# Electronic Structure, Spectroscopic (IR, Raman, UV-Vis, NMR), Optoelectronic, and NLO Properties Investigations of Rubescin E (C31H36O7) Molecule in Gas Phase and Chloroform Solution Using Ab Initio and DFT Methods

Authors: Richard Arnaud Yossa Kamsi; Geh Wilson Ejuh; Fidèle Tchoffo; Pierre Mkounga; Jean-Marie Bienvenu Ndjaka
Journal: Advances in Condensed Matter Physics
 (2019)

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## Abstract

Quantum chemical methods were used to study the electronic structure and some physicochemical properties of Rubescin E molecule. Good agreement with experiment was found forJ3H-H coupling constant, IR, 1H NMR, and 13C NMR. The excitation energy and oscillator strength calculated by TD-DFT also complement with experiment. Large values were obtained for dipole moment, polarizability, first static hyperpolarizability, electric susceptibility, refractive index, and dielectric constant, meaning that Rubescin E has strong optical and phonon application and can be a good candidate as NLOs material. The 3D analysis of the title molecule leads us to the conclusion that electron can easily be transferred from furan to tetrahydrofuran ring. The global reactivity descriptors were evaluated. Mulliken, ESP, and NBO charges comparisons were carried out and described.


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## Body

## 1. Introduction

Many molecules from plant research were found nowadays to have application in the field of medicine, where there are use for the treatment of many diseases among which we found malaria caused by plasmodium falciparum. The new limonoid name Rubescin E (C31H36O7), extracted from the roots of Trichilia Rubescens, collected from Cameroon, has been evaluated against erythrocytic stages of strain 3D7 plasmodium falciparum and also exhibited significant antiplasmodial in vitro activity with IC50 value of 1.13μM [1]. The FT-IR performed on Rubescin E molecule revealed the presence of α, β-unsaturated carbonyl moiety at 1720 cm−1 and 1664 cm−1. These values can be obtained theoretically by performing the vibrational frequencies calculation on the title molecule and used to explain the different motion of atoms or group of atoms in a molecular system. The 1D (1H, 13C NMR) and 2D NMR spectra were run on a Bruker AV spectrometer [1] in order to predict the structure of the title molecule and were done in this work in order to take out similarities between experiment done previously and theoretical calculation performed here.In this work, quantum chemical calculation was performed in order to take out the electronic structure (energy gap, charge distributions, NLO properties, vibrational frequencies, NMR, and UV-vis calculation) and some physicochemical properties (J3H-H chemical coupling-coupling constant, the global reactivity descriptors, and some geometrical parameters such as bonds lengths and bonds angles) of Rubescin E molecule. To the best of our knowledge, no theoretical study was performed yet on the title molecule, that is what motivated us to investigate the electronic structure, the spectroscopic, and some physicochemical properties of Rubescin E molecule. Except for NMR, UV-vis, J3H-H chemical coupling-coupling constant, and the vibrational frequencies obtained for the two α, β-unsaturated carbonyl moiety, most of our results were not compared and we are optimistic that it can be used as threshold for future experimental or theoretical research. Hartree Fock and DFT (using B3LYP and B3PW91 functionals) methods were used for these purposes. These properties were calculated by employing the triple split valence basis set along with polarization functions with and without diffuse functions as implemented in Gaussian 09, Rev. A02 in both gas phase and in a solution of chloroform. The methods and basis sets used are among the most widely used [2–5] and provide excellent results which are generally very close to experiments [6–8].


## 2. Computational Methods

Theoretical calculations were performed on Rubescin E using HF and DFT methods at the B3LYP and B3PW91 levels as implemented in Gaussian 09W code [9]. All these calculations were done in gas phase and in a solution of chloroform. No geometry restriction was applied during the optimization procedure. The solvent effects were treated within the conductor-like polarizable continuum model (CPCM). For the geometry optimization, the 6-311G(d,p) and 6-311++G(d,p) basis set were used in both gas and solvent. Convergence criteria in which both the maximum force and displacement are smaller than the cut-off of 0.000015 and 0.000060 and RMS force and displacement less than the cut-off values of 0.000010 and 0.000040 were used in the calculations in order to increase the accuracy of our results. The chemical J3H-H proton-proton coupling constant function of angle between two C-H vectors was calculated from the optimization output using the original Karplus equation [10]. The optimized form of our molecule was then used to determine the global reactivity descriptors, electronic and NLOs properties. The net charges were also evaluated using MPA, ESP, and NBOs methods at the three levels mentioned above, and all this was done in both gas phase and chloroform with the 6-311++G(d,p) basis set. In order to confirm the stability of our molecule, the vibrational frequencies (IR and Raman) were evaluated at the 6-311G(d,p) and no imaginary frequencies were found leading us to the results that our molecule was stable at the levels and basis set considered. The time dependent density functional theory (TD-DFT) field was used in gas phase with the 6-311++G(d,p) basis in order to understand the electronic transition of our molecule and the obtained results were compared to experiment. The GIAO (gauge independent atomic orbital) method was used on the optimized form of our molecule in a solution of chloroform to determine the 1H and 13C NMR spectra parameters at the three levels and with the 6-311++G(d,p) basis set. In order to compare the calculated values of 1H and 13C chemical shift with experimental results, the reference and widely used molecule TMS (tetramethylsilane) for this purpose were exploited at the same level, at the same phase, and with the same basis set.


## 3. Results and Discussion

### 3.1. Optimized Structure

The optimized geometry of Rubescin E obtained using the B3LYP/6-311++G(d,p) method in chloroform is shown in Figure1. The value of the total electronic energy of the molecule obtained at the B3LYP shows that Figure 1 is the most stable structure of the molecule. The total electronic energy calculated within the two methods in gas and in a solution of chloroform with the 6-311++G(d,p) is given in Table 1.Table 1
Optimized geometric parameters in gas phase and in chloroform solution of Rubescin E at the RHF, B3LYP, and B3PW91 level with the 6-311++G (d,p) basis sets.
Levels RHF B3LYP B3PW91 Theory a[11], b[12], c[13] Basis set Gaz CDCl3 Gaz CDCl3 Gaz CDCl3 Bond length  R1 (C1-C2) 1.5503 1.5490 1.5603 1.5583 1.5521 1.5500 R2 (C1-C3) 1.5698 1.5672 1.5811 1.5777 1.5719 1.5684 R3 (C1-C20) 1.5167 1.5157 1.5221 1.5215 1.5153 1.5147 R4 (C1-C22) 1.5474 1.5481 1.5510 1.5509 1.5439 1.5438 R5 (C2=O7) 1.1900 1.1948 1.2167 1.2213 1.2152 1.2197 2.10 b R6 (C2-C34) 1.5041 1.4992 1.4966 1.4910 1.4920 1.4867 R7 (C3-C4) 1.5898 1.5887 1.5973 1.5968 1.5866 1.5860 R8 (C3-C40) 1.4814 1.4800 1.4972 1.4958 1.4931 1.4918 1.462 b R9 (C3-O59) 1.3994 1.4024 1.4311 1.4335 1.4236 1.4256 1.428 b R10 (C4-C5) 1.5515 1.5518 1.5549 1.5548 1.5473 1.5471 R11 (C4-C12) 1.5707 1.5733 1.5756 1.5787 1.5676 1.5707 R12 (C4-C36) 1.5501 1.5503 1.5543 1.5543 1.5471 1.5472 R13 (C5-C6) 1.5428 1.5442 1.5477 1.5487 1.5401 1.5410 R14 (C5-C46) 1.4556 1.4553 1.4720 1.4717 1.4686 1.4684 1.462 b R15 (C5-O61) 1.4206 1.4235 1.4568 1.4590 1.4473 1.4492 1.428 b R16 (C6-C26) 1.5259 1.5260 1.5306 1.5307 1.5246 1.5248 R17 (C6-C42) 1.5352 1.5350 1.5373 1.5373 1.5298 1.5298 R18 (C6-C51) 1.5703 1.5708 1.5810 1.5814 1.5724 1.5728 R19 (C8-C16) 1.5423 1.5424 1.5477 1.5481 1.5405 1.5408 R20 (C8-C20) 1.5256 1.5244 1.5348 1.5335 1.5276 1.5264 1.536 c R21 (C8-C29) 1.5405 1.5402 1.5479 1.5468 1.5416 1.5406 1.536 c R22 (C8-C32) 1.5036 1.5036 1.5010 1.5010 1.4958 1.4960 R23 (C9-O11) 1.4120 1.4133 1.4389 1.4411 1.4304 1.4324 1.428 c R24 (C9-C12) 1.5288 1.5302 1.5357 1.5373 1.5311 1.5329 R25 (C9-C20) 1.4997 1.4993 1.5044 1.5042 1.4999 1.4998 1.536 c R26 (O11-C29) 1.4261 1.4287 1.4530 1.4551 1.4438 1.4457 1.428 c R27 (C12-O60) 1.4104 1.4131 1.4339 1.4369 1.4255 1.4283 R28 (C14-C51) 1.5035 1.5041 1.5003 1.5010 1.4953 1.4959 R29 (C14-C53) 1.4493 1.4505 1.4428 1.4438 1.4387 1.4397 1.430 a R30 (C14=C57) 1.3411 1.3410 1.3621 1.3619 1.3614 1.3614 1.364 a R31 (O15-C55) 1.3382 1.3412 1.3609 1.3638 1.3548 1.3574 1.364 a R32 (O15-C57) 1.3467 1.3496 1.3659 1.3686 1.3592 1.3616 1.364 a R33 (C26-C40) 1.5162 1.5158 1.5190 1.5181 1.5137 1.5129 R34 (C32=C34) 1.3270 1.3285 1.3431 1.3445 1.3422 1.3436 R35 (C40-O59) 1.4010 1.4054 1.4353 1.4395 1.4282 1.4320 1.428 b R36 (C46-C48) 1.5086 1.5076 1.5135 1.5123 1.5088 1.5077 R37 (C46-O61) 1.4005 1.4051 1.4326 1.4376 1.4254 1.4297 1.428 b R38 (C48-C51) 1.5407 1.5405 1.5478 1.5475 1.5408 1.5405 R39 (C53=C55) 1.3381 1.3381 1.3567 1.3567 1.3559 1.3559 1.364 a R40 (O60-C62) 1.3485 1.3397 1.3805 1.3700 1.3743 1.3650 R41 (C62-C63) 1.5033 1.5030 1.4998 1.5000 1.4956 1.4952 R42 (C62=O65) 1.1810 1.1873 1.2059 1.2113 1.2046 1.2098 R43 (C63=C64) 1.3222 1.3230 1.3402 1.3403 1.3394 1.3398 R44 (C63-C71) 1.5153 1.5159 1.5127 1.5135 1.5071 1.5083 R45 (C64-C67) 1.5001 1.5002 1.4954 1.4959 1.4898 1.4901  Bond angles  A1 (C2-C1-C3) 115.3869 115.1538 115.3519 115.0591 115.3042 114.9661 A2 (C2-C1-C20) 104.9116 105.2360 104.8861 105.3058 105.0195 105.4353 A3 (C2-C1-C22) 104.6632 104.8093 104.8467 105.0548 104.7619 105.0065 A4 (C3-C1-C20) 105.4487 104.9239 106.0693 105.3428 105.9491 105.1727 A5 (C3-C1-C22) 110.0598 110.4677 109.3407 109.9326 109.4774 110.1062 A6 (C20-C1-C22) 116.6507 116.5134 116.6409 116.4160 116.6212 116.4196 A7 (C1-C2-O7) 122.6712 122.1731 122.5890 122.0461 122.6012 122.0599 A8 (C1-C2-C34) 118.8294 119.0297 118.5520 118.8580 118.5112 118.8095 A9 (O7-C2-C34) 118.3115 118.6060 118.6750 118.9135 118.6899 118.9368 A10 (C1-C3-C4) 117.4677 117.2546 117.5179 117.3499 117.4703 117.2908 A11 (C1-C3-C40) 120.4116 120.3391 120.5229 120.3696 120.4781 120.3201 A12 (C1-C3-O59) 113.5239 113.6346 113.2288 113.4708 113.2740 113.5007 A13 (C4-C3-C40) 119.7989 119.8618 119.6777 119.7275 119.7605 119.8264 A14 (C4-C3-O59) 110.9192 111.3348 110.6687 111.0566 110.7288 111.1433 A15 (C3-C4-C5) 108.2815 108.0767 108.5292 108.3020 108.4460 108.1898 A16 (C3-C4-C12) 116.9097 116.9148 116.6545 116.8466 116.8336 117.0260 A17 (C3-C4-C36) 107.3533 107.5825 107.2145 107.3890 107.2213 107.3820 A18 (C5-C4-C12) 110.9502 111.2590 110.8879 111.1131 111.0310 111.3284 A19 (C5-C4-C36) 108.2096 108.3900 108.2857 108.5557 108.0890 108.3471 A20 (C12-C4-C36) 104.7402 104.2361 104.883 104.2585 104.7988 104.1530 A21 (C4-C5-C6) 122.3963 122.5160 122.2095 122.2513 122.2181 122.2697 A22 (C4-C5-C46) 126.1434 126.0858 126.2488 126.1993 126.1315 126.0739 A23 (C4-C5-O61) 113.7557 113.5947 113.7382 113.6922 114.0173 113.9553 A24 (C6-C5-C46) 108.4092 108.4312 108.2407 108.2667 108.2513 108.2900 A25 (C6-C5-O61) 109.3436 109.1575 109.7850 109.6384 109.6935 109.5481 A26 (C5-C6-C26) 106.9225 107.1323 107.1725 107.3025 107.1359 107.2931 A27 (C5-C6-C42) 114.7934 114.8607 114.4807 114.5006 114.5313 114.5541 A28 (C5-C6-C51) 101.8612 101.8830 101.9281 102.0115 101.8916 101.9777 A29 (C26-C6-C42) 108.8679 108.6162 109.1102 108.9149 109.1443 108.9314 A30 (C26-C6-C51) 113.8205 113.8653 113.9931 114.0014 113.9406 113.9367 A31 (C42-C6-C51) 110.5307 110.4727 110.1102 110.0888 110.1443 110.1222 A32 (C16-C8-C20) 117.8467 117.8806 117.5220 117.5381 117.3986 117.3974 A33 (C16-C8-C29) 108.3950 108.5431 108.4117 108.5195 108.5270 108.6672 A34 (C16-C8-C32) 109.5455 109.4283 109.5034 109.3293 109.6190 109.4415 A35 (C20-C8-C29) 96.3773 96.4321 96.6032 96.6193 96.4146 96.4285 101.5 c A36 (C20-C8-C32) 106.3315 106.2487 106.4280 106.3876 106.432 106.3732 A37 (C29-C8-C32) 118.2843 118.2659 118.3155 118.4200 118.3462 118.4575 A38 (O11-C9-C12) 113.2108 113.1065 113.2048 113.2060 113.1493 113.1724 A39 (O11-C9-C20) 103.3360 103.1494 103.8285 103.6622 103.8971 103.7399 104.0 c A40 (C12-C9-C20) 109.2549 109.4574 108.7908 108.9954 108.4814 108.6640 A41 (C9-O11-C29) 111.1841 111.2217 109.8976 109.9018 109.8190 109.8362 110.6 c A42 (C4-C12-C9) 110.4259 110.6951 110.0123 110.3980 109.8110 110.1418 A43 (C4-C12-O60) 111.1499 111.4570 110.9644 111.4849 111.3257 111.9073 A44 (C9-C12-O60) 109.0864 108.7044 108.7314 108.2508 108.4512 107.9972 A45 (C51-C14-C53) 126.042 126.0928 126.1043 126.1692 126.2986 126.3771 A46 (C51-C14-C57) 129.3418 129.1716 128.8385 128.6558 128.7371 128.5448 A47 (C53-C14-C57) 104.5893 104.7043 105.0493 105.1666 104.9597 105.0728 106.14 a A48 (C55-O15-C57) 107.1084 107.1499 106.7602 106.8013 106.8133 106.8678 106.74 a A49 (C1-C20-C8) 121.1479 121.0073 120.9097 120.7705 120.9914 120.8439 A50 (C1-C20-C9) 118.7226 118.5220 118.7478 118.3732 118.6818 118.2898 A51 (C8-C20-C9) 103.8120 103.9439 104.2023 104.3600 104.0389 104.2216 104.4 c A52 (C6-C26-C40) 111.4945 111.6304 111.4804 111.5216 111.4199 111.4969 A53 (C8-C29-O11) 104.4386 104.4819 104.6594 104.594 104.6712 104.6043 107.5 c A54 (C8-C32-C34) 120.4664 120.4528 120.5688 120.4387 120.4312 120.2925 A55 (C2-C34-C32) 125.2907 124.9802 125.5569 125.2584 125.5114 125.1913 A56 (C3-C40-C26) 124.7594 125.1561 124.3752 124.7373 124.3541 124.7241 A57 (C26-C40-O59) 116.1404 115.9652 116.0868 116.0753 115.9905 115.9607 A58 (C5-C46-C48) 110.0006 110.0212 109.8202 109.8537 109.6430 109.6699 A59 (C48-C46-O61) 111.5740 111.5456 111.7313 111.7203 111.8859 111.8641 A60 (C46-C48-C51) 102.6704 102.7788 102.8570 103.0253 102.6915 102.8703 A61 (C6-C51-C14) 116.8638 116.8705 116.6829 116.6156 116.3993 116.3329 A62 (C6-C51-C48) 104.4966 104.5425 104.2867 104.3539 104.3511 104.4332 A63 (C14-C51-C48) 114.9685 114.8714 115.2826 115.1809 115.2757 115.1468 A64 (C14-C53-C55) 106.1668 106.2381 106.7966 106.8606 106.6618 106.7168 106.14 a A65 (O15-C55-C53) 110.7484 110.6455 110.3339 110.2350 110.4305 110.3331 110.49 a A66 (C14-C57-O15) 111.3857 111.2607 111.0591 110.9356 111.1339 111.0086 110.49 a A67 (C12-O60-C62) 123.1805 123.4264 122.4520 122.2629 121.8099 121.5920 A68 (O60-C62-C63) 118.3342 119.1473 118.6681 119.4932 118.6273 119.3485 A69 (O60-C62-O65) 118.3753 117.9395 117.5454 117.1467 117.6414 117.2568 A70 (C63-C62-O65) 123.0766 122.6884 123.4720 123.0718 123.4069 123.1015 A71 (C62-C63-C64) 116.9655 117.1950 116.2922 116.7661 116.1754 116.6519 A72 (C62-C63-C71) 117.8479 117.3833 119.4971 118.5815 119.7175 119.0158 A74 (C64-C63-C71) 125.0717 125.2904 124.1105 124.5124 123.9876 124.1815 A75 (C63-C64-C67) 127.2664 127.2197 127.2301 127.2514 126.9123 126.7855  Total energy (Hartree) -1719.15539 -1719.17648 -1729.82917 -1729.84726 -1729.17724 -1729.19498Figure 1
Ground state geometry of Rubescin E at B3LYP/6-311++G(d,p) in chloroform solution.


