# Density Functional Theoretical Computational Studies on 3-Methyl 2-Vinyl Pyridinium Phosphate

Authors: N. Kanagathara; V. J. Thanigaiarasu; V. Sabari; S. Elangovan
Journal: Advances in Condensed Matter Physics
 (2022)

---

## Abstract

The molecular structure of 3-methyl 2-vinyl pyridinium phosphate (3M2VPP) has been optimized by using Density Functional Theory using B3LYP hybrid functional with 6-311++G (d, p) basis set in order to find the whole characteristics of the molecular complex. The theoretical structural parameters such as bond length, bond angle, and dihedral angle are determined by DFT methods and are well agreed with the single crystal X-ray diffraction parameters. Theoretical vibrational, highest occupied molecular orbital - lowest unoccupied molecular orbital (HOMO-LUMO), natural bonding orbital (NBO), and electrostatic potential (ESP) analyses have also been performed. Based on the potential energy distribution (PED), the complete vibrational assignments, analysis, and correlation of the compound’s fundamental modes have been determined. Natural bonding orbital (NBO) analysis is used to evaluate the intramolecular charge transfer and hyper-conjugative interaction of the molecule. B3LYP/6-311++G (d, p) basis set determines the electronic properties such as HOMO–LUMO energies and is used to understand the kinetic stability and chemical reactivity of the studied compound. Molecular electrostatic potential (MEP) is used to investigate the electron density distribution and chemical reactive sites of 3M2VPP. The dipole moment, total polarizability, and the first-order hyperpolarizability calculations have been carried out for the studied molecule. Hirshfeld surface analysis has been done to study the intermolecular interactions in the studied complex.


---

## Body

## 1. Introduction

Organic aromatic materials with the ability of charge transfer have attracted many researchers for the past two decades and have been recognized as a material for the development of nonlinear optical materials [1, 2]. Organic phosphates are highly lustrous, adherent, and ductile, and their additives are used in electroplating baths. Structure, as well as biological activities of thiazolo-pyridine dicarboxylic derivatives, were reported by Yahia et al. [3]. Linear, as well as nonlinear optical properties of pyridine N-oxide, were reported by Soscun et al. [4]. Phosphoric acid pyridine-1-ium-2-carboxylate has been identified as a potential nonlinear optical material and is useful for device fabrication [5]. There are many reports available for the pyridine derivatives applications in the nonlinear optical field [6–10]. Pyridinium salts and its derivatives are found in various natural and bioactive compounds [11]. It has wide applications such as acylating agents and phase transfer catalysts and has found use in industrial applications such as dyes, surfactants, cosmetics, pharmaceuticals, polymerization, phase transfer agents, catalysis, sensors, and electrolytes [12]. In continuation of research on possible and potential applications of pyridine and its salts, the present study is aimed to study the quantum chemical computations of 3-methyl 2-vinyl pyridinium phosphate. The structure of 3-methyl 2-vinyl pyridinium phosphate was reported by Kalaiselvi et al. [13]. The title crystal crystallizes in a monoclinic system having a P21/c space group with lattice parameters a = 7.7089 (6) Å, b = 16.366 (13) Å, c = 8.0649 (6) Å, α = 90o, β = 109.689 (4)o, γ = 90o and V = 958.06 (13) Å3. The 3-methyl 2-vinyl pyridinium cations are bonded to phosphate anions via N-H⋯O and C-H⋯O interactions [13]. In the present communication, the optimized geometry, vibrational, NBO, and other electronic parameters have been discussed theoretically with DFT/B3LYP-6-311++G (d, p) basis set.


## 2. Materials and Methods

### 2.1. Synthesis of 3-Methyl 2-Vinyl Pyridinium Phosphate

1 g (0.0084 mol) of freshly distilled 3-methyl,2-vinyl pyridine was dissolved in 15 mL of diethyl ether at −10°C under a nitrogen atmosphere. To the above solution, 0.5 mL of H3PO4 and 10 mL of diethyl ether mixture were added in drops with continuous stirring. The product obtained as a white solid was filtered, washed with diethyl ether, and dried under a vacuum, the product was recrystallized from methanol. Yield: 100% (1.82 g) [13].


## 2.1. Synthesis of 3-Methyl 2-Vinyl Pyridinium Phosphate

1 g (0.0084 mol) of freshly distilled 3-methyl,2-vinyl pyridine was dissolved in 15 mL of diethyl ether at −10°C under a nitrogen atmosphere. To the above solution, 0.5 mL of H3PO4 and 10 mL of diethyl ether mixture were added in drops with continuous stirring. The product obtained as a white solid was filtered, washed with diethyl ether, and dried under a vacuum, the product was recrystallized from methanol. Yield: 100% (1.82 g) [13].


## 3. Results and Discussion

### 3.1. Structural Analysis

The molecular structure along with the numbering of atoms of 3-methyl 2-vinyl pyridinium phosphate is obtained from Gaussian 09 and GaussView programs and is shown in Figure1. [14, 15]. The most optimized structural parameters (bond length and bond angle) are calculated by B3LYP/6-311++G (d, p) basis sets are compared with experimental data from the results the bond lengths and angles have normal values. The asymmetric unit is composed of one 3-methyl 2-vinyl pyridinium cation and one phosphate anion. The C1—N1—C5 angle in the pyridinium ring is widened to 123.35 (2)°, compared to 115.25 (13)° in 4-aminopyridine, 121.20 (15)° in 1-(2-carboxy-ethyl)-5-ethyl-2-methylpyridinium and 120.7 (2)° in Aminopyridinium. The 3-methyl 2-vinyl pyridinium ring is essentially planar with the maximum deviation from planarity being 0.008 (2) Å for atom C5. The sum of the bond angles around the N1 atom (359.89°) indicates sp2 hybridization. The phosphate anions form centrosymmetric R22 (8) dimers via O—H⋯O hydrogen bonds. These dimers are further linked to chains running along the c axis. The cations are boned to the anions via N—H⋯O hydrogen bonds and C—H⋯O contacts [13]. Table1 list the geometric parameters of 3M2VPP. Theoretically computed bond distance and bond angles are very well matches with experimentally observed geometric parameters.Figure 1
Optimized structure 3M2VPP.Table 1
Selected bond parameters of 3M2VPP.
AtomBond distance (Å)CalculatedExpt.1C-2H1.091.0291C-3C1.38381.3721C-15N1.34181.3343C-4H1.08170.9303C-5C1.39091.3845C-6H1.08490.9305C-7C1.3961.3897C-8C1.4111.3967C-11C1.50891.5028C-9C1.4661.4688C-15N1.35491.3519C-10C1.33921.2949C-17H1.08290.99210C-18H1.08411.06410C-19H1.08491.02011C-12H1.09340.96011C-13H1.09070.96011C-14H1.09360.96015N-16H1.12551.08916H-21O1.41161.41220O-24P1.49391.49221O-24P1.53441.51222O-24P1.63841.647220-25H0.96410.88023O-24P1.63411.58923O-26H0.9640.889AtomBond angle (o)CalculatedExpt.2H-1C-3C124.9693119.942H-1C-15N115.0102119.943C-1C-15N120.0187120.111C-3C-4H119.9727120.791C-3C-5C118.3786118.384H-3C-5C121.6486120.833C-5C-6H119.6955119.313C-5C-7C121.4081121.326H-5C-7C118.8962118.375C-7C-8C117.9677118.055C-7C-11C120.1661120.778C-7C-11C121.8654121.897C-8C-9C121.6164120.577C-8C-15N118.7077118.769C-8C-15N119.6758118.668C-9C-10C126.7544126.998C-9C-17H114.6652115.2810C-9C-17H118.5775117.689C-10C-18H119.1689119.099C-10C-19H123.6603121.7418H-10C-19H117.1705113.197C-11C-12H111.6949109.527C-11C-13H110.3074109.397C-11C-14H111.722109.4012H-11C-13H107.7316109.4612H-11C-14H107.532109.5213H-11C-14H107.667109.481C-15N-8C123.5167123.351C-15N-16H113.4781112.908C-15N-16H123.0017123.6416H-21O-24P118.5485120.1924P-22O-25H110.5635110.9224P-23O-26H111.5211111.9120O-24P-21O119.1096119.2020O-24P-22O111.7533110.9220O-24P-23O108.9413107.4521O-24P-22O104.5152106.0421O-24P-23O107.7098108.5622O-24P-23O103.6473106.43AtomDihedral angle (o)CalculatedExpt.2H-1C-3C-4H−0.4648−1.142H-1C-3C-5C179.587178.9115N-1C-3C-4H−179.955178.8415N-1C-3C-5C0.0969−1.122H-1C-15N-8C−179.197−179.922H-1C-15N-16H1.4626−3.743C-1C-15N-8C0.342−0.053C-1C-15N-16H−178.999−176.281C-3C-5C-6H179.8694178.821C-3C-5C-7C−0.27141.124H-3C-5C-6H−0.0781.184H-3C-5C-7C179.7813−178.063C-5C-7C-8C0.02920.013C-5C-7C-11C−179.666−179.906H-5C-7C-8C179.8895179.996H-5C-7C-11C0.19470.095C-7C-8C-9C−179.461178.175C-7C-8C-15N0.3859−1.1611C-7C-8C-9C0.2286−1.0211C-7C-8C-15N−179.925−178.765C-7C-11C-12H119.7356120.935C-7C-11C-13H−0.048−1.005C-7C-11C-14H−119.768−119.038C-7C-11C-12H−59.9471−60.898C-7C-11C-13H−179.731−179.018C-7C-11C-14H60.5493−60.897C-8C-9C-10C175.3397166.297C-8C-9C-17H−4.030911.4015N-8C-9C-10C−4.505513.0315N-8C-9C-17H176.1239−169.227C-8C-15N-1C−0.58621.227C-8C-15N-16H178.6925174.739C-8C-15N-1C179.2634178.149C-8C-15N-16H−1.45795.928C-9C-10C-18H−179.652179.408C-9C-10C-19H0.5768−0.4717H-9C-10C-18H−0.3029−1.0417H-9C-10C-19H179.9254178.1716H-21O-24P-20O6.253523.5516H-21O-24P-22O−119.362−120.4316H-21O-24P-23O130.8515144.6625H-22O-24P-20O35.22240.2825H-22O-24P-21O165.3396167.4025H-22O-24P-23O−81.9411−78.6626H-23O-24P-20O169.2019160.8926H-23O-24P-21O38.697434.8026H-23O-24P-22O−71.6849−79.92


