# Efficient ZrO(NO3)2.2H2O Catalyzed Synthesis of 1H-Indazolo[1,2-b] phthalazine-1,6,11(13H)-triones and Electronic Properties Analyses, Vibrational Frequencies, NMR Chemical Shift Analysis, MEP: A DFT Study

Authors: Forozan Piryaei; Nahid Shajari; Hooriye Yahyaei
Journal: Heteroatom Chemistry
 (2020)

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## Abstract

The synthesis of 1H-indazolo[1,2-b]phthalazine-1,6,11(13H)-trione derivatives, using one-pot three-component condensation reaction of 3-nitrophthalic anhydride, hydrazine monohydrate, dimedone, and aromatic aldehydes in the presence of ZrO(NO3)2.2H2O as the novel catalyst and in reflux conditions in EtOH was reported. Quantum theoretical calculations for three structures of compounds (5a, 5b, and 5c) were performed using the Hartree–Fock (HF) and density functional theory (DFT). From the optimized structure, geometric parameters were obtained and experimental measurements were compared with the calculated data. The structures of the products were confirmed by IR, 1H NMR, 13C NMR, mass spectra, and elemental analyses. The IR spectra data and 1H NMR and 13C NMR chemical shift computations of the 1H-indazolo[1,2-b]phthalazine-1,6,11(13H)-trione derivatives in the ground state were calculated. Frontier molecular orbitals (FMOs), total density of states (DOS), thermodynamic parameters, and molecular electrostatic potential (MEP) of the title compounds were investigated by theoretical calculations. Molecular properties such as the ionization potential (I), electron affinity (A), chemical hardness (η), electronic chemical potential (µ), and electrophilicity (ω) were investigated for the structures. Thus, there was an excellent agreement between experimental and theoretical results.


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## Body

## 1. Introduction

The nitrogen-containing heterocyclic compounds are extensive in nature and play a unique role in biological systems [1–3]. Heterocycles containing the phthalazine ring are important compounds with broad biological activities, such as anticonvulsant [4], vasorelaxant [5], cardiotonic [6], cytotoxic [7], antimicrobial [8], anticonvulsant [9], antifungal [10], anticancer [11], and anti-inflammatory [12]. Several methods have been reported in the literature for the synthesis of 1H-indazolo[1,2-b]phthalazine-1,6,11(13H)-trione derivatives which have been reported using Mg(HSO4)2 [13], [Bmim]Br [14], p-TSA [15], silica sulfuric acid [16], PPA–SiO2 [17], H2SO4/H2O–EtOH and H2SO4/[bmim]BF4 [18], Ce(SO4)2.4H2O [19], and starch sulfate [20], as catalysts. Given the interest in the synthesis of heterocycles [21–24], we described herein a simple synthesis of 1H-indazolo[1, 2-b]phthalazinetriones by three-component condensation reaction of phthalhydrazide, dimedone, and aromatic aldehydes in the presence of a catalytic amount of ZrO(NO3)2.2H2O at reflux conditions in EtOH. In recent years, computational chemistry has become an important tool for chemists and a well-accepted partner for experimental chemistry [25]. Computational chemistry is the application of computer simulation to predict or interpret chemical reactivity. Computational organic chemistry is an important area within which occur the determination of the mechanisms of chemical reactions [26, 27] especially catalysis [28, 29]structural determination of organic compounds [30, 31] prediction of spectroscopic data such as 1H NMR and 13C NMR chemical shifts [32, 33] properties calculation of organic molecules [34, 35] and the interaction of a substrate with an enzyme [36]. This study has revealed some potential leads for possible pharmaceutical applications, and further research may help in the development of new antioxidative agents for important metabolic functions. Also, three new crystal structures of the compounds 5a, 5b, and 5c are reported. In the present work, we investigated the energetic and structural properties of three compounds of 1H-indazolo[1,2-b]phthalazine-1,6,11(13H)-trione derivatives (5a, 5b, and 5c), using the DFT calculations. The optimized geometries, quantum molecular descriptors, IR spectra data, 1H NMR and 13C NMR chemical shift computations, molecular electrostatic potential (MEP), thermodynamic and electronic properties, and NBO analysis were calculated through density functional theory (DFT) and Hartree–Fock (HF) methods.


## 2. Materials and Methods

The starting materials and solvents were obtained from Merck (Germany) and Fluka (Switzerland) and were used without further purification. The melting points were measured with an Electrothermal 9100 apparatus and were uncorrected. The IR spectra were recorded on a Jasco FT-IR 6300 spectrometer. The1H NMR and 13C NMR spectra were measured (CDCl3 solution) with a Bruker DRX-250 Avance spectrometer at 250.0 and 62.9 MHz, respectively. Mass spectra were recorded with an Agilent Technologies 5975°C mass spectrometer. The elemental analyses were carried out using a Heraeus CHN-O-rapid analyzer.


### 2.1. General Procedure for the Synthesis of1H-indazolo[1,2-b]phthalazine-1,6,11(13H)-triones

3-Nitrophthalic anhydride (1, 1 mmol) and hydrazine monohydrate (2, 1 mmol)) were refluxed in ethanol for 15 minutes to form phthalhydrazide as an intermediate. Then, we added dimedone (3, 1 mmol) and aromatic aldehydes (4, 1 mmol) to the mixture of this reaction one by one in the presence of ZrO(NO3)2.2H2O (2 mol%) and the mixture was refluxed again for 2-3 hours. The completion of the reaction was checked by TLC. The solvent was removed under reduced pressure, and the viscous residue was purified by a preparative layer chromatography (silica gel; petroleum ether–ethyl acetate (8 : 2)). The solvent was removed under a reduced pressure and the products 5a–c were obtained.


### 2.2. Computational Studies

In the present study, we carried out quantum theoretical calculations for the compounds5a, 5b, and 5c using the HF/6-31+G∗, HF/6–311+G∗∗, B3LYP/6-31+G∗, and B3LYP/6–311+G∗∗ levels [37] by the Gaussian 03W program package [38] and calculated their properties. During the beginning stage, we obtained an optimized structure using Gaussian 03W program (see Figure 1). Then, we calculated the 1H NMR chemical shifts using the HF/6-31+G∗, HF/6–311+G∗∗, B3LYP/6-31+G∗, and B3LYP/6–311+G∗∗ levels for the title compounds (5a, 5b, and 5c) and 13C NMR [39]. The electronic properties included energy of the highest occupied molecular orbital (EHOMO), energy of the lowest unoccupied molecular orbital (ELUMO), HOMO-LUMO energy gap (∆E), ELUMO, natural charges, and molecular properties [40]. The optimized molecular structure, HOMO and LUMO surfaces were visualized using GaussView 03 program [41].Figure 1
(a) Calculated frontier molecular orbitals of compounds5a, 5b, and 5c (ΔE: energy gap between LUMO and HOMO). (b) Calculated DOS plots of the title compounds (using B3LYP/6-311+G(d)).


## 2.1. General Procedure for the Synthesis of1H-indazolo[1,2-b]phthalazine-1,6,11(13H)-triones

3-Nitrophthalic anhydride (1, 1 mmol) and hydrazine monohydrate (2, 1 mmol)) were refluxed in ethanol for 15 minutes to form phthalhydrazide as an intermediate. Then, we added dimedone (3, 1 mmol) and aromatic aldehydes (4, 1 mmol) to the mixture of this reaction one by one in the presence of ZrO(NO3)2.2H2O (2 mol%) and the mixture was refluxed again for 2-3 hours. The completion of the reaction was checked by TLC. The solvent was removed under reduced pressure, and the viscous residue was purified by a preparative layer chromatography (silica gel; petroleum ether–ethyl acetate (8 : 2)). The solvent was removed under a reduced pressure and the products 5a–c were obtained.


## 2.2. Computational Studies

In the present study, we carried out quantum theoretical calculations for the compounds5a, 5b, and 5c using the HF/6-31+G∗, HF/6–311+G∗∗, B3LYP/6-31+G∗, and B3LYP/6–311+G∗∗ levels [37] by the Gaussian 03W program package [38] and calculated their properties. During the beginning stage, we obtained an optimized structure using Gaussian 03W program (see Figure 1). Then, we calculated the 1H NMR chemical shifts using the HF/6-31+G∗, HF/6–311+G∗∗, B3LYP/6-31+G∗, and B3LYP/6–311+G∗∗ levels for the title compounds (5a, 5b, and 5c) and 13C NMR [39]. The electronic properties included energy of the highest occupied molecular orbital (EHOMO), energy of the lowest unoccupied molecular orbital (ELUMO), HOMO-LUMO energy gap (∆E), ELUMO, natural charges, and molecular properties [40]. The optimized molecular structure, HOMO and LUMO surfaces were visualized using GaussView 03 program [41].Figure 1
(a) Calculated frontier molecular orbitals of compounds5a, 5b, and 5c (ΔE: energy gap between LUMO and HOMO). (b) Calculated DOS plots of the title compounds (using B3LYP/6-311+G(d)).


## 3. Results and Discussion

The three-component reaction between 3-nitro phthalhydrazide(6), dimedone (3), and aromatic aldehydes (4) proceeded very smoothly and cleanly in the presence of a catalytic amount of ZrO(NO3)2.2H2O at reflux conditions in ethanol and afforded the corresponding 1H-indazolo[1,2-b]phthalazine-1,6,11(13H)-trione derivatives (5a-c) in high yields (Scheme 1 and Table 1), and no undesirable side reactions were observed. A mechanistic rationalization for this reaction is provided in Scheme 2. The structures of the products were deduced from their IR, 1H NMR, 13C NMR, mass spectra and elemental analyses. For example, the 1H NMR spectrum of 5a exhibited distinct signals arising from two CH3 groups of dimedone (0.96 and 1.00 ppm, 2 s), two CH2 groups of dimedone ring (2.07–2.33 ppm, m) and (3.65 ppm, s), one OCH3 group of 4-methoxyphenyl ring (3.80 ppm, s), aliphatic CH (5.25 ppm, s), and seven aromatic CH (7.02 ppm, d,3JHH = 8.25 Hz), (7.78 ppm, d,3JHH = 8.25 Hz), and (8.50–8.82, m). The 13C NMR spectrum of 5a shows 22 distinct resonances arising from two CH3 groups (26.91 and 28.16 ppm), C (32.24 ppm), two CH2 groups (42.49 and 50.74 ppm), OCH3 (55.81 ppm), aliphatic CH (64.46 ppm), aromatic and olefinic carbons (113.66, 114.83, 127.03, 127.99, 128.71, 129.08, 129.41, 129.96, 130.40, 131.97, 135.29, and 136.87 ppm), and C=O carbons (160.84, 162.12, and 196.47 ppm). The mass spectrum of 5a displays a molecular ion peak at m/z 447.Scheme 1
Three-component reaction of 3-nitrophthalic anhydride, hydrazine monohydrate, dimedone, and aromatic aldehydes (see Table1).Table 1
Synthesis of 1H-indazolo[1,2-b]phthalazine-1,6,11(13H)-trione derivatives (5a-c).
5
Ar
% Yield
a
4-Methoxyphenyl
75
b
Phenyl group
80
c
4-Chlorophenyl group
78Scheme 2
A proposed mechanism for the formulation of 1H-indazolo[1,2-b]phthalazine-1,6,11(13H)-trione derivatives (5a-c).


