Bhawani Dutt Joshi / BIBECHANA 14 (2017) 86-97 : RCOST p.86 (Online Publication: Dec., 2016) BIBECHANA A Multidisciplinary Journal of Science, Technology and Mathematics ISSN 2091-0762 (Print), 2382-5340 (0nline) Journal homepage: http://nepjol.info/index.php/BIBECHANA Publisher: Research Council of Science and Technology, Biratnagar, Nepal NBO, chemical reactivity, thermodynamic properties and hyperpolarizability analysis of aristolochic acid II Bhawani Datt Joshi Department of Physics, Tribhuvan University, Siddhanath Sc. Campus, Mahendranagar, Nepal * Email bdjoshi_007@yahoo.com, pbdjoshi@gmail.com Article history: Received 3 September, 2016; Accepted 8 October, 2016 DOI: http://dx.doi.org/10.3126/bibechana.v14i0.15892 This work is licensed under the Creative Commons CC BY-NC License. https://creativecommons.org/licenses/by-nc/4.0/ Abstract Alkaloids are a group of naturally occurring chemical compounds and show immense potential of medicinal uses in traditional systems. In this work, a computational study on an alkaloid aristolochc acidid II (AA II) is presented using density functional theory, B3LYP functional employing 6-311G (d,p) basis set. Natural bond orbital analysis has been carried out to investigate the various conjugative and hyperconjugative interactions within the molecule and their second-order stabilisation energy (E(2)). The local nucleophilic reactivity descriptors such as Fukui functions (π‘“π‘˜ +, π‘“π‘˜ βˆ’), local softness (π‘ π‘˜ +, π‘ π‘˜ βˆ’) and electrophilicity indices (Ο‰π‘˜, + , Ο‰π‘˜ βˆ’) analyses have been carried out to determine the reactive sites within the molecule. The non-linear optical properties have been calculated using the same basis set. The calculated value of the first order hyperpolarisability (Ξ²0), suggests that the investigated molecule is an attractive object in future for non-linear optical properties. Keywords: AA II; DFT; NBO; chemical reactivity; hyperpolarizability. . 1. Introduction Majority of drugs in use today are natural products, natural product mimics or semi synthetic derivatives. Therefore in recent times, focus on plant research has increased all over the world and large body of evidence has been collected to show immense potential of medicinal plants used in various traditional systems. Plants are sources of natural antioxidants, and some of the compounds have significant antioxidative properties and health benefits. Aristolochic acids (AAs) which mainly include aristolochic acid I (AA I), aristolochic acid II (AA II) and aristolochic acid III (AA III) are normally present in Aristolochia and Asarum of Aristolochiaceae [1]. In oriental medicine the fruit of Aristolochia is given for cough and dyspnea. Their roots have biological functions including treatment of stomach-ache, http://nepjol.info/index.php/BIBECHANA mailto:bdjoshi_007@yahoo.com mailto:pbdjoshi@gmail.com http://dx.doi.org/10.3126/bibechana.v14i0.15 https://creativecommons.org/licenses/by-nc/4.0/ https://creativecommons.org/licenses/by-nc/4.0/ https://en.wikipedia.org/wiki/Natural_product https://en.wikipedia.org/wiki/Chemical_compound https://creativecommons.org/licenses/by-nc/4.0/ Bhawani Dutt Joshi / BIBECHANA 14 (2017) 86-97 : RCOST p.87 (Online Publication: Dec., 2016) toothache, eczema, hypertension relief, rheumatism relief, leukocyte enhancement, edema therapy, poisonous snake bites as well as analgesic and diuretic effects [2,3]. In the family of natural