### 3.2. Vibrational Analysis

The analytical techniques of infrared (IR) absorption and Raman spectroscopy are frequently utilised in the quest for novel materials. Experimental methods become even better adopted for the complexity of highly functionalized materials when combined with the strength of recent computational chemistry technologies. The computational element aids in the analysis of the data-rich spectroscopic results, while the latter also confirms the computational approach used. The title molecule has 26 atoms and has 72 (3N-6) normal modes of vibration. The theoretically constructed FT-IR and FT Raman spectrum is shown in Figure2. The vibrational frequencies obtained using the B3LYP method with the standard 6-311++G (d, p) basis set calculations together with the approximate description of each normal mode are tabulated in Table 2.Figure 2
Theoretical FT-IR and FT Raman spectrum of 3M2VPP.Table 2
Wave numbers (cm−1) and relative intensities of observed and calculated Fourier infrared and Raman spectra of 3M2VPP.
Unscaled frequency (cm−1)Scaled frequency (cm−1)IR intensityRaman activityBand assignment description (PED (%))3839.2313710.61651.2159140.5984νasym (O-H) (54)3836.7013708.171100.714466.9707νasym (O-H) (46)3226.9763118.87223.920591.6865νasym (O-H) (95)3213.2253105.5810.9295160.0995νasym (C-H) (96)3186.8013080.04314.340175.7115νasym (C-H) (96)3172.2283065.9587.1712112.926νasym (C-H) (93)3130.3853025.51759.4681131.9634νasym (C-H) (54)3113.993009.67111.533261.8349νsym (C-H) (50)3107.2473003.154187.0633104.438νsym (C-H) (82)3086.2522982.8628.390466.7826νsym (C-H) (49)3033.5152931.89312.621211.6118νsym (C-H) (42)1945.2181880.0541707.74721.352δ(N-H) (51)1683.4891627.092115.4109127.6561ν (C-C) (32)1653.9111598.505309.36372.1817ν (C-C) (20)1631.2081576.562205.1555200.4535ν (C-C) (15)1568.8631516.306385.10272.6362ν (C-C) (32)1513.4351462.735136.063410.9424δ(H-C-H) (12)1490.2561440.3329.48699.7149δ(H-C-H) (13)1489.4371439.54156.175372.3044δ(H-C-H) (13)1484.9671435.2257.95665.349ν(P-O) (26)1422.9621375.2931.385412.4871δ(H-C-H) (23)1419.7551372.19361.56376.5647δ(H-C-C) (13)1366.9211321.1290.622751.4184ν(C-C) (16)1332.9721288.3184.65267.6211ν(C-N) (12)1287.9371244.79153.224110.7206ν(C-N) (15)1259.9071217.77.561756.5216ν(C-C) (12)1236.0011194.595199.43740.9401ν(P-O) (58)1221.5391180.61753.98980.2654ν(P-O) (26) (/τ(H-N-C-C) (36)1190.4521150.5729.93194.8839δ(H-C-C) (10)1128.7141090.90219.96766.2068δ(H-C-C) (16)1109.1891072.03119.579539.2419δ(H-C-C) (12)1065.3151029.6270.74810.8269δ(H-C-C) (39)1063.821028.1827.29987.8261δ(H-N-C) (11)1050.6961015.498371.209612.7771ν(P-O) (16)1035.4931000.80450.89851.6426τ(H-C-C-C) (18)1032.588997.99650.85750.3042τ(H-C-C-C) (40)1019.36985.211291.80155.831ν(P-O) (15) δ(H-O-P) (13)1012.457978.53964.47465.3341τ(H-C-C-C) (31)1010.606976.750224.35937.459τ(H-C-C-C) (39)986.0833953.0495255.53563.7348τ(H-C-C-C) (35)984.8057951.8147517.7846.6565τ(H-C-C-C) (16)849.3175820.8654322.57632.467ν(P-O) (50)840.6951812.531846.97174.622ν(P-O)/δ(C-C-C) (14)821.4817793.962126.92440.5279ν(P-O) (38)/δ(C-C-C)(17)801.2227774.381776.596320.3339ν(P-O) (42)797.2224770.515411.41831.1044τ(H-C-C-C) (13)/τ(C-N-C-C) (28)731.3239706.8245299.710512.8903ν(C-C) (11)638.8264617.42570.07431.1833τ(H-C-C-C) (19)/τ(C-N-C-C) (15)593.9972574.0983104.42927.774δ(H-N-C) (14)531.8615514.044116.47137.2788ν(C-C) (15)507.6132490.6082206.57325.752ω(O-H)/ω(O-P-O) (16)497.2902480.63151.73881.9153δ(H-O-P) (11)494.3387477.778416.58271.6197ω(H-O-P) (11)/τ(H-C-C-C) (10)483.3281467.136650.63032.0877τ(O-O-O-P) (26)456.1658440.884266.67651.7577τ(O-O-O-P) (27)442.7693427.93653.92890.4109τ(O-O-O-P) (18)406.9055393.27427.6020.4082τ(H-O-P-O) (24)350.1837338.45255.36134.5604τ(H-O-P-O) (19)344.8172333.26588.11881.7445ω(O-O-O-P) (19)277.187267.901274.55510.1594τ(C-C-C-C) (25)/τ(H-O-P-O) (41)261.6002252.83663.3650.6734τ(C-C-C-C) (12)/(C-C-N-C)(20)245.9159237.67770.50945.0403τ(C-N-H-O) (20)220.2828212.9033192.39811.6911τ(H-O-P-O) (30)178.0645172.09932.44750.8118τ(C-C-N-C) (14)/τ(O-O-O-P) (13)173.0998167.30120.35731.6346τ(C-C-N-C) (14)/τ(O-O-O-P) (13)166.1433160.57753.31572.0295τ(H-C-C-C) (16)120.4188116.38487.95220.4634τ(H-N-C-C) (13)/τ(C-C-C-C) (14)94.678891.507060.5880.4054τ(C-C-C-N) (27)87.829884.88750.46090.379τ(C-C-C-N) (45)62.589760.492952.43082.2013τ(H-O-P-O) (10)36.571535.346350.68112.168τ(C-N-H-O) (20)28.003327.065192.50261.8538τ(C-N-H-O) (72)