### 3.1. Characterization Data for the Synthesis of 1H-indazolo[1,2-b]phthalazine-1,6,11(13H)-trione Derivatives (5a-c)

#### 3.1.1. 3,3-Dimethyl-13-(4-methoxyphenyl)-10-nitro-2,3,4,13-tetrahydro-1H-indazolo[1,2-b] phthalazine-1,6,11(13H)-trione (5a)

Yellow solid; m.p.>250°C; Yield: 75%; Anal. Calcd for C24H21N3O6 (447.4): C, 64.42; H, 4.73; N, 9.39 %. Found: C, 64.38; H, 4.75; N, 9.33; IR (KBr) (υmax, cm−1): 3439, 2959, 1728 (C=O), 1666 (C=O), 1602 (C=O), 1535 (NO2-Asymmetric Str.), 1464, 1358 (NO2-Symmetric Str.); 1H NMR (DMSO. d6, 250.0 MHz): δH 0.96 (3H, s, CH3), 1.00 (3H, s, CH3), 2.07–2.33 (2H, m, CH2), 3.65 (2H, s, CH2), 3.80 (3H, s, OCH3), 5.25 (1H, s, CH), 7.02 (2H, d, 3JHH = 8.25 HZ, arom CH), 7.78 (2H, d, 3JHH = 8.25 HZ, arom CH), 8.50–8.82 (3H, m, arom CH); 13C NMR (DMSO. d6, 62.9 MHz): δC 26.91 and 28.16 (2CH3), 32.24 (C), 42.49 (CH2), 50.74 (CH2), 55.81 (OCH3), 64.46 (CH), 113.66, 114.83, 127.03, 127.99, 128.71, 129.08, 129.41, 129.96, 130.40, 131.97, 135.29, and 136.87 (aromatic and olefinic carbons), 160.84, 162.12, and 196.47 (3C=O); MS (EI): m/z 447 (M+, 0.02), 286 (5), 269 (100), 253 (9), 241 (27), 161 (76), 134 (27), 91 (24), 77 (33), and 63 (13).


#### 3.1.2. 3,3-Dimethyl-10-nitro-13-phenyl-2,3,4,13-tetrahydro-1H-indazolo[1,2-b]phthalazine-1,6,11(13H)-trione (5b)

Yellow solid; m.p.>250°C; Yield: 80%; Anal. Calcd for C23H19N3O5 (417.4): C, 66.18; H, 4.59; N, 10.07 %. Found: C, 66.25; H, 4.54; N, 10.00; IR (KBr) (υmax, cm−1): 2931, 2358, 1724 (C=O), 1617 (C=O), 1588 (C=O), 1539 (NO2-Asymmetric Str.), 1460, 1410 (NO2 - Symmetric Str.); 1H NMR (DMSO. d6, 250.0 MHz): δH 0.96 (3H, s, CH3), 1.24 (3H, s, CH3), 2.07–2.23 (2H, m, CH2), 3.87–3.92 (2H, m, CH2), 5.26 (1H, s, CH), 7.36–8.69 (9H, m, arom CH); 13C NMR (DMSO. d6, 62.9 MHz): δC 28.15 and 28.50 (2CH3), 32.47 (C), 42.49 (CH2), 50.74 (CH2), 64.44 (CH), 126.81, 128.29, 128.44, 128.56, 128.79, 129.14, 129.32, 130.78, 131.76, 131.95, 134.25, and 135.31 (aromatic and olefinic carbons), 161.82, 165.50, and 198.19 (3C=O).


#### 3.1.3. 13-(4-Chlorophenyl)-3,3-dimethyl-10-nitro-2,3,4,13-tetrahydro-1H-indazolo[1,2-b]phthalazine-1,6,11(13H)-trione (5c)

Yellow Solid; m.p. >250°C; Yield: 78%; Anal. Calcd for C23H18ClN3O5 (451.9): C, 61.14; H, 4.02; N, 9.30 %. Found: C, 61.10; H, 4.04; N, 9.24; IR (KBr) (υmax, cm−1): 2928, 2358, 1728 (C=O), 1611 (C=O), 1591 (C=O), 1474 (NO2- Asymmetric Str.), 1393 (NO2-Symmetric Str.), 1085 (C–Cl); 1H NMR (DMSO. d6, 250.0 MHz): δH 0.94 (3H, s, CH3), 1.22 (3H, s, CH3), 2.05–2.20 (2H, m, CH2), 3.87 (2H, s, CH2), 5.23 (1H, s, CH), 7.15–8.66 (8H, m, arom CH); 13C NMR (DMSO. d6, 62.9 MHz): δC 26.82 and 28.12 (2CH3), 32.45(C), 42.43 (CH2), 50.68 (CH2), 64.45 (CH), 114.38, 123.32, 128.22, 128.67, 128.90, 129.07, 129.26, 129.46, 129.89, 130.34, 133.01, and 134.70 (aromatic and olefinic carbons), 161.00, 163.41, and 196.43 (3C=O).


### 3.2. Computational Section

#### 3.2.1. IR Spectroscopy

Harmonic vibrational frequencies of the title compounds were calculated using the B3LYP/3-21G, HF/3-21G, B3LYP/6-311+G(d), and HF/6-311+G(d) levels. The vibrational frequencies assignments were made using the GaussView program. Some of the characteristic frequencies are provided in Tables2–4. The harmonic frequencies calculated by DFT are usually higher than the corresponding experimental values due to the approximate treatment of the electron correlation, anharmonicity effects, and basis set deficiencies [39].Table 2
The selected experimental and theoretical frequencies of the title compounds using the B3LYP and HF methods for compound(5a).
Experimental wavenumbers by FT-IR (cm−1)
Calculated vibrational wavenumbers by HF and DFT methods (cm−1)
B3LYP
HF
3-21G
6-311+G∗∗
3-21G
6-311+G∗∗
Assignment
C=O
3439
3441
3440
3438
3450
2959
2967
2955
2964
2960
1728
1721
1729
1720
1733
C=O
1666
1691
1673
1689
1682
C=O
1602
1602
1608
1615
1600
C=C
1535
1599
1530
1542
1535
Ar C=C
1464
1466
1466
1463
1469
CH3
1358
1351
1359
1368
1366Table 3
The selected experimental and theoretical frequencies of the title compounds using the B3LYP and HF methods for compound(5b).
Experimental wavenumbers by FT-IR (cm−1)
Calculated vibrational wavenumbers by HF and DFT methods (cm−1)
B3LYP
HF
3-21G
6-311+G∗∗
3-21G
6-311+G∗∗
Assignment
C=O
3413
3413
3405
3461
3423
2955
2972
2915
2952
2962
1661
1660
1663
1668
1671
C=O
1626
1619
1628
1630
1629
C=H
1583
1573
1588
1589
1573
Ar C=C
1489
1489
1490
1498
1499
CH3
1362
1397
1362
1373
1307
C–Cl, bending
1090
1080
1090
1099
1088Table 4
The selected experimental and theoretical frequencies of the title compounds using the B3LYP and HF methods for compound(5c).
Experimental wavenumbers by FT-IR (cm−1)
Calculated vibrational wavenumbers by HF and DFT methods (cm−1)
B3LYP
HF
3-21G
6-311+G∗∗
3-21G
6-311+G∗∗
Assignment
C=O
3436
3430
3430
3449
3435
2951
2971
2962
2973
2943
1661
1669
1661
1750
1665
C=O
1625
1638
1640
1615
1635
C=C
1576
1583
1579
1580
1579
Ar C=C
1492
1483
1492
1489
1497
CH3
1361
1361
1361
1373
1360For the title compound(5a), the strong band at 3376 cm−1 in the FT-IR spectrum is assigned as vC=O mode. The calculated values for this mode are 3375, 3204, 3227, and 3360 cm−1 for HF/6-31+G∗, HF/6–311+G∗∗, B3LYP/6-31+G∗, and B3LYP/6–311+G∗∗ levels, respectively. For the title compound (5a), the strong band at 3439, 2959, and 1728 cm−1 in the FT-IR spectrum is assigned as vC=O mode. The calculated values for this mode are the same as those calculated for HF/3-21G, HF/6-311+G∗∗, B3LYP/3-21G, and B3LYP/6-311+G∗∗ levels, respectively. The DFT computation predicts this vibrational mode in ArC=C at 1464 cm−1 for A, 1489 cm−1 for the compound 5b, and 1493 cm−1 for the compound 5c. This observed frequency coincides well with the expected value [42]. There was an excellent agreement between experimental and theoretical results for all used methods. In order to compare this agreement, the correlation graphic based on the theoretical and experimental data was investigated. A small difference between the experimental and calculated vibrational modes was observed. This difference might have been due to intermolecular hydrogen bonding formation. Also, the experimental results belong to the solid phase while theoretical calculations belong to the isolated gaseous phase.