### 3.2. Structural Properties

A part of the optimized geometrical parameters (bond length, bond angle) and total electronic energy of the title molecule both in gas and in a solution of chloroform are given in Table1 using the three levels and with the 6-311++G(d,p) basis set. The total description of the molecular geometry of Rubescin E molecule in gas phase and in a solution of chloroform using ab initio (RHF) and DFT (B3LYP and B3PW91) methods with the 6-311++G(d,p) basis set can be obtained from Supplementary Material S1.The atom numbering scheme adopted for this purpose is the same as in Figure1. The energy differences between the two used phases increase when we move from B3PW91 to B3LYP and to RHF and are found to be approximatively 0.48 eV, 0.49 eV, and 0.57 eV, respectively. The optimized bond length and bond angle of Rubescin E are also listed in Table 1 with some specific experimental values [12–14] found in the literature for some groups of compounds such as furan, ethylene oxide, and tetrahydrofuran present in our molecule. It can be observed from Table 1 that the values of the bond length obtained at B3LYP are slightly higher than those obtained at the B3PW91 level. These differences are found between 0.0034 Å and 0.0107 Å for C-C; 0.0061 Å and 0.0095 Å for C-O; and 0.0007 Å and 0.0013 Å for C=C in gas phase. The value of C=O bond length is better at the DFT methods since its values are closer to 2.10 Å found in literature [11]. It can also been observed that the calculated bonds length using Hartree Fock and DFT methods are very close to the values found in literature for the specific groups of compounds present in our molecule. These observed differences varied from 0.0012 Å at the B3LYP level to 0.0363 Å at the RHF level; from 0.0002 Å at the B3PW91 level to 0.0288 Å at the B3LYP level; and from 0.0019 Å at the B3LYP level to 0.0259 Å at the RHF level for C-C, C-O, and C=C bonds both in gas phase and in chloroform solution, respectively.The bonds angles of the studied molecule are slightly different when we move from one phase to another at each level with larger values obtained at the RHF level. From our results, it can be seen that the C-C-C bond angle varies from 96.3773° to 129.3418°, from 96.6032° to 128.8385°, and from 96.4146° to 128.7371° at the gas phase, respectively, at the RHF, B3LYP, and B3PW91 level of the theory. In CDCl3, the C-C-C bond angles are similar to those obtained at the gas phase. The smallest value of C-C-C bond angle was C20-C8-C29 bond angle and the largest C51-C14-C57 bond angle. For the C-C-O angle, the smallest value was 104.4386° obtained at the RHF and the largest value was 123.472° obtained at the B3LYP level both in the gas phase. The C-O-C bond angle was found between 107.1084° and 123.4264° obtained at the RHF level. These bonds angles compared to some known values found in literature [12, 14] for specific compound present in our structure show good similarities. The little differences are found between 0.0268° and 1.5507° for C-C-C bond, between 0.0595° and 3.0614° for C-C-O bond, and between 0.0202° and 0.781° for C-O-C bond. These observed differences are due to the fact that these groups of compounds were not isolated.


### 3.3. CalculatedJ3H-H Coupling Constant

The chemicalJ3H-H proton-proton coupling constant was calculated using the original Karplus [10] equation in gas and solvent and its results compared to experimental values [1] obtained by extracting Rubescin E in a solution of chloroform. From our results, we found that the calculated parameters both in gas and in chloroform are all similar at all the levels used. These obtained results are also very close to experiment. As predicted in literature [10], we observed from Table 2 that when the angles between the two C-H vectors are close enough to 00 or 1800, the value of J3H-H coupling constant is greater (with J31800>J300) and is very small when the angle is close to 900.Table 2
Experimental and calculatedJ3H-H proton-proton coupling constant of Rubescin E in gas phase and in chloroform solution.
PARAMETERS RHF B3LYP B3PW91 EXP [1] Gaz CDCl3 Gaz CDCl3 Gaz CDCl3 Angles(°) J   3 H - H (Hz) Angles(°) J   3 H - H (Hz) Angles(°) J   3 H - H (Hz) Angles(°) J   3 H - H (Hz) Angles(°) J   3 H - H (Hz) Angles(°) J   3 H - H (Hz) H10-C9-C12-H13 45.5506 6.20 43.8143 6.49 48.1393 5.79 45.9537 6.14 48.3285 5.76 46.1662 6.10 4.0 H10-C9-C20-H21 169.5395 12.65 169.8194 12.67 168.824 12.61 168.658 12.59 168.5 12.58 168.2201 12.56 12.0 H27-C26-C40-H41 -11.0718 10.65 -12.0311 10.59 -10.1794 10.70 -10.89 10.66 -10.4324 10.69 -11.298 10.64 6.5 H28-C26-C40-H41 105.3029 2.96 103.995 2.83 106.3433 3.07 105.3319 2.96 106.1668 3.05 104.964 2.92 1.3 H33-C32-C34-H35 -0.2873 11 -0.123 11 -0.5893 11 -0.366 11 -0.566 11 -0.3331 11 10.0 H47-C46-C48-H49 -61.3614 3.82 -61.1286 3.85 -61.9356 3.74 -61.8438 3.75 -61.5482 3.79 -61.4875 3.80 4.2 H47-C46-C48-H50 58.7437 4.17 58.7503 4.17 58.0428 4.27 57.8579 4.30 58.534 4.20 58.3044 4.24 4.2 H49-C48-C51-H52 -42.5704 6.69 -42.1786 6.75 -43.9616 6.46 -43.3642 6.56 -44.5718 6.36 -43.9227 6.47 4.2 H50-C48-C51-H52 -164.093 12.21 -163.817 12.18 -165.22 12.32 -164.673 12.27 -165.874 12.37 -165.259 12.32 11 H54-C53-C55-H56 -0.3838 11 -0.2856 11 -0.3275 11 -0.2429 11 -0.3921 11 -0.3074 11 H66-C64-C67-H68 -177.906 12.99 -177.979 12.99 178.4674 12.99 178.7874 13 178.4147 12.99 178.548 12.99 H66-C64-C67-H69 -56.9125 4.43 -56.9428 4.43 -60.3746 3.95 -59.9903 4 -60.4007 3.95 -60.1923 3.97 7.0 H66-C64-C67-H70 60.6324 3.91 60.4696 3.94 56.6811 4.47 56.9449 4.42 56.6504 4.47 56.7234 4.46 7.0


### 3.4. Electronic Properties

#### 3.4.1. Mulliken, ESP, and Natural Charge Distribution

The Mulliken atomic charges of our molecule calculated at all the levels in gas phase and chloroform show positive charge for all the hydrogen atoms. The net charge on all the atoms varies from -1.109653e to 1.980512e, from -1.164916e to 1.904034e, and from -0.891775e to 1.524787e, respectively, in gas phase at the RHF, B3PW91, and B3LYP levels. In a solution of chloroform, the charges varied from -1.064962e to 1.826589e, from -1.206706e to 1.904292e, and from -0.945041e to 1.550492e with some oxygen atoms charges being positive and can be explained by the fact that the oxygen is related to extremely negative carbon atoms. The most positive charge atoms are C63, C5, C8 and the most negative charge atoms are C71, C62, C67.The electrostatic charges were evaluated in this work using the CHelpG scheme of Breneman model. We found from our results that the most positive charges atom is C4 followed by C62 and C2 and the most negative charge atom is C12 followed by C5 and C7. The observation made at all levels and basis set in gas phase and in a solution of chloroform is that the most positive charge atoms are directly related to the most negative charge atoms.The natural atomic charges, obtained using the natural bonding orbital method, were also used to evaluate the atomic charge of Rubescin E. Positive and negative charges were found for all hydrogen and oxygen atoms, respectively. In this case, all carbon atoms directly linked to hydrogen atoms were found to have negative charges except for those linked to oxygen atoms. The most negative charge atom was calculated using HF method and was observed for O65 (-0.69456e) and O60 (-0.68330e), respectively, in chloroform and gas phase. The most positive charge atom was found to be C62 in both gas (0.97067e, 0.80601e, and 0.81407e, respectively, at the RHF, B3PW91, and B3LYP levels) and solvent (0.98887e, 0.81804e, and 0.82650e, respectively, at the RHF, B3PW91, and B3LYP levels); this is due to the fact that C62 is related to negative charge atoms (O65, O60, and C63). Mulliken, electrostatic, and natural atomic charge distributions are graphically shown in Figure 2. From Figure 2, one can observe that, for almost all the methods used for charge description, the most positive and negative charge atoms were calculated at the RHF level in both gas and chloroform and this is due to the fact that the effect of electron correlation is not well described in HF method.Figure 2
Charge distribution on Rubescin E calculated at the RHF, B3PW91, and B3LYP levels in both gas phase and chloroform solution and with the 6-311++G(d,p) basis set.


#### 3.4.2. Global Reactivity Descriptors

In order to understand the relationships between structure, stability, and reactivity of Rubescin E molecule, the global reactivity descriptors parameters such as chemical hardness (H), chemical potential (μcp), chemical softness (s), electronegativity (X), and electrophilicity index (ω) were calculated. The finite difference equation given by (1) was used to calculate the ionization potential and electron affinity, which are generally used to calculate the above cited parameters.(1)IP=Eq=N+1-Eq=NEA=Eq=N-Eq=N-1The IP and EA calculated from (1) were then used to calculate H, μcp, s, X, and ω using equations found in the literature [15–17]. All these parameters calculated using the two methods in gas phase are presented in Table 3. A high value of μcp and ω characterizes a good electrophile, while a small value stands for good nucleophile.Table 3
Global reactivity descriptors of Rubescin E at the RHF, B3LYP, and B3PW91 levels in gas phase and in chloroform solution using the 6-311++G(d,p) basis set.
RHF B3LYP B3PW91 Gas Chloroform Gas Chloroform Gas Chloroform IP (eV) 7.151 5.662 7.875 6.819 7.861 6.819 EA (eV) -0.841 0.684 0.461 1.804 0.450 1.825 μ c p (eV) -3.155 -3.173 -4.168 -4.312 -4.156 -4.322 X (eV) 3.155 3.173 4.168 4.312 4.156 4.322 H (eV) 3.996 2.489 3.707 2.508 3.706 2.497 s (eV)−1 0.250 0.402 0.270 0.399 0.270 0.400 ω (eV) 1.245 2.022 2.343 3.707 2.330 3.740The calculated vertical IP values in gas phase are bigger than their corresponding values in solvent. From Table3, we also found that putting the molecule in solvent increases its electron affinity. From the calculated IP and EA values, one can conclude that solvent effect increases the capacity of molecule of gaining an electron compared to donating it. It also reduces the harness of our molecule and increases the softness. Hence, the presence of solvent increases the reactivity of the molecule Rubescin.


#### 3.4.3. Frontier Molecular Orbitals

The frontier molecular orbitals of Rubescin E were evaluated using the ab initio and DFT methods. The 6-311G(d,p) and 6-311++G(d,p) basis sets were used for this purpose in gas phase and in chloroform solution. The results show that the energy gap of our molecule decreases when diffuse functions are added onto all the atoms. We also found that whenever the basis set and methods used, the energy gap is greater than 4, showing that our molecule is hard and can be used as insulator in many electronic devices. In Figure3, the 3D plots of the HOMO and LUMO orbitals computed at the RHF, B3PW91, and B3LYP levels with the 6-311G(d,p) basis set are illustrated in gas phase. We observed that the HOMO of Rubescin E is located over the furan ring at the three levels and also at the C-C of cyclohexane ring and C-O of oxiran ring. By contrast, the LUMO orbital is located over the cyclohex-2-enone ring, C-C and C-O bond of tetrahydrofuran ring. We can therefore conclude that electron can easily be transferred from furan ring to tetrahydrofuran ring.Figure 3
Molecular orbital and the HOMO and LUMO energy of Rubescin E in gas phase.The total density of states (DOS) spectrum of Rubescin E at the gas phase and in chloroform is given in Figure4 for each level at the 6-311++G(d,p) basis set. These DOSs spectra presented in Figure 4 were obtained from Gauss-Sum 3.0 program [18] which was used in order to show the contributions of different group to molecular orbital (HOMO and LUMO). From Figure 4, we observe that the HOMO-LUMO energy gap is smaller when we move from RHF to B3PW91 and from B3PW91 to B3LYP level, respectively, for both gas and chloroform phases, with larger values obtained in chloroform.Figure 4
Total density of state (DOS) spectrum of Rubescin E at the RHF, B3PW91, and B3LYP levels in both gas and chloroform phase and with the 6-311++G(d,p) basis set.


#### 3.4.4. UV-Vis Spectra Analysis

Time dependent density functional theory (TD-DFT) was used in gas phase at the two levels B3PW91 and B3LYP with the 6-311++G(d,p) basis set in order to determine the first six excited states to investigate the UV-vis absorption spectra of the molecule. The excitation energy (E), wavelength (λ), and oscillator strength (f) along with their major contributions are given in Table 4 and their results are compared to experiment.Table 4
Theoretical absorption wavelength (λ), excitation energy (E), and oscillator strengths of Rubescin E at the B3PW91 and B3LYP levels in gas with the 6-311++G(d,p) basis set.
Excited states Exp [1] B3PW91 B3LYP λ (nm) λ (nm) E (eV) f Major contributions λ (nm) E (eV) f Major contributions 1 365 360.27 3.4415 0.0014 H-1 → L (93%) 358.31 3.4603 0.0014 H-1 → L (93%) 2  312.18 3.9715 0.0000 H → L (99%) 313.69 3.9524 0.0000 H → L (99%) 3 254 275.92 4.4934 0.0043 H-4 → L (24%) 274.77 4.5123 0.0041 H-4 → L (28%) 4  272.66 4.5473 0.0006 H-4 → L (50%) 272.27 4.5538 0.0004 H-4 → L (44%) 5  269.56 4.5994 0.0001 H-4 → L (19%) 268.47 4.6182 0.0001 H-4 → L (20%) 6  261.21 4.7465 0.0000 H → L+1 (100%) 263.16 4.7113 0.0000 H → L+1 (100%)Two intense electronic transitions were predicted at 4.4934 eV (275.92 nm) and 3.4415 eV (360.27 nm) with oscillator strengths of 0.0043 and 0.0014, respectively, at the B3PW91 level and 4.5123 eV (274.77 nm) and 3.4603 eV (358.31 nm) with oscillator strengths of 0.0041 and 0.0014, respectively, at the B3LYP level. We observed from the spectra that the maximum absorption wavelength corresponds to the electronic transition from HOMO to LUMO+1 with 100% contribution followed by the electronic transition from HOMO to LUMO with 99% contribution at the two levels. The experimental absorption spectra of the title molecule predict two bands at 254 nm and 365 nm. The error between the theoretical and experimental results range from - 4.73 nm to 21.92 nm at the B3PW91 and from - 6.69 nm to 20.77 nm at the B3LYP level. These errors are due to the fact that only one molecule was considered for simulation. The theoretical UV-vis absorption spectra of Rubescin E in gas phase are shown in Figure5.Figure 5
Theoretical absorption spectra of Rubescin E at the B3PW91 and B3LYP levels in gas with the 6-311++G(d,p) basis set.


#### 3.4.5. Dipole Moment (μDM), Average Polarizability (α), First Static Hyperpolarizability (β), and Anisotropy of Polarization

In this work, the dipole momentμDM, average polarizability α, first static hyperpolarizability β, and anisotropy of polarizability Δα of Rubescin E were evaluated in both gas phase and chloroform solution in order to define the nonlinearity of Rubescin E. The finite-field approach was used for this purpose. Equations (2), (3), (4), and (5) were used to calculate the polarizability, dipole moment, anisotropy of polarizability, and first static hyperpolarizability, respectively, using the x,y,z components obtained from Gaussian 09 W output. The calculated parameters were presented in Table 5 at the three levels with the 6-311++G(d,p) basis set.(2)α=13αxx+αyy+αzz(3)μDM=μx2+μy2+μz21/2(4)∆α=12αxx-αyy2+αyy-αzz2+αzz-αxx2+6αxz2+6αxy2+6αyz21/2(5)β=βxxx+βxyy+βxzz2+βyyy+βyzz+βyxx2+βzzz+βzxx+βzyy21/2The calculated values of polarizability and first static hyperpolarizability obtained from Gaussian output are in atomic unit. These values were then converted into electrostatic unit (esu) for comparison purpose (for α: 1 a.u = 0.1482 x 10−24 esu, for β: 1 a.u = 8.6393 x 10−33 esu) [19–22]. From a giving molecule, when these values (μDM and β) are greater than those of urea, the molecule is said to have good active NLO properties. We observed from our results that the values of α, β, and μDM are higher in solvent than their corresponding value in gas phase. β and μDM of Rubescin E calculated at the 6-311++G(d,p) basis set using different methods were greater than those of urea. These values calculated using the HF/6-311D(d,p) method (μDM=5.2175D and β=1760.3169x10-33 esu) were also higher than those of urea (μDM=3.8851D and β=372.8x10-33esu), obtained using the same method and basis set [21]. Hence Rubescin E can be considered to have good active NLO properties and this is due to the delocalize ᴫ electron on the furan ring.Table 5
Electric dipole moment, polarizability, anisotropy of polarization, first-order hyperpolarizability, and molar refractivity of Rubescin E at the RHF, B3LYP, and B3PW91 levels with the 6-311G (d, p) and 6-311++G (d, p) basis sets.
RHF B3LYP B3PW91 Gas Chloroform Gas Chloroform Gas Chloroform μ D M (D) 5.3966 7.0953 5.2074 6.7654 5.1176 6.6663  α x x 352.266 421.425 387.992 470.193 384.258 465.488 α x y 17.3299 24.2341 19.6436 29.6995 19.3544 29.0512 α y y 336.148 424.889 374.795 479.493 371.091 475.445 α x z 1.50612 0.677331 0.715703 -0.411779 0.795242 -0.371934 α y z 3.39268 -1.23142 4.44903 0.0306216 4.53244 0.450373 α z z 278.550 371.379 305.049 415.461 301.619 411.131  α t o t (∗10−24 esu) 47.7036 60.0729 52.6799 67.3473 52.1438 66.7018  Δα (∗10−24 esu) 10.9240 9.8814 12.5387 11.6890 12.4723 11.5857  β x x x 58.5850 116.324 77.8905 117.687 82.0568 124.840 β x x y -34.3404 -40.3762 -33.9536 -66.5203 -29.0441 -60.4155 β x y y 22.5993 15.4126 -29.6091 -106.843 -36.6541 -122.127 β y y y 92.3349 129.004 27.6922 -58.5834 26.8972 -63.6805 β x x z -16.3605 -23.5326 -55.0267 -81.7313 -58.0975 -89.6785 β x y z -8.72859 -0.242861 -11.9414 10.3722 -12.8764 6.24556 β y y z -38.9332 -65.6523 -107.633 -207.304 -108.216 -214.866 β x z z -14.4537 -58.3711 -7.34826 -70.3072 -7.94692 -69.1599 β y z z -50.8004 -109.450 -77.7921 -196.200 -71.2685 -182.588 β z z z -6.38532 23.9632 -16.7476 -0.675756 -9.68167 5.78764  β (∗10−33 esu) 787.4783 866.9154 1747.7167 3772.6270 1678.8815 3743.0498


#### 3.4.6. Optoelectronic Properties

In order to recognize the optoelectronic nature of Rubescin E for different devices applications, some parameters such as electric field (E), electric polarization (P), electric susceptibility (χ), permittivity (ℰ), refractive index (η), and electric displacement (D) were calculated using equations given in the literature [23–25]. We observed from Table 6 that the results of the calculated parameters are slightly different when we move from one level to another and also when the medium changes. The value of electric field is greater in a solution of chloroform than its corresponding value in gas phase. This is because the polarizability increases in presence of a solvent. The values of electric susceptibility, dielectric constant, and refractive index are greater at B3LYP level compared to their corresponding value at the RHF. All the calculated parameters of optoelectronic properties obtained at the B3LYP level are similar to those obtained at the B3PW91 level. None of these parameters have been determined before either theoretically or experimentally.Table 6
Calculated values of polarization density (P), average electric field (E), electric susceptibility (χ), refractive index (η), dielectric constant (E), magnitude of the displacement (D), and molar refractivity (MR) of Rubescin E molecule obtained at the RHF, B3LYP, and B3PW91 levels with the 6-311++G(d,p) basis set.
Parameters RHF B3LYP B3PW91 Gas Chloroform Gas Chloroform Gas Chloroform E (V.m−1)∗ 109 3.3873 3.5365 2.9597 3.0078 2.9386 2.9924 P (C.m−2)∗10−2 8.3339 10.7944 7.5778 8.6086 8.3117 7.9130 χ 2.7787 3.4473 2.8916 3.2324 3.1945 2.9865 E ∗10−11 3.3458 3.9377 3.4457 3.7475 3.7139 3.5297 η 1.9439 2.1089 1.9727 2.0573 2.0480 1.9966 D (C.m−2)∗10−2 0.1133 0.1393 0.1020 0.1127 0.1091 0.1056 MR (esu.mol−1) 120.3345 151.5366 132.8875 169.8866 131.5351 168.2585One of the central goals of this study is to understand the underlying structure–property relationships which might form the basis for a “molecular engineering” approach to electronics, optoelectronics, and photonics. The molar refractivity of our molecule, known to be an important parameter in quantitative structure–property relationship analysis was calculated for this purpose. The value of the molar refractivity was calculated at the three levels, in both gas and chloroform using the 6-311++G(d,p) basis set. The Lorenz-Lorentz equation was used for this calculation [26, 27] and its results are listed in Table 6.The high values of molar refractivity, polarizability, anisotropy of polarizability, and first static hyperpolarizability of Rubescin E molecule show that the molecule has good quantitative structure–property relationship analysis and might therefore form the basis for a “molecular engineering” approach to electronics, optoelectronics, and photonics.