products, the alkaloids occupy a unique place and provide challenging problems for structural elucidation, synthetic and biosynthetic studies. Because of their very complex structure and unique places the determination of their constitution and the discovery of the methods producing them synthetically offer attractive problems to the chemist and though a great deal has been accomplished much still remains to be done in this field. Vibrational spectroscopy is a very valuable method for studying the dynamical behavior and to gain insight into the electronic structures of alkaloids at microscopic level [4]. However, both the Raman and IR are the best traditional methods for the vibrational analysis and particularly for the non-destructive characterization of the substances [5], but in the recent years there has been interest in the application of ab initio calculations to the alkaloids as it provide the additional vibrational spectroscopic data [3-6]. In the present work the chemical reactivity descriptors, thermodynamic properties and the natural bond orbitals (NBOs) analysis of an alkaloid aristolochic acid II have been communicated. The aim of this study was to determine the stabilization energy when the system acquires an additional charge from the environment and the direction of the charge transfer. Similarly, the variation of the thermodynamic properties with the temperature and, hybridization, conjugation and charge transfer in the polyatomic wave functions theoretically using ab initio HF and density functional theory (DFT) [7]. We had presented some spectroscopic analysis on the title molecule in our previous work [8]. The crystal structure and optimized structure of AA II are as shown in the Figure 1a and b. Fig. 1(a): Crystal structure of AA II. Fig. 1(b): Optimized structure of AA II. 2. Materials and Methods 2.1 Computational Details Geometry optimization has been performed as the first task of the computational work. The geometric parameters available from the PubChem data base [9] have been used as the basis for the optimization. These optimized parameters were computed by ab intio HF and the DFT using Gaussian 09 [10] program package employing B3LYP/6-311G (d,p) basis set. The DFT calculations were mainly carried out in the Bhawani Dutt Joshi / BIBECHANA 14 (2017) 86-97 : RCOST p.88 (Online Publication: Dec., 2016) frame-work of the Becke–Lee-Yang-Parr [B3LYP] functional, in which the exchange functional is a local spin density exchange with Becke gradient correction [11] and the correlation functional is that of Lee, Yang and Parr with both local and nonlocal terms [12,13]. 3. Results and Discussion 3.1 Natural bond Orbital (NBO) Analysis NBO analysis is one of the efficient methods for studying hybridization, conjugative interactions, covalence effects and charge transfer in polyatomic wave functions [4]. In the present work, utilizing the second-order micro-disturbance theory analysis, we have reported some of the electron donor orbital, acceptor orbital and the interacting stabilization energy. Higher the value of stabilization energy E(2) more is the intensity of the interaction between electron donors and electron acceptors, i.e. the more donating tendency from electron donors to electron acceptors. The hyperconjugative interaction energy was deduced from the second-order perturbation approach [14-16]. 