#### 3.2.2. NMR Parameters

The calculation of1H NMR and 13C NMR chemical shifts of compounds 5a, 5b, and 5c is done at B3LYP/3-21G, HF/3-21G, B3LYP/6-311+G(d), and HF/6-311+G(d) levels. The experimental and calculated 1H NMR and 13C NMR chemical shifts of 1H-indazolo[1,2-b] phthalazine-1,6,11(13H)-trione derivatives (5a, 5b and 5c) are presented in Tables 5–10. Based on our calculations and experimental spectra, we made a reliable one-to-one correspondence between our fundamentals, and all of the chemical shifts were calculated by the HF and B3LYP methods. For the title compound (5a), the aromatic CH protons appeared at δH 7.02–8.82 ppm, and the calculated amounts at HF/6-311+G∗∗ and B3LYP/6-311+G∗∗ basis set levels were at 7.30–8.19 and 7.00–8.89 ppm, respectively. Protons of two methyl groups appeared at δH 0.96 and 1.00 ppm, the calculated amounts at HF/6-311+G∗∗ and B3LYP/6-311+G∗∗ basis set levels were at 0.67 and 1.28 ppm and 0.86 and 1.19 ppm, respectively. Also, chemical shifts of three carbonyl groups appeared at δc 160.84, 162.12, and 196.47 ppm, the calculated amounts at HF/6-311+G∗∗ and B3LYP/6-311+G∗∗ basis set levels were at 149.88, 153.99, and 190.97 ppm and 159.51, 161.27, and 197.32 ppm, respectively. The same was true for other compounds.Table 5
Experimentally measured and calculated1H chemical shifts δ (ppm vs TMS) of the compound (5a).
1H NMR
EXP
Calculated
B3LYP/3-21G
B3LYP/6-311+G∗∗
HF/3-21G
HF/6-311+G∗∗
3H, s, CH
3
0.96
0.33
0.86
0.66
0.67
3H, s, CH
3
1.00
1.41
1.19
1.15
1.28
2H, m, CH
2
2.07–2.33
2.38–2.52
2.03–2.33
1.95–2.60
1.95–2.60
2H, s, CH
2
3.65
3.32
3.60
3.13
3.13
3H, s, OCH
3
3.80
3.78
3.88
3.66
3.66
1H, s, CH
5.25
5.25
5.50
5.81
5.81
2H, d, arom C–H
7.02
7.02
7.00
7.30
7.30
2H, d, arom C–H
7.78
7.11
7.70
7.44
7.44
4H, m, arom C–H
8.50–8.82
8.22–8.75
8.51–8.89
8.08–8.17
8.08–8.19Table 6
Experimentally measured and calculated13C chemical shifts δ (ppm vs TMS) of the compound (5a).
13C NMR
EXP
Calculated
B3LYP/3-21G
B3LYP/6-311+G∗∗
HF/3-21G
HF/6-311+G∗∗
2CH
3
26.91–28.16
26.26–27.78
26.90–27.99
18.82–30.50
26.80–27.01
C
32.24
31.10
31.99
32.62
30.37
CH
2
42.49
42.83
42.73
45.54
44.99
CH
2
50.74
49.01
49.41
46.01
46.89
CH
64.46
63.98
62.99
58.79
60.74
OCH
3
55.81
50.11
55.88
48.72
50.11
C-H aromatic and olefinic carbons
113.66
93.78
113.52
101.98
107.09
114.83
94.99
113.99
108.88
111.90
127.99
95.08
126.31
110.44
123.53
128.71
95.39
130.07
111.47
123.43
128.71
96.14
131.05
112.90
122.90
129.08
96.87
130.66
113.02
125.51
129.41
97.60
133.98
114.13
124.39
129.96
97.65
136.75
114.48
124.19
130.40
119.1
138.41
114.56
124.97
131.97
122.79
127.99
126.65
135.29
127.76
137.19
137.19
136.87
129.30
138.90
144.90
C=O(1)
160.84
—
159.51
—
149.88
C=O(2)
162.12
—
161.27
—
153.99
C=O(3)
196.47
—
197.32
—
190.97Table 7
Experimentally measured and calculated1H chemical shifts δ (ppm vs TMS) of the compound (5b).
1H NMR
EXP
Calculated
B3LYP/3-21G
B3LYP/6-311+G∗∗
HF/3-21G
HF/6-311+G∗∗
3H, s, CH
3
0.94
0.43
0.98
0.48
0.97
3H, s, CH
3
1.22
1.42
1.27
1.30
1.30
2H, m, CH
2
2.05–2.20
2.11–2.32
2.08–2.28
2.17–2.96
2.09–2.48
2H, s, CH
2
3.87
3.94
3.90
4.00
3.98
1H, s, C–H
5.23
5.63
5.32
5.85
5.42
8H, m, arom C–H
7.15–8.66
7.10–7.97
7.17–8.62
7.19–8.91
7.19–8.76Table 8
Experimentally measured and calculated13C chemical shifts δ (ppm vs TMS) of the compound (5b).
13C NMR
EXP
Calculated
B3LYP/3-21G
B3LYP/6-311+G∗∗
HF/3-21G
HF/6-311+G∗∗
2CH
3
26.82–28.12
26.43–29.11
26.83–29.11
25.31–31.74
28.88–30.11
C
32.45
37.41
32.51
36.42
36.77
CH
2
42.43
43.33
42.51
41.23
42.21
CH
2
50.68
58.13
51.67
59.11
57.32
CH
64.45
70.41
63.78
72.31
71.20
Aromatic and olefinic carbons
114.38
86.90
115.77
89.99
85.90
123.32
93.88
123.46
97.67
91.63
128.22
94.84
129.22
97.91
96.41
128.67
97.22
129.63
83.23
126.99
128.90
97.71
129.77
84.89
128.71
129.07
97.97
130.11
85.99
128.86
129.26
100.82
130.28
112.92
128.32
129.46
101.89
130.49
113.55
129.27
129.89
119.29
130.80
114.41
129.64
130.34
127.48
131.45
129.99
129.83
133.01
129.17
134.89
130.89
130.22
134.70
148.29
135.03
137.98
134.60
C=O(1)
161.00
—
160.27
—
159.21
C=O(2)
163.41
—
162.11
—
160.41Table 9
Experimentally measured and calculated1H chemical shifts δ (ppm vs TMS) of the compound (5c).
1H NMR
EXP
Calculated
B3LYP/3-21G
B3LYP/6-311+G∗∗
HF/3-21G
HF/6-311+G∗∗
3H, s, CH
3
0.96
0.53
0.97
0.69
0.78
3H, s, CH
3
1.24
1.40
1.29
1.84
1.48
2H, m, CH
2
2.07–2.23
1.83–2.32
2.11–2.29
1.95–2.10
1.96–2.11
2H, m, CH
2
3.87–3.92
2.86
3.80–3.94
3.10–3.51
3.18–3.68
1H, s, C-H
5.26
5.59
5.23
5.88
5.40
9H, m, arom C-H
7.36–8.69
7.06–7.19
7.33–8.68
7.18–8.16
7.11–8.39Table 10
Experimentally measured and calculated13C chemical shifts δ (ppm vs TMS) of the compound (5c).
13C NMR
EXP
Calculated
B3LYP/3-21G
B3LYP/6-311+G∗∗
HF/3-21G
HF/6-311+G∗∗
CH
3
28.15
26.66
28.19
18.20
28.21
CH
3
28.50
28.19
28.93
18.70
28.87
C
32.47
30.11
33.11
30.65
32.76
CH
2
42.49
43.86
47.22
45.64
48.32
CH
2
50.74
50.11
50.66
48.11
50.98
CH
64.44
73.11
64.32
48.91
67.11
Aromatic and olefinic carbons
126.81
87.066
127.93
107.92
128.01
128.29
92.77
129.48
108.21
128.32
128.44
92.93
129.32
108.43
128.66
128.67
93.60
129.51
108.74
128.51
128.86
93.23
129.69
108.56
128.90
129.14
96.53
130.11
109.85
133.66
129.32
97.06
130.30
110.05
133.68
130.78
97.73
130.79
110.48
133.99
131.76
102.53
133.35
112.03
136.98
131.95
119.2
133.78
113.08
136.31
134.25
127.6
133.86
114.19
136.32
135.31
129.46
139.21
118.79
137.38
C=O(1)
161.82
—
163.23
151.46
160.20
C=O(2)
165.50
—
169.93
153.24
161.39
C=O(3)
198.19
—
197.11
169.84
193.22There was an excellent agreement between experimental and theoretical results for all methods employed. In order to compare this agreement, the correlation graphic based on the theoretical and experimental data was investigated. The correlation value (R2) for compounds at HF/3-21G, B3LYP/3-21G, HF/6-311+G∗∗, and B3LYP/6-311+G∗∗ is presented in Table 11. There was an excellent agreement between experimental and theoretical results [39]. A small difference between the experimental and calculated vibrational modes was observed. This difference might have been due to the intermolecular hydrogen bonding formation. Furthermore, the experimental results belong to the solid phase while and theoretical calculations belong to the isolated gaseous phase.Table 11
Correlation of calculated and experimental1H NMR,13C NMR, and IR of the compounds.
Compounds
B3LYP/3-21G
B3LYP/6-311+G∗∗
HF/3-21G
HF/6-311+G∗∗
5a
HNMR
0.9975
0.9999
0.9991
0.9974
5b
0.9986
0.9999
0.9985
0.9997
5c
0.9996
0.9995
0.9990
0.9998
5a
CNMR
0.9977
0.9995
0.9992
0.9975
5b
0.9983
0.9999
0.9990
0.9998
5c
0.9986
0.9998
0.9998
0.9999
5a
IR
0.9953
0.9995
0.9995
0.9978
5b
0.9986
0.9999
0.9988
0.9990
5c
0.9970
0.9997
0.9983
0.9991


#### 3.2.3. Electronic Properties

Quantum chemical methods are important for obtaining information about molecular structure and electrochemical behavior. A frontier molecular orbital (FMO) analysis was performed for the compounds using the B3LYP/6-311+G(d) level [38]. FMO results such as EHOMO, ELUMO, and the HOMO-LUMO energy gap (∆E) of the title compounds are summarized in Table 7. The energy of the LUMO, HOMO, and their energy gaps reflected the chemical reactivity of the molecule [43]. In addition, the HOMO could act as an electron donor and the LUMO as an electron acceptor. A higher HOMO energy (EHOMO) for the molecule indicated a higher electron-donating ability to an appropriate acceptor molecule with a low-energy empty molecular orbital [44]. As shown in Figure 1 the HOMO energy of the compound 5c had the highest value (−0.29 eV). A large energy gap implied high stability for the molecule. The calculated values of the HOMO-LUMO energy gap (∆E) for the structures 5a, 5b, and 5c were 0.07, 0.08, and 0.06 eV, respectively. DOS plots [45] also demonstrated the calculated energy gaps (∆E) for the compounds 5a, 5b, and 5c (see Figure 2). It is obvious that the energy gap of the compound 5b was the highest (0.08 eV); therefore, it was less reactive than the other structures, whereas the energy gap of the compound 5c was the lowest (0.06 eV), which indicates that it was the most reactive. As presented in Figure 2, charge transfer could take place within the three molecules.Figure 2
Molecular electrostatic potential (MEP) maps of the title compounds calculated using the B3LYP/6-311+G(d) level.
(a)
(b)
(c)The electronic properties such as ionization potential, electron affinity, global hardness, electronic chemical potential, and electrophilicity are calculated in Table12. The first ionization potential (I) and electron affinity (A) could be expressed through HOMO and LUMO orbital energies by connecting it with Hartree–Fock SCF theory and invoking Koopmans' theorem [46] as I = −EHOMO and A = −ELUMO. The chemical hardness (η = I−A/2) is an important property that measures the molecular stability and reactivity [47]. A hard molecule has a large energy gap (∆E) and a soft molecule has a small energy gap (∆E) [48]. The chemical hardness (η) values of the compounds 5a, 5b, and 5c were 0.170, 0.176, and 0.175 eV, respectively. Compound 5b had the highest chemical hardness (η = 0.176 eV); therefore, it was a hard molecule with less reactivity and a high energy gap (∆E = 0.08 eV). The electronic chemical potential (µ = −(I + A)/2) is a form of the potential energy that can be absorbed or released during a chemical reaction and that may also change during a phase transition [49]. The electronic chemical potential of 5c had the most negative value (−0.26 eV). The electrophilicity (ω) measures the stabilization in energy when the system acquires an additional electronic charge from the environment. The electrophilicity index (ω = µ2/2η) contains information about both electron transfer (chemical potential) and stability (hardness) and is a better descriptor of global chemical reactivity [50]. The higher value of electrophilicity index shows the high capacity of the molecule to accept electrons. The electrophilicity index for the compounds 5a, 5b, and 5c was 0.0040, 0.0046, and 0.0059 eV, respectively. The compound 5c had the highest electrophilicity index; therefore, it had a high capacity for accepting electrons. The dipole moment (µD) is a good measure of the asymmetric nature of a molecule. The size of the dipole moment depends on the composition and dimensionality of the 3D structures. As shown in Table 12, all structures had a high value of dipole moment and point group of C1, which reflected no symmetry in the structures. The dipole moment for the compound 5b (B3LYP/6-311+G(d) = 6.172 Debye) was higher than that for the compounds 5a and 5c (4.988 and 4.396 Debye, respectively).The high value for 5c was due to its asymmetric character.Table 12
Absolute energy (a.u), dipole moment (μ, Debye), frontier orbital energies (HOMO and LUMO, eV), hardness (η, eV), chemical potential (μ, eV), and electrophilicity (ω, eV) of 5a, 5b, and 5c molecules.
E
HOMO
E
LUMO
I
A
µ
η
ω
µ
D
Point group
5a
−0.27
−0.20
0.27
0.20
−0.235
0.170
0.0040
4.988
C1
5b
−0.27
−0.19
0.27
0.19
−0.230
0.176
0.0046
6.172
C1
5c
−0.29
−0.23
0.29
0.23
−0.260
0.175
0.0059
4.396
C1