### 3.5. NMR Study of Rubescin E

After the optimization of the Rubescin E molecule, the1H and 13C chemical shifts were calculated at the RHF, B3LYP, and B3PW91 levels of the theory using the 6-311++G(d,p) basis set. In order to compare the calculated values of 1H and 13C chemical shifts with experimental results, we also need to calculate the absolute shielding value of 1H and 13C for the tetramethylsilane (TMS) using the same methods above. The GIAO (Gauge Invariant Atomic Orbitals) approach known to provide satisfactory chemical shifts for different nuclei with larger molecules [28] was used for this purpose and the following equation:(6)δippm=isotropicTMSi-isotropici,where i is the atom type and was used to convert the chemical shielding to chemical shifts.The experimental and calculated chemical shifts of1H along with their corresponding error are listed in Table 7. From our results we observed that all the methods provide results which are very close to experiment since the errors between the experimental and calculated results are smaller.Table 7
Experimental and calculated1H NMR chemical shifts δ (ppm) of Rubescin E at the RHF, B3LYP, and B3PW91 levels in chloroform solution using the 6-311++G(d,p) basis set.
Nuclei Calculatedδ (ppm) Experimentalδ (ppm) [1] Nuclei Calculatedδ (ppm) Experimentalδ (ppm) [1] RHF B3LYP B3PW91 RHF B3LYP B3PW91 H10 3,6354 4,4787 4,5162 4,44 H41 3,2764 3,8070 3,7375 3,97 H13 3,7599 4,5046 4,4656 5,5 H43 0,0206 0,1390 0,1217 - H17 1,1735 1,3264 1,2850 - H44 0,5304 0,6752 0,6653 0,65 H18 1,4006 1,4842 1,5205 1,34 H45 1,1410 1,2581 1,2916 - H19 0,8843 0,9632 0,9055 - H47 2,9441 3,4299 3,3665 3,45 H21 2,2212 3,1228 3,2220 2,9 H49 1,8799 2,0794 2,0578 2,11 H23 0,7480 0,8702 0,8499 - H50 1,6401 2,0098 2,0019 1,51 H24 0,9682 1,2471 1,2747 1,43 H52 2,1382 2,6231 2,6453 2,52 H25 1,6905 1,7201 1,7225 - H54 6,4241 6,4756 6,5064 6,23 H27 1,7833 2,0352 1,9975 1,9 H56 7,6008 7,6737 7,6347 7,34 H28 1,7575 2,1239 2,1319 1,9 H58 7,2432 7,2352 7,1892 7,24 H30 3,1956 3,7283 3,7158 3,77 H66 6,5053 6,5963 6,7294 6,73 H31 3,3513 3,5791 3,5410 3,55 H68 1,9939 2,0486 2,0556 - H33 7,4298 7,4428 7,5055 7,07 H69 1,6905 1,8891 1,9108 1,82 H35 5,9894 6,1274 6,1740 5,95 H70 1,7037 1,8508 1,8560 - H37 0,3741 0,4953 0,4827 - H72 1,3371 1,5726 1,5006 - H38 1,4776 1,8588 1,8632 1,22 H73 1,7489 1,8289 1,8340 1,87 H39 0,7281 1,2414 1,3276 - H74 2,1737 2,2617 2,2408 -In order to compare experimental and theoretical results, a linear correlation of1H-NMR chemical shifts was established as shown in Figure 6. The regression line was plotted using the following equations: δcal=0.98880δexp-0.17198, δcal=0.97379δexp+0.18796, and δcal=0.97069δexp+0.19387, respectively, at the RHF, B3PW91, and B3LYP levels of the theory. The theoretical results obtained from using the 6-311++G(d,p) basis set show good correlation with experiment since, and the calculated R-square values are found to be close to 1 at each level as shown by Figure 6.Figure 6
Comparison of experimental and theoretical1H chemical shifts of Rubescin E calculated at the RHF, B3PW91, and B3LYP using the 6-311++G(d,p) basis set in chloroform.The calculated and experimental13C chemical shifts of our molecule are given in Table 8 and their comparison can be found in Figure 7. The linear regression line plotted in Figure 7 shows that theoretical results are in good agreement with experiment. This is confirmed by the linear correlation coefficient calculated here as R-square at the RHF, B3PW91, and B3LYP levels using the 6-311++G(d,p) basis set.Table 8
Experimental and calculated13C NMR chemical shift δ (ppm) of Rubescin E at the RHF, B3LYP, and B3PW91 levels in chloroform solution using the 6-311++G(d,p) basis set.
Nuclei Calculatedδ (ppm) Experimentalδ (ppm) [1] Nuclei Calculatedδ (ppm) Experimentalδ (ppm) [1] RHF B3LYP B3PW91 RHF B3LYP B3PW91 C1 44,217875 56,667075 53,80495 47,5 s C34 134,341675 139,383575 138,51605 131,3 d C2 206,549275 213,070575 210,62615 200,3 s C36 21,545175 24,454275 24,23345 22,7 q C3 56,393275 73,459075 70,54015 64,6 s C40 53,124275 65,723775 64,21635 60,3 d C4 43,854075 56,324675 52,83685 44,9 s C42 22,468475 24,495375 24,17495 21,5 q C5 60,103575 77,293875 74,30925 68,3 d C46 48,923175 61,540375 59,53515 55,2 d C6 39,115675 49,868075 47,23345 41,3 s C48 29,511075 34,706875 33,33385 31,1 t C8 39,020275 51,568975 49,31465 41,3 s C51 38,272375 48,003275 46,38035 38,8 d C9 65,951775 79,364675 77,38455 71,4 d C53 117,347375 119,574075 118,57695 110,8 d C12 72,763675 87,369975 84,63375 74,7 d C55 149,815075 151,680375 149,71195 142,9 d C14 130,650675 133,767875 131,73785 123,1 s C57 144,528075 147,708875 145,91185 139,2 d C16 21,641175 23,522875 22,88275 21,1 q C62 178,475775 182,888075 180,33025 167,4 s C20 44,504575 54,261975 53,16905 50,6 d C63 132,986175 138,281375 136,47755 128,8 s C22 16,680575 18,585575 18,72435 17,5 q C64 148,221575 150,697975 151,11665 138,3 d C26 34,988975 41,161875 39,99065 35,4 t C67 15,275775 17,096475 17,51975 14,6 q C29 71,816475 83,425975 81,35795 79,5 t C71 13,518375 15,400475 15,47155 12,6 q C32 164,415875 166,172275 165,17515 151,6 dFigure 7
Comparison of experimental and theoretical13C chemical shifts of Rubescin E calculated at the RHF, B3PW91, and B3LYP using the 6-311++G(d,p) basis set.The following regression line plotted for each level using the general equationδcal=aδexp+b, where a and b are given in Figure 7, shows that the calculated 13C chemical shifts correlate very well with experiment. The linear correlation coefficient calculated as R-square found in Figure 7 also confirms this.