𝐸(2) = βˆ’ π‘›πœŽβŸ¨πœŽ|𝐹|𝜎⟩ 2 πΈπœŽβˆ—βˆ’πΈπœŽ = βˆ’π‘›πœŽ | 𝐹𝑖𝑗 2 βˆ†πΈ | where ⟨𝜎|𝐹|𝜎⟩2, or 𝐹𝑖𝑗 2 is the Fock matrix element between i and j NBO orbital, 𝐸𝜎 and πΈπœŽβˆ— are the energies of 𝜎 and 𝜎* NBO’s, and π‘›πœŽ is the population of the donor orbital. The larger the E(2) value the more intensive is interaction, the greater the extent of conjugation of the whole system [16]. Hyperconjugation may be given as a stabilizing effect that arises from overlap between an occupied orbital with another neighboring electron deficient orbital when these orbitals are properly oriented. The most important interaction between β€˜β€˜filled’’ (donor) Lewis type NBOs and β€˜β€˜empty’’ (acceptor) non- Lewis NBOs are reported in Table 1. There occurs a strong intramolecular hyperconjugative interactions of πœ‹ electrons of the rings R2 and R3 from C11 - C15, C13 - C17, C10 - C12 and C14 - C16 to the πœ‹*(C8 - C9) bond of which increases the electron density 0.474e leading to the stabilization. This enhanced the further conjugation of the πœ‹*(C8 - C9) NBO mainly with πœ‹*(C10 – C12) and πœ‹*(C14 – C16) resulting to the high stabilization of 236.16 and 134.76 kcal/mol, respectively. Also, there occur some another hypercinjugative interactions of πœ‹ electrons from C13 – C17 β†’ πœ‹*(C11 – C15) with ED 0.40135e, C14 – C16 β†’ πœ‹*(O5 – N7) with ED 0.60349e, C18 – C21 β†’ πœ‹*(C10 – C12) with ED 0.44633e and C20 – C22 β†’ πœ‹*(C18 – C21) with ED 0.27488e leading to the stabilization energies 21.06, 16.48, 18.62 and 18.77 kcal/mol, respectively. Similarly, the enhanced NBOs πœ‹*(C11 – C15) conjugate with πœ‹*(C13 – C17) in ring R2 which further conjugates with πœ‹*(O4 – C23) of the carboxyl group leading to the corresponding stabilization energies 276.35 and 112.33 kcal/mol, respectively. The electron donation related to the resonance in the molecule is from LP(2) O3 to antibonding acceptor πœ‹*(O4 – C23) of carboxyl group (41.00 kcal/mol) and from LP(2) O6 to πœ‹*(O5 – N7) of NO2 group (168.74 kcal/mol). The interactions are mainly confined between the rings and the lone pair electron groups. These charge transfer in the system lead to the structure activity of the molecule. A comparison of the NBO and Mullikan charges is given in the Table 2. Bhawani Dutt Joshi / BIBECHANA 14 (2017) 86-97 : RCOST p.89 (Online Publication: Dec., 2016) Table 1: Second order perturbation theory analysis of Fock matrix in NBO basis for AA II. Donor NBIO(i) ED (i)/e Acceptor NBO(j) ED (j)/e E(2)a (kcl/mol) [E(j) –E(i)]b F(i,j)c LP(2)O1 1.85366 πœ‹* (C11 – C15) 0.40135 23.22 0.35 0.087 LP(2)O2 1.85651 πœ‹* (C11 – C15) 0.40135 23.59 0.35 0.086 LP(2)O3 1.82127 πœ‹* (O4 – C23) 0.24140 41.00 0.36 0.111 LP(2)O4 1.83912 𝜎*(O3 - C23) 0.09844 32.38 0.61 0.128 𝜎*(C13 - C23) 0.06750 18.44 0.68 0.102 LP(2)O5 1.89423 𝜎*(O6 – N7) 0.07135 19.19 0.71 0.105 𝜎*(N7 – C14) 0.10978 14.26 0.55 0.079 LP(2)O6 1.89355 𝜎*(O6 – N7) 0.07135 18.60 0.73 0.105 πœ‹*(O5 – N7) 0.60349 168.74 0.15 0.144 𝜎(C11 - C15) 1.97681 𝜎*(C8 - C11) 0.02801 6.07 1.27 0.079 𝜎(C14 - C16) 1.97140 𝜎*(C9 - C14) 0.03163 5.49 1.24 0.074 𝜎(C16 – H24) 1.97338 𝜎*(C9 - C14) 0.03163 6.26 1.02 0.072 πœ‹(C8 - C9) 1.58253 𝜎*(O1 - C11) 0.02832 6.00 0.99 0.069 πœ‹(C10 – C12) 1.56437 πœ‹* (C8 – C9) 0.47400 16.91 0.26 0.060 πœ‹* (C14 – C16) 0.22748 16.78 0.28 0.065 πœ‹* (C18 – C21) 0.27488 17.31 0.28 0.065 πœ‹* (C20 – C22) 0.27301 17.26 0.28 0.065 πœ‹(C11 – C15) 1.63802 πœ‹* (C8 – C9) 0.47400 17.68 0.30 0.067 πœ‹* (C13 – C17) 0.36737 20.25 0.31 0.071 πœ‹(C13 – C17) 1.68334 πœ‹* (O4