#### 3.2.1. 3-Methyl 2-Vinyl Pyridinium Cation Vibrations

2-vinylpyridine is a polymer that is extensively utilised in the fabrication of multilayer films and as a matrix for the embedding of semiconductor nanoparticles. It exhibits unique photochemical properties as a result of the lone pair of sp2 electrons, leading to a variety of applications such as pH-responsive coatings. Absorption bands due to the stretching modes of CH and CH2 groups can be seen in the frequency range of 2800–3200 cm−1. The variations in this spectral region were obvious but modest since the molar strength of the CH stretching vibration is quite small. The loss of methyne protons in the 2-vinyl pyridine structure was blamed for the reduction of strength in the methyne bands at 3010–3030 cm−1 in the gel spectrum. The NH+ stretching vibration of the pyridinium ion was attributed to a new, very strong infrared band at 3400 cm−1 [16]. Theoretically, these peaks are computed at 3120–2930 cm−1. The computed peak at 1880 cm−1 is attributed to N-H in-plane bending vibration. According to PED calculations, there are weak peaks observed in the range 1150–1029 cm−1 and are attributed to C-C-H bending vibrations. The torsional vibrations of HCCC are computed in the region 980–950 cm−1 with weak infrared and Raman intensity except at 953 cm−1 with strong infrared intensity. 1630–1510 cm−1 range of frequencies are ascribed to C-C stretching vibrations of the 2-vinylpyridine ring. Methyl group bending vibrations are calculated at 1462 and 1440 cm−1. Similar peaks were observed at 1375 and 1372 cm−1 with medium intensity. The other peak vibrations are computed and provided in Table 2.


#### 3.2.2. Phosphate Anion Vibrations

Phosphate anion includes vibrations of PO4 stretching as well P-O-H bending mode. The internal vibrations of each H2PO4− ion are divided into vibrations of the two groups, PO2 and P(OH)2 which is due to the presence of two P-OH longer bonds and P-O shorter bonds [17, 18]. PED computed values at 3710 and 3708 cm−1 is contributed to O-H asymmetric stretching vibrations of a phosphate anion. The stretching vibrations of the P-O bonds are theoretically computed at 1194, 1180, 1015, 985, 820, 812, 793, and 774 cm−1. P-O2 asymmetric stretching ranges from 1060 to 1175 cm−1 whereas symmetric stretching ranges from 1035 to 1065 cm−1. Asymmetric stretching vibrations of P(OH)2 lie in the region 950–980 cm−1 and symmetric stretching vibrations of P(OH)2 are in the region 900 to 920 cm−1. This type of P-O stretching bond is experimentally found at 1175 and 900 cm−1 [19, 20].


### 3.3. Natural Bonding Orbitals Analysis

NBOs analysis gives deep insight into the chemical bonding of all the complexes. It also makes available substantial information regarding the nature of bonding orbitals, their occupancies as well as the type and nature of the interaction (intermolecular or intramolecular, hyper-conjugative or charge transfer) existing between virtual and occupied Lewis orbitals. The analysis is conducted by considering all probable interactions between donor (occupied Lewis NBOs) and acceptors (vacant) non-Lewis NBOs, and approximating their energetic significance by second-order perturbation theory of the Fock matrix [21, 22]. For this analysis, all potential interactions between “full” (donor) Lewis-type NBOs and “empty” (acceptor) non-Lewis NBOs are examined, and their energy significance is estimated using second-order perturbation theory. These interactions are known as “delocalization” corrections to the zeroth-order natural Lewis structure because they cause a loss of occupancy from the localised NBOs of the idealised Lewis structure into the empty non-Lewis orbitals (and thus, to departures from the idealised Lewis structure description) [23]. In the present study, donor–acceptor interactions were applied for investigating interactions in the 3M2VPP molecular complex. Table 3 shows some of the significant donor–acceptor interactions and their stabilization energies E(2). The NBO charges on the particular atoms computed for 3M2VPP are shown in Table 3. According to the calculation, the methyl group attached carbon atom in the pyridine ring (7C) have smaller negative charges (−0.598e) than the carbon atom (10C) in the CH2 groups (−0.265e). The nitrogen atom (15N) of the pyridine ring which is involved in hydrogen bonds (H16) shows the highest positive charge 0.4765e confirms the occurrence of protonation. For singly protonated 2-vinyl pyridinium cation, the most charge difference i.e., −0.466 e is observed at 15N where the proton is attached. The methyl group hydrogen atoms (12H, 13H, and 14H) have higher similar positive charges (0.215e to 0.222e) than the other hydrogen atoms (18H and 19H) of the C-H groups. The calculated charges for carbon atoms C1, C3, C5, C7, and C8 in the pyridine ring are completely different. The adjacent carbon atoms 1C and 8C carry positive charges whereas 3C, 5C, 7C, and 8C have negative charges. The phosphor atom (24P) has a more positive charge of 2.471e and all the oxygen atoms have negative charges. Hydrogen atoms 25H and 26H have more positive charges. Thus, the positive and negative charges are balanced and establishes the stability of the molecule as shown in Figure 3. The donor–acceptor interactions of the inclusion complex of phosphoric acid into 3-methyl 2-vinyl pyridine are investigated using the NBO program. The obtained results are illustrated in Table 3. The interaction energies of these contacts are in the range of 4–363 kJmol−1. The highest intramolecular stabilization energy of 91.12 kJmol−1 is found in 3-methyl-2-vinylpyridine between antibonding π orbitals of C1-N15 to C3-C5. The next highest stabilization energy is due to the lone pair of carbon atom C7 with π∗(C3-C5)−71.58 kJmol−1 and C8 with π∗(C1-N15)−67.09 kJmol−1. The strongest intermolecular stabilization energy occurs in between the lone pair of electronegative nitrogen atom N15 in 3-methyl-2-vinyl pyridine to H16 in phosphoric acid establishing energy of 362.82 kJmol−1. The lone pair of oxygen atom O21 with antibonding H16 has 14.13 kJmol−1 confirming the protonation between the molecules. Intramolecular stabilization energy of phosophoric acid lies in the range of 10 to 22 kJmol−1 [24, 25]. The other type of intermolecular and intramolecular interactions and their energies are tabulated in Table 3.Table 3
Second-order perturbation theory analysis of the Fock matrix in NBO basis for 3M2VPP.
Donor NBO (i)Acceptor NBO (j)E(2) (kcal/mol)E(j)-E(i) a.u.F(i, j) a.uWithin unit 1BD∗(2)C1-N15BD∗(2) C3-C591.120.040.090LP (1)C7BD∗(2) C3-C571.580.140.110LP∗(1)C8BD∗(2) C1-N1567.090.100.090BD (2)C3-C5LP(1) C748.580.150.090BD (2)C1-N15LP∗(1) C843.840.210.108BD (2)C3-C5BD∗(2) C1-N1535.690.240.084BD (2)C9-C10LP∗(1) C833.670.140.081LP∗(1)C8BD∗(2) C9-C1026.130.170.086From unit 1 to unit 2LP (1)N15LP∗(1) H16362.820.480.385BD (1)C1-N15LP∗(1) H1614.090.980.121BD (1)C8-N15LP∗(1) H1612.220.980.113From unit 2 to unit 3LP∗(1) H16BD∗(1) O21-P244.560.260.054From unit 3 to unit 1LP (3) O20BD∗(1) C1-H24.260.670.050From unit 3 to unit 2LP (3)O21LP∗(1) H16114.130.480.228LP (1)O21LP∗(1) H1615.900.710.108Within unit 3LP (2)O20BD∗(1) O22-P2422.030.490.093LP (3)O20BD∗(1) O21-P2417.700.590.092LP (2)O21BD∗(1) O22-P2413.220.520.076LP (3)O20BD∗(1) O23-P2411.280.490.067LP (2)O20BD∗(1) O23-P2410.790.490.065LP (2)O21BD∗(1) O23-P2410.520.530.068LP (2)O22BD∗(1) O23-P2410.480.570.071LP (2)O23BD∗(1) O22-P2410.070.560.069Figure 3
NBO charges of 3M2VPP.