#### 3.2.4. Thermodynamic Analysis

The total energy of a molecule consists of the sum of translational, rotational, vibrational, and electronic energies. The statistical thermochemical analysis of title compounds is carried out considering the molecule to be at room temperature of 25°C and 1 atmospheric pressure. The thermodynamic parameters such as zero-point vibrational energy, rotational constant, heat capacity (C), and the entropy (S) of the title compound by B3LYP/6-311+G(d) level are listed in Table13. According to Table 13, the calculated values for compound 5a and 5b are larger than compound 5c; therefore, compounds 5a and 5b have maximum stability compared to compound 5c due to formation of intramolecular hydrogen bonding.Table 13
Thermodynamic parameters of the5a, 5b, and 5c molecules using the B3LYP/6-311+G(d) level.
5a
5b
5c
Zero-point correctiona
0.439579
0.394413
0.405306
Thermal correction to energyb
0.468575
0.422073
0.431620
Thermal correction to enthalpyc
0.469519
0.423017
0.432564
Thermal correction to Gibbs free energyd
0.377501
0.333551
0.346912
Sum of electronic and zero-point energiese
−1522.507825
−1864.121732
−1409.523823
Sum of electronic and thermal energiesf
−1522.478830
−1864.094072
−1409.497509
Sum of electronic and thermal enthalpiesg
−1522.477886
−1864.093128
−1409.496565
Sum of electronic and thermal free energiesh
−1522.569904
−1864.182594
−1409.582218
E (Thermal)i
294.035
264.855
270.846
CVj
109.323
104.085
100.028
Sk
193.668
188.297
180.271
a-hHartree/particle; iKCal/Mol; j,kCal/Mol-Kelvin.


#### 3.2.5. Molecular Electrostatic Potential (MEP)

The molecular electrostatic potential (MEP) was calculated by the B3LYP/6-311+G (d) level. The MEP is related to the electronic density and is a very useful descriptor in understanding sites for electrophilic attack and nucleophilic reactions as well as hydrogen bonding interactions [45]. The negative regions (red color) of the MEP are related to electrophilic reactivity, and the positive (blue color) region is related to nucleophilic reactivity, as shown in Figure 2.Molecular electrostatic potential (MEP) surface aims at locating the positive and negative charged electrostatic potential in the molecule. In each MEP surface, there is a color scale which indicates the negative and positive value. The red color is a sign for the negative extreme, and the blue color represents the positive extreme. The red color with a negative sign indicates the minimum electrostatic potential (which means it is bound loosely or has excess electrons), and it acts as electrophilic attack. The blue color also indicates the maximum of electrostatic potential, and it acts in the opposite manner.Starting from the above note, if we plot all MEP surfaces with all isosurface values, we see only the top surface. It is observed from the MEP map in Figure2 that the nitrogen-bonded oxygen atoms in the NO2 group and the oxygen atoms in the carbonyl groups (C=O) of the rings are negative regions in all compounds because in the resonance form of the nitro group, the oxygen atoms have a negative charge and the nitrogen atom has a positive charge, and in the resonance form of the carbonyl groups, the oxygen atoms have a negative charge and the carbon atom has a positive charge. Thus, oxygen atoms are sites for electrophilic activity. The nitrogen atoms in the ring, which are attached to carbonyl lethal electron groups, are also positively charged; therefore, nitrogen atoms are sites for nucleophilic attraction. As such, these sites provide information about the regions where the compounds can have strong intermolecular interactions.


## 3.1. Characterization Data for the Synthesis of 1H-indazolo[1,2-b]phthalazine-1,6,11(13H)-trione Derivatives (5a-c)

### 3.1.1. 3,3-Dimethyl-13-(4-methoxyphenyl)-10-nitro-2,3,4,13-tetrahydro-1H-indazolo[1,2-b] phthalazine-1,6,11(13H)-trione (5a)

Yellow solid; m.p.>250°C; Yield: 75%; Anal. Calcd for C24H21N3O6 (447.4): C, 64.42; H, 4.73; N, 9.39 %. Found: C, 64.38; H, 4.75; N, 9.33; IR (KBr) (υmax, cm−1): 3439, 2959, 1728 (C=O), 1666 (C=O), 1602 (C=O), 1535 (NO2-Asymmetric Str.), 1464, 1358 (NO2-Symmetric Str.); 1H NMR (DMSO. d6, 250.0 MHz): δH 0.96 (3H, s, CH3), 1.00 (3H, s, CH3), 2.07–2.33 (2H, m, CH2), 3.65 (2H, s, CH2), 3.80 (3H, s, OCH3), 5.25 (1H, s, CH), 7.02 (2H, d, 3JHH = 8.25 HZ, arom CH), 7.78 (2H, d, 3JHH = 8.25 HZ, arom CH), 8.50–8.82 (3H, m, arom CH); 13C NMR (DMSO. d6, 62.9 MHz): δC 26.91 and 28.16 (2CH3), 32.24 (C), 42.49 (CH2), 50.74 (CH2), 55.81 (OCH3), 64.46 (CH), 113.66, 114.83, 127.03, 127.99, 128.71, 129.08, 129.41, 129.96, 130.40, 131.97, 135.29, and 136.87 (aromatic and olefinic carbons), 160.84, 162.12, and 196.47 (3C=O); MS (EI): m/z 447 (M+, 0.02), 286 (5), 269 (100), 253 (9), 241 (27), 161 (76), 134 (27), 91 (24), 77 (33), and 63 (13).


### 3.1.2. 3,3-Dimethyl-10-nitro-13-phenyl-2,3,4,13-tetrahydro-1H-indazolo[1,2-b]phthalazine-1,6,11(13H)-trione (5b)

Yellow solid; m.p.>250°C; Yield: 80%; Anal. Calcd for C23H19N3O5 (417.4): C, 66.18; H, 4.59; N, 10.07 %. Found: C, 66.25; H, 4.54; N, 10.00; IR (KBr) (υmax, cm−1): 2931, 2358, 1724 (C=O), 1617 (C=O), 1588 (C=O), 1539 (NO2-Asymmetric Str.), 1460, 1410 (NO2 - Symmetric Str.); 1H NMR (DMSO. d6, 250.0 MHz): δH 0.96 (3H, s, CH3), 1.24 (3H, s, CH3), 2.07–2.23 (2H, m, CH2), 3.87–3.92 (2H, m, CH2), 5.26 (1H, s, CH), 7.36–8.69 (9H, m, arom CH); 13C NMR (DMSO. d6, 62.9 MHz): δC 28.15 and 28.50 (2CH3), 32.47 (C), 42.49 (CH2), 50.74 (CH2), 64.44 (CH), 126.81, 128.29, 128.44, 128.56, 128.79, 129.14, 129.32, 130.78, 131.76, 131.95, 134.25, and 135.31 (aromatic and olefinic carbons), 161.82, 165.50, and 198.19 (3C=O).


### 3.1.3. 13-(4-Chlorophenyl)-3,3-dimethyl-10-nitro-2,3,4,13-tetrahydro-1H-indazolo[1,2-b]phthalazine-1,6,11(13H)-trione (5c)

Yellow Solid; m.p. >250°C; Yield: 78%; Anal. Calcd for C23H18ClN3O5 (451.9): C, 61.14; H, 4.02; N, 9.30 %. Found: C, 61.10; H, 4.04; N, 9.24; IR (KBr) (υmax, cm−1): 2928, 2358, 1728 (C=O), 1611 (C=O), 1591 (C=O), 1474 (NO2- Asymmetric Str.), 1393 (NO2-Symmetric Str.), 1085 (C–Cl); 1H NMR (DMSO. d6, 250.0 MHz): δH 0.94 (3H, s, CH3), 1.22 (3H, s, CH3), 2.05–2.20 (2H, m, CH2), 3.87 (2H, s, CH2), 5.23 (1H, s, CH), 7.15–8.66 (8H, m, arom CH); 13C NMR (DMSO. d6, 62.9 MHz): δC 26.82 and 28.12 (2CH3), 32.45(C), 42.43 (CH2), 50.68 (CH2), 64.45 (CH), 114.38, 123.32, 128.22, 128.67, 128.90, 129.07, 129.26, 129.46, 129.89, 130.34, 133.01, and 134.70 (aromatic and olefinic carbons), 161.00, 163.41, and 196.43 (3C=O).


## 3.1.1. 3,3-Dimethyl-13-(4-methoxyphenyl)-10-nitro-2,3,4,13-tetrahydro-1H-indazolo[1,2-b] phthalazine-1,6,11(13H)-trione (5a)

Yellow solid; m.p.>250°C; Yield: 75%; Anal. Calcd for C24H21N3O6 (447.4): C, 64.42; H, 4.73; N, 9.39 %. Found: C, 64.38; H, 4.75; N, 9.33; IR (KBr) (υmax, cm−1): 3439, 2959, 1728 (C=O), 1666 (C=O), 1602 (C=O), 1535 (NO2-Asymmetric Str.), 1464, 1358 (NO2-Symmetric Str.); 1H NMR (DMSO. d6, 250.0 MHz): δH 0.96 (3H, s, CH3), 1.00 (3H, s, CH3), 2.07–2.33 (2H, m, CH2), 3.65 (2H, s, CH2), 3.80 (3H, s, OCH3), 5.25 (1H, s, CH), 7.02 (2H, d, 3JHH = 8.25 HZ, arom CH), 7.78 (2H, d, 3JHH = 8.25 HZ, arom CH), 8.50–8.82 (3H, m, arom CH); 13C NMR (DMSO. d6, 62.9 MHz): δC 26.91 and 28.16 (2CH3), 32.24 (C), 42.49 (CH2), 50.74 (CH2), 55.81 (OCH3), 64.46 (CH), 113.66, 114.83, 127.03, 127.99, 128.71, 129.08, 129.41, 129.96, 130.40, 131.97, 135.29, and 136.87 (aromatic and olefinic carbons), 160.84, 162.12, and 196.47 (3C=O); MS (EI): m/z 447 (M+, 0.02), 286 (5), 269 (100), 253 (9), 241 (27), 161 (76), 134 (27), 91 (24), 77 (33), and 63 (13).


## 3.1.2. 3,3-Dimethyl-10-nitro-13-phenyl-2,3,4,13-tetrahydro-1H-indazolo[1,2-b]phthalazine-1,6,11(13H)-trione (5b)

Yellow solid; m.p.>250°C; Yield: 80%; Anal. Calcd for C23H19N3O5 (417.4): C, 66.18; H, 4.59; N, 10.07 %. Found: C, 66.25; H, 4.54; N, 10.00; IR (KBr) (υmax, cm−1): 2931, 2358, 1724 (C=O), 1617 (C=O), 1588 (C=O), 1539 (NO2-Asymmetric Str.), 1460, 1410 (NO2 - Symmetric Str.); 1H NMR (DMSO. d6, 250.0 MHz): δH 0.96 (3H, s, CH3), 1.24 (3H, s, CH3), 2.07–2.23 (2H, m, CH2), 3.87–3.92 (2H, m, CH2), 5.26 (1H, s, CH), 7.36–8.69 (9H, m, arom CH); 13C NMR (DMSO. d6, 62.9 MHz): δC 28.15 and 28.50 (2CH3), 32.47 (C), 42.49 (CH2), 50.74 (CH2), 64.44 (CH), 126.81, 128.29, 128.44, 128.56, 128.79, 129.14, 129.32, 130.78, 131.76, 131.95, 134.25, and 135.31 (aromatic and olefinic carbons), 161.82, 165.50, and 198.19 (3C=O).