### 3.6. Vibrational Frequencies Analysis

The vibrational frequencies of our molecule were computed by using B3LYP/6-311G(d,p) method in both gas phase and chloroform. The experimental IR vibrational frequencies obtained for the two carbonyl moiety present in our structure along with the calculated scaled and unscaled vibrational frequencies, IR, and Raman frequencies with their approximate descriptions are given in Table9. The rest of the vibrational parameter of Rubescin E molecule which is not described in Table 9 can be obtained from Supplementary Material S2. The scale factor was determined as the mean value of the scale factor that matches correctly for the C=O stretching and the given experimental value. The obtained scale factor was 0.9706. No imaginary frequencies were found showing that structure of the molecule Rubescin E is stable in both gas and solvent. Figure 8 gives the representation of the scaled IR intensity and Raman scattering activity.Table 9
Some calculated scaled and unscaled vibrational frequencies (cm−1), IR (km.mol−1), and Raman scattering activities (Å4.amu−1) of Rubescin E in gas phase and chloroform solution obtained at the B3LYP/6-311G(d,p) level.
Gas phase Chloroform solution Vibrational frequencies  Vibrational frequencies Exp. [1] Unscaled Scaled IR Raman Unscaled Scaled IR Raman Approximate descriptions 3277.8244 3179.489668 0.1483 154.454 3277.3381 3179.017957 0.2265 260.5952 Symνs C-H groups on furan ring 3272.9127 3174.725319 1.6469 66.8185 3272.4528 3174.279216 1.0819 83.7804 Asymνs C-H groups on furan ring 3240.2105 3143.004185 0.9505 45.7116 3240.612 3143.39364 1.6053 100.3155 Asymνs of (C53-H54; C55-H56) 3189.511 3093.82567 3.5332 66.4094 3189.3244 3093.644668 8.3712 160.0412 ν s C40-H41 3175.4637 3080.199789 11.8025 201.1091 3175.3082 3080.048954 19.8811 372.2174 Symνs (C34-H35; C32-H33) 3172.7225 3077.540825 4.8286 43.2929 3170.4225 3075.309825 12.9561 111.1091 Asymνs of CH3 (C36) 3164.5342 3069.598174 5.4628 42.0037 3160.4647 3065.650759 13.1398 103.7241 ν s C64-H66 3140.7401 3046.517897 10.7253 48.1146 3141.8739 3047.617683 28.9110 111.4035 Asymνs of CH3 (C36. C22) 3096.4047 3003.512559 37.8710 128.8493 3103.9325 3010.814525 53.3513 256.448 Asymνs of (C29-H30; C29-H31) 3087.0614 2994.449558 18.8484 62.1458 3094.289 3001.46033 37.2141 110.584 Asymνs of CH3 (C71); νs C12-H13 3056.0169 2964.336393 13.0488 74.2148 3062.0737 2970.211489 17.9489 162.7148 Symνs of CH3 (C22) 3055.6408 2963.971576 14.4803 142.8654 3056.849 2965.14353 21.0392 234.8621 Asymνs of (C67-H69; C67-H70) 3023.1661 2932.471117 14.1323 120.9272 3029.0714 2938.199258 23.4132 269.1079 Symνs of CH3 (C71) 3016.7818 2926.278346 23.9892 318.0136 3018.0608 2927.518976 25.8983 486.6073 Symνs of CH3 (C67) 2999.7383 2909.746151 1.0004 31.9507 2998.9246 2908.956862 3.4528 89.9972 ν s of C20-H21 1720 1779.5912 1726.203464 172.5832 16.0679 1753.6214 1701.012758 326.2675 24.7567 ν s of C62=O65 and βs of C62-C63=C64-C67 1664 1742.8596 1690.573812 191.5410 32.6047 1719.1678 1667.592766 374.9763 96.2937 ν s of C2=O7 and βs of C1-C2-C34-H35 1699.8624 1648.866528 90.7515 127.5998 1692.7491 1641.966627 159.0973 264.4437 ν s C63=C64; βs H66-C64-C67-H68 and βs C62-C63-C71-H72 1655.4051 1605.742947 20.9946 48.7257 1648.5716 1599.114452 54.0221 158.0979 ν s C34=C32; δs of H33-C32-C8 and δs of H35-C34-C2 1627.2588 1578.441036 1.1593 11.251 1625.9499 1577.171403 1.4847 24.0532 Asymνs of C=C on furan ring 1532.8277 1486.842869 17.3545 52.0428 1530.1712 1484.266064 23.5845 101.1704 Symνs of C=C on furan ring 1531.0536 1485.121992 4.3738 6.1013 1522.5028 1476.827716 5.4574 13.4777 s c i s . s of (C29-H30; C29-H31) 1518.4514 1472.897858 13.9129 13.9129 1514.0912 1468.668464 12.9483 27.3727 τ s of CH3 (C22; C16) and scis.w of (C29-H30; C29-H31) 1503.6728 1458.562616 9.8386 5.7612 1498.5877 1453.630069 19.7850 13.2898 τ s of CH3 (C16; C22; C36) 1499.3956 1454.413732 5.1940 7.4533 1492.6161 1447.837617 9.3270 17.4033 τ s of CH3 (C42); scis.m of (C26-H27; C26-H28) and scis.w of (C48-H49; C48-H50) 1488.4029 1443.750813 0.9776 2.8672 1485.682 1441.11154 6.7043 7.8167 τ s of CH3 (C16; C22; C36) and δm of C20-H21 1485.5561 1440.989417 2.9100 5.2938 1481.7402 1437.287994 4.3280 14.1082 s c i s . s of (C48-H49; C48-H50) and τs of CH3 (C42) 1483.6563 1439.146611 0.4862 7.8554 1478.0624 1433.720528 1.4889 21.2082 s c i s . s of (C26-H27; C26-H28) and τm of CH3 (C42) 1479.4465 1435.063105 7.9832 38.0149 1470.3189 1426.209333 12.7942 58.6094 τ s of CH3 (C67; C71) 1463.5075 1419.602275 2.5457 1.0126 1459.7847 1415.991159 4.0997 2.0734 τ s of H21-C20-C9-H10 and τw of CH3 (C22) 1442.8169 1399.532393 5.3126 6.5726 1441.0254 1397.794638 8.4482 14.8596 ν m of C3-C40; νm of C5-C46; rock.s of (C26-H27; C40-H41) and τm of H10-C9-C20-H21 1422.4074 1379.735178 42.8712 4.011 1420.5762 1377.958914 63.3216 10.8875 Sym CH3 umbrella mode 1418.7082 1376.146954 0.6510 1.2396 1416.3711 1373.879967 0.6332 11.5796 Asym CH3 umbrella mode; rock.m (C34-H35;C32-H33); δm C51-H52 1417.9087 1375.371439 6.7934 3.5193 1414.8341 1372.389077 5.2808 12.6492 ν m of C14-C53; δs of H52-C51 and sym CH3 umbrella mode 1411.6946 1369.343762 3.6967 24.766 1405.5801 1363.412697 6.3221 38.7377 asym CH3 umbrella mode (C67; C71) and δm of H66-C64 1404.0182 1361.897654 5.7921 1.3462 1402.0625 1360.000625 12.7684 4.8755 r o c k . m of (H35-C34; C32-H33); CH3 umbrella mode (C22; C16) and τm of H21-C20-C9-H10 1399.4114 1357.429058 7.3054 2.6928 1399.317 1357.33749 5.4113 6.6084 τ s of H10-C9-C20-H21; rock.m of (H35-C34; C32-H33) and δm of H13-C12-O60 1392.7814 1350.997958 4.4872 7.7674 1393.9199 1352.102303 8.7259 13.1186 τ s of H10-C9-C20-H21; rock.s of (H35-C34; C32-H33) and δs of H13-C12-O6 1381.3486 1339.908142 0.8619 1.6091 1378.5237 1337.167989 2.7575 3.5116 w a g g . s of (C29-H30; C29-H31); τs of H10-C9-C20-H21; δm of H13-C12-C9 and CH3 umbrella mode (C16) 1373.7055 1332.494335 4.3307 9.0916 1371.0783 1329.945951 5.0163 17.666 ν m of C63-C71; CH3 umbrella mode (C67; C71); δs of C64-H66 and τm of H10-C9-C20-H21 1368.9888 1327.919136 4.4971 10.4931 1367.4102 1326.387894 5.4518 20.2257 r o c k . s of (H56-C55; C53-H54); δs of C51-H52; wagg.s of (C48-H49; C48H50) and wagg.m of (C26-H27; C26H28) 1365.648 1324.67856 4.2088 1.0219 1364.8154 1323.870938 6.4354 2.7506 τ s of H10-C9-C12-H13; δm of C64-H66; rock.m (H35-C34; C32-H33); wagg.m of (C29-H30; C29H31) and CH3 umbrella mode (C16; C36) 1351.6819 1311.131443 2.3942 1.8233 1351.4078 1310.865566 3.8793 2.9367 w a g g . s of (C26-H27; C26-H28); δs of C51-H52 1343.0612 1302.769364 0.8245 6.8235 1343.2284 1302.931548 0.0396 7.8405 τ m of H10-C9-C20-H21; δs of C12-H13; δs of C51-H52 1326.3406 1286.550382 6.0965 5.2766 1322.4392 1282.766024 7.9781 13.8929 ν s of C3-C40; δs of C40-H41 1301.2149 1262.178453 4.1883 6.2643 1301.7097 1262.658409 7.1261 6.9678 ν m of C5-C6; twist.s of (C26-H27; C26-H28); wagg.m of (C48-H49; C48-H50); δm of H47-C46-C5; rock.s of (H56-C55; C53-H54) 1297.0244 1258.113668 1.7948 7.1956 1297.4084 1258.486148 1.3878 21.5171 ν w of C9-C12; wagg.s of (C48-H49; C48-H50); δm of H47-C46-C48; δs of C51-H52; twist.m of (C26-H27; C26-H28) 1288.4675 1249.813475 3.5313 1.5262 1287.909 1249.27173 1.5765 14.1367 δ s of C46-H47; δs of C12-H13; τm of H10-C9-C20-H21 and twist.m of (C26-H27; C26-H28) 1278.2074 1239.861178 1.4763 18.6173 1278.0044 1239.664268 2.9774 29.5326 ν m of C14-C51; δs of C57-H58; twist.m of (C48-H49; C48-H50) and δs of C51-H52 1273.4643 1235.260371 3.1680 10.1375 1271.8325 1233.677525 4.2401 20.9966 δ s of C46-H47; δs of C12-H13; δs of C57-H58; τs of H10-C9-C20-H21 and twist.m of (C26-H27; C26-H28) 1266.8541 1228.848477 3.8717 5.3878 1266.4233 1228.430601 6.8831 16.4996 τ s of H10-C9-C20-C8 and δm of C32-H33 1253.2129 1215.616513 59.1657 19.3282 1253.6896 1216.078912 120.7089 57.0914 s c i s . s of (C32-H33; C34-H35) and τm of C2-C1-C20-C9 1252.2694 1214.701318 0.7185 4.8164 1251.9233 1214.365601 0.6008 8.7087 δ m of CH on furan ring; twist.s of (C48-H49; C48-H50); twist.m of (C26-H27; C26-H28) and τm of H52-C51-C6-C42 1245.9092 1208.531924 177.9705 5.7457 1246.65 1209.2505 254.8417 9.1404 ν m of C62C63; τm of H66-C64-C67-H68; twist.s of (C29-H30; C29H31) 1237.0891 1199.976427 12.8957 8.0876 1236.5792 1199.481824 11.7625 18.8578 t w i s t . s of (C29-H30; C29-H31); τm of H21-C20-C8-C16 and rock.w of (C32-H33; C34-H35) 1220.0711 1183.468967 14.9312 3.1637 1219.3148 1182.735356 19.5929 7.8591 t w i s t . s of (C26-H27; C26-H28) and of (C48-H49; C48-H50); δs of C51-H52; δm of C55-H56 and τm of C6-C5-C4-C36 1201.9071 1165.849887 3.4760 6.7455 1199.1897 1163.214009 8.0422 13.5718 δ s of C40-H41; δm of C46-H47 and τm of H13-C12-C4-C3 1185.406 1149.84382 15.4074 0.3306 1180.1007 1144.697679 18.7873 1.4104 t w i s t . s of (C48-H49; C48-H50); τm of H52-C51-C14-C57; scis.s of (C55-H56; C53-H54) 1179.6911 1144.300367 1.9628 1.119 1178.2209 1142.874273 2.8925 1.7435 t w i s t . m of (C48-H49; C48-H50); τm of H28-C26-C40-H41; δm of C51-H52 and τm of C42-C6-C5-C4 1166.7314 1131.729458 14.6259 5.1602 1164.8183 1129.873751 9.3342 9.3366 τ m C1-C20-C8-C32  twist.s of (C29-H30; C29-H31); τm C3-C4-C12-C9 1157.5523 1122.825731 15.5290 4.7107 1156.1874 1121.501778 28.1722 11.6347 S c i s . m of (C32-H33; C34-H35); δs of C9-H10 and τm C12-C4-C5-C6 1148.5582 1114.101454 146.5450 3.5872 1149.5402 1115.053994 200.0358 6.6811 ν m of C62-O60 and βs C63-C64-C67-H68 1144.341 1110.01077 178416 3.5877 1144.4015 1110.069455 27.0332 7.8819 t w i s t . m of (C26-H27; C26-H28); τm C4-C5-C6-C4; τm C10-C9-C20-C8 1136.9705 1102.861385 1.6907 9.6148 1134.337 1100.30689 2.0658 19.6536 τ s H28-C26-C40-H41; τm H37-C36-C46-C47; scis.s (C32-H33; C34-H35) 1122.8634 1089.177498 21.5468 4.0892 1120.5923 1086.974531 35.6177 10.2656 τ m H33-C32-C8-C20; τm C9-C12-C4-C36; τm C41-C40-C26-C28 and τm C42-C6-C51-C48 1099.4941 1066.509277 48.0338 2.0757 1096.2182 1063.331654 62.1695 5.261 ν m C12-O60; δm of C46-H47; δm of C51-H52;τm C9-C20-C1-C22 and twist.m of (C48-H49; C48-H50) 1091.4985 1058.753545 28.1743 1.6861 1085.2223 1052.665631 29.9371 3.0875 ν m C57-O15 and scis.s of (C53-H54; C55-H56) 1080.7072 1048.285984 92.4087 0.7097 1080.9064 1048.479208 144.3970 1.9949 ν m C12-O60; sym δs CH3; scis.s of (C32-H33; C34-H35) and τm C2-C1-C3-C40 1071.7177 1039.566169 123.1938 6.7128 1073.0176 1040.827072 197.5919 15.9455 ν m C62-O60; δs of C46-H47 and asym δs of CH3 (C71) 1068.3452 1036.294844 9.8016 1.8104 1067.1028 1035.089716 24.1877 5.7115 τ s C67C64C63C71 1050.9373 1019.409181 13.3402 0.7713 1048.853 1017.38741 37.6705 1.8533 δ m of C46-H47; δm of C64-H66; τm C67-C64-C63-C71 1045.5983 1014.230351 69.2901 6.619 1044.7341 1013.392077 62.2356 12.9459 t w i s t . m of (C71-H73; C71-H74); δm of C26-H27; δm of C53-H54; δm of C48-H50 1027.1407 996.326479 1.7797 5.289 1027.2885 996.469845 30.2585 3.8663 t w i s t . s (C34H35; C32H33) 1022.4549 991.781253 0.9472 2.7037 1020.7406 990.118382 6.3182 4.1772 ν m of C48-C51; asym δs of CH3; βm H66-C64-C63-C62 and τm H13-C12-C4-C5 1017.7638 987.230886 30.0425 3.9798 1015.3161 984.856617 43.5319 8.8798 asymδs of CH3; rock.s of (C29-H30; C29-H31); τm C9-C20-C1-C3 1011.5509 981.204373 4.8801 6.6943 1009.814 979.51958 6.3114 13.7312 β s C51-C14-C53-H54; asym δm of CH3 (C42); βs H58-C57-O15-C55 1002.0581 971.996357 12.1626 2.5574 998.7131 968.751707 27.5923 6.2284 ν m of C46-C48; τm H47-C46-C48-C49; βm C1-C3-C40-C26 994.6222 964.783534 14.7581 1.7537 993.1115 963.318155 22.8186 4.3633 asymδm of CH3 groups; τm C3-C4-C5-C46; τm C48-C51-C6-C26 984.7888 955.245136 9.9824 2.1081 982.8653 953.379341 23.0630 4.4849 τ m C32-C8-C29-H31; asym δm of CH3 groups; τm H13-C12-C9-H10 935.5082 907.442954 21.5974 1.5821 933.456 905.45232 35.1689 4.3679 r o c k . s of (C26-H27; C26-H28); asym δm of CH3; τm C40-C3-C1-C22 894.4122 867.579834 6.7651 6.1001 892.2404 865.473188 16.1490 13.2213 t w i s t . s (C67-H69; C67-H70) and δs C64-H66 888.7652 862.102244 7.1646 2.8098 886.3304 859.740488 9.5352 6.1863 δ s C64-H66; rock.m (C48-H49; C48-H50); twist.s (C67-H69; C67-H70) 866.5271 840.531287 1.1709 0.6223 870.9888 844.859136 1.8110 2.3985 t w i s t . s of (C53-H54; C55-H56) 863.4892 837.584524 11.2475 6.7108 862.9942 837.104374 10.4041 13.1553 τ m H52-C51-C48-H49; rock.m (C26-H27; C26-H28); rock.m (C22-H23; C22-H24); τm H45-C42-C6-H5 843.0488 817.757336 17.4461 2.5204 843.0694 817.777318 32.2094 5.1332 w a g g . s (C34-H35; C32-H33) and τw O7=C2-C1-C22 834.8182 809.773654 8.7574 3.1907 831.3156 806.376132 15.1706 6.936 τ s H47-C46-C5-C4; τs C48-C51-C6-H42 813.7477 789.335269 1.0138 6.0149 810.0882 785.785554 0.7347 13.0197 τ m C26-C40-C3-C4 801.2001 777.164097 32.6376 0.9129 802.8851 778.798547 51.1580 3.2321 Symδs CH groups on furan ring 772.7524 749.569828 40.1779 4.4199 769.619 746.53043 62.4072 8.3682 τ s of C71-C63-C62-O60; τm of H66-C64-C67-H69 765.4691 742.505027 7.1326 7.398 765.0018 742.051746 11.7201 14.1992 Symδm CH on furan ring and τm C42-C6-C51-C48 751.3513 728.810761 2.6045 2.4905 750.9877 728.458069 5.0319 4.4818 τ m C5-C4-C12-C9 and τm C34-C32-C8-C29 738.9121 716.744737 11.6448 0.2055 739.1239 716.950183 16.1963 0.0788 Asymδs CH on furan ring 722.1832 700.517704 12.3489 2.6117 723.4458 701.742426 18.8683 4.4984 τ m C1-C2-C34-C32; τm C4-C12-O60-C62 686.9578 666.349066 5.4224 1.4738 685.8912 665.314464 10.7183 2.8493 τ m H58-C57-C14-C53 and τm C48-C51-C6-C42 668.865 648.79905 12.8788 0.9188 667.6324 647.603428 18.4726 1.8119 τ m C9-C12-C4-C36 646.4378 627.044666 11.8100 0.5746 646.7719 627.368743 21.9688 1.442 β m C67-C64-C63-C71 619.5628 600.975916 14.5359 2.821 617.9459 599.407523 19.3158 4.5248 τ s C53-C55-O15-C57 616.8961 598.389217 4.4856 1.6795 615.6735 597.203295 10.3745 2.8885 τ s C57-C14-C51-C48 590.7602 573.037394 2.2255 8.0984 590.8644 573.138468 4.8686 15.7435 τ m O60-C62-C63-C71; τm C26-C6-C5-C46 545.9651 529.586147 0.9299 3.7502 549.5733 533.086101 3.8923 7.7962 τ m C62-C63-C64-C67; δm of CH3 (C71) 538.3894 522.237718 17.1612 0.4714 536.6383 520.539151 25.1977 1.1212 τ m C4-C5-C6-C51 508.9443 493.675971 1.2889 2.069 507.5983 492.370351 1.4410 4.1594 τ m C3-C4-C5-C46; rock.m (C26-H27; C26-H28) 475.643 461.37371 1.2962 4.5398 474.4059 460.173723 2.4947 10.7229 δ s C16-C8-C29 461.5318 447.685846 2.3465 0.597 461.4543 447.610671 4.0236 0.9512 τ m C48-C46-C5-C4 451.0159 437.485423 2.9275 4.0628 448.867 435.40099 4.9702 8.8493 δ s C32-H33; τm C29-C8-C32-C34 437.1112 423.997864 1.4877 1.6801 437.3603 424.239491 4.9702 2.869 τ m O60-C62-C63-C64 and rock.m (C26-H27; C26-H28) 416.2717 403.783549 7.0349 2.9785 413.098 400.70506 9.3286 5.9324 τ m C62-C63-C64-C67 376.4872 365.192584 0.6057 1.5014 375.9518 364.673246 0.8549 2.7432 δ s C36-C4-C12 359.436 348.65292 1.0513 0.2212 357.6319 346.902943 0.4099 3.4574 τ m C22-C1-C3-C40 347.1844 336.768868 0.2931 1.3363 346.0298 335.648906 0.6318 1.8682 Asymδm of CH3 groups 309.437 300.15389 1.4908 0.891 306.2399 297.052703 1.5054 1.1169 β m C67-C64-C63-C71 231.0043 224.074171 3.5498 0.8619 229.9752 223.075944 7.8008 1.6674 β m O60-C62-C63-C64 42.7727 41.489519 0.3353 1.5162 39.5275 38.341675 0.5007 4.2131 t w i s t . m of (C14-C57; C14-C53) δ = bending; τ = out of plane deformation; β = in plane deformation; w = weak; m = medium; s = strong; wagg. = wagging; twist. = twisting; rock. = rocking; scis. = scissoring; ν = stretching; sym = symmetrical and asym = anti-symmetrical.Figure 8
IR spectra (blue) and Raman spectra (red) of Rubescin E in both gas phase (top) and chloroform solution (bottom) using B3LYP/6-311G(d,p).The C=O double bond gives rise to a very intense absorption band in IR spectrum. The position and intensity of this band range from 1870 cm−1 to 1540 cm−1 depending on the physical state, electronic, and mass effects of neighboring substituents, intra- and intermolecular interactions, and conjugations [29]. The C=O double bond absorption spectra were observed experimentally at 1720 cm−1 and 1664 cm−1 [1]. In this study, the vibrational mode of C=O was found at 1726.20 cm−1 and 1690.57 cm−1 gas phase and at 1701.01 cm−1 and 1667.59 cm−1 in chloroform. There is good agreement between the vibrational modes with experimental values.