### 3.4. Frontier Molecular Orbitals (FMOs) Analysis

Frontier molecular orbitals (FMO) theory allows a chemist to make predictions about a reaction by knowing the placement of the HOMO and LUMO energy levels. Fukui developed the frontier molecular orbital theory to explain the chemical reactivity of the sample [26]. The Frontier molecular orbitals such as HOMO and LUMO affords information about the chemical stability and electrical and optical properties of the compounds; also it is used to explain various types of reactions in conjugated systems. The HOMO-LUMO orbitals are referred to as frontier molecular orbitals (FMOs) as they lie at the outermost boundaries for the electrons in a system. The pictorial representations of HOMO and LUMO orbitals have been calculated by using the B3LYP/6-311++G (d, p) basis set as depicted in Figure 4. HOMO is completely occupied in the 3-methyl 2-vinyl pyridinium ring and LUMO is partially occupied in the 3-methyl 2-vinyl pyridinium ring which seems that the majority of interaction takes place within the ring. The calculated energy values of HOMO and LUMO in 3-methyl 2-vinyl pyridinium phosphate are -9.987 eV and -6.443 eV and the frontier orbital energy gap value is 3.544 eV as listed in Table 4. HOMO and LUMO energy gap explains the eventual charge transfer interactions taking place within the molecule. The high stability and chemical inertness are due to the presence of high ionization energy. Global chemical descriptors like chemical potential, electrophilicity, hardness, softness, and electronegativity varies the chemical reactivity of the molecule [27–30]. All the calculated parameters indicate the high reactive nature of the grown sample. Also, high electrophilicity values indicate the good electrophile nature of the material [31, 32].Figure 4
HOMO-LUMO plot of 3M2VPP.Table 4
Chemical descriptors of 3M2VPP.
ParametersValue (eV)EHOMO−9.987ELUMO−6.443ΔEgap3.544Ionization potential (I)+9.987Electron affinity (A)+6.443Chemical potential (μ)−8.215Electronegativity (χ)8.215Global hardness (η)1.772Global softness (S)0.282Electrophilicity (ω)19.042


### 3.5. Molecular Electrostatic Potential Studies

Molecular Electrostatic Potential (MEP) is an essential tool for interpreting electrostatic (electron and nuclei) distribution potential and envisage the reactive site of wide ranges in both electrophilic and nucleophilic attacks in chemical reactions, and hydrogen-bonding interactions. This map is useful as an indicator of the sites or regions of a molecule to which an approaching electrophile and nucleophile are initially attracted. This is in turn related to the electronic density and is a very useful descriptor for determining sites for electrophilic attack and related to nucleophilic reactions as well as hydrogen-bonding interactions [33, 34]. The molecular electrostatic potential projection map for 3-methyl 2-vinyl pyridinium phosphate is calculated using the B3LYP/6-311++G (d, p) method. MEP surface map of 3-methyl 2-vinyl pyridinium phosphate is shown in Figure 5. The reactive sites are located by different colour codes and are highly beneficial to explore the molecular structure with its physiochemical property relationship [35, 36]. Molecular electrostatic potential map ranges from −4.324 × 10−2 to +4.324 × 10−2 esu. The total density spectrum ranges from 4.074 × 10−4 to +4.074 × 10−4 esu. Electrophilic and nucleophilic areas are represented by red and blue colour regions respectively as shown in Figure 6.Figure 5
MEP map of 3M2VPP.Figure 6
Total density spectrum of 3M2VPP.


### 3.6. Nonlinear Optical Properties

The first-order hyperpolarizability (β) is a measure of how easily a dipole is induced in a molecule in the presence of an electric field. The first-order hyperpolarizability calculations have been done using the DFT method based on the finite field approach. The first-order hyperpolarizability is a third-rank tensor that can be described by a 3 × 3 × 3 matrix. The 27 components of the 3D matrix can be reduced to 10 components due to the Kleinman symmetry [37].The total induced dipole moment by the applied field is calculated using the Taylor series expansion.(1)μ=μ0+αijEj+βijkEjEk+⋯,where α, linear polarizability; μ0, the permanent dipole moment; and βijk, first order hyperpolarizability tensor component.The expression for the static dipole moment is given as(2)μ=μx2+μy2+μz21/2.The following expression gives the isotropic (or average) linear polarizability:(3)αTotal=αxx+αyy+αzz3.The magnitude of the first order hyperpolarizability tensor is calculated using the relation,(4)βi=βiii+13∑i≠jβijj+βjij+βjji.The output of Gaussian 09W for calculating the magnitude ofβTotal is given as follows:(5)βTotal=βxxx+βxyy+βxzz2+βyyy+βyzz+βyxx2+βzzz+βzxx+βzyy2.Gaussian 09W program using B3YLP/6-311++G (d, p) methodology to compute first order hyperpolarizability calculations. The total molecular dipole moment (μ), linear polarizability (α), and first-order hyperpolarizability (β) were calculated in atomic units and are converted into electrostatic units. (α: 1 a.u = 0.1482 × 10−24 esu, β: 1 a.u = 8.6393 × 10−30esu). Table 5 lists the calculated parameters of an electric dipole moment µ(D), the average polarizability αtot (×10−24 esu), and first-order hyperpolarizability βtot (×10−31 esu). The calculated dipole moment is 8.9064 Debye and reveals the ionic nature of the compound. The maximum value of 1.1298 Debye occurs in the Y direction. The maximum hyperpolarizability value is 21.2852 × 10−31 esu and it is computed for βxzz direction which is due to the substantial delocalization of electron cloud in that region. The next highest hyperpolarizabiltiy is computed to be 16.8041 × 10−31 esu and 11.3499 × 10−31 esu for the direction βzxx & βyyy respectively. Urea–a well-known standard nonlinear optical material has total polarizability (α = 3.8312 × 10−24 esu) and first-order hyperpolarizability (β = 3.7289 × 10−31 esu). The total polarizability is computed to be 39.878 × 10−31 esu. It is found that 3M2VPP is 10.694 times that of urea and may be expected as a potential candidate for the development of NLO materials [38–42].Table 5
Calculated electric dipole moment, polarizability, and first-order hyperpolarizability of 3M2VPP.
ParametersB3LYP/6-311++G (d, p)ParametersB3LYP/6-311++G (d, p)μx−8.8313βxxx−27.9812μy1.1298βxxy13.3782μz0.2376βxyy−21.3378μ (D)8.9064βyyy11.3499αxx−77.4601βzxx16.8041αxy7.9872βxyz−17.5345αyy−83.7978βzyy−4.4329αxz2.3012βxzz21.2853αyz−4.0765βyzz−0.2132αzz−93.5580βzzz1.8827αtot(esu)84.938 × 10−24βtot(esu)39.878 × 10−31


### 3.7. Hirshfeld Surface Analysis

CrystalExplorer 3.1 [43] program is used to understand the interactions and the connectivity among the molecules efficiently. The crystallographic information file (.cif) was imported to the crystal explorer to generate the Hirshfeld surfaces. The Hirshfeld surface (HS) is the region around the molecule in the crystal space which can be considered as the boundary separating two regions—the interior (the reference molecule) and the exterior (neighboring molecules) [44]. The 2D fingerprint plot provides a precise two-dimensional graphical representation of the intermolecular interactions in the crystal as shown in Figure 7. The contributions from different contacts to the total Hirshfeld surface area are shown in Figure8. The major contribution (42.0%) is from H⋯H and (38.6%) from O⋯H contacts. The wings are due to the C–H⋯π interactions. The π···π type of interaction is clearly seen on the shape decorated HSs where the characteristic blue and red triangles are present. Hydrogen bonding contacts are represented by red spots which are shown in Figure 8. The dnorm parameter exhibits a surface with a red-white-blue colour scheme. Bright red spots show the intermolecular contacts less than their vdW radii, while the blue spots show intermolecular contacts longer than their vdW radii. White spots are the sum of their vdW radii. The red regions in Figure 9 are apparent around the phosphor atom participating in the P-O···H contacts.Figure 7
Fingerprint of LHLTHH (100%).Figure 8
Hirshfeld surface analysisdi, de, dnorm, shape index, and curvedness of 3M2VPP.Figure 9
Relative contributions to the percentage of Hirshfeld surface area for the various intermolecular contacts in 3M2VPP.