## 3.1.3. 13-(4-Chlorophenyl)-3,3-dimethyl-10-nitro-2,3,4,13-tetrahydro-1H-indazolo[1,2-b]phthalazine-1,6,11(13H)-trione (5c)

Yellow Solid; m.p. >250°C; Yield: 78%; Anal. Calcd for C23H18ClN3O5 (451.9): C, 61.14; H, 4.02; N, 9.30 %. Found: C, 61.10; H, 4.04; N, 9.24; IR (KBr) (υmax, cm−1): 2928, 2358, 1728 (C=O), 1611 (C=O), 1591 (C=O), 1474 (NO2- Asymmetric Str.), 1393 (NO2-Symmetric Str.), 1085 (C–Cl); 1H NMR (DMSO. d6, 250.0 MHz): δH 0.94 (3H, s, CH3), 1.22 (3H, s, CH3), 2.05–2.20 (2H, m, CH2), 3.87 (2H, s, CH2), 5.23 (1H, s, CH), 7.15–8.66 (8H, m, arom CH); 13C NMR (DMSO. d6, 62.9 MHz): δC 26.82 and 28.12 (2CH3), 32.45(C), 42.43 (CH2), 50.68 (CH2), 64.45 (CH), 114.38, 123.32, 128.22, 128.67, 128.90, 129.07, 129.26, 129.46, 129.89, 130.34, 133.01, and 134.70 (aromatic and olefinic carbons), 161.00, 163.41, and 196.43 (3C=O).


## 3.2. Computational Section

### 3.2.1. IR Spectroscopy

Harmonic vibrational frequencies of the title compounds were calculated using the B3LYP/3-21G, HF/3-21G, B3LYP/6-311+G(d), and HF/6-311+G(d) levels. The vibrational frequencies assignments were made using the GaussView program. Some of the characteristic frequencies are provided in Tables2–4. The harmonic frequencies calculated by DFT are usually higher than the corresponding experimental values due to the approximate treatment of the electron correlation, anharmonicity effects, and basis set deficiencies [39].Table 2
The selected experimental and theoretical frequencies of the title compounds using the B3LYP and HF methods for compound(5a).
Experimental wavenumbers by FT-IR (cm−1)
Calculated vibrational wavenumbers by HF and DFT methods (cm−1)
B3LYP
HF
3-21G
6-311+G∗∗
3-21G
6-311+G∗∗
Assignment
C=O
3439
3441
3440
3438
3450
2959
2967
2955
2964
2960
1728
1721
1729
1720
1733
C=O
1666
1691
1673
1689
1682
C=O
1602
1602
1608
1615
1600
C=C
1535
1599
1530
1542
1535
Ar C=C
1464
1466
1466
1463
1469
CH3
1358
1351
1359
1368
1366Table 3
The selected experimental and theoretical frequencies of the title compounds using the B3LYP and HF methods for compound(5b).
Experimental wavenumbers by FT-IR (cm−1)
Calculated vibrational wavenumbers by HF and DFT methods (cm−1)
B3LYP
HF
3-21G
6-311+G∗∗
3-21G
6-311+G∗∗
Assignment
C=O
3413
3413
3405
3461
3423
2955
2972
2915
2952
2962
1661
1660
1663
1668
1671
C=O
1626
1619
1628
1630
1629
C=H
1583
1573
1588
1589
1573
Ar C=C
1489
1489
1490
1498
1499
CH3
1362
1397
1362
1373
1307
C–Cl, bending
1090
1080
1090
1099
1088Table 4
The selected experimental and theoretical frequencies of the title compounds using the B3LYP and HF methods for compound(5c).
Experimental wavenumbers by FT-IR (cm−1)
Calculated vibrational wavenumbers by HF and DFT methods (cm−1)
B3LYP
HF
3-21G
6-311+G∗∗
3-21G
6-311+G∗∗
Assignment
C=O
3436
3430
3430
3449
3435
2951
2971
2962
2973
2943
1661
1669
1661
1750
1665
C=O
1625
1638
1640
1615
1635
C=C
1576
1583
1579
1580
1579
Ar C=C
1492
1483
1492
1489
1497
CH3
1361
1361
1361
1373
1360For the title compound(5a), the strong band at 3376 cm−1 in the FT-IR spectrum is assigned as vC=O mode. The calculated values for this mode are 3375, 3204, 3227, and 3360 cm−1 for HF/6-31+G∗, HF/6–311+G∗∗, B3LYP/6-31+G∗, and B3LYP/6–311+G∗∗ levels, respectively. For the title compound (5a), the strong band at 3439, 2959, and 1728 cm−1 in the FT-IR spectrum is assigned as vC=O mode. The calculated values for this mode are the same as those calculated for HF/3-21G, HF/6-311+G∗∗, B3LYP/3-21G, and B3LYP/6-311+G∗∗ levels, respectively. The DFT computation predicts this vibrational mode in ArC=C at 1464 cm−1 for A, 1489 cm−1 for the compound 5b, and 1493 cm−1 for the compound 5c. This observed frequency coincides well with the expected value [42]. There was an excellent agreement between experimental and theoretical results for all used methods. In order to compare this agreement, the correlation graphic based on the theoretical and experimental data was investigated. A small difference between the experimental and calculated vibrational modes was observed. This difference might have been due to intermolecular hydrogen bonding formation. Also, the experimental results belong to the solid phase while theoretical calculations belong to the isolated gaseous phase.


### 3.2.2. NMR Parameters

The calculation of1H NMR and 13C NMR chemical shifts of compounds 5a, 5b, and 5c is done at B3LYP/3-21G, HF/3-21G, B3LYP/6-311+G(d), and HF/6-311+G(d) levels. The experimental and calculated 1H NMR and 13C NMR chemical shifts of 1H-indazolo[1,2-b] phthalazine-1,6,11(13H)-trione derivatives (5a, 5b and 5c) are presented in Tables 5–10. Based on our calculations and experimental spectra, we made a reliable one-to-one correspondence between our fundamentals, and all of the chemical shifts were calculated by the HF and B3LYP methods. For the title compound (5a), the aromatic CH protons appeared at δH 7.02–8.82 ppm, and the calculated amounts at HF/6-311+G∗∗ and B3LYP/6-311+G∗∗ basis set levels were at 7.30–8.19 and 7.00–8.89 ppm, respectively. Protons of two methyl groups appeared at δH 0.96 and 1.00 ppm, the calculated amounts at HF/6-311+G∗∗ and B3LYP/6-311+G∗∗ basis set levels were at 0.67 and 1.28 ppm and 0.86 and 1.19 ppm, respectively. Also, chemical shifts of three carbonyl groups appeared at δc 160.84, 162.12, and 196.47 ppm, the calculated amounts at HF/6-311+G∗∗ and B3LYP/6-311+G∗∗ basis set levels were at 149.88, 153.99, and 190.97 ppm and 159.51, 161.27, and 197.32 ppm, respectively. The same was true for other compounds.Table 5
Experimentally measured and calculated1H chemical shifts δ (ppm vs TMS) of the compound (5a).
1H NMR
EXP
Calculated
B3LYP/3-21G
B3LYP/6-311+G∗∗
HF/3-21G
HF/6-311+G∗∗
3H, s, CH
3
0.96
0.33
0.86
0.66
0.67
3H, s, CH
3
1.00
1.41
1.19
1.15
1.28
2H, m, CH
2
2.07–2.33
2.38–2.52
2.03–2.33
1.95–2.60
1.95–2.60
2H, s, CH
2
3.65
3.32
3.60
3.13
3.13
3H, s, OCH
3
3.80
3.78
3.88
3.66
3.66
1H, s, CH
5.25
5.25
5.50
5.81
5.81
2H, d, arom C–H
7.02
7.02
7.00
7.30
7.30
2H, d, arom C–H
7.78
7.11
7.70
7.44
7.44
4H, m, arom C–H
8.50–8.82
8.22–8.75
8.51–8.89
8.08–8.17
8.08–8.19Table 6
Experimentally measured and calculated13C chemical shifts δ (ppm vs TMS) of the compound (5a).
13C NMR
EXP
Calculated
B3LYP/3-21G
B3LYP/6-311+G∗∗
HF/3-21G
HF/6-311+G∗∗
2CH
3
26.91–28.16
26.26–27.78
26.90–27.99
18.82–30.50
26.80–27.01
C
32.24
31.10
31.99
32.62
30.37
CH
2
42.49
42.83
42.73
45.54
44.99
CH
2
50.74
49.01
49.41
46.01
46.89
CH
64.46
63.98
62.99
58.79
60.74
OCH
3
55.81
50.11
55.88
48.72
50.11
C-H aromatic and olefinic carbons
113.66
93.78
113.52
101.98
107.09
114.83
94.99
113.99
108.88
111.90
127.99
95.08
126.31
110.44
123.53
128.71
95.39
130.07
111.47
123.43
128.71
96.14
131.05
112.90
122.90
129.08
96.87
130.66
113.02
125.51
129.41
97.60
133.98
114.13
124.39
129.96
97.65
136.75
114.48
124.19
130.40
119.1
138.41
114.56
124.97
131.97
122.79
127.99
126.65
135.29
127.76
137.19
137.19
136.87
129.30
138.90
144.90
C=O(1)
160.84
—
159.51
—
149.88
C=O(2)
162.12
—
161.27
—
153.99
C=O(3)
196.47
—
197.32
—
190.97Table 7
Experimentally measured and calculated1H chemical shifts δ (ppm vs TMS) of the compound (5b).
1H NMR
EXP
Calculated
B3LYP/3-21G
B3LYP/6-311+G∗∗
HF/3-21G
HF/6-311+G∗∗
3H, s, CH
3
0.94
0.43
0.98
0.48
0.97
3H, s, CH
3
1.22
1.42
1.27
1.30
1.30
2H, m, CH
2
2.05–2.20
2.11–2.32
2.08–2.28
2.17–2.96
2.09–2.48
2H, s, CH
2
3.87
3.94
3.90
4.00
3.98
1H, s, C–H
5.23
5.63
5.32
5.85
5.42
8H, m, arom C–H
7.15–8.66
7.10–7.97
7.17–8.62
7.19–8.91
7.19–8.76Table 8
Experimentally measured and calculated13C chemical shifts δ (ppm vs TMS) of the compound (5b).
13C NMR
EXP
Calculated
B3LYP/3-21G
B3LYP/6-311+G∗∗
HF/3-21G
HF/6-311+G∗∗
2CH
3
26.82–28.12
26.43–29.11
26.83–29.11
25.31–31.74
28.88–30.11
C
32.45
37.41
32.51
36.42
36.77
CH
2
42.43
43.33
42.51
41.23
42.21
CH
2
50.68
58.13
51.67
59.11
57.32
CH
64.45
70.41
63.78
72.31
71.20
Aromatic and olefinic carbons
114.38
86.90
115.77
89.99
85.90
123.32
93.88
123.46
97.67
91.63
128.22
94.84
129.22
97.91
96.41
128.67
97.22
129.63
83.23
126.99
128.90
97.71
129.77
84.89
128.71
129.07
97.97
130.11
85.99
128.86
129.26
100.82
130.28
112.92
128.32
129.46
101.89
130.49
113.55
129.27
129.89
119.29
130.80
114.41
129.64
130.34
127.48
131.45
129.99
129.83
133.01
129.17
134.89
130.89
130.22
134.70
148.29
135.03
137.98
134.60
C=O(1)
161.00
—
160.27
—
159.21
C=O(2)
163.41
—
162.11
—
160.41Table 9
Experimentally measured and calculated1H chemical shifts δ (ppm vs TMS) of the compound (5c).
1H NMR
EXP
Calculated
B3LYP/3-21G
B3LYP/6-311+G∗∗
HF/3-21G
HF/6-311+G∗∗
3H, s, CH
3
0.96
0.53
0.97
0.69
0.78
3H, s, CH
3
1.24
1.40
1.29
1.84
1.48
2H, m, CH
2
2.07–2.23
1.83–2.32
2.11–2.29
1.95–2.10
1.96–2.11
2H, m, CH
2
3.87–3.92
2.86
3.80–3.94
3.10–3.51
3.18–3.68
1H, s, C-H
5.26
5.59
5.23
5.88
5.40
9H, m, arom C-H
7.36–8.69
7.06–7.19
7.33–8.68
7.18–8.16
7.11–8.39Table 10
Experimentally measured and calculated13C chemical shifts δ (ppm vs TMS) of the compound (5c).
13C NMR
EXP
Calculated
B3LYP/3-21G
B3LYP/6-311+G∗∗
HF/3-21G
HF/6-311+G∗∗
CH
3
28.15
26.66
28.19
18.20
28.21
CH
3
28.50
28.19
28.93
18.70
28.87
C
32.47
30.11
33.11
30.65
32.76
CH
2
42.49
43.86
47.22
45.64
48.32
CH
2
50.74
50.11
50.66
48.11
50.98
CH
64.44
73.11
64.32
48.91
67.11
Aromatic and olefinic carbons
126.81
87.066
127.93
107.92
128.01
128.29
92.77
129.48
108.21
128.32
128.44
92.93
129.32
108.43
128.66
128.67
93.60
129.51
108.74
128.51
128.86
93.23
129.69
108.56
128.90
129.14
96.53
130.11
109.85
133.66
129.32
97.06
130.30
110.05
133.68
130.78
97.73
130.79
110.48
133.99
131.76
102.53
133.35
112.03
136.98
131.95
119.2
133.78
113.08
136.31
134.25
127.6
133.86
114.19
136.32
135.31
129.46
139.21
118.79
137.38
C=O(1)
161.82
—
163.23
151.46
160.20
C=O(2)
165.50
—
169.93
153.24
161.39
C=O(3)
198.19
—
197.11
169.84
193.22There was an excellent agreement between experimental and theoretical results for all methods employed. In order to compare this agreement, the correlation graphic based on the theoretical and experimental data was investigated. The correlation value (R2) for compounds at HF/3-21G, B3LYP/3-21G, HF/6-311+G∗∗, and B3LYP/6-311+G∗∗ is presented in Table 11. There was an excellent agreement between experimental and theoretical results [39]. A small difference between the experimental and calculated vibrational modes was observed. This difference might have been due to the intermolecular hydrogen bonding formation. Furthermore, the experimental results belong to the solid phase while and theoretical calculations belong to the isolated gaseous phase.Table 11
Correlation of calculated and experimental1H NMR,13C NMR, and IR of the compounds.
Compounds
B3LYP/3-21G
B3LYP/6-311+G∗∗
HF/3-21G
HF/6-311+G∗∗
5a
HNMR
0.9975
0.9999
0.9991
0.9974
5b
0.9986
0.9999
0.9985
0.9997
5c
0.9996
0.9995
0.9990
0.9998
5a
CNMR
0.9977
0.9995
0.9992
0.9975
5b
0.9983
0.9999
0.9990
0.9998
5c
0.9986
0.9998
0.9998
0.9999
5a
IR
0.9953
0.9995
0.9995
0.9978
5b
0.9986
0.9999
0.9988
0.9990
5c
0.9970
0.9997
0.9983
0.9991