## 3.1. Optimized Structure

The optimized geometry of Rubescin E obtained using the B3LYP/6-311++G(d,p) method in chloroform is shown in Figure1. The value of the total electronic energy of the molecule obtained at the B3LYP shows that Figure 1 is the most stable structure of the molecule. The total electronic energy calculated within the two methods in gas and in a solution of chloroform with the 6-311++G(d,p) is given in Table 1.Table 1
Optimized geometric parameters in gas phase and in chloroform solution of Rubescin E at the RHF, B3LYP, and B3PW91 level with the 6-311++G (d,p) basis sets.
Levels RHF B3LYP B3PW91 Theory a[11], b[12], c[13] Basis set Gaz CDCl3 Gaz CDCl3 Gaz CDCl3 Bond length  R1 (C1-C2) 1.5503 1.5490 1.5603 1.5583 1.5521 1.5500 R2 (C1-C3) 1.5698 1.5672 1.5811 1.5777 1.5719 1.5684 R3 (C1-C20) 1.5167 1.5157 1.5221 1.5215 1.5153 1.5147 R4 (C1-C22) 1.5474 1.5481 1.5510 1.5509 1.5439 1.5438 R5 (C2=O7) 1.1900 1.1948 1.2167 1.2213 1.2152 1.2197 2.10 b R6 (C2-C34) 1.5041 1.4992 1.4966 1.4910 1.4920 1.4867 R7 (C3-C4) 1.5898 1.5887 1.5973 1.5968 1.5866 1.5860 R8 (C3-C40) 1.4814 1.4800 1.4972 1.4958 1.4931 1.4918 1.462 b R9 (C3-O59) 1.3994 1.4024 1.4311 1.4335 1.4236 1.4256 1.428 b R10 (C4-C5) 1.5515 1.5518 1.5549 1.5548 1.5473 1.5471 R11 (C4-C12) 1.5707 1.5733 1.5756 1.5787 1.5676 1.5707 R12 (C4-C36) 1.5501 1.5503 1.5543 1.5543 1.5471 1.5472 R13 (C5-C6) 1.5428 1.5442 1.5477 1.5487 1.5401 1.5410 R14 (C5-C46) 1.4556 1.4553 1.4720 1.4717 1.4686 1.4684 1.462 b R15 (C5-O61) 1.4206 1.4235 1.4568 1.4590 1.4473 1.4492 1.428 b R16 (C6-C26) 1.5259 1.5260 1.5306 1.5307 1.5246 1.5248 R17 (C6-C42) 1.5352 1.5350 1.5373 1.5373 1.5298 1.5298 R18 (C6-C51) 1.5703 1.5708 1.5810 1.5814 1.5724 1.5728 R19 (C8-C16) 1.5423 1.5424 1.5477 1.5481 1.5405 1.5408 R20 (C8-C20) 1.5256 1.5244 1.5348 1.5335 1.5276 1.5264 1.536 c R21 (C8-C29) 1.5405 1.5402 1.5479 1.5468 1.5416 1.5406 1.536 c R22 (C8-C32) 1.5036 1.5036 1.5010 1.5010 1.4958 1.4960 R23 (C9-O11) 1.4120 1.4133 1.4389 1.4411 1.4304 1.4324 1.428 c R24 (C9-C12) 1.5288 1.5302 1.5357 1.5373 1.5311 1.5329 R25 (C9-C20) 1.4997 1.4993 1.5044 1.5042 1.4999 1.4998 1.536 c R26 (O11-C29) 1.4261 1.4287 1.4530 1.4551 1.4438 1.4457 1.428 c R27 (C12-O60) 1.4104 1.4131 1.4339 1.4369 1.4255 1.4283 R28 (C14-C51) 1.5035 1.5041 1.5003 1.5010 1.4953 1.4959 R29 (C14-C53) 1.4493 1.4505 1.4428 1.4438 1.4387 1.4397 1.430 a R30 (C14=C57) 1.3411 1.3410 1.3621 1.3619 1.3614 1.3614 1.364 a R31 (O15-C55) 1.3382 1.3412 1.3609 1.3638 1.3548 1.3574 1.364 a R32 (O15-C57) 1.3467 1.3496 1.3659 1.3686 1.3592 1.3616 1.364 a R33 (C26-C40) 1.5162 1.5158 1.5190 1.5181 1.5137 1.5129 R34 (C32=C34) 1.3270 1.3285 1.3431 1.3445 1.3422 1.3436 R35 (C40-O59) 1.4010 1.4054 1.4353 1.4395 1.4282 1.4320 1.428 b R36 (C46-C48) 1.5086 1.5076 1.5135 1.5123 1.5088 1.5077 R37 (C46-O61) 1.4005 1.4051 1.4326 1.4376 1.4254 1.4297 1.428 b R38 (C48-C51) 1.5407 1.5405 1.5478 1.5475 1.5408 1.5405 R39 (C53=C55) 1.3381 1.3381 1.3567 1.3567 1.3559 1.3559 1.364 a R40 (O60-C62) 1.3485 1.3397 1.3805 1.3700 1.3743 1.3650 R41 (C62-C63) 1.5033 1.5030 1.4998 1.5000 1.4956 1.4952 R42 (C62=O65) 1.1810 1.1873 1.2059 1.2113 1.2046 1.2098 R43 (C63=C64) 1.3222 1.3230 1.3402 1.3403 1.3394 1.3398 R44 (C63-C71) 1.5153 1.5159 1.5127 1.5135 1.5071 1.5083 R45 (C64-C67) 1.5001 1.5002 1.4954 1.4959 1.4898 1.4901  Bond angles  A1 (C2-C1-C3) 115.3869 115.1538 115.3519 115.0591 115.3042 114.9661 A2 (C2-C1-C20) 104.9116 105.2360 104.8861 105.3058 105.0195 105.4353 A3 (C2-C1-C22) 104.6632 104.8093 104.8467 105.0548 104.7619 105.0065 A4 (C3-C1-C20) 105.4487 104.9239 106.0693 105.3428 105.9491 105.1727 A5 (C3-C1-C22) 110.0598 110.4677 109.3407 109.9326 109.4774 110.1062 A6 (C20-C1-C22) 116.6507 116.5134 116.6409 116.4160 116.6212 116.4196 A7 (C1-C2-O7) 122.6712 122.1731 122.5890 122.0461 122.6012 122.0599 A8 (C1-C2-C34) 118.8294 119.0297 118.5520 118.8580 118.5112 118.8095 A9 (O7-C2-C34) 118.3115 118.6060 118.6750 118.9135 118.6899 118.9368 A10 (C1-C3-C4) 117.4677 117.2546 117.5179 117.3499 117.4703 117.2908 A11 (C1-C3-C40) 120.4116 120.3391 120.5229 120.3696 120.4781 120.3201 A12 (C1-C3-O59) 113.5239 113.6346 113.2288 113.4708 113.2740 113.5007 A13 (C4-C3-C40) 119.7989 119.8618 119.6777 119.7275 119.7605 119.8264 A14 (C4-C3-O59) 110.9192 111.3348 110.6687 111.0566 110.7288 111.1433 A15 (C3-C4-C5) 108.2815 108.0767 108.5292 108.3020 108.4460 108.1898 A16 (C3-C4-C12) 116.9097 116.9148 116.6545 116.8466 116.8336 117.0260 A17 (C3-C4-C36) 107.3533 107.5825 107.2145 107.3890 107.2213 107.3820 A18 (C5-C4-C12) 110.9502 111.2590 110.8879 111.1131 111.0310 111.3284 A19 (C5-C4-C36) 108.2096 108.3900 108.2857 108.5557 108.0890 108.3471 A20 (C12-C4-C36) 104.7402 104.2361 104.883 104.2585 104.7988 104.1530 A21 (C4-C5-C6) 122.3963 122.5160 122.2095 122.2513 122.2181 122.2697 A22 (C4-C5-C46) 126.1434 126.0858 126.2488 126.1993 126.1315 126.0739 A23 (C4-C5-O61) 113.7557 113.5947 113.7382 113.6922 114.0173 113.9553 A24 (C6-C5-C46) 108.4092 108.4312 108.2407 108.2667 108.2513 108.2900 A25 (C6-C5-O61) 109.3436 109.1575 109.7850 109.6384 109.6935 109.5481 A26 (C5-C6-C26) 106.9225 107.1323 107.1725 107.3025 107.1359 107.2931 A27 (C5-C6-C42) 114.7934 114.8607 114.4807 114.5006 114.5313 114.5541 A28 (C5-C6-C51) 101.8612 101.8830 101.9281 102.0115 101.8916 101.9777 A29 (C26-C6-C42) 108.8679 108.6162 109.1102 108.9149 109.1443 108.9314 A30 (C26-C6-C51) 113.8205 113.8653 113.9931 114.0014 113.9406 113.9367 A31 (C42-C6-C51) 110.5307 110.4727 110.1102 110.0888 110.1443 110.1222 A32 (C16-C8-C20) 117.8467 117.8806 117.5220 117.5381 117.3986 117.3974 A33 (C16-C8-C29) 108.3950 108.5431 108.4117 108.5195 108.5270 108.6672 A34 (C16-C8-C32) 109.5455 109.4283 109.5034 109.3293 109.6190 109.4415 A35 (C20-C8-C29) 96.3773 96.4321 96.6032 96.6193 96.4146 96.4285 101.5 c A36 (C20-C8-C32) 106.3315 106.2487 106.4280 106.3876 106.432 106.3732 A37 (C29-C8-C32) 118.2843 118.2659 118.3155 118.4200 118.3462 118.4575 A38 (O11-C9-C12) 113.2108 113.1065 113.2048 113.2060 113.1493 113.1724 A39 (O11-C9-C20) 103.3360 103.1494 103.8285 103.6622 103.8971 103.7399 104.0 c A40 (C12-C9-C20) 109.2549 109.4574 108.7908 108.9954 108.4814 108.6640 A41 (C9-O11-C29) 111.1841 111.2217 109.8976 109.9018 109.8190 109.8362 110.6 c A42 (C4-C12-C9) 110.4259 110.6951 110.0123 110.3980 109.8110 110.1418 A43 (C4-C12-O60) 111.1499 111.4570 110.9644 111.4849 111.3257 111.9073 A44 (C9-C12-O60) 109.0864 108.7044 108.7314 108.2508 108.4512 107.9972 A45 (C51-C14-C53) 126.042 126.0928 126.1043 126.1692 126.2986 126.3771 A46 (C51-C14-C57) 129.3418 129.1716 128.8385 128.6558 128.7371 128.5448 A47 (C53-C14-C57) 104.5893 104.7043 105.0493 105.1666 104.9597 105.0728 106.14 a A48 (C55-O15-C57) 107.1084 107.1499 106.7602 106.8013 106.8133 106.8678 106.74 a A49 (C1-C20-C8) 121.1479 121.0073 120.9097 120.7705 120.9914 120.8439 A50 (C1-C20-C9) 118.7226 118.5220 118.7478 118.3732 118.6818 118.2898 A51 (C8-C20-C9) 103.8120 103.9439 104.2023 104.3600 104.0389 104.2216 104.4 c A52 (C6-C26-C40) 111.4945 111.6304 111.4804 111.5216 111.4199 111.4969 A53 (C8-C29-O11) 104.4386 104.4819 104.6594 104.594 104.6712 104.6043 107.5 c A54 (C8-C32-C34) 120.4664 120.4528 120.5688 120.4387 120.4312 120.2925 A55 (C2-C34-C32) 125.2907 124.9802 125.5569 125.2584 125.5114 125.1913 A56 (C3-C40-C26) 124.7594 125.1561 124.3752 124.7373 124.3541 124.7241 A57 (C26-C40-O59) 116.1404 115.9652 116.0868 116.0753 115.9905 115.9607 A58 (C5-C46-C48) 110.0006 110.0212 109.8202 109.8537 109.6430 109.6699 A59 (C48-C46-O61) 111.5740 111.5456 111.7313 111.7203 111.8859 111.8641 A60 (C46-C48-C51) 102.6704 102.7788 102.8570 103.0253 102.6915 102.8703 A61 (C6-C51-C14) 116.8638 116.8705 116.6829 116.6156 116.3993 116.3329 A62 (C6-C51-C48) 104.4966 104.5425 104.2867 104.3539 104.3511 104.4332 A63 (C14-C51-C48) 114.9685 114.8714 115.2826 115.1809 115.2757 115.1468 A64 (C14-C53-C55) 106.1668 106.2381 106.7966 106.8606 106.6618 106.7168 106.14 a A65 (O15-C55-C53) 110.7484 110.6455 110.3339 110.2350 110.4305 110.3331 110.49 a A66 (C14-C57-O15) 111.3857 111.2607 111.0591 110.9356 111.1339 111.0086 110.49 a A67 (C12-O60-C62) 123.1805 123.4264 122.4520 122.2629 121.8099 121.5920 A68 (O60-C62-C63) 118.3342 119.1473 118.6681 119.4932 118.6273 119.3485 A69 (O60-C62-O65) 118.3753 117.9395 117.5454 117.1467 117.6414 117.2568 A70 (C63-C62-O65) 123.0766 122.6884 123.4720 123.0718 123.4069 123.1015 A71 (C62-C63-C64) 116.9655 117.1950 116.2922 116.7661 116.1754 116.6519 A72 (C62-C63-C71) 117.8479 117.3833 119.4971 118.5815 119.7175 119.0158 A74 (C64-C63-C71) 125.0717 125.2904 124.1105 124.5124 123.9876 124.1815 A75 (C63-C64-C67) 127.2664 127.2197 127.2301 127.2514 126.9123 126.7855  Total energy (Hartree) -1719.15539 -1719.17648 -1729.82917 -1729.84726 -1729.17724 -1729.19498Figure 1
Ground state geometry of Rubescin E at B3LYP/6-311++G(d,p) in chloroform solution.


## 3.2. Structural Properties

A part of the optimized geometrical parameters (bond length, bond angle) and total electronic energy of the title molecule both in gas and in a solution of chloroform are given in Table1 using the three levels and with the 6-311++G(d,p) basis set. The total description of the molecular geometry of Rubescin E molecule in gas phase and in a solution of chloroform using ab initio (RHF) and DFT (B3LYP and B3PW91) methods with the 6-311++G(d,p) basis set can be obtained from Supplementary Material S1.The atom numbering scheme adopted for this purpose is the same as in Figure1. The energy differences between the two used phases increase when we move from B3PW91 to B3LYP and to RHF and are found to be approximatively 0.48 eV, 0.49 eV, and 0.57 eV, respectively. The optimized bond length and bond angle of Rubescin E are also listed in Table 1 with some specific experimental values [12–14] found in the literature for some groups of compounds such as furan, ethylene oxide, and tetrahydrofuran present in our molecule. It can be observed from Table 1 that the values of the bond length obtained at B3LYP are slightly higher than those obtained at the B3PW91 level. These differences are found between 0.0034 Å and 0.0107 Å for C-C; 0.0061 Å and 0.0095 Å for C-O; and 0.0007 Å and 0.0013 Å for C=C in gas phase. The value of C=O bond length is better at the DFT methods since its values are closer to 2.10 Å found in literature [11]. It can also been observed that the calculated bonds length using Hartree Fock and DFT methods are very close to the values found in literature for the specific groups of compounds present in our molecule. These observed differences varied from 0.0012 Å at the B3LYP level to 0.0363 Å at the RHF level; from 0.0002 Å at the B3PW91 level to 0.0288 Å at the B3LYP level; and from 0.0019 Å at the B3LYP level to 0.0259 Å at the RHF level for C-C, C-O, and C=C bonds both in gas phase and in chloroform solution, respectively.The bonds angles of the studied molecule are slightly different when we move from one phase to another at each level with larger values obtained at the RHF level. From our results, it can be seen that the C-C-C bond angle varies from 96.3773° to 129.3418°, from 96.6032° to 128.8385°, and from 96.4146° to 128.7371° at the gas phase, respectively, at the RHF, B3LYP, and B3PW91 level of the theory. In CDCl3, the C-C-C bond angles are similar to those obtained at the gas phase. The smallest value of C-C-C bond angle was C20-C8-C29 bond angle and the largest C51-C14-C57 bond angle. For the C-C-O angle, the smallest value was 104.4386° obtained at the RHF and the largest value was 123.472° obtained at the B3LYP level both in the gas phase. The C-O-C bond angle was found between 107.1084° and 123.4264° obtained at the RHF level. These bonds angles compared to some known values found in literature [12, 14] for specific compound present in our structure show good similarities. The little differences are found between 0.0268° and 1.5507° for C-C-C bond, between 0.0595° and 3.0614° for C-C-O bond, and between 0.0202° and 0.781° for C-O-C bond. These observed differences are due to the fact that these groups of compounds were not isolated.


## 3.3. CalculatedJ3H-H Coupling Constant

The chemicalJ3H-H proton-proton coupling constant was calculated using the original Karplus [10] equation in gas and solvent and its results compared to experimental values [1] obtained by extracting Rubescin E in a solution of chloroform. From our results, we found that the calculated parameters both in gas and in chloroform are all similar at all the levels used. These obtained results are also very close to experiment. As predicted in literature [10], we observed from Table 2 that when the angles between the two C-H vectors are close enough to 00 or 1800, the value of J3H-H coupling constant is greater (with J31800>J300) and is very small when the angle is close to 900.Table 2
Experimental and calculatedJ3H-H proton-proton coupling constant of Rubescin E in gas phase and in chloroform solution.
PARAMETERS RHF B3LYP B3PW91 EXP [1] Gaz CDCl3 Gaz CDCl3 Gaz CDCl3 Angles(°) J   3 H - H (Hz) Angles(°) J   3 H - H (Hz) Angles(°) J   3 H - H (Hz) Angles(°) J   3 H - H (Hz) Angles(°) J   3 H - H (Hz) Angles(°) J   3 H - H (Hz) H10-C9-C12-H13 45.5506 6.20 43.8143 6.49 48.1393 5.79 45.9537 6.14 48.3285 5.76 46.1662 6.10 4.0 H10-C9-C20-H21 169.5395 12.65 169.8194 12.67 168.824 12.61 168.658 12.59 168.5 12.58 168.2201 12.56 12.0 H27-C26-C40-H41 -11.0718 10.65 -12.0311 10.59 -10.1794 10.70 -10.89 10.66 -10.4324 10.69 -11.298 10.64 6.5 H28-C26-C40-H41 105.3029 2.96 103.995 2.83 106.3433 3.07 105.3319 2.96 106.1668 3.05 104.964 2.92 1.3 H33-C32-C34-H35 -0.2873 11 -0.123 11 -0.5893 11 -0.366 11 -0.566 11 -0.3331 11 10.0 H47-C46-C48-H49 -61.3614 3.82 -61.1286 3.85 -61.9356 3.74 -61.8438 3.75 -61.5482 3.79 -61.4875 3.80 4.2 H47-C46-C48-H50 58.7437 4.17 58.7503 4.17 58.0428 4.27 57.8579 4.30 58.534 4.20 58.3044 4.24 4.2 H49-C48-C51-H52 -42.5704 6.69 -42.1786 6.75 -43.9616 6.46 -43.3642 6.56 -44.5718 6.36 -43.9227 6.47 4.2 H50-C48-C51-H52 -164.093 12.21 -163.817 12.18 -165.22 12.32 -164.673 12.27 -165.874 12.37 -165.259 12.32 11 H54-C53-C55-H56 -0.3838 11 -0.2856 11 -0.3275 11 -0.2429 11 -0.3921 11 -0.3074 11 H66-C64-C67-H68 -177.906 12.99 -177.979 12.99 178.4674 12.99 178.7874 13 178.4147 12.99 178.548 12.99 H66-C64-C67-H69 -56.9125 4.43 -56.9428 4.43 -60.3746 3.95 -59.9903 4 -60.4007 3.95 -60.1923 3.97 7.0 H66-C64-C67-H70 60.6324 3.91 60.4696 3.94 56.6811 4.47 56.9449 4.42 56.6504 4.47 56.7234 4.46 7.0


## 3.4. Electronic Properties

### 3.4.1. Mulliken, ESP, and Natural Charge Distribution

The Mulliken atomic charges of our molecule calculated at all the levels in gas phase and chloroform show positive charge for all the hydrogen atoms. The net charge on all the atoms varies from -1.109653e to 1.980512e, from -1.164916e to 1.904034e, and from -0.891775e to 1.524787e, respectively, in gas phase at the RHF, B3PW91, and B3LYP levels. In a solution of chloroform, the charges varied from -1.064962e to 1.826589e, from -1.206706e to 1.904292e, and from -0.945041e to 1.550492e with some oxygen atoms charges being positive and can be explained by the fact that the oxygen is related to extremely negative carbon atoms. The most positive charge atoms are C63, C5, C8 and the most negative charge atoms are C71, C62, C67.The electrostatic charges were evaluated in this work using the CHelpG scheme of Breneman model. We found from our results that the most positive charges atom is C4 followed by C62 and C2 and the most negative charge atom is C12 followed by C5 and C7. The observation made at all levels and basis set in gas phase and in a solution of chloroform is that the most positive charge atoms are directly related to the most negative charge atoms.The natural atomic charges, obtained using the natural bonding orbital method, were also used to evaluate the atomic charge of Rubescin E. Positive and negative charges were found for all hydrogen and oxygen atoms, respectively. In this case, all carbon atoms directly linked to hydrogen atoms were found to have negative charges except for those linked to oxygen atoms. The most negative charge atom was calculated using HF method and was observed for O65 (-0.69456e) and O60 (-0.68330e), respectively, in chloroform and gas phase. The most positive charge atom was found to be C62 in both gas (0.97067e, 0.80601e, and 0.81407e, respectively, at the RHF, B3PW91, and B3LYP levels) and solvent (0.98887e, 0.81804e, and 0.82650e, respectively, at the RHF, B3PW91, and B3LYP levels); this is due to the fact that C62 is related to negative charge atoms (O65, O60, and C63). Mulliken, electrostatic, and natural atomic charge distributions are graphically shown in Figure 2. From Figure 2, one can observe that, for almost all the methods used for charge description, the most positive and negative charge atoms were calculated at the RHF level in both gas and chloroform and this is due to the fact that the effect of electron correlation is not well described in HF method.Figure 2
Charge distribution on Rubescin E calculated at the RHF, B3PW91, and B3LYP levels in both gas phase and chloroform solution and with the 6-311++G(d,p) basis set.


### 3.4.2. Global Reactivity Descriptors

In order to understand the relationships between structure, stability, and reactivity of Rubescin E molecule, the global reactivity descriptors parameters such as chemical hardness (H), chemical potential (μcp), chemical softness (s), electronegativity (X), and electrophilicity index (ω) were calculated. The finite difference equation given by (1) was used to calculate the ionization potential and electron affinity, which are generally used to calculate the above cited parameters.(1)IP=Eq=N+1-Eq=NEA=Eq=N-Eq=N-1The IP and EA calculated from (1) were then used to calculate H, μcp, s, X, and ω using equations found in the literature [15–17]. All these parameters calculated using the two methods in gas phase are presented in Table 3. A high value of μcp and ω characterizes a good electrophile, while a small value stands for good nucleophile.Table 3
Global reactivity descriptors of Rubescin E at the RHF, B3LYP, and B3PW91 levels in gas phase and in chloroform solution using the 6-311++G(d,p) basis set.
RHF B3LYP B3PW91 Gas Chloroform Gas Chloroform Gas Chloroform IP (eV) 7.151 5.662 7.875 6.819 7.861 6.819 EA (eV) -0.841 0.684 0.461 1.804 0.450 1.825 μ c p (eV) -3.155 -3.173 -4.168 -4.312 -4.156 -4.322 X (eV) 3.155 3.173 4.168 4.312 4.156 4.322 H (eV) 3.996 2.489 3.707 2.508 3.706 2.497 s (eV)−1 0.250 0.402 0.270 0.399 0.270 0.400 ω (eV) 1.245 2.022 2.343 3.707 2.330 3.740The calculated vertical IP values in gas phase are bigger than their corresponding values in solvent. From Table3, we also found that putting the molecule in solvent increases its electron affinity. From the calculated IP and EA values, one can conclude that solvent effect increases the capacity of molecule of gaining an electron compared to donating it. It also reduces the harness of our molecule and increases the softness. Hence, the presence of solvent increases the reactivity of the molecule Rubescin.