## 3.1. Structural Analysis

The molecular structure along with the numbering of atoms of 3-methyl 2-vinyl pyridinium phosphate is obtained from Gaussian 09 and GaussView programs and is shown in Figure1. [14, 15]. The most optimized structural parameters (bond length and bond angle) are calculated by B3LYP/6-311++G (d, p) basis sets are compared with experimental data from the results the bond lengths and angles have normal values. The asymmetric unit is composed of one 3-methyl 2-vinyl pyridinium cation and one phosphate anion. The C1—N1—C5 angle in the pyridinium ring is widened to 123.35 (2)°, compared to 115.25 (13)° in 4-aminopyridine, 121.20 (15)° in 1-(2-carboxy-ethyl)-5-ethyl-2-methylpyridinium and 120.7 (2)° in Aminopyridinium. The 3-methyl 2-vinyl pyridinium ring is essentially planar with the maximum deviation from planarity being 0.008 (2) Å for atom C5. The sum of the bond angles around the N1 atom (359.89°) indicates sp2 hybridization. The phosphate anions form centrosymmetric R22 (8) dimers via O—H⋯O hydrogen bonds. These dimers are further linked to chains running along the c axis. The cations are boned to the anions via N—H⋯O hydrogen bonds and C—H⋯O contacts [13]. Table1 list the geometric parameters of 3M2VPP. Theoretically computed bond distance and bond angles are very well matches with experimentally observed geometric parameters.Figure 1
Optimized structure 3M2VPP.Table 1
Selected bond parameters of 3M2VPP.
AtomBond distance (Å)CalculatedExpt.1C-2H1.091.0291C-3C1.38381.3721C-15N1.34181.3343C-4H1.08170.9303C-5C1.39091.3845C-6H1.08490.9305C-7C1.3961.3897C-8C1.4111.3967C-11C1.50891.5028C-9C1.4661.4688C-15N1.35491.3519C-10C1.33921.2949C-17H1.08290.99210C-18H1.08411.06410C-19H1.08491.02011C-12H1.09340.96011C-13H1.09070.96011C-14H1.09360.96015N-16H1.12551.08916H-21O1.41161.41220O-24P1.49391.49221O-24P1.53441.51222O-24P1.63841.647220-25H0.96410.88023O-24P1.63411.58923O-26H0.9640.889AtomBond angle (o)CalculatedExpt.2H-1C-3C124.9693119.942H-1C-15N115.0102119.943C-1C-15N120.0187120.111C-3C-4H119.9727120.791C-3C-5C118.3786118.384H-3C-5C121.6486120.833C-5C-6H119.6955119.313C-5C-7C121.4081121.326H-5C-7C118.8962118.375C-7C-8C117.9677118.055C-7C-11C120.1661120.778C-7C-11C121.8654121.897C-8C-9C121.6164120.577C-8C-15N118.7077118.769C-8C-15N119.6758118.668C-9C-10C126.7544126.998C-9C-17H114.6652115.2810C-9C-17H118.5775117.689C-10C-18H119.1689119.099C-10C-19H123.6603121.7418H-10C-19H117.1705113.197C-11C-12H111.6949109.527C-11C-13H110.3074109.397C-11C-14H111.722109.4012H-11C-13H107.7316109.4612H-11C-14H107.532109.5213H-11C-14H107.667109.481C-15N-8C123.5167123.351C-15N-16H113.4781112.908C-15N-16H123.0017123.6416H-21O-24P118.5485120.1924P-22O-25H110.5635110.9224P-23O-26H111.5211111.9120O-24P-21O119.1096119.2020O-24P-22O111.7533110.9220O-24P-23O108.9413107.4521O-24P-22O104.5152106.0421O-24P-23O107.7098108.5622O-24P-23O103.6473106.43AtomDihedral angle (o)CalculatedExpt.2H-1C-3C-4H−0.4648−1.142H-1C-3C-5C179.587178.9115N-1C-3C-4H−179.955178.8415N-1C-3C-5C0.0969−1.122H-1C-15N-8C−179.197−179.922H-1C-15N-16H1.4626−3.743C-1C-15N-8C0.342−0.053C-1C-15N-16H−178.999−176.281C-3C-5C-6H179.8694178.821C-3C-5C-7C−0.27141.124H-3C-5C-6H−0.0781.184H-3C-5C-7C179.7813−178.063C-5C-7C-8C0.02920.013C-5C-7C-11C−179.666−179.906H-5C-7C-8C179.8895179.996H-5C-7C-11C0.19470.095C-7C-8C-9C−179.461178.175C-7C-8C-15N0.3859−1.1611C-7C-8C-9C0.2286−1.0211C-7C-8C-15N−179.925−178.765C-7C-11C-12H119.7356120.935C-7C-11C-13H−0.048−1.005C-7C-11C-14H−119.768−119.038C-7C-11C-12H−59.9471−60.898C-7C-11C-13H−179.731−179.018C-7C-11C-14H60.5493−60.897C-8C-9C-10C175.3397166.297C-8C-9C-17H−4.030911.4015N-8C-9C-10C−4.505513.0315N-8C-9C-17H176.1239−169.227C-8C-15N-1C−0.58621.227C-8C-15N-16H178.6925174.739C-8C-15N-1C179.2634178.149C-8C-15N-16H−1.45795.928C-9C-10C-18H−179.652179.408C-9C-10C-19H0.5768−0.4717H-9C-10C-18H−0.3029−1.0417H-9C-10C-19H179.9254178.1716H-21O-24P-20O6.253523.5516H-21O-24P-22O−119.362−120.4316H-21O-24P-23O130.8515144.6625H-22O-24P-20O35.22240.2825H-22O-24P-21O165.3396167.4025H-22O-24P-23O−81.9411−78.6626H-23O-24P-20O169.2019160.8926H-23O-24P-21O38.697434.8026H-23O-24P-22O−71.6849−79.92