### 3.2.3. Electronic Properties

Quantum chemical methods are important for obtaining information about molecular structure and electrochemical behavior. A frontier molecular orbital (FMO) analysis was performed for the compounds using the B3LYP/6-311+G(d) level [38]. FMO results such as EHOMO, ELUMO, and the HOMO-LUMO energy gap (∆E) of the title compounds are summarized in Table 7. The energy of the LUMO, HOMO, and their energy gaps reflected the chemical reactivity of the molecule [43]. In addition, the HOMO could act as an electron donor and the LUMO as an electron acceptor. A higher HOMO energy (EHOMO) for the molecule indicated a higher electron-donating ability to an appropriate acceptor molecule with a low-energy empty molecular orbital [44]. As shown in Figure 1 the HOMO energy of the compound 5c had the highest value (−0.29 eV). A large energy gap implied high stability for the molecule. The calculated values of the HOMO-LUMO energy gap (∆E) for the structures 5a, 5b, and 5c were 0.07, 0.08, and 0.06 eV, respectively. DOS plots [45] also demonstrated the calculated energy gaps (∆E) for the compounds 5a, 5b, and 5c (see Figure 2). It is obvious that the energy gap of the compound 5b was the highest (0.08 eV); therefore, it was less reactive than the other structures, whereas the energy gap of the compound 5c was the lowest (0.06 eV), which indicates that it was the most reactive. As presented in Figure 2, charge transfer could take place within the three molecules.Figure 2
Molecular electrostatic potential (MEP) maps of the title compounds calculated using the B3LYP/6-311+G(d) level.
(a)
(b)
(c)The electronic properties such as ionization potential, electron affinity, global hardness, electronic chemical potential, and electrophilicity are calculated in Table12. The first ionization potential (I) and electron affinity (A) could be expressed through HOMO and LUMO orbital energies by connecting it with Hartree–Fock SCF theory and invoking Koopmans' theorem [46] as I = −EHOMO and A = −ELUMO. The chemical hardness (η = I−A/2) is an important property that measures the molecular stability and reactivity [47]. A hard molecule has a large energy gap (∆E) and a soft molecule has a small energy gap (∆E) [48]. The chemical hardness (η) values of the compounds 5a, 5b, and 5c were 0.170, 0.176, and 0.175 eV, respectively. Compound 5b had the highest chemical hardness (η = 0.176 eV); therefore, it was a hard molecule with less reactivity and a high energy gap (∆E = 0.08 eV). The electronic chemical potential (µ = −(I + A)/2) is a form of the potential energy that can be absorbed or released during a chemical reaction and that may also change during a phase transition [49]. The electronic chemical potential of 5c had the most negative value (−0.26 eV). The electrophilicity (ω) measures the stabilization in energy when the system acquires an additional electronic charge from the environment. The electrophilicity index (ω = µ2/2η) contains information about both electron transfer (chemical potential) and stability (hardness) and is a better descriptor of global chemical reactivity [50]. The higher value of electrophilicity index shows the high capacity of the molecule to accept electrons. The electrophilicity index for the compounds 5a, 5b, and 5c was 0.0040, 0.0046, and 0.0059 eV, respectively. The compound 5c had the highest electrophilicity index; therefore, it had a high capacity for accepting electrons. The dipole moment (µD) is a good measure of the asymmetric nature of a molecule. The size of the dipole moment depends on the composition and dimensionality of the 3D structures. As shown in Table 12, all structures had a high value of dipole moment and point group of C1, which reflected no symmetry in the structures. The dipole moment for the compound 5b (B3LYP/6-311+G(d) = 6.172 Debye) was higher than that for the compounds 5a and 5c (4.988 and 4.396 Debye, respectively).The high value for 5c was due to its asymmetric character.Table 12
Absolute energy (a.u), dipole moment (μ, Debye), frontier orbital energies (HOMO and LUMO, eV), hardness (η, eV), chemical potential (μ, eV), and electrophilicity (ω, eV) of 5a, 5b, and 5c molecules.
E
HOMO
E
LUMO
I
A
µ
η
ω
µ
D
Point group
5a
−0.27
−0.20
0.27
0.20
−0.235
0.170
0.0040
4.988
C1
5b
−0.27
−0.19
0.27
0.19
−0.230
0.176
0.0046
6.172
C1
5c
−0.29
−0.23
0.29
0.23
−0.260
0.175
0.0059
4.396
C1


### 3.2.4. Thermodynamic Analysis

The total energy of a molecule consists of the sum of translational, rotational, vibrational, and electronic energies. The statistical thermochemical analysis of title compounds is carried out considering the molecule to be at room temperature of 25°C and 1 atmospheric pressure. The thermodynamic parameters such as zero-point vibrational energy, rotational constant, heat capacity (C), and the entropy (S) of the title compound by B3LYP/6-311+G(d) level are listed in Table13. According to Table 13, the calculated values for compound 5a and 5b are larger than compound 5c; therefore, compounds 5a and 5b have maximum stability compared to compound 5c due to formation of intramolecular hydrogen bonding.Table 13
Thermodynamic parameters of the5a, 5b, and 5c molecules using the B3LYP/6-311+G(d) level.
5a
5b
5c
Zero-point correctiona
0.439579
0.394413
0.405306
Thermal correction to energyb
0.468575
0.422073
0.431620
Thermal correction to enthalpyc
0.469519
0.423017
0.432564
Thermal correction to Gibbs free energyd
0.377501
0.333551
0.346912
Sum of electronic and zero-point energiese
−1522.507825
−1864.121732
−1409.523823
Sum of electronic and thermal energiesf
−1522.478830
−1864.094072
−1409.497509
Sum of electronic and thermal enthalpiesg
−1522.477886
−1864.093128
−1409.496565
Sum of electronic and thermal free energiesh
−1522.569904
−1864.182594
−1409.582218
E (Thermal)i
294.035
264.855
270.846
CVj
109.323
104.085
100.028
Sk
193.668
188.297
180.271
a-hHartree/particle; iKCal/Mol; j,kCal/Mol-Kelvin.


### 3.2.5. Molecular Electrostatic Potential (MEP)

The molecular electrostatic potential (MEP) was calculated by the B3LYP/6-311+G (d) level. The MEP is related to the electronic density and is a very useful descriptor in understanding sites for electrophilic attack and nucleophilic reactions as well as hydrogen bonding interactions [45]. The negative regions (red color) of the MEP are related to electrophilic reactivity, and the positive (blue color) region is related to nucleophilic reactivity, as shown in Figure 2.Molecular electrostatic potential (MEP) surface aims at locating the positive and negative charged electrostatic potential in the molecule. In each MEP surface, there is a color scale which indicates the negative and positive value. The red color is a sign for the negative extreme, and the blue color represents the positive extreme. The red color with a negative sign indicates the minimum electrostatic potential (which means it is bound loosely or has excess electrons), and it acts as electrophilic attack. The blue color also indicates the maximum of electrostatic potential, and it acts in the opposite manner.Starting from the above note, if we plot all MEP surfaces with all isosurface values, we see only the top surface. It is observed from the MEP map in Figure2 that the nitrogen-bonded oxygen atoms in the NO2 group and the oxygen atoms in the carbonyl groups (C=O) of the rings are negative regions in all compounds because in the resonance form of the nitro group, the oxygen atoms have a negative charge and the nitrogen atom has a positive charge, and in the resonance form of the carbonyl groups, the oxygen atoms have a negative charge and the carbon atom has a positive charge. Thus, oxygen atoms are sites for electrophilic activity. The nitrogen atoms in the ring, which are attached to carbonyl lethal electron groups, are also positively charged; therefore, nitrogen atoms are sites for nucleophilic attraction. As such, these sites provide information about the regions where the compounds can have strong intermolecular interactions.