### 3.4.3. Frontier Molecular Orbitals

The frontier molecular orbitals of Rubescin E were evaluated using the ab initio and DFT methods. The 6-311G(d,p) and 6-311++G(d,p) basis sets were used for this purpose in gas phase and in chloroform solution. The results show that the energy gap of our molecule decreases when diffuse functions are added onto all the atoms. We also found that whenever the basis set and methods used, the energy gap is greater than 4, showing that our molecule is hard and can be used as insulator in many electronic devices. In Figure3, the 3D plots of the HOMO and LUMO orbitals computed at the RHF, B3PW91, and B3LYP levels with the 6-311G(d,p) basis set are illustrated in gas phase. We observed that the HOMO of Rubescin E is located over the furan ring at the three levels and also at the C-C of cyclohexane ring and C-O of oxiran ring. By contrast, the LUMO orbital is located over the cyclohex-2-enone ring, C-C and C-O bond of tetrahydrofuran ring. We can therefore conclude that electron can easily be transferred from furan ring to tetrahydrofuran ring.Figure 3
Molecular orbital and the HOMO and LUMO energy of Rubescin E in gas phase.The total density of states (DOS) spectrum of Rubescin E at the gas phase and in chloroform is given in Figure4 for each level at the 6-311++G(d,p) basis set. These DOSs spectra presented in Figure 4 were obtained from Gauss-Sum 3.0 program [18] which was used in order to show the contributions of different group to molecular orbital (HOMO and LUMO). From Figure 4, we observe that the HOMO-LUMO energy gap is smaller when we move from RHF to B3PW91 and from B3PW91 to B3LYP level, respectively, for both gas and chloroform phases, with larger values obtained in chloroform.Figure 4
Total density of state (DOS) spectrum of Rubescin E at the RHF, B3PW91, and B3LYP levels in both gas and chloroform phase and with the 6-311++G(d,p) basis set.


### 3.4.4. UV-Vis Spectra Analysis

Time dependent density functional theory (TD-DFT) was used in gas phase at the two levels B3PW91 and B3LYP with the 6-311++G(d,p) basis set in order to determine the first six excited states to investigate the UV-vis absorption spectra of the molecule. The excitation energy (E), wavelength (λ), and oscillator strength (f) along with their major contributions are given in Table 4 and their results are compared to experiment.Table 4
Theoretical absorption wavelength (λ), excitation energy (E), and oscillator strengths of Rubescin E at the B3PW91 and B3LYP levels in gas with the 6-311++G(d,p) basis set.
Excited states Exp [1] B3PW91 B3LYP λ (nm) λ (nm) E (eV) f Major contributions λ (nm) E (eV) f Major contributions 1 365 360.27 3.4415 0.0014 H-1 → L (93%) 358.31 3.4603 0.0014 H-1 → L (93%) 2  312.18 3.9715 0.0000 H → L (99%) 313.69 3.9524 0.0000 H → L (99%) 3 254 275.92 4.4934 0.0043 H-4 → L (24%) 274.77 4.5123 0.0041 H-4 → L (28%) 4  272.66 4.5473 0.0006 H-4 → L (50%) 272.27 4.5538 0.0004 H-4 → L (44%) 5  269.56 4.5994 0.0001 H-4 → L (19%) 268.47 4.6182 0.0001 H-4 → L (20%) 6  261.21 4.7465 0.0000 H → L+1 (100%) 263.16 4.7113 0.0000 H → L+1 (100%)Two intense electronic transitions were predicted at 4.4934 eV (275.92 nm) and 3.4415 eV (360.27 nm) with oscillator strengths of 0.0043 and 0.0014, respectively, at the B3PW91 level and 4.5123 eV (274.77 nm) and 3.4603 eV (358.31 nm) with oscillator strengths of 0.0041 and 0.0014, respectively, at the B3LYP level. We observed from the spectra that the maximum absorption wavelength corresponds to the electronic transition from HOMO to LUMO+1 with 100% contribution followed by the electronic transition from HOMO to LUMO with 99% contribution at the two levels. The experimental absorption spectra of the title molecule predict two bands at 254 nm and 365 nm. The error between the theoretical and experimental results range from - 4.73 nm to 21.92 nm at the B3PW91 and from - 6.69 nm to 20.77 nm at the B3LYP level. These errors are due to the fact that only one molecule was considered for simulation. The theoretical UV-vis absorption spectra of Rubescin E in gas phase are shown in Figure5.Figure 5
Theoretical absorption spectra of Rubescin E at the B3PW91 and B3LYP levels in gas with the 6-311++G(d,p) basis set.


### 3.4.5. Dipole Moment (μDM), Average Polarizability (α), First Static Hyperpolarizability (β), and Anisotropy of Polarization

In this work, the dipole momentμDM, average polarizability α, first static hyperpolarizability β, and anisotropy of polarizability Δα of Rubescin E were evaluated in both gas phase and chloroform solution in order to define the nonlinearity of Rubescin E. The finite-field approach was used for this purpose. Equations (2), (3), (4), and (5) were used to calculate the polarizability, dipole moment, anisotropy of polarizability, and first static hyperpolarizability, respectively, using the x,y,z components obtained from Gaussian 09 W output. The calculated parameters were presented in Table 5 at the three levels with the 6-311++G(d,p) basis set.(2)α=13αxx+αyy+αzz(3)μDM=μx2+μy2+μz21/2(4)∆α=12αxx-αyy2+αyy-αzz2+αzz-αxx2+6αxz2+6αxy2+6αyz21/2(5)β=βxxx+βxyy+βxzz2+βyyy+βyzz+βyxx2+βzzz+βzxx+βzyy21/2The calculated values of polarizability and first static hyperpolarizability obtained from Gaussian output are in atomic unit. These values were then converted into electrostatic unit (esu) for comparison purpose (for α: 1 a.u = 0.1482 x 10−24 esu, for β: 1 a.u = 8.6393 x 10−33 esu) [19–22]. From a giving molecule, when these values (μDM and β) are greater than those of urea, the molecule is said to have good active NLO properties. We observed from our results that the values of α, β, and μDM are higher in solvent than their corresponding value in gas phase. β and μDM of Rubescin E calculated at the 6-311++G(d,p) basis set using different methods were greater than those of urea. These values calculated using the HF/6-311D(d,p) method (μDM=5.2175D and β=1760.3169x10-33 esu) were also higher than those of urea (μDM=3.8851D and β=372.8x10-33esu), obtained using the same method and basis set [21]. Hence Rubescin E can be considered to have good active NLO properties and this is due to the delocalize ᴫ electron on the furan ring.Table 5
Electric dipole moment, polarizability, anisotropy of polarization, first-order hyperpolarizability, and molar refractivity of Rubescin E at the RHF, B3LYP, and B3PW91 levels with the 6-311G (d, p) and 6-311++G (d, p) basis sets.
RHF B3LYP B3PW91 Gas Chloroform Gas Chloroform Gas Chloroform μ D M (D) 5.3966 7.0953 5.2074 6.7654 5.1176 6.6663  α x x 352.266 421.425 387.992 470.193 384.258 465.488 α x y 17.3299 24.2341 19.6436 29.6995 19.3544 29.0512 α y y 336.148 424.889 374.795 479.493 371.091 475.445 α x z 1.50612 0.677331 0.715703 -0.411779 0.795242 -0.371934 α y z 3.39268 -1.23142 4.44903 0.0306216 4.53244 0.450373 α z z 278.550 371.379 305.049 415.461 301.619 411.131  α t o t (∗10−24 esu) 47.7036 60.0729 52.6799 67.3473 52.1438 66.7018  Δα (∗10−24 esu) 10.9240 9.8814 12.5387 11.6890 12.4723 11.5857  β x x x 58.5850 116.324 77.8905 117.687 82.0568 124.840 β x x y -34.3404 -40.3762 -33.9536 -66.5203 -29.0441 -60.4155 β x y y 22.5993 15.4126 -29.6091 -106.843 -36.6541 -122.127 β y y y 92.3349 129.004 27.6922 -58.5834 26.8972 -63.6805 β x x z -16.3605 -23.5326 -55.0267 -81.7313 -58.0975 -89.6785 β x y z -8.72859 -0.242861 -11.9414 10.3722 -12.8764 6.24556 β y y z -38.9332 -65.6523 -107.633 -207.304 -108.216 -214.866 β x z z -14.4537 -58.3711 -7.34826 -70.3072 -7.94692 -69.1599 β y z z -50.8004 -109.450 -77.7921 -196.200 -71.2685 -182.588 β z z z -6.38532 23.9632 -16.7476 -0.675756 -9.68167 5.78764  β (∗10−33 esu) 787.4783 866.9154 1747.7167 3772.6270 1678.8815 3743.0498


### 3.4.6. Optoelectronic Properties

In order to recognize the optoelectronic nature of Rubescin E for different devices applications, some parameters such as electric field (E), electric polarization (P), electric susceptibility (χ), permittivity (ℰ), refractive index (η), and electric displacement (D) were calculated using equations given in the literature [23–25]. We observed from Table 6 that the results of the calculated parameters are slightly different when we move from one level to another and also when the medium changes. The value of electric field is greater in a solution of chloroform than its corresponding value in gas phase. This is because the polarizability increases in presence of a solvent. The values of electric susceptibility, dielectric constant, and refractive index are greater at B3LYP level compared to their corresponding value at the RHF. All the calculated parameters of optoelectronic properties obtained at the B3LYP level are similar to those obtained at the B3PW91 level. None of these parameters have been determined before either theoretically or experimentally.Table 6
Calculated values of polarization density (P), average electric field (E), electric susceptibility (χ), refractive index (η), dielectric constant (E), magnitude of the displacement (D), and molar refractivity (MR) of Rubescin E molecule obtained at the RHF, B3LYP, and B3PW91 levels with the 6-311++G(d,p) basis set.
Parameters RHF B3LYP B3PW91 Gas Chloroform Gas Chloroform Gas Chloroform E (V.m−1)∗ 109 3.3873 3.5365 2.9597 3.0078 2.9386 2.9924 P (C.m−2)∗10−2 8.3339 10.7944 7.5778 8.6086 8.3117 7.9130 χ 2.7787 3.4473 2.8916 3.2324 3.1945 2.9865 E ∗10−11 3.3458 3.9377 3.4457 3.7475 3.7139 3.5297 η 1.9439 2.1089 1.9727 2.0573 2.0480 1.9966 D (C.m−2)∗10−2 0.1133 0.1393 0.1020 0.1127 0.1091 0.1056 MR (esu.mol−1) 120.3345 151.5366 132.8875 169.8866 131.5351 168.2585One of the central goals of this study is to understand the underlying structure–property relationships which might form the basis for a “molecular engineering” approach to electronics, optoelectronics, and photonics. The molar refractivity of our molecule, known to be an important parameter in quantitative structure–property relationship analysis was calculated for this purpose. The value of the molar refractivity was calculated at the three levels, in both gas and chloroform using the 6-311++G(d,p) basis set. The Lorenz-Lorentz equation was used for this calculation [26, 27] and its results are listed in Table 6.The high values of molar refractivity, polarizability, anisotropy of polarizability, and first static hyperpolarizability of Rubescin E molecule show that the molecule has good quantitative structure–property relationship analysis and might therefore form the basis for a “molecular engineering” approach to electronics, optoelectronics, and photonics.


## 3.4.1. Mulliken, ESP, and Natural Charge Distribution

The Mulliken atomic charges of our molecule calculated at all the levels in gas phase and chloroform show positive charge for all the hydrogen atoms. The net charge on all the atoms varies from -1.109653e to 1.980512e, from -1.164916e to 1.904034e, and from -0.891775e to 1.524787e, respectively, in gas phase at the RHF, B3PW91, and B3LYP levels. In a solution of chloroform, the charges varied from -1.064962e to 1.826589e, from -1.206706e to 1.904292e, and from -0.945041e to 1.550492e with some oxygen atoms charges being positive and can be explained by the fact that the oxygen is related to extremely negative carbon atoms. The most positive charge atoms are C63, C5, C8 and the most negative charge atoms are C71, C62, C67.The electrostatic charges were evaluated in this work using the CHelpG scheme of Breneman model. We found from our results that the most positive charges atom is C4 followed by C62 and C2 and the most negative charge atom is C12 followed by C5 and C7. The observation made at all levels and basis set in gas phase and in a solution of chloroform is that the most positive charge atoms are directly related to the most negative charge atoms.The natural atomic charges, obtained using the natural bonding orbital method, were also used to evaluate the atomic charge of Rubescin E. Positive and negative charges were found for all hydrogen and oxygen atoms, respectively. In this case, all carbon atoms directly linked to hydrogen atoms were found to have negative charges except for those linked to oxygen atoms. The most negative charge atom was calculated using HF method and was observed for O65 (-0.69456e) and O60 (-0.68330e), respectively, in chloroform and gas phase. The most positive charge atom was found to be C62 in both gas (0.97067e, 0.80601e, and 0.81407e, respectively, at the RHF, B3PW91, and B3LYP levels) and solvent (0.98887e, 0.81804e, and 0.82650e, respectively, at the RHF, B3PW91, and B3LYP levels); this is due to the fact that C62 is related to negative charge atoms (O65, O60, and C63). Mulliken, electrostatic, and natural atomic charge distributions are graphically shown in Figure 2. From Figure 2, one can observe that, for almost all the methods used for charge description, the most positive and negative charge atoms were calculated at the RHF level in both gas and chloroform and this is due to the fact that the effect of electron correlation is not well described in HF method.Figure 2
Charge distribution on Rubescin E calculated at the RHF, B3PW91, and B3LYP levels in both gas phase and chloroform solution and with the 6-311++G(d,p) basis set.


## 3.4.2. Global Reactivity Descriptors

In order to understand the relationships between structure, stability, and reactivity of Rubescin E molecule, the global reactivity descriptors parameters such as chemical hardness (H), chemical potential (μcp), chemical softness (s), electronegativity (X), and electrophilicity index (ω) were calculated. The finite difference equation given by (1) was used to calculate the ionization potential and electron affinity, which are generally used to calculate the above cited parameters.(1)IP=Eq=N+1-Eq=NEA=Eq=N-Eq=N-1The IP and EA calculated from (1) were then used to calculate H, μcp, s, X, and ω using equations found in the literature [15–17]. All these parameters calculated using the two methods in gas phase are presented in Table 3. A high value of μcp and ω characterizes a good electrophile, while a small value stands for good nucleophile.Table 3
Global reactivity descriptors of Rubescin E at the RHF, B3LYP, and B3PW91 levels in gas phase and in chloroform solution using the 6-311++G(d,p) basis set.
RHF B3LYP B3PW91 Gas Chloroform Gas Chloroform Gas Chloroform IP (eV) 7.151 5.662 7.875 6.819 7.861 6.819 EA (eV) -0.841 0.684 0.461 1.804 0.450 1.825 μ c p (eV) -3.155 -3.173 -4.168 -4.312 -4.156 -4.322 X (eV) 3.155 3.173 4.168 4.312 4.156 4.322 H (eV) 3.996 2.489 3.707 2.508 3.706 2.497 s (eV)−1 0.250 0.402 0.270 0.399 0.270 0.400 ω (eV) 1.245 2.022 2.343 3.707 2.330 3.740The calculated vertical IP values in gas phase are bigger than their corresponding values in solvent. From Table3, we also found that putting the molecule in solvent increases its electron affinity. From the calculated IP and EA values, one can conclude that solvent effect increases the capacity of molecule of gaining an electron compared to donating it. It also reduces the harness of our molecule and increases the softness. Hence, the presence of solvent increases the reactivity of the molecule Rubescin.


## 3.4.3. Frontier Molecular Orbitals

The frontier molecular orbitals of Rubescin E were evaluated using the ab initio and DFT methods. The 6-311G(d,p) and 6-311++G(d,p) basis sets were used for this purpose in gas phase and in chloroform solution. The results show that the energy gap of our molecule decreases when diffuse functions are added onto all the atoms. We also found that whenever the basis set and methods used, the energy gap is greater than 4, showing that our molecule is hard and can be used as insulator in many electronic devices. In Figure3, the 3D plots of the HOMO and LUMO orbitals computed at the RHF, B3PW91, and B3LYP levels with the 6-311G(d,p) basis set are illustrated in gas phase. We observed that the HOMO of Rubescin E is located over the furan ring at the three levels and also at the C-C of cyclohexane ring and C-O of oxiran ring. By contrast, the LUMO orbital is located over the cyclohex-2-enone ring, C-C and C-O bond of tetrahydrofuran ring. We can therefore conclude that electron can easily be transferred from furan ring to tetrahydrofuran ring.Figure 3
Molecular orbital and the HOMO and LUMO energy of Rubescin E in gas phase.The total density of states (DOS) spectrum of Rubescin E at the gas phase and in chloroform is given in Figure4 for each level at the 6-311++G(d,p) basis set. These DOSs spectra presented in Figure 4 were obtained from Gauss-Sum 3.0 program [18] which was used in order to show the contributions of different group to molecular orbital (HOMO and LUMO). From Figure 4, we observe that the HOMO-LUMO energy gap is smaller when we move from RHF to B3PW91 and from B3PW91 to B3LYP level, respectively, for both gas and chloroform phases, with larger values obtained in chloroform.Figure 4
Total density of state (DOS) spectrum of Rubescin E at the RHF, B3PW91, and B3LYP levels in both gas and chloroform phase and with the 6-311++G(d,p) basis set.


## 3.4.4. UV-Vis Spectra Analysis

Time dependent density functional theory (TD-DFT) was used in gas phase at the two levels B3PW91 and B3LYP with the 6-311++G(d,p) basis set in order to determine the first six excited states to investigate the UV-vis absorption spectra of the molecule. The excitation energy (E), wavelength (λ), and oscillator strength (f) along with their major contributions are given in Table 4 and their results are compared to experiment.Table 4
Theoretical absorption wavelength (λ), excitation energy (E), and oscillator strengths of Rubescin E at the B3PW91 and B3LYP levels in gas with the 6-311++G(d,p) basis set.
Excited states Exp [1] B3PW91 B3LYP λ (nm) λ (nm) E (eV) f Major contributions λ (nm) E (eV) f Major contributions 1 365 360.27 3.4415 0.0014 H-1 → L (93%) 358.31 3.4603 0.0014 H-1 → L (93%) 2  312.18 3.9715 0.0000 H → L (99%) 313.69 3.9524 0.0000 H → L (99%) 3 254 275.92 4.4934 0.0043 H-4 → L (24%) 274.77 4.5123 0.0041 H-4 → L (28%) 4  272.66 4.5473 0.0006 H-4 → L (50%) 272.27 4.5538 0.0004 H-4 → L (44%) 5  269.56 4.5994 0.0001 H-4 → L (19%) 268.47 4.6182 0.0001 H-4 → L (20%) 6  261.21 4.7465 0.0000 H → L+1 (100%) 263.16 4.7113 0.0000 H → L+1 (100%)Two intense electronic transitions were predicted at 4.4934 eV (275.92 nm) and 3.4415 eV (360.27 nm) with oscillator strengths of 0.0043 and 0.0014, respectively, at the B3PW91 level and 4.5123 eV (274.77 nm) and 3.4603 eV (358.31 nm) with oscillator strengths of 0.0041 and 0.0014, respectively, at the B3LYP level. We observed from the spectra that the maximum absorption wavelength corresponds to the electronic transition from HOMO to LUMO+1 with 100% contribution followed by the electronic transition from HOMO to LUMO with 99% contribution at the two levels. The experimental absorption spectra of the title molecule predict two bands at 254 nm and 365 nm. The error between the theoretical and experimental results range from - 4.73 nm to 21.92 nm at the B3PW91 and from - 6.69 nm to 20.77 nm at the B3LYP level. These errors are due to the fact that only one molecule was considered for simulation. The theoretical UV-vis absorption spectra of Rubescin E in gas phase are shown in Figure5.Figure 5
Theoretical absorption spectra of Rubescin E at the B3PW91 and B3LYP levels in gas with the 6-311++G(d,p) basis set.