## 3.2. Vibrational Analysis

The analytical techniques of infrared (IR) absorption and Raman spectroscopy are frequently utilised in the quest for novel materials. Experimental methods become even better adopted for the complexity of highly functionalized materials when combined with the strength of recent computational chemistry technologies. The computational element aids in the analysis of the data-rich spectroscopic results, while the latter also confirms the computational approach used. The title molecule has 26 atoms and has 72 (3N-6) normal modes of vibration. The theoretically constructed FT-IR and FT Raman spectrum is shown in Figure2. The vibrational frequencies obtained using the B3LYP method with the standard 6-311++G (d, p) basis set calculations together with the approximate description of each normal mode are tabulated in Table 2.Figure 2
Theoretical FT-IR and FT Raman spectrum of 3M2VPP.Table 2
Wave numbers (cm−1) and relative intensities of observed and calculated Fourier infrared and Raman spectra of 3M2VPP.
Unscaled frequency (cm−1)Scaled frequency (cm−1)IR intensityRaman activityBand assignment description (PED (%))3839.2313710.61651.2159140.5984νasym (O-H) (54)3836.7013708.171100.714466.9707νasym (O-H) (46)3226.9763118.87223.920591.6865νasym (O-H) (95)3213.2253105.5810.9295160.0995νasym (C-H) (96)3186.8013080.04314.340175.7115νasym (C-H) (96)3172.2283065.9587.1712112.926νasym (C-H) (93)3130.3853025.51759.4681131.9634νasym (C-H) (54)3113.993009.67111.533261.8349νsym (C-H) (50)3107.2473003.154187.0633104.438νsym (C-H) (82)3086.2522982.8628.390466.7826νsym (C-H) (49)3033.5152931.89312.621211.6118νsym (C-H) (42)1945.2181880.0541707.74721.352δ(N-H) (51)1683.4891627.092115.4109127.6561ν (C-C) (32)1653.9111598.505309.36372.1817ν (C-C) (20)1631.2081576.562205.1555200.4535ν (C-C) (15)1568.8631516.306385.10272.6362ν (C-C) (32)1513.4351462.735136.063410.9424δ(H-C-H) (12)1490.2561440.3329.48699.7149δ(H-C-H) (13)1489.4371439.54156.175372.3044δ(H-C-H) (13)1484.9671435.2257.95665.349ν(P-O) (26)1422.9621375.2931.385412.4871δ(H-C-H) (23)1419.7551372.19361.56376.5647δ(H-C-C) (13)1366.9211321.1290.622751.4184ν(C-C) (16)1332.9721288.3184.65267.6211ν(C-N) (12)1287.9371244.79153.224110.7206ν(C-N) (15)1259.9071217.77.561756.5216ν(C-C) (12)1236.0011194.595199.43740.9401ν(P-O) (58)1221.5391180.61753.98980.2654ν(P-O) (26) (/τ(H-N-C-C) (36)1190.4521150.5729.93194.8839δ(H-C-C) (10)1128.7141090.90219.96766.2068δ(H-C-C) (16)1109.1891072.03119.579539.2419δ(H-C-C) (12)1065.3151029.6270.74810.8269δ(H-C-C) (39)1063.821028.1827.29987.8261δ(H-N-C) (11)1050.6961015.498371.209612.7771ν(P-O) (16)1035.4931000.80450.89851.6426τ(H-C-C-C) (18)1032.588997.99650.85750.3042τ(H-C-C-C) (40)1019.36985.211291.80155.831ν(P-O) (15) δ(H-O-P) (13)1012.457978.53964.47465.3341τ(H-C-C-C) (31)1010.606976.750224.35937.459τ(H-C-C-C) (39)986.0833953.0495255.53563.7348τ(H-C-C-C) (35)984.8057951.8147517.7846.6565τ(H-C-C-C) (16)849.3175820.8654322.57632.467ν(P-O) (50)840.6951812.531846.97174.622ν(P-O)/δ(C-C-C) (14)821.4817793.962126.92440.5279ν(P-O) (38)/δ(C-C-C)(17)801.2227774.381776.596320.3339ν(P-O) (42)797.2224770.515411.41831.1044τ(H-C-C-C) (13)/τ(C-N-C-C) (28)731.3239706.8245299.710512.8903ν(C-C) (11)638.8264617.42570.07431.1833τ(H-C-C-C) (19)/τ(C-N-C-C) (15)593.9972574.0983104.42927.774δ(H-N-C) (14)531.8615514.044116.47137.2788ν(C-C) (15)507.6132490.6082206.57325.752ω(O-H)/ω(O-P-O) (16)497.2902480.63151.73881.9153δ(H-O-P) (11)494.3387477.778416.58271.6197ω(H-O-P) (11)/τ(H-C-C-C) (10)483.3281467.136650.63032.0877τ(O-O-O-P) (26)456.1658440.884266.67651.7577τ(O-O-O-P) (27)442.7693427.93653.92890.4109τ(O-O-O-P) (18)406.9055393.27427.6020.4082τ(H-O-P-O) (24)350.1837338.45255.36134.5604τ(H-O-P-O) (19)344.8172333.26588.11881.7445ω(O-O-O-P) (19)277.187267.901274.55510.1594τ(C-C-C-C) (25)/τ(H-O-P-O) (41)261.6002252.83663.3650.6734τ(C-C-C-C) (12)/(C-C-N-C)(20)245.9159237.67770.50945.0403τ(C-N-H-O) (20)220.2828212.9033192.39811.6911τ(H-O-P-O) (30)178.0645172.09932.44750.8118τ(C-C-N-C) (14)/τ(O-O-O-P) (13)173.0998167.30120.35731.6346τ(C-C-N-C) (14)/τ(O-O-O-P) (13)166.1433160.57753.31572.0295τ(H-C-C-C) (16)120.4188116.38487.95220.4634τ(H-N-C-C) (13)/τ(C-C-C-C) (14)94.678891.507060.5880.4054τ(C-C-C-N) (27)87.829884.88750.46090.379τ(C-C-C-N) (45)62.589760.492952.43082.2013τ(H-O-P-O) (10)36.571535.346350.68112.168τ(C-N-H-O) (20)28.003327.065192.50261.8538τ(C-N-H-O) (72)


### 3.2.1. 3-Methyl 2-Vinyl Pyridinium Cation Vibrations

2-vinylpyridine is a polymer that is extensively utilised in the fabrication of multilayer films and as a matrix for the embedding of semiconductor nanoparticles. It exhibits unique photochemical properties as a result of the lone pair of sp2 electrons, leading to a variety of applications such as pH-responsive coatings. Absorption bands due to the stretching modes of CH and CH2 groups can be seen in the frequency range of 2800–3200 cm−1. The variations in this spectral region were obvious but modest since the molar strength of the CH stretching vibration is quite small. The loss of methyne protons in the 2-vinyl pyridine structure was blamed for the reduction of strength in the methyne bands at 3010–3030 cm−1 in the gel spectrum. The NH+ stretching vibration of the pyridinium ion was attributed to a new, very strong infrared band at 3400 cm−1 [16]. Theoretically, these peaks are computed at 3120–2930 cm−1. The computed peak at 1880 cm−1 is attributed to N-H in-plane bending vibration. According to PED calculations, there are weak peaks observed in the range 1150–1029 cm−1 and are attributed to C-C-H bending vibrations. The torsional vibrations of HCCC are computed in the region 980–950 cm−1 with weak infrared and Raman intensity except at 953 cm−1 with strong infrared intensity. 1630–1510 cm−1 range of frequencies are ascribed to C-C stretching vibrations of the 2-vinylpyridine ring. Methyl group bending vibrations are calculated at 1462 and 1440 cm−1. Similar peaks were observed at 1375 and 1372 cm−1 with medium intensity. The other peak vibrations are computed and provided in Table 2.


### 3.2.2. Phosphate Anion Vibrations

Phosphate anion includes vibrations of PO4 stretching as well P-O-H bending mode. The internal vibrations of each H2PO4− ion are divided into vibrations of the two groups, PO2 and P(OH)2 which is due to the presence of two P-OH longer bonds and P-O shorter bonds [17, 18]. PED computed values at 3710 and 3708 cm−1 is contributed to O-H asymmetric stretching vibrations of a phosphate anion. The stretching vibrations of the P-O bonds are theoretically computed at 1194, 1180, 1015, 985, 820, 812, 793, and 774 cm−1. P-O2 asymmetric stretching ranges from 1060 to 1175 cm−1 whereas symmetric stretching ranges from 1035 to 1065 cm−1. Asymmetric stretching vibrations of P(OH)2 lie in the region 950–980 cm−1 and symmetric stretching vibrations of P(OH)2 are in the region 900 to 920 cm−1. This type of P-O stretching bond is experimentally found at 1175 and 900 cm−1 [19, 20].


## 3.2.1. 3-Methyl 2-Vinyl Pyridinium Cation Vibrations

2-vinylpyridine is a polymer that is extensively utilised in the fabrication of multilayer films and as a matrix for the embedding of semiconductor nanoparticles. It exhibits unique photochemical properties as a result of the lone pair of sp2 electrons, leading to a variety of applications such as pH-responsive coatings. Absorption bands due to the stretching modes of CH and CH2 groups can be seen in the frequency range of 2800–3200 cm−1. The variations in this spectral region were obvious but modest since the molar strength of the CH stretching vibration is quite small. The loss of methyne protons in the 2-vinyl pyridine structure was blamed for the reduction of strength in the methyne bands at 3010–3030 cm−1 in the gel spectrum. The NH+ stretching vibration of the pyridinium ion was attributed to a new, very strong infrared band at 3400 cm−1 [16]. Theoretically, these peaks are computed at 3120–2930 cm−1. The computed peak at 1880 cm−1 is attributed to N-H in-plane bending vibration. According to PED calculations, there are weak peaks observed in the range 1150–1029 cm−1 and are attributed to C-C-H bending vibrations. The torsional vibrations of HCCC are computed in the region 980–950 cm−1 with weak infrared and Raman intensity except at 953 cm−1 with strong infrared intensity. 1630–1510 cm−1 range of frequencies are ascribed to C-C stretching vibrations of the 2-vinylpyridine ring. Methyl group bending vibrations are calculated at 1462 and 1440 cm−1. Similar peaks were observed at 1375 and 1372 cm−1 with medium intensity. The other peak vibrations are computed and provided in Table 2.