## 3.2.1. IR Spectroscopy

Harmonic vibrational frequencies of the title compounds were calculated using the B3LYP/3-21G, HF/3-21G, B3LYP/6-311+G(d), and HF/6-311+G(d) levels. The vibrational frequencies assignments were made using the GaussView program. Some of the characteristic frequencies are provided in Tables2–4. The harmonic frequencies calculated by DFT are usually higher than the corresponding experimental values due to the approximate treatment of the electron correlation, anharmonicity effects, and basis set deficiencies [39].Table 2
The selected experimental and theoretical frequencies of the title compounds using the B3LYP and HF methods for compound(5a).
Experimental wavenumbers by FT-IR (cm−1)
Calculated vibrational wavenumbers by HF and DFT methods (cm−1)
B3LYP
HF
3-21G
6-311+G∗∗
3-21G
6-311+G∗∗
Assignment
C=O
3439
3441
3440
3438
3450
2959
2967
2955
2964
2960
1728
1721
1729
1720
1733
C=O
1666
1691
1673
1689
1682
C=O
1602
1602
1608
1615
1600
C=C
1535
1599
1530
1542
1535
Ar C=C
1464
1466
1466
1463
1469
CH3
1358
1351
1359
1368
1366Table 3
The selected experimental and theoretical frequencies of the title compounds using the B3LYP and HF methods for compound(5b).
Experimental wavenumbers by FT-IR (cm−1)
Calculated vibrational wavenumbers by HF and DFT methods (cm−1)
B3LYP
HF
3-21G
6-311+G∗∗
3-21G
6-311+G∗∗
Assignment
C=O
3413
3413
3405
3461
3423
2955
2972
2915
2952
2962
1661
1660
1663
1668
1671
C=O
1626
1619
1628
1630
1629
C=H
1583
1573
1588
1589
1573
Ar C=C
1489
1489
1490
1498
1499
CH3
1362
1397
1362
1373
1307
C–Cl, bending
1090
1080
1090
1099
1088Table 4
The selected experimental and theoretical frequencies of the title compounds using the B3LYP and HF methods for compound(5c).
Experimental wavenumbers by FT-IR (cm−1)
Calculated vibrational wavenumbers by HF and DFT methods (cm−1)
B3LYP
HF
3-21G
6-311+G∗∗
3-21G
6-311+G∗∗
Assignment
C=O
3436
3430
3430
3449
3435
2951
2971
2962
2973
2943
1661
1669
1661
1750
1665
C=O
1625
1638
1640
1615
1635
C=C
1576
1583
1579
1580
1579
Ar C=C
1492
1483
1492
1489
1497
CH3
1361
1361
1361
1373
1360For the title compound(5a), the strong band at 3376 cm−1 in the FT-IR spectrum is assigned as vC=O mode. The calculated values for this mode are 3375, 3204, 3227, and 3360 cm−1 for HF/6-31+G∗, HF/6–311+G∗∗, B3LYP/6-31+G∗, and B3LYP/6–311+G∗∗ levels, respectively. For the title compound (5a), the strong band at 3439, 2959, and 1728 cm−1 in the FT-IR spectrum is assigned as vC=O mode. The calculated values for this mode are the same as those calculated for HF/3-21G, HF/6-311+G∗∗, B3LYP/3-21G, and B3LYP/6-311+G∗∗ levels, respectively. The DFT computation predicts this vibrational mode in ArC=C at 1464 cm−1 for A, 1489 cm−1 for the compound 5b, and 1493 cm−1 for the compound 5c. This observed frequency coincides well with the expected value [42]. There was an excellent agreement between experimental and theoretical results for all used methods. In order to compare this agreement, the correlation graphic based on the theoretical and experimental data was investigated. A small difference between the experimental and calculated vibrational modes was observed. This difference might have been due to intermolecular hydrogen bonding formation. Also, the experimental results belong to the solid phase while theoretical calculations belong to the isolated gaseous phase.


## 3.2.2. NMR Parameters

The calculation of1H NMR and 13C NMR chemical shifts of compounds 5a, 5b, and 5c is done at B3LYP/3-21G, HF/3-21G, B3LYP/6-311+G(d), and HF/6-311+G(d) levels. The experimental and calculated 1H NMR and 13C NMR chemical shifts of 1H-indazolo[1,2-b] phthalazine-1,6,11(13H)-trione derivatives (5a, 5b and 5c) are presented in Tables 5–10. Based on our calculations and experimental spectra, we made a reliable one-to-one correspondence between our fundamentals, and all of the chemical shifts were calculated by the HF and B3LYP methods. For the title compound (5a), the aromatic CH protons appeared at δH 7.02–8.82 ppm, and the calculated amounts at HF/6-311+G∗∗ and B3LYP/6-311+G∗∗ basis set levels were at 7.30–8.19 and 7.00–8.89 ppm, respectively. Protons of two methyl groups appeared at δH 0.96 and 1.00 ppm, the calculated amounts at HF/6-311+G∗∗ and B3LYP/6-311+G∗∗ basis set levels were at 0.67 and 1.28 ppm and 0.86 and 1.19 ppm, respectively. Also, chemical shifts of three carbonyl groups appeared at δc 160.84, 162.12, and 196.47 ppm, the calculated amounts at HF/6-311+G∗∗ and B3LYP/6-311+G∗∗ basis set levels were at 149.88, 153.99, and 190.97 ppm and 159.51, 161.27, and 197.32 ppm, respectively. The same was true for other compounds.Table 5
Experimentally measured and calculated1H chemical shifts δ (ppm vs TMS) of the compound (5a).
1H NMR
EXP
Calculated
B3LYP/3-21G
B3LYP/6-311+G∗∗
HF/3-21G
HF/6-311+G∗∗
3H, s, CH
3
0.96
0.33
0.86
0.66
0.67
3H, s, CH
3
1.00
1.41
1.19
1.15
1.28
2H, m, CH
2
2.07–2.33
2.38–2.52
2.03–2.33
1.95–2.60
1.95–2.60
2H, s, CH
2
3.65
3.32
3.60
3.13
3.13
3H, s, OCH
3
3.80
3.78
3.88
3.66
3.66
1H, s, CH
5.25
5.25
5.50
5.81
5.81
2H, d, arom C–H
7.02
7.02
7.00
7.30
7.30
2H, d, arom C–H
7.78
7.11
7.70
7.44
7.44
4H, m, arom C–H
8.50–8.82
8.22–8.75
8.51–8.89
8.08–8.17
8.08–8.19Table 6
Experimentally measured and calculated13C chemical shifts δ (ppm vs TMS) of the compound (5a).
13C NMR
EXP
Calculated
B3LYP/3-21G
B3LYP/6-311+G∗∗
HF/3-21G
HF/6-311+G∗∗
2CH
3
26.91–28.16
26.26–27.78
26.90–27.99
18.82–30.50
26.80–27.01
C
32.24
31.10
31.99
32.62
30.37
CH
2
42.49
42.83
42.73
45.54
44.99
CH
2
50.74
49.01
49.41
46.01
46.89
CH
64.46
63.98
62.99
58.79
60.74
OCH
3
55.81
50.11
55.88
48.72
50.11
C-H aromatic and olefinic carbons
113.66
93.78
113.52
101.98
107.09
114.83
94.99
113.99
108.88
111.90
127.99
95.08
126.31
110.44
123.53
128.71
95.39
130.07
111.47
123.43
128.71
96.14
131.05
112.90
122.90
129.08
96.87
130.66
113.02
125.51
129.41
97.60
133.98
114.13
124.39
129.96
97.65
136.75
114.48
124.19
130.40
119.1
138.41
114.56
124.97
131.97
122.79
127.99
126.65
135.29
127.76
137.19
137.19
136.87
129.30
138.90
144.90
C=O(1)
160.84
—
159.51
—
149.88
C=O(2)
162.12
—
161.27
—
153.99
C=O(3)
196.47
—
197.32
—
190.97Table 7
Experimentally measured and calculated1H chemical shifts δ (ppm vs TMS) of the compound (5b).
1H NMR
EXP
Calculated
B3LYP/3-21G
B3LYP/6-311+G∗∗
HF/3-21G
HF/6-311+G∗∗
3H, s, CH
3
0.94
0.43
0.98
0.48
0.97
3H, s, CH
3
1.22
1.42
1.27
1.30
1.30
2H, m, CH
2
2.05–2.20
2.11–2.32
2.08–2.28
2.17–2.96
2.09–2.48
2H, s, CH
2
3.87
3.94
3.90
4.00
3.98
1H, s, C–H
5.23
5.63
5.32
5.85
5.42
8H, m, arom C–H
7.15–8.66
7.10–7.97
7.17–8.62
7.19–8.91
7.19–8.76Table 8
Experimentally measured and calculated13C chemical shifts δ (ppm vs TMS) of the compound (5b).
13C NMR
EXP
Calculated
B3LYP/3-21G
B3LYP/6-311+G∗∗
HF/3-21G
HF/6-311+G∗∗
2CH
3
26.82–28.12
26.43–29.11
26.83–29.11
25.31–31.74
28.88–30.11
C
32.45
37.41
32.51
36.42
36.77
CH
2
42.43
43.33
42.51
41.23
42.21
CH
2
50.68
58.13
51.67
59.11
57.32
CH
64.45
70.41
63.78
72.31
71.20
Aromatic and olefinic carbons
114.38
86.90
115.77
89.99
85.90
123.32
93.88
123.46
97.67
91.63
128.22
94.84
129.22
97.91
96.41
128.67
97.22
129.63
83.23
126.99
128.90
97.71
129.77
84.89
128.71
129.07
97.97
130.11
85.99
128.86
129.26
100.82
130.28
112.92
128.32
129.46
101.89
130.49
113.55
129.27
129.89
119.29
130.80
114.41
129.64
130.34
127.48
131.45
129.99
129.83
133.01
129.17
134.89
130.89
130.22
134.70
148.29
135.03
137.98
134.60
C=O(1)
161.00
—
160.27
—
159.21
C=O(2)
163.41
—
162.11
—
160.41Table 9
Experimentally measured and calculated1H chemical shifts δ (ppm vs TMS) of the compound (5c).
1H NMR
EXP
Calculated
B3LYP/3-21G
B3LYP/6-311+G∗∗
HF/3-21G
HF/6-311+G∗∗
3H, s, CH
3
0.96
0.53
0.97
0.69
0.78
3H, s, CH
3
1.24
1.40
1.29
1.84
1.48
2H, m, CH
2
2.07–2.23
1.83–2.32
2.11–2.29
1.95–2.10
1.96–2.11
2H, m, CH
2
3.87–3.92
2.86
3.80–3.94
3.10–3.51
3.18–3.68
1H, s, C-H
5.26
5.59
5.23
5.88
5.40
9H, m, arom C-H
7.36–8.69
7.06–7.19
7.33–8.68
7.18–8.16
7.11–8.39Table 10
Experimentally measured and calculated13C chemical shifts δ (ppm vs TMS) of the compound (5c).
13C NMR
EXP
Calculated
B3LYP/3-21G
B3LYP/6-311+G∗∗
HF/3-21G
HF/6-311+G∗∗
CH
3
28.15
26.66
28.19
18.20
28.21
CH
3
28.50
28.19
28.93
18.70
28.87
C
32.47
30.11
33.11
30.65
32.76
CH
2
42.49
43.86
47.22
45.64
48.32
CH
2
50.74
50.11
50.66
48.11
50.98
CH
64.44
73.11
64.32
48.91
67.11
Aromatic and olefinic carbons
126.81
87.066
127.93
107.92
128.01
128.29
92.77
129.48
108.21
128.32
128.44
92.93
129.32
108.43
128.66
128.67
93.60
129.51
108.74
128.51
128.86
93.23
129.69
108.56
128.90
129.14
96.53
130.11
109.85
133.66
129.32
97.06
130.30
110.05
133.68
130.78
97.73
130.79
110.48
133.99
131.76
102.53
133.35
112.03
136.98
131.95
119.2
133.78
113.08
136.31
134.25
127.6
133.86
114.19
136.32
135.31
129.46
139.21
118.79
137.38
C=O(1)
161.82
—
163.23
151.46
160.20
C=O(2)
165.50
—
169.93
153.24
161.39
C=O(3)
198.19
—
197.11
169.84
193.22There was an excellent agreement between experimental and theoretical results for all methods employed. In order to compare this agreement, the correlation graphic based on the theoretical and experimental data was investigated. The correlation value (R2) for compounds at HF/3-21G, B3LYP/3-21G, HF/6-311+G∗∗, and B3LYP/6-311+G∗∗ is presented in Table 11. There was an excellent agreement between experimental and theoretical results [39]. A small difference between the experimental and calculated vibrational modes was observed. This difference might have been due to the intermolecular hydrogen bonding formation. Furthermore, the experimental results belong to the solid phase while and theoretical calculations belong to the isolated gaseous phase.Table 11
Correlation of calculated and experimental1H NMR,13C NMR, and IR of the compounds.
Compounds
B3LYP/3-21G
B3LYP/6-311+G∗∗
HF/3-21G
HF/6-311+G∗∗
5a
HNMR
0.9975
0.9999
0.9991
0.9974
5b
0.9986
0.9999
0.9985
0.9997
5c
0.9996
0.9995
0.9990
0.9998
5a
CNMR
0.9977
0.9995
0.9992
0.9975
5b
0.9983
0.9999
0.9990
0.9998
5c
0.9986
0.9998
0.9998
0.9999
5a
IR
0.9953
0.9995
0.9995
0.9978
5b
0.9986
0.9999
0.9988
0.9990
5c
0.9970
0.9997
0.9983
0.9991