## 3.4.5. Dipole Moment (μDM), Average Polarizability (α), First Static Hyperpolarizability (β), and Anisotropy of Polarization

In this work, the dipole momentμDM, average polarizability α, first static hyperpolarizability β, and anisotropy of polarizability Δα of Rubescin E were evaluated in both gas phase and chloroform solution in order to define the nonlinearity of Rubescin E. The finite-field approach was used for this purpose. Equations (2), (3), (4), and (5) were used to calculate the polarizability, dipole moment, anisotropy of polarizability, and first static hyperpolarizability, respectively, using the x,y,z components obtained from Gaussian 09 W output. The calculated parameters were presented in Table 5 at the three levels with the 6-311++G(d,p) basis set.(2)α=13αxx+αyy+αzz(3)μDM=μx2+μy2+μz21/2(4)∆α=12αxx-αyy2+αyy-αzz2+αzz-αxx2+6αxz2+6αxy2+6αyz21/2(5)β=βxxx+βxyy+βxzz2+βyyy+βyzz+βyxx2+βzzz+βzxx+βzyy21/2The calculated values of polarizability and first static hyperpolarizability obtained from Gaussian output are in atomic unit. These values were then converted into electrostatic unit (esu) for comparison purpose (for α: 1 a.u = 0.1482 x 10−24 esu, for β: 1 a.u = 8.6393 x 10−33 esu) [19–22]. From a giving molecule, when these values (μDM and β) are greater than those of urea, the molecule is said to have good active NLO properties. We observed from our results that the values of α, β, and μDM are higher in solvent than their corresponding value in gas phase. β and μDM of Rubescin E calculated at the 6-311++G(d,p) basis set using different methods were greater than those of urea. These values calculated using the HF/6-311D(d,p) method (μDM=5.2175D and β=1760.3169x10-33 esu) were also higher than those of urea (μDM=3.8851D and β=372.8x10-33esu), obtained using the same method and basis set [21]. Hence Rubescin E can be considered to have good active NLO properties and this is due to the delocalize ᴫ electron on the furan ring.Table 5
Electric dipole moment, polarizability, anisotropy of polarization, first-order hyperpolarizability, and molar refractivity of Rubescin E at the RHF, B3LYP, and B3PW91 levels with the 6-311G (d, p) and 6-311++G (d, p) basis sets.
RHF B3LYP B3PW91 Gas Chloroform Gas Chloroform Gas Chloroform μ D M (D) 5.3966 7.0953 5.2074 6.7654 5.1176 6.6663  α x x 352.266 421.425 387.992 470.193 384.258 465.488 α x y 17.3299 24.2341 19.6436 29.6995 19.3544 29.0512 α y y 336.148 424.889 374.795 479.493 371.091 475.445 α x z 1.50612 0.677331 0.715703 -0.411779 0.795242 -0.371934 α y z 3.39268 -1.23142 4.44903 0.0306216 4.53244 0.450373 α z z 278.550 371.379 305.049 415.461 301.619 411.131  α t o t (∗10−24 esu) 47.7036 60.0729 52.6799 67.3473 52.1438 66.7018  Δα (∗10−24 esu) 10.9240 9.8814 12.5387 11.6890 12.4723 11.5857  β x x x 58.5850 116.324 77.8905 117.687 82.0568 124.840 β x x y -34.3404 -40.3762 -33.9536 -66.5203 -29.0441 -60.4155 β x y y 22.5993 15.4126 -29.6091 -106.843 -36.6541 -122.127 β y y y 92.3349 129.004 27.6922 -58.5834 26.8972 -63.6805 β x x z -16.3605 -23.5326 -55.0267 -81.7313 -58.0975 -89.6785 β x y z -8.72859 -0.242861 -11.9414 10.3722 -12.8764 6.24556 β y y z -38.9332 -65.6523 -107.633 -207.304 -108.216 -214.866 β x z z -14.4537 -58.3711 -7.34826 -70.3072 -7.94692 -69.1599 β y z z -50.8004 -109.450 -77.7921 -196.200 -71.2685 -182.588 β z z z -6.38532 23.9632 -16.7476 -0.675756 -9.68167 5.78764  β (∗10−33 esu) 787.4783 866.9154 1747.7167 3772.6270 1678.8815 3743.0498


## 3.4.6. Optoelectronic Properties

In order to recognize the optoelectronic nature of Rubescin E for different devices applications, some parameters such as electric field (E), electric polarization (P), electric susceptibility (χ), permittivity (ℰ), refractive index (η), and electric displacement (D) were calculated using equations given in the literature [23–25]. We observed from Table 6 that the results of the calculated parameters are slightly different when we move from one level to another and also when the medium changes. The value of electric field is greater in a solution of chloroform than its corresponding value in gas phase. This is because the polarizability increases in presence of a solvent. The values of electric susceptibility, dielectric constant, and refractive index are greater at B3LYP level compared to their corresponding value at the RHF. All the calculated parameters of optoelectronic properties obtained at the B3LYP level are similar to those obtained at the B3PW91 level. None of these parameters have been determined before either theoretically or experimentally.Table 6
Calculated values of polarization density (P), average electric field (E), electric susceptibility (χ), refractive index (η), dielectric constant (E), magnitude of the displacement (D), and molar refractivity (MR) of Rubescin E molecule obtained at the RHF, B3LYP, and B3PW91 levels with the 6-311++G(d,p) basis set.
Parameters RHF B3LYP B3PW91 Gas Chloroform Gas Chloroform Gas Chloroform E (V.m−1)∗ 109 3.3873 3.5365 2.9597 3.0078 2.9386 2.9924 P (C.m−2)∗10−2 8.3339 10.7944 7.5778 8.6086 8.3117 7.9130 χ 2.7787 3.4473 2.8916 3.2324 3.1945 2.9865 E ∗10−11 3.3458 3.9377 3.4457 3.7475 3.7139 3.5297 η 1.9439 2.1089 1.9727 2.0573 2.0480 1.9966 D (C.m−2)∗10−2 0.1133 0.1393 0.1020 0.1127 0.1091 0.1056 MR (esu.mol−1) 120.3345 151.5366 132.8875 169.8866 131.5351 168.2585One of the central goals of this study is to understand the underlying structure–property relationships which might form the basis for a “molecular engineering” approach to electronics, optoelectronics, and photonics. The molar refractivity of our molecule, known to be an important parameter in quantitative structure–property relationship analysis was calculated for this purpose. The value of the molar refractivity was calculated at the three levels, in both gas and chloroform using the 6-311++G(d,p) basis set. The Lorenz-Lorentz equation was used for this calculation [26, 27] and its results are listed in Table 6.The high values of molar refractivity, polarizability, anisotropy of polarizability, and first static hyperpolarizability of Rubescin E molecule show that the molecule has good quantitative structure–property relationship analysis and might therefore form the basis for a “molecular engineering” approach to electronics, optoelectronics, and photonics.


## 3.5. NMR Study of Rubescin E

After the optimization of the Rubescin E molecule, the1H and 13C chemical shifts were calculated at the RHF, B3LYP, and B3PW91 levels of the theory using the 6-311++G(d,p) basis set. In order to compare the calculated values of 1H and 13C chemical shifts with experimental results, we also need to calculate the absolute shielding value of 1H and 13C for the tetramethylsilane (TMS) using the same methods above. The GIAO (Gauge Invariant Atomic Orbitals) approach known to provide satisfactory chemical shifts for different nuclei with larger molecules [28] was used for this purpose and the following equation:(6)δippm=isotropicTMSi-isotropici,where i is the atom type and was used to convert the chemical shielding to chemical shifts.The experimental and calculated chemical shifts of1H along with their corresponding error are listed in Table 7. From our results we observed that all the methods provide results which are very close to experiment since the errors between the experimental and calculated results are smaller.Table 7
Experimental and calculated1H NMR chemical shifts δ (ppm) of Rubescin E at the RHF, B3LYP, and B3PW91 levels in chloroform solution using the 6-311++G(d,p) basis set.
Nuclei Calculatedδ (ppm) Experimentalδ (ppm) [1] Nuclei Calculatedδ (ppm) Experimentalδ (ppm) [1] RHF B3LYP B3PW91 RHF B3LYP B3PW91 H10 3,6354 4,4787 4,5162 4,44 H41 3,2764 3,8070 3,7375 3,97 H13 3,7599 4,5046 4,4656 5,5 H43 0,0206 0,1390 0,1217 - H17 1,1735 1,3264 1,2850 - H44 0,5304 0,6752 0,6653 0,65 H18 1,4006 1,4842 1,5205 1,34 H45 1,1410 1,2581 1,2916 - H19 0,8843 0,9632 0,9055 - H47 2,9441 3,4299 3,3665 3,45 H21 2,2212 3,1228 3,2220 2,9 H49 1,8799 2,0794 2,0578 2,11 H23 0,7480 0,8702 0,8499 - H50 1,6401 2,0098 2,0019 1,51 H24 0,9682 1,2471 1,2747 1,43 H52 2,1382 2,6231 2,6453 2,52 H25 1,6905 1,7201 1,7225 - H54 6,4241 6,4756 6,5064 6,23 H27 1,7833 2,0352 1,9975 1,9 H56 7,6008 7,6737 7,6347 7,34 H28 1,7575 2,1239 2,1319 1,9 H58 7,2432 7,2352 7,1892 7,24 H30 3,1956 3,7283 3,7158 3,77 H66 6,5053 6,5963 6,7294 6,73 H31 3,3513 3,5791 3,5410 3,55 H68 1,9939 2,0486 2,0556 - H33 7,4298 7,4428 7,5055 7,07 H69 1,6905 1,8891 1,9108 1,82 H35 5,9894 6,1274 6,1740 5,95 H70 1,7037 1,8508 1,8560 - H37 0,3741 0,4953 0,4827 - H72 1,3371 1,5726 1,5006 - H38 1,4776 1,8588 1,8632 1,22 H73 1,7489 1,8289 1,8340 1,87 H39 0,7281 1,2414 1,3276 - H74 2,1737 2,2617 2,2408 -In order to compare experimental and theoretical results, a linear correlation of1H-NMR chemical shifts was established as shown in Figure 6. The regression line was plotted using the following equations: δcal=0.98880δexp-0.17198, δcal=0.97379δexp+0.18796, and δcal=0.97069δexp+0.19387, respectively, at the RHF, B3PW91, and B3LYP levels of the theory. The theoretical results obtained from using the 6-311++G(d,p) basis set show good correlation with experiment since, and the calculated R-square values are found to be close to 1 at each level as shown by Figure 6.Figure 6
Comparison of experimental and theoretical1H chemical shifts of Rubescin E calculated at the RHF, B3PW91, and B3LYP using the 6-311++G(d,p) basis set in chloroform.The calculated and experimental13C chemical shifts of our molecule are given in Table 8 and their comparison can be found in Figure 7. The linear regression line plotted in Figure 7 shows that theoretical results are in good agreement with experiment. This is confirmed by the linear correlation coefficient calculated here as R-square at the RHF, B3PW91, and B3LYP levels using the 6-311++G(d,p) basis set.Table 8
Experimental and calculated13C NMR chemical shift δ (ppm) of Rubescin E at the RHF, B3LYP, and B3PW91 levels in chloroform solution using the 6-311++G(d,p) basis set.
Nuclei Calculatedδ (ppm) Experimentalδ (ppm) [1] Nuclei Calculatedδ (ppm) Experimentalδ (ppm) [1] RHF B3LYP B3PW91 RHF B3LYP B3PW91 C1 44,217875 56,667075 53,80495 47,5 s C34 134,341675 139,383575 138,51605 131,3 d C2 206,549275 213,070575 210,62615 200,3 s C36 21,545175 24,454275 24,23345 22,7 q C3 56,393275 73,459075 70,54015 64,6 s C40 53,124275 65,723775 64,21635 60,3 d C4 43,854075 56,324675 52,83685 44,9 s C42 22,468475 24,495375 24,17495 21,5 q C5 60,103575 77,293875 74,30925 68,3 d C46 48,923175 61,540375 59,53515 55,2 d C6 39,115675 49,868075 47,23345 41,3 s C48 29,511075 34,706875 33,33385 31,1 t C8 39,020275 51,568975 49,31465 41,3 s C51 38,272375 48,003275 46,38035 38,8 d C9 65,951775 79,364675 77,38455 71,4 d C53 117,347375 119,574075 118,57695 110,8 d C12 72,763675 87,369975 84,63375 74,7 d C55 149,815075 151,680375 149,71195 142,9 d C14 130,650675 133,767875 131,73785 123,1 s C57 144,528075 147,708875 145,91185 139,2 d C16 21,641175 23,522875 22,88275 21,1 q C62 178,475775 182,888075 180,33025 167,4 s C20 44,504575 54,261975 53,16905 50,6 d C63 132,986175 138,281375 136,47755 128,8 s C22 16,680575 18,585575 18,72435 17,5 q C64 148,221575 150,697975 151,11665 138,3 d C26 34,988975 41,161875 39,99065 35,4 t C67 15,275775 17,096475 17,51975 14,6 q C29 71,816475 83,425975 81,35795 79,5 t C71 13,518375 15,400475 15,47155 12,6 q C32 164,415875 166,172275 165,17515 151,6 dFigure 7
Comparison of experimental and theoretical13C chemical shifts of Rubescin E calculated at the RHF, B3PW91, and B3LYP using the 6-311++G(d,p) basis set.The following regression line plotted for each level using the general equationδcal=aδexp+b, where a and b are given in Figure 7, shows that the calculated 13C chemical shifts correlate very well with experiment. The linear correlation coefficient calculated as R-square found in Figure 7 also confirms this.