## 3.2.2. Phosphate Anion Vibrations

Phosphate anion includes vibrations of PO4 stretching as well P-O-H bending mode. The internal vibrations of each H2PO4− ion are divided into vibrations of the two groups, PO2 and P(OH)2 which is due to the presence of two P-OH longer bonds and P-O shorter bonds [17, 18]. PED computed values at 3710 and 3708 cm−1 is contributed to O-H asymmetric stretching vibrations of a phosphate anion. The stretching vibrations of the P-O bonds are theoretically computed at 1194, 1180, 1015, 985, 820, 812, 793, and 774 cm−1. P-O2 asymmetric stretching ranges from 1060 to 1175 cm−1 whereas symmetric stretching ranges from 1035 to 1065 cm−1. Asymmetric stretching vibrations of P(OH)2 lie in the region 950–980 cm−1 and symmetric stretching vibrations of P(OH)2 are in the region 900 to 920 cm−1. This type of P-O stretching bond is experimentally found at 1175 and 900 cm−1 [19, 20].


## 3.3. Natural Bonding Orbitals Analysis

NBOs analysis gives deep insight into the chemical bonding of all the complexes. It also makes available substantial information regarding the nature of bonding orbitals, their occupancies as well as the type and nature of the interaction (intermolecular or intramolecular, hyper-conjugative or charge transfer) existing between virtual and occupied Lewis orbitals. The analysis is conducted by considering all probable interactions between donor (occupied Lewis NBOs) and acceptors (vacant) non-Lewis NBOs, and approximating their energetic significance by second-order perturbation theory of the Fock matrix [21, 22]. For this analysis, all potential interactions between “full” (donor) Lewis-type NBOs and “empty” (acceptor) non-Lewis NBOs are examined, and their energy significance is estimated using second-order perturbation theory. These interactions are known as “delocalization” corrections to the zeroth-order natural Lewis structure because they cause a loss of occupancy from the localised NBOs of the idealised Lewis structure into the empty non-Lewis orbitals (and thus, to departures from the idealised Lewis structure description) [23]. In the present study, donor–acceptor interactions were applied for investigating interactions in the 3M2VPP molecular complex. Table 3 shows some of the significant donor–acceptor interactions and their stabilization energies E(2). The NBO charges on the particular atoms computed for 3M2VPP are shown in Table 3. According to the calculation, the methyl group attached carbon atom in the pyridine ring (7C) have smaller negative charges (−0.598e) than the carbon atom (10C) in the CH2 groups (−0.265e). The nitrogen atom (15N) of the pyridine ring which is involved in hydrogen bonds (H16) shows the highest positive charge 0.4765e confirms the occurrence of protonation. For singly protonated 2-vinyl pyridinium cation, the most charge difference i.e., −0.466 e is observed at 15N where the proton is attached. The methyl group hydrogen atoms (12H, 13H, and 14H) have higher similar positive charges (0.215e to 0.222e) than the other hydrogen atoms (18H and 19H) of the C-H groups. The calculated charges for carbon atoms C1, C3, C5, C7, and C8 in the pyridine ring are completely different. The adjacent carbon atoms 1C and 8C carry positive charges whereas 3C, 5C, 7C, and 8C have negative charges. The phosphor atom (24P) has a more positive charge of 2.471e and all the oxygen atoms have negative charges. Hydrogen atoms 25H and 26H have more positive charges. Thus, the positive and negative charges are balanced and establishes the stability of the molecule as shown in Figure 3. The donor–acceptor interactions of the inclusion complex of phosphoric acid into 3-methyl 2-vinyl pyridine are investigated using the NBO program. The obtained results are illustrated in Table 3. The interaction energies of these contacts are in the range of 4–363 kJmol−1. The highest intramolecular stabilization energy of 91.12 kJmol−1 is found in 3-methyl-2-vinylpyridine between antibonding π orbitals of C1-N15 to C3-C5. The next highest stabilization energy is due to the lone pair of carbon atom C7 with π∗(C3-C5)−71.58 kJmol−1 and C8 with π∗(C1-N15)−67.09 kJmol−1. The strongest intermolecular stabilization energy occurs in between the lone pair of electronegative nitrogen atom N15 in 3-methyl-2-vinyl pyridine to H16 in phosphoric acid establishing energy of 362.82 kJmol−1. The lone pair of oxygen atom O21 with antibonding H16 has 14.13 kJmol−1 confirming the protonation between the molecules. Intramolecular stabilization energy of phosophoric acid lies in the range of 10 to 22 kJmol−1 [24, 25]. The other type of intermolecular and intramolecular interactions and their energies are tabulated in Table 3.Table 3
Second-order perturbation theory analysis of the Fock matrix in NBO basis for 3M2VPP.
Donor NBO (i)Acceptor NBO (j)E(2) (kcal/mol)E(j)-E(i) a.u.F(i, j) a.uWithin unit 1BD∗(2)C1-N15BD∗(2) C3-C591.120.040.090LP (1)C7BD∗(2) C3-C571.580.140.110LP∗(1)C8BD∗(2) C1-N1567.090.100.090BD (2)C3-C5LP(1) C748.580.150.090BD (2)C1-N15LP∗(1) C843.840.210.108BD (2)C3-C5BD∗(2) C1-N1535.690.240.084BD (2)C9-C10LP∗(1) C833.670.140.081LP∗(1)C8BD∗(2) C9-C1026.130.170.086From unit 1 to unit 2LP (1)N15LP∗(1) H16362.820.480.385BD (1)C1-N15LP∗(1) H1614.090.980.121BD (1)C8-N15LP∗(1) H1612.220.980.113From unit 2 to unit 3LP∗(1) H16BD∗(1) O21-P244.560.260.054From unit 3 to unit 1LP (3) O20BD∗(1) C1-H24.260.670.050From unit 3 to unit 2LP (3)O21LP∗(1) H16114.130.480.228LP (1)O21LP∗(1) H1615.900.710.108Within unit 3LP (2)O20BD∗(1) O22-P2422.030.490.093LP (3)O20BD∗(1) O21-P2417.700.590.092LP (2)O21BD∗(1) O22-P2413.220.520.076LP (3)O20BD∗(1) O23-P2411.280.490.067LP (2)O20BD∗(1) O23-P2410.790.490.065LP (2)O21BD∗(1) O23-P2410.520.530.068LP (2)O22BD∗(1) O23-P2410.480.570.071LP (2)O23BD∗(1) O22-P2410.070.560.069Figure 3
NBO charges of 3M2VPP.


## 3.4. Frontier Molecular Orbitals (FMOs) Analysis

Frontier molecular orbitals (FMO) theory allows a chemist to make predictions about a reaction by knowing the placement of the HOMO and LUMO energy levels. Fukui developed the frontier molecular orbital theory to explain the chemical reactivity of the sample [26]. The Frontier molecular orbitals such as HOMO and LUMO affords information about the chemical stability and electrical and optical properties of the compounds; also it is used to explain various types of reactions in conjugated systems. The HOMO-LUMO orbitals are referred to as frontier molecular orbitals (FMOs) as they lie at the outermost boundaries for the electrons in a system. The pictorial representations of HOMO and LUMO orbitals have been calculated by using the B3LYP/6-311++G (d, p) basis set as depicted in Figure 4. HOMO is completely occupied in the 3-methyl 2-vinyl pyridinium ring and LUMO is partially occupied in the 3-methyl 2-vinyl pyridinium ring which seems that the majority of interaction takes place within the ring. The calculated energy values of HOMO and LUMO in 3-methyl 2-vinyl pyridinium phosphate are -9.987 eV and -6.443 eV and the frontier orbital energy gap value is 3.544 eV as listed in Table 4. HOMO and LUMO energy gap explains the eventual charge transfer interactions taking place within the molecule. The high stability and chemical inertness are due to the presence of high ionization energy. Global chemical descriptors like chemical potential, electrophilicity, hardness, softness, and electronegativity varies the chemical reactivity of the molecule [27–30]. All the calculated parameters indicate the high reactive nature of the grown sample. Also, high electrophilicity values indicate the good electrophile nature of the material [31, 32].Figure 4
HOMO-LUMO plot of 3M2VPP.Table 4
Chemical descriptors of 3M2VPP.
ParametersValue (eV)EHOMO−9.987ELUMO−6.443ΔEgap3.544Ionization potential (I)+9.987Electron affinity (A)+6.443Chemical potential (μ)−8.215Electronegativity (χ)8.215Global hardness (η)1.772Global softness (S)0.282Electrophilicity (ω)19.042


## 3.5. Molecular Electrostatic Potential Studies

Molecular Electrostatic Potential (MEP) is an essential tool for interpreting electrostatic (electron and nuclei) distribution potential and envisage the reactive site of wide ranges in both electrophilic and nucleophilic attacks in chemical reactions, and hydrogen-bonding interactions. This map is useful as an indicator of the sites or regions of a molecule to which an approaching electrophile and nucleophile are initially attracted. This is in turn related to the electronic density and is a very useful descriptor for determining sites for electrophilic attack and related to nucleophilic reactions as well as hydrogen-bonding interactions [33, 34]. The molecular electrostatic potential projection map for 3-methyl 2-vinyl pyridinium phosphate is calculated using the B3LYP/6-311++G (d, p) method. MEP surface map of 3-methyl 2-vinyl pyridinium phosphate is shown in Figure 5. The reactive sites are located by different colour codes and are highly beneficial to explore the molecular structure with its physiochemical property relationship [35, 36]. Molecular electrostatic potential map ranges from −4.324 × 10−2 to +4.324 × 10−2 esu. The total density spectrum ranges from 4.074 × 10−4 to +4.074 × 10−4 esu. Electrophilic and nucleophilic areas are represented by red and blue colour regions respectively as shown in Figure 6.Figure 5
MEP map of 3M2VPP.Figure 6
Total density spectrum of 3M2VPP.