## 3.2.3. Electronic Properties

Quantum chemical methods are important for obtaining information about molecular structure and electrochemical behavior. A frontier molecular orbital (FMO) analysis was performed for the compounds using the B3LYP/6-311+G(d) level [38]. FMO results such as EHOMO, ELUMO, and the HOMO-LUMO energy gap (∆E) of the title compounds are summarized in Table 7. The energy of the LUMO, HOMO, and their energy gaps reflected the chemical reactivity of the molecule [43]. In addition, the HOMO could act as an electron donor and the LUMO as an electron acceptor. A higher HOMO energy (EHOMO) for the molecule indicated a higher electron-donating ability to an appropriate acceptor molecule with a low-energy empty molecular orbital [44]. As shown in Figure 1 the HOMO energy of the compound 5c had the highest value (−0.29 eV). A large energy gap implied high stability for the molecule. The calculated values of the HOMO-LUMO energy gap (∆E) for the structures 5a, 5b, and 5c were 0.07, 0.08, and 0.06 eV, respectively. DOS plots [45] also demonstrated the calculated energy gaps (∆E) for the compounds 5a, 5b, and 5c (see Figure 2). It is obvious that the energy gap of the compound 5b was the highest (0.08 eV); therefore, it was less reactive than the other structures, whereas the energy gap of the compound 5c was the lowest (0.06 eV), which indicates that it was the most reactive. As presented in Figure 2, charge transfer could take place within the three molecules.Figure 2
Molecular electrostatic potential (MEP) maps of the title compounds calculated using the B3LYP/6-311+G(d) level.
(a)
(b)
(c)The electronic properties such as ionization potential, electron affinity, global hardness, electronic chemical potential, and electrophilicity are calculated in Table12. The first ionization potential (I) and electron affinity (A) could be expressed through HOMO and LUMO orbital energies by connecting it with Hartree–Fock SCF theory and invoking Koopmans' theorem [46] as I = −EHOMO and A = −ELUMO. The chemical hardness (η = I−A/2) is an important property that measures the molecular stability and reactivity [47]. A hard molecule has a large energy gap (∆E) and a soft molecule has a small energy gap (∆E) [48]. The chemical hardness (η) values of the compounds 5a, 5b, and 5c were 0.170, 0.176, and 0.175 eV, respectively. Compound 5b had the highest chemical hardness (η = 0.176 eV); therefore, it was a hard molecule with less reactivity and a high energy gap (∆E = 0.08 eV). The electronic chemical potential (µ = −(I + A)/2) is a form of the potential energy that can be absorbed or released during a chemical reaction and that may also change during a phase transition [49]. The electronic chemical potential of 5c had the most negative value (−0.26 eV). The electrophilicity (ω) measures the stabilization in energy when the system acquires an additional electronic charge from the environment. The electrophilicity index (ω = µ2/2η) contains information about both electron transfer (chemical potential) and stability (hardness) and is a better descriptor of global chemical reactivity [50]. The higher value of electrophilicity index shows the high capacity of the molecule to accept electrons. The electrophilicity index for the compounds 5a, 5b, and 5c was 0.0040, 0.0046, and 0.0059 eV, respectively. The compound 5c had the highest electrophilicity index; therefore, it had a high capacity for accepting electrons. The dipole moment (µD) is a good measure of the asymmetric nature of a molecule. The size of the dipole moment depends on the composition and dimensionality of the 3D structures. As shown in Table 12, all structures had a high value of dipole moment and point group of C1, which reflected no symmetry in the structures. The dipole moment for the compound 5b (B3LYP/6-311+G(d) = 6.172 Debye) was higher than that for the compounds 5a and 5c (4.988 and 4.396 Debye, respectively).The high value for 5c was due to its asymmetric character.Table 12
Absolute energy (a.u), dipole moment (μ, Debye), frontier orbital energies (HOMO and LUMO, eV), hardness (η, eV), chemical potential (μ, eV), and electrophilicity (ω, eV) of 5a, 5b, and 5c molecules.
E
HOMO
E
LUMO
I
A
µ
η
ω
µ
D
Point group
5a
−0.27
−0.20
0.27
0.20
−0.235
0.170
0.0040
4.988
C1
5b
−0.27
−0.19
0.27
0.19
−0.230
0.176
0.0046
6.172
C1
5c
−0.29
−0.23
0.29
0.23
−0.260
0.175
0.0059
4.396
C1


## 3.2.4. Thermodynamic Analysis

The total energy of a molecule consists of the sum of translational, rotational, vibrational, and electronic energies. The statistical thermochemical analysis of title compounds is carried out considering the molecule to be at room temperature of 25°C and 1 atmospheric pressure. The thermodynamic parameters such as zero-point vibrational energy, rotational constant, heat capacity (C), and the entropy (S) of the title compound by B3LYP/6-311+G(d) level are listed in Table13. According to Table 13, the calculated values for compound 5a and 5b are larger than compound 5c; therefore, compounds 5a and 5b have maximum stability compared to compound 5c due to formation of intramolecular hydrogen bonding.Table 13
Thermodynamic parameters of the5a, 5b, and 5c molecules using the B3LYP/6-311+G(d) level.
5a
5b
5c
Zero-point correctiona
0.439579
0.394413
0.405306
Thermal correction to energyb
0.468575
0.422073
0.431620
Thermal correction to enthalpyc
0.469519
0.423017
0.432564
Thermal correction to Gibbs free energyd
0.377501
0.333551
0.346912
Sum of electronic and zero-point energiese
−1522.507825
−1864.121732
−1409.523823
Sum of electronic and thermal energiesf
−1522.478830
−1864.094072
−1409.497509
Sum of electronic and thermal enthalpiesg
−1522.477886
−1864.093128
−1409.496565
Sum of electronic and thermal free energiesh
−1522.569904
−1864.182594
−1409.582218
E (Thermal)i
294.035
264.855
270.846
CVj
109.323
104.085
100.028
Sk
193.668
188.297
180.271
a-hHartree/particle; iKCal/Mol; j,kCal/Mol-Kelvin.


## 3.2.5. Molecular Electrostatic Potential (MEP)

The molecular electrostatic potential (MEP) was calculated by the B3LYP/6-311+G (d) level. The MEP is related to the electronic density and is a very useful descriptor in understanding sites for electrophilic attack and nucleophilic reactions as well as hydrogen bonding interactions [45]. The negative regions (red color) of the MEP are related to electrophilic reactivity, and the positive (blue color) region is related to nucleophilic reactivity, as shown in Figure 2.Molecular electrostatic potential (MEP) surface aims at locating the positive and negative charged electrostatic potential in the molecule. In each MEP surface, there is a color scale which indicates the negative and positive value. The red color is a sign for the negative extreme, and the blue color represents the positive extreme. The red color with a negative sign indicates the minimum electrostatic potential (which means it is bound loosely or has excess electrons), and it acts as electrophilic attack. The blue color also indicates the maximum of electrostatic potential, and it acts in the opposite manner.Starting from the above note, if we plot all MEP surfaces with all isosurface values, we see only the top surface. It is observed from the MEP map in Figure2 that the nitrogen-bonded oxygen atoms in the NO2 group and the oxygen atoms in the carbonyl groups (C=O) of the rings are negative regions in all compounds because in the resonance form of the nitro group, the oxygen atoms have a negative charge and the nitrogen atom has a positive charge, and in the resonance form of the carbonyl groups, the oxygen atoms have a negative charge and the carbon atom has a positive charge. Thus, oxygen atoms are sites for electrophilic activity. The nitrogen atoms in the ring, which are attached to carbonyl lethal electron groups, are also positively charged; therefore, nitrogen atoms are sites for nucleophilic attraction. As such, these sites provide information about the regions where the compounds can have strong intermolecular interactions.


## 4. Conclusion

In the present study, the three-component reaction between 3-nitrophthalic anhydride, hydrazine monohydrate, dimedone, and aromatic aldehydes in the presence of a novel catalytic amount of ZrO(NO3)2.2H2O to produce 1H-indazolo[1,2-b]phthalazine-1,6,11(13H)-trione derivatives was reported. The reported method offers a mild and efficient procedure for the preparation of these compounds. These compounds of the products were confirmed by IR, 1H NMR, 13C NMR, mass spectra, and elemental analyses. The IR spectra data and 1H NMR and 13C NMR chemical shift computations of the 1H-indazolo[1,2-b] phthalazine-1,6,11(13H)-trione derivatives in the ground state were calculated. There was an excellent agreement between experimental and theoretical results. Frontier molecular orbitals (FMOs), total density of states (DOS), and molecular electrostatic potential (MEP) of the title compounds were investigated through theoretical calculations.



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