## 3.6. Vibrational Frequencies Analysis

The vibrational frequencies of our molecule were computed by using B3LYP/6-311G(d,p) method in both gas phase and chloroform. The experimental IR vibrational frequencies obtained for the two carbonyl moiety present in our structure along with the calculated scaled and unscaled vibrational frequencies, IR, and Raman frequencies with their approximate descriptions are given in Table9. The rest of the vibrational parameter of Rubescin E molecule which is not described in Table 9 can be obtained from Supplementary Material S2. The scale factor was determined as the mean value of the scale factor that matches correctly for the C=O stretching and the given experimental value. The obtained scale factor was 0.9706. No imaginary frequencies were found showing that structure of the molecule Rubescin E is stable in both gas and solvent. Figure 8 gives the representation of the scaled IR intensity and Raman scattering activity.Table 9
Some calculated scaled and unscaled vibrational frequencies (cm−1), IR (km.mol−1), and Raman scattering activities (Å4.amu−1) of Rubescin E in gas phase and chloroform solution obtained at the B3LYP/6-311G(d,p) level.
Gas phase Chloroform solution Vibrational frequencies  Vibrational frequencies Exp. [1] Unscaled Scaled IR Raman Unscaled Scaled IR Raman Approximate descriptions 3277.8244 3179.489668 0.1483 154.454 3277.3381 3179.017957 0.2265 260.5952 Symνs C-H groups on furan ring 3272.9127 3174.725319 1.6469 66.8185 3272.4528 3174.279216 1.0819 83.7804 Asymνs C-H groups on furan ring 3240.2105 3143.004185 0.9505 45.7116 3240.612 3143.39364 1.6053 100.3155 Asymνs of (C53-H54; C55-H56) 3189.511 3093.82567 3.5332 66.4094 3189.3244 3093.644668 8.3712 160.0412 ν s C40-H41 3175.4637 3080.199789 11.8025 201.1091 3175.3082 3080.048954 19.8811 372.2174 Symνs (C34-H35; C32-H33) 3172.7225 3077.540825 4.8286 43.2929 3170.4225 3075.309825 12.9561 111.1091 Asymνs of CH3 (C36) 3164.5342 3069.598174 5.4628 42.0037 3160.4647 3065.650759 13.1398 103.7241 ν s C64-H66 3140.7401 3046.517897 10.7253 48.1146 3141.8739 3047.617683 28.9110 111.4035 Asymνs of CH3 (C36. C22) 3096.4047 3003.512559 37.8710 128.8493 3103.9325 3010.814525 53.3513 256.448 Asymνs of (C29-H30; C29-H31) 3087.0614 2994.449558 18.8484 62.1458 3094.289 3001.46033 37.2141 110.584 Asymνs of CH3 (C71); νs C12-H13 3056.0169 2964.336393 13.0488 74.2148 3062.0737 2970.211489 17.9489 162.7148 Symνs of CH3 (C22) 3055.6408 2963.971576 14.4803 142.8654 3056.849 2965.14353 21.0392 234.8621 Asymνs of (C67-H69; C67-H70) 3023.1661 2932.471117 14.1323 120.9272 3029.0714 2938.199258 23.4132 269.1079 Symνs of CH3 (C71) 3016.7818 2926.278346 23.9892 318.0136 3018.0608 2927.518976 25.8983 486.6073 Symνs of CH3 (C67) 2999.7383 2909.746151 1.0004 31.9507 2998.9246 2908.956862 3.4528 89.9972 ν s of C20-H21 1720 1779.5912 1726.203464 172.5832 16.0679 1753.6214 1701.012758 326.2675 24.7567 ν s of C62=O65 and βs of C62-C63=C64-C67 1664 1742.8596 1690.573812 191.5410 32.6047 1719.1678 1667.592766 374.9763 96.2937 ν s of C2=O7 and βs of C1-C2-C34-H35 1699.8624 1648.866528 90.7515 127.5998 1692.7491 1641.966627 159.0973 264.4437 ν s C63=C64; βs H66-C64-C67-H68 and βs C62-C63-C71-H72 1655.4051 1605.742947 20.9946 48.7257 1648.5716 1599.114452 54.0221 158.0979 ν s C34=C32; δs of H33-C32-C8 and δs of H35-C34-C2 1627.2588 1578.441036 1.1593 11.251 1625.9499 1577.171403 1.4847 24.0532 Asymνs of C=C on furan ring 1532.8277 1486.842869 17.3545 52.0428 1530.1712 1484.266064 23.5845 101.1704 Symνs of C=C on furan ring 1531.0536 1485.121992 4.3738 6.1013 1522.5028 1476.827716 5.4574 13.4777 s c i s . s of (C29-H30; C29-H31) 1518.4514 1472.897858 13.9129 13.9129 1514.0912 1468.668464 12.9483 27.3727 τ s of CH3 (C22; C16) and scis.w of (C29-H30; C29-H31) 1503.6728 1458.562616 9.8386 5.7612 1498.5877 1453.630069 19.7850 13.2898 τ s of CH3 (C16; C22; C36) 1499.3956 1454.413732 5.1940 7.4533 1492.6161 1447.837617 9.3270 17.4033 τ s of CH3 (C42); scis.m of (C26-H27; C26-H28) and scis.w of (C48-H49; C48-H50) 1488.4029 1443.750813 0.9776 2.8672 1485.682 1441.11154 6.7043 7.8167 τ s of CH3 (C16; C22; C36) and δm of C20-H21 1485.5561 1440.989417 2.9100 5.2938 1481.7402 1437.287994 4.3280 14.1082 s c i s . s of (C48-H49; C48-H50) and τs of CH3 (C42) 1483.6563 1439.146611 0.4862 7.8554 1478.0624 1433.720528 1.4889 21.2082 s c i s . s of (C26-H27; C26-H28) and τm of CH3 (C42) 1479.4465 1435.063105 7.9832 38.0149 1470.3189 1426.209333 12.7942 58.6094 τ s of CH3 (C67; C71) 1463.5075 1419.602275 2.5457 1.0126 1459.7847 1415.991159 4.0997 2.0734 τ s of H21-C20-C9-H10 and τw of CH3 (C22) 1442.8169 1399.532393 5.3126 6.5726 1441.0254 1397.794638 8.4482 14.8596 ν m of C3-C40; νm of C5-C46; rock.s of (C26-H27; C40-H41) and τm of H10-C9-C20-H21 1422.4074 1379.735178 42.8712 4.011 1420.5762 1377.958914 63.3216 10.8875 Sym CH3 umbrella mode 1418.7082 1376.146954 0.6510 1.2396 1416.3711 1373.879967 0.6332 11.5796 Asym CH3 umbrella mode; rock.m (C34-H35;C32-H33); δm C51-H52 1417.9087 1375.371439 6.7934 3.5193 1414.8341 1372.389077 5.2808 12.6492 ν m of C14-C53; δs of H52-C51 and sym CH3 umbrella mode 1411.6946 1369.343762 3.6967 24.766 1405.5801 1363.412697 6.3221 38.7377 asym CH3 umbrella mode (C67; C71) and δm of H66-C64 1404.0182 1361.897654 5.7921 1.3462 1402.0625 1360.000625 12.7684 4.8755 r o c k . m of (H35-C34; C32-H33); CH3 umbrella mode (C22; C16) and τm of H21-C20-C9-H10 1399.4114 1357.429058 7.3054 2.6928 1399.317 1357.33749 5.4113 6.6084 τ s of H10-C9-C20-H21; rock.m of (H35-C34; C32-H33) and δm of H13-C12-O60 1392.7814 1350.997958 4.4872 7.7674 1393.9199 1352.102303 8.7259 13.1186 τ s of H10-C9-C20-H21; rock.s of (H35-C34; C32-H33) and δs of H13-C12-O6 1381.3486 1339.908142 0.8619 1.6091 1378.5237 1337.167989 2.7575 3.5116 w a g g . s of (C29-H30; C29-H31); τs of H10-C9-C20-H21; δm of H13-C12-C9 and CH3 umbrella mode (C16) 1373.7055 1332.494335 4.3307 9.0916 1371.0783 1329.945951 5.0163 17.666 ν m of C63-C71; CH3 umbrella mode (C67; C71); δs of C64-H66 and τm of H10-C9-C20-H21 1368.9888 1327.919136 4.4971 10.4931 1367.4102 1326.387894 5.4518 20.2257 r o c k . s of (H56-C55; C53-H54); δs of C51-H52; wagg.s of (C48-H49; C48H50) and wagg.m of (C26-H27; C26H28) 1365.648 1324.67856 4.2088 1.0219 1364.8154 1323.870938 6.4354 2.7506 τ s of H10-C9-C12-H13; δm of C64-H66; rock.m (H35-C34; C32-H33); wagg.m of (C29-H30; C29H31) and CH3 umbrella mode (C16; C36) 1351.6819 1311.131443 2.3942 1.8233 1351.4078 1310.865566 3.8793 2.9367 w a g g . s of (C26-H27; C26-H28); δs of C51-H52 1343.0612 1302.769364 0.8245 6.8235 1343.2284 1302.931548 0.0396 7.8405 τ m of H10-C9-C20-H21; δs of C12-H13; δs of C51-H52 1326.3406 1286.550382 6.0965 5.2766 1322.4392 1282.766024 7.9781 13.8929 ν s of C3-C40; δs of C40-H41 1301.2149 1262.178453 4.1883 6.2643 1301.7097 1262.658409 7.1261 6.9678 ν m of C5-C6; twist.s of (C26-H27; C26-H28); wagg.m of (C48-H49; C48-H50); δm of H47-C46-C5; rock.s of (H56-C55; C53-H54) 1297.0244 1258.113668 1.7948 7.1956 1297.4084 1258.486148 1.3878 21.5171 ν w of C9-C12; wagg.s of (C48-H49; C48-H50); δm of H47-C46-C48; δs of C51-H52; twist.m of (C26-H27; C26-H28) 1288.4675 1249.813475 3.5313 1.5262 1287.909 1249.27173 1.5765 14.1367 δ s of C46-H47; δs of C12-H13; τm of H10-C9-C20-H21 and twist.m of (C26-H27; C26-H28) 1278.2074 1239.861178 1.4763 18.6173 1278.0044 1239.664268 2.9774 29.5326 ν m of C14-C51; δs of C57-H58; twist.m of (C48-H49; C48-H50) and δs of C51-H52 1273.4643 1235.260371 3.1680 10.1375 1271.8325 1233.677525 4.2401 20.9966 δ s of C46-H47; δs of C12-H13; δs of C57-H58; τs of H10-C9-C20-H21 and twist.m of (C26-H27; C26-H28) 1266.8541 1228.848477 3.8717 5.3878 1266.4233 1228.430601 6.8831 16.4996 τ s of H10-C9-C20-C8 and δm of C32-H33 1253.2129 1215.616513 59.1657 19.3282 1253.6896 1216.078912 120.7089 57.0914 s c i s . s of (C32-H33; C34-H35) and τm of C2-C1-C20-C9 1252.2694 1214.701318 0.7185 4.8164 1251.9233 1214.365601 0.6008 8.7087 δ m of CH on furan ring; twist.s of (C48-H49; C48-H50); twist.m of (C26-H27; C26-H28) and τm of H52-C51-C6-C42 1245.9092 1208.531924 177.9705 5.7457 1246.65 1209.2505 254.8417 9.1404 ν m of C62C63; τm of H66-C64-C67-H68; twist.s of (C29-H30; C29H31) 1237.0891 1199.976427 12.8957 8.0876 1236.5792 1199.481824 11.7625 18.8578 t w i s t . s of (C29-H30; C29-H31); τm of H21-C20-C8-C16 and rock.w of (C32-H33; C34-H35) 1220.0711 1183.468967 14.9312 3.1637 1219.3148 1182.735356 19.5929 7.8591 t w i s t . s of (C26-H27; C26-H28) and of (C48-H49; C48-H50); δs of C51-H52; δm of C55-H56 and τm of C6-C5-C4-C36 1201.9071 1165.849887 3.4760 6.7455 1199.1897 1163.214009 8.0422 13.5718 δ s of C40-H41; δm of C46-H47 and τm of H13-C12-C4-C3 1185.406 1149.84382 15.4074 0.3306 1180.1007 1144.697679 18.7873 1.4104 t w i s t . s of (C48-H49; C48-H50); τm of H52-C51-C14-C57; scis.s of (C55-H56; C53-H54) 1179.6911 1144.300367 1.9628 1.119 1178.2209 1142.874273 2.8925 1.7435 t w i s t . m of (C48-H49; C48-H50); τm of H28-C26-C40-H41; δm of C51-H52 and τm of C42-C6-C5-C4 1166.7314 1131.729458 14.6259 5.1602 1164.8183 1129.873751 9.3342 9.3366 τ m C1-C20-C8-C32  twist.s of (C29-H30; C29-H31); τm C3-C4-C12-C9 1157.5523 1122.825731 15.5290 4.7107 1156.1874 1121.501778 28.1722 11.6347 S c i s . m of (C32-H33; C34-H35); δs of C9-H10 and τm C12-C4-C5-C6 1148.5582 1114.101454 146.5450 3.5872 1149.5402 1115.053994 200.0358 6.6811 ν m of C62-O60 and βs C63-C64-C67-H68 1144.341 1110.01077 178416 3.5877 1144.4015 1110.069455 27.0332 7.8819 t w i s t . m of (C26-H27; C26-H28); τm C4-C5-C6-C4; τm C10-C9-C20-C8 1136.9705 1102.861385 1.6907 9.6148 1134.337 1100.30689 2.0658 19.6536 τ s H28-C26-C40-H41; τm H37-C36-C46-C47; scis.s (C32-H33; C34-H35) 1122.8634 1089.177498 21.5468 4.0892 1120.5923 1086.974531 35.6177 10.2656 τ m H33-C32-C8-C20; τm C9-C12-C4-C36; τm C41-C40-C26-C28 and τm C42-C6-C51-C48 1099.4941 1066.509277 48.0338 2.0757 1096.2182 1063.331654 62.1695 5.261 ν m C12-O60; δm of C46-H47; δm of C51-H52;τm C9-C20-C1-C22 and twist.m of (C48-H49; C48-H50) 1091.4985 1058.753545 28.1743 1.6861 1085.2223 1052.665631 29.9371 3.0875 ν m C57-O15 and scis.s of (C53-H54; C55-H56) 1080.7072 1048.285984 92.4087 0.7097 1080.9064 1048.479208 144.3970 1.9949 ν m C12-O60; sym δs CH3; scis.s of (C32-H33; C34-H35) and τm C2-C1-C3-C40 1071.7177 1039.566169 123.1938 6.7128 1073.0176 1040.827072 197.5919 15.9455 ν m C62-O60; δs of C46-H47 and asym δs of CH3 (C71) 1068.3452 1036.294844 9.8016 1.8104 1067.1028 1035.089716 24.1877 5.7115 τ s C67C64C63C71 1050.9373 1019.409181 13.3402 0.7713 1048.853 1017.38741 37.6705 1.8533 δ m of C46-H47; δm of C64-H66; τm C67-C64-C63-C71 1045.5983 1014.230351 69.2901 6.619 1044.7341 1013.392077 62.2356 12.9459 t w i s t . m of (C71-H73; C71-H74); δm of C26-H27; δm of C53-H54; δm of C48-H50 1027.1407 996.326479 1.7797 5.289 1027.2885 996.469845 30.2585 3.8663 t w i s t . s (C34H35; C32H33) 1022.4549 991.781253 0.9472 2.7037 1020.7406 990.118382 6.3182 4.1772 ν m of C48-C51; asym δs of CH3; βm H66-C64-C63-C62 and τm H13-C12-C4-C5 1017.7638 987.230886 30.0425 3.9798 1015.3161 984.856617 43.5319 8.8798 asymδs of CH3; rock.s of (C29-H30; C29-H31); τm C9-C20-C1-C3 1011.5509 981.204373 4.8801 6.6943 1009.814 979.51958 6.3114 13.7312 β s C51-C14-C53-H54; asym δm of CH3 (C42); βs H58-C57-O15-C55 1002.0581 971.996357 12.1626 2.5574 998.7131 968.751707 27.5923 6.2284 ν m of C46-C48; τm H47-C46-C48-C49; βm C1-C3-C40-C26 994.6222 964.783534 14.7581 1.7537 993.1115 963.318155 22.8186 4.3633 asymδm of CH3 groups; τm C3-C4-C5-C46; τm C48-C51-C6-C26 984.7888 955.245136 9.9824 2.1081 982.8653 953.379341 23.0630 4.4849 τ m C32-C8-C29-H31; asym δm of CH3 groups; τm H13-C12-C9-H10 935.5082 907.442954 21.5974 1.5821 933.456 905.45232 35.1689 4.3679 r o c k . s of (C26-H27; C26-H28); asym δm of CH3; τm C40-C3-C1-C22 894.4122 867.579834 6.7651 6.1001 892.2404 865.473188 16.1490 13.2213 t w i s t . s (C67-H69; C67-H70) and δs C64-H66 888.7652 862.102244 7.1646 2.8098 886.3304 859.740488 9.5352 6.1863 δ s C64-H66; rock.m (C48-H49; C48-H50); twist.s (C67-H69; C67-H70) 866.5271 840.531287 1.1709 0.6223 870.9888 844.859136 1.8110 2.3985 t w i s t . s of (C53-H54; C55-H56) 863.4892 837.584524 11.2475 6.7108 862.9942 837.104374 10.4041 13.1553 τ m H52-C51-C48-H49; rock.m (C26-H27; C26-H28); rock.m (C22-H23; C22-H24); τm H45-C42-C6-H5 843.0488 817.757336 17.4461 2.5204 843.0694 817.777318 32.2094 5.1332 w a g g . s (C34-H35; C32-H33) and τw O7=C2-C1-C22 834.8182 809.773654 8.7574 3.1907 831.3156 806.376132 15.1706 6.936 τ s H47-C46-C5-C4; τs C48-C51-C6-H42 813.7477 789.335269 1.0138 6.0149 810.0882 785.785554 0.7347 13.0197 τ m C26-C40-C3-C4 801.2001 777.164097 32.6376 0.9129 802.8851 778.798547 51.1580 3.2321 Symδs CH groups on furan ring 772.7524 749.569828 40.1779 4.4199 769.619 746.53043 62.4072 8.3682 τ s of C71-C63-C62-O60; τm of H66-C64-C67-H69 765.4691 742.505027 7.1326 7.398 765.0018 742.051746 11.7201 14.1992 Symδm CH on furan ring and τm C42-C6-C51-C48 751.3513 728.810761 2.6045 2.4905 750.9877 728.458069 5.0319 4.4818 τ m C5-C4-C12-C9 and τm C34-C32-C8-C29 738.9121 716.744737 11.6448 0.2055 739.1239 716.950183 16.1963 0.0788 Asymδs CH on furan ring 722.1832 700.517704 12.3489 2.6117 723.4458 701.742426 18.8683 4.4984 τ m C1-C2-C34-C32; τm C4-C12-O60-C62 686.9578 666.349066 5.4224 1.4738 685.8912 665.314464 10.7183 2.8493 τ m H58-C57-C14-C53 and τm C48-C51-C6-C42 668.865 648.79905 12.8788 0.9188 667.6324 647.603428 18.4726 1.8119 τ m C9-C12-C4-C36 646.4378 627.044666 11.8100 0.5746 646.7719 627.368743 21.9688 1.442 β m C67-C64-C63-C71 619.5628 600.975916 14.5359 2.821 617.9459 599.407523 19.3158 4.5248 τ s C53-C55-O15-C57 616.8961 598.389217 4.4856 1.6795 615.6735 597.203295 10.3745 2.8885 τ s C57-C14-C51-C48 590.7602 573.037394 2.2255 8.0984 590.8644 573.138468 4.8686 15.7435 τ m O60-C62-C63-C71; τm C26-C6-C5-C46 545.9651 529.586147 0.9299 3.7502 549.5733 533.086101 3.8923 7.7962 τ m C62-C63-C64-C67; δm of CH3 (C71) 538.3894 522.237718 17.1612 0.4714 536.6383 520.539151 25.1977 1.1212 τ m C4-C5-C6-C51 508.9443 493.675971 1.2889 2.069 507.5983 492.370351 1.4410 4.1594 τ m C3-C4-C5-C46; rock.m (C26-H27; C26-H28) 475.643 461.37371 1.2962 4.5398 474.4059 460.173723 2.4947 10.7229 δ s C16-C8-C29 461.5318 447.685846 2.3465 0.597 461.4543 447.610671 4.0236 0.9512 τ m C48-C46-C5-C4 451.0159 437.485423 2.9275 4.0628 448.867 435.40099 4.9702 8.8493 δ s C32-H33; τm C29-C8-C32-C34 437.1112 423.997864 1.4877 1.6801 437.3603 424.239491 4.9702 2.869 τ m O60-C62-C63-C64 and rock.m (C26-H27; C26-H28) 416.2717 403.783549 7.0349 2.9785 413.098 400.70506 9.3286 5.9324 τ m C62-C63-C64-C67 376.4872 365.192584 0.6057 1.5014 375.9518 364.673246 0.8549 2.7432 δ s C36-C4-C12 359.436 348.65292 1.0513 0.2212 357.6319 346.902943 0.4099 3.4574 τ m C22-C1-C3-C40 347.1844 336.768868 0.2931 1.3363 346.0298 335.648906 0.6318 1.8682 Asymδm of CH3 groups 309.437 300.15389 1.4908 0.891 306.2399 297.052703 1.5054 1.1169 β m C67-C64-C63-C71 231.0043 224.074171 3.5498 0.8619 229.9752 223.075944 7.8008 1.6674 β m O60-C62-C63-C64 42.7727 41.489519 0.3353 1.5162 39.5275 38.341675 0.5007 4.2131 t w i s t . m of (C14-C57; C14-C53) δ = bending; τ = out of plane deformation; β = in plane deformation; w = weak; m = medium; s = strong; wagg. = wagging; twist. = twisting; rock. = rocking; scis. = scissoring; ν = stretching; sym = symmetrical and asym = anti-symmetrical.Figure 8
IR spectra (blue) and Raman spectra (red) of Rubescin E in both gas phase (top) and chloroform solution (bottom) using B3LYP/6-311G(d,p).The C=O double bond gives rise to a very intense absorption band in IR spectrum. The position and intensity of this band range from 1870 cm−1 to 1540 cm−1 depending on the physical state, electronic, and mass effects of neighboring substituents, intra- and intermolecular interactions, and conjugations [29]. The C=O double bond absorption spectra were observed experimentally at 1720 cm−1 and 1664 cm−1 [1]. In this study, the vibrational mode of C=O was found at 1726.20 cm−1 and 1690.57 cm−1 gas phase and at 1701.01 cm−1 and 1667.59 cm−1 in chloroform. There is good agreement between the vibrational modes with experimental values.


## 4. Conclusion

In this study, the geometry optimization of Rubescin E has been carried out using ab initio HF and density functional theory DFT (B3LYP and B3PW91) methods in both gas phase and chloroform solution with the 6-311++G(d,p) basis set. The optimized parameters were compared to those of some existing groups of compound present in our molecule, since none of this have been done before for the title molecule and good agreement was found. In order to confirm the geometry of our molecule, theJ3H-H proton-proton coupling constant was evaluated and the results compared to experiment were similar. The calculated results have showed that Rubescin E possesses a HOMO-LUMO energy gap greater than 4, which indicate a hard molecule that can be used as an insulator in many electronic devices. We can also conclude from the HOMO-LUMO analysis that the electron can easily be transferred from the furan to tetrahydrofuran ring. The charge analysis performed using Mulliken population, CHepG, and NBO methods showed positive charge for all hydrogen atoms; it was observed that the most positive (respectively, negative) charge atoms were directly linked to the most negative (respectively, positive) charge atoms and also that all the carbon atoms linked to hydrogen were all negatively charged. The calculated first static hyperpolarizability was found to be more than four times greater than the reported value found in the literature for urea leading us to the conclusion that Rubescin E has very good NLO properties. The calculated optoelectronic properties show large values of refractive index, dielectric constant, and electrical susceptibility, leading us to the conclusion that Rubescin E has strong optical and phonon application. Good agreement was found between the calculated and experimental UV spectrum. The theoretical proton (1H) and carbon (13C) chemical shift values (with respect to TMS) were reported and compared with experimental data, showing a very good agreement for both 1H and 13C NMR. The calculated vibrational frequencies done using the B3LYP/6-311G(d,p) functional in both gas and chloroform solutions were all positive leading us to the conclusion that Rubescin E was stable. Approximate descriptions of the vibrational assignments were done in order to take out the different motions of atoms in the title molecule.



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*Source: 4246810-2019-01-02.xml*