## 3.6. Nonlinear Optical Properties

The first-order hyperpolarizability (β) is a measure of how easily a dipole is induced in a molecule in the presence of an electric field. The first-order hyperpolarizability calculations have been done using the DFT method based on the finite field approach. The first-order hyperpolarizability is a third-rank tensor that can be described by a 3 × 3 × 3 matrix. The 27 components of the 3D matrix can be reduced to 10 components due to the Kleinman symmetry [37].The total induced dipole moment by the applied field is calculated using the Taylor series expansion.(1)μ=μ0+αijEj+βijkEjEk+⋯,where α, linear polarizability; μ0, the permanent dipole moment; and βijk, first order hyperpolarizability tensor component.The expression for the static dipole moment is given as(2)μ=μx2+μy2+μz21/2.The following expression gives the isotropic (or average) linear polarizability:(3)αTotal=αxx+αyy+αzz3.The magnitude of the first order hyperpolarizability tensor is calculated using the relation,(4)βi=βiii+13∑i≠jβijj+βjij+βjji.The output of Gaussian 09W for calculating the magnitude ofβTotal is given as follows:(5)βTotal=βxxx+βxyy+βxzz2+βyyy+βyzz+βyxx2+βzzz+βzxx+βzyy2.Gaussian 09W program using B3YLP/6-311++G (d, p) methodology to compute first order hyperpolarizability calculations. The total molecular dipole moment (μ), linear polarizability (α), and first-order hyperpolarizability (β) were calculated in atomic units and are converted into electrostatic units. (α: 1 a.u = 0.1482 × 10−24 esu, β: 1 a.u = 8.6393 × 10−30esu). Table 5 lists the calculated parameters of an electric dipole moment µ(D), the average polarizability αtot (×10−24 esu), and first-order hyperpolarizability βtot (×10−31 esu). The calculated dipole moment is 8.9064 Debye and reveals the ionic nature of the compound. The maximum value of 1.1298 Debye occurs in the Y direction. The maximum hyperpolarizability value is 21.2852 × 10−31 esu and it is computed for βxzz direction which is due to the substantial delocalization of electron cloud in that region. The next highest hyperpolarizabiltiy is computed to be 16.8041 × 10−31 esu and 11.3499 × 10−31 esu for the direction βzxx & βyyy respectively. Urea–a well-known standard nonlinear optical material has total polarizability (α = 3.8312 × 10−24 esu) and first-order hyperpolarizability (β = 3.7289 × 10−31 esu). The total polarizability is computed to be 39.878 × 10−31 esu. It is found that 3M2VPP is 10.694 times that of urea and may be expected as a potential candidate for the development of NLO materials [38–42].Table 5
Calculated electric dipole moment, polarizability, and first-order hyperpolarizability of 3M2VPP.
ParametersB3LYP/6-311++G (d, p)ParametersB3LYP/6-311++G (d, p)μx−8.8313βxxx−27.9812μy1.1298βxxy13.3782μz0.2376βxyy−21.3378μ (D)8.9064βyyy11.3499αxx−77.4601βzxx16.8041αxy7.9872βxyz−17.5345αyy−83.7978βzyy−4.4329αxz2.3012βxzz21.2853αyz−4.0765βyzz−0.2132αzz−93.5580βzzz1.8827αtot(esu)84.938 × 10−24βtot(esu)39.878 × 10−31


## 3.7. Hirshfeld Surface Analysis

CrystalExplorer 3.1 [43] program is used to understand the interactions and the connectivity among the molecules efficiently. The crystallographic information file (.cif) was imported to the crystal explorer to generate the Hirshfeld surfaces. The Hirshfeld surface (HS) is the region around the molecule in the crystal space which can be considered as the boundary separating two regions—the interior (the reference molecule) and the exterior (neighboring molecules) [44]. The 2D fingerprint plot provides a precise two-dimensional graphical representation of the intermolecular interactions in the crystal as shown in Figure 7. The contributions from different contacts to the total Hirshfeld surface area are shown in Figure8. The major contribution (42.0%) is from H⋯H and (38.6%) from O⋯H contacts. The wings are due to the C–H⋯π interactions. The π···π type of interaction is clearly seen on the shape decorated HSs where the characteristic blue and red triangles are present. Hydrogen bonding contacts are represented by red spots which are shown in Figure 8. The dnorm parameter exhibits a surface with a red-white-blue colour scheme. Bright red spots show the intermolecular contacts less than their vdW radii, while the blue spots show intermolecular contacts longer than their vdW radii. White spots are the sum of their vdW radii. The red regions in Figure 9 are apparent around the phosphor atom participating in the P-O···H contacts.Figure 7
Fingerprint of LHLTHH (100%).Figure 8
Hirshfeld surface analysisdi, de, dnorm, shape index, and curvedness of 3M2VPP.Figure 9
Relative contributions to the percentage of Hirshfeld surface area for the various intermolecular contacts in 3M2VPP.


## 4. Conclusion

The compound - 3-methyl 2-vinyl pyridinium phosphate (3M2VPP) was optimized with DFT-B3LYP using a 6-311++G (d, p) basis set. The complete molecular structural parameters of the optimized geometry of the compound have been obtained from DFT calculations. The calculated bond length, bond angle, and dihedral angles are compared with the XRD data of 3M2VPP. All the experimental and theoretical data are in a good agreement with each other. The vibrational frequencies of the fundamental modes of the compound have been precisely assigned, and analysed and the theoretical results are provided with a clear assignment description. The electronic properties such as highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO)) energies are determined by the B3LYP/6-311++G (d, p) basis set. The calculated HOMO-LUMO energy gap of 3.544eV reveals that the molecule possesses good kinetic stability and low chemical reactivity. Further global chemical descriptors explain the possible reactive sites and provide a firm explanation for the reactivity of the 3M2VPP molecule. The intramolecular charge transfer and hyper-conjugative interaction of the compound are investigated from natural bonding orbitals (NBOs) analysis. The highest intramolecular stabilization energy of 91.12 kJmol−1 is found in 3-methyl-2-vinylpyridine between antibonding π orbitals of the atoms C1-N15 to C3-C5. The strongest intermolecular stabilization energy between lone pair of electronegative nitrogen atom N15 in 3-methyl-2-vinyl pyridine to H16 phosphoric acid establishes with an energy of 362.82 kJmol−1 and lone pair of oxygen atom O21 with antibonding H16 has the energy 114.13 kJmol−1 confirms the protonation occurrence between the molecules. Intramolecular stabilization energy of phosophoric acid lies in the range of 10 to 22 kJmol−1. Molecular electrostatic potential envisages the presence of reactive sites of both electrophilic and nucleophilic reactions. The calculated first-order hyperpolarizability of 3M2VPP is 10.694 times greater than that of urea and may be expected as a potential candidate for the development of NLO materials. Hirshfeld surface analysis was performed to determine the intermolecular interactions and the crystal packing. Hirshfeld surface analysis shows H⋯H (42.0%) followed by O⋯H (38.6%) as a major contribution towards crystal surface. All the above results confirm the potential candidature of the chosen material for optoelectronic and photonic applications.



---

*Source: 6488234-2022-08-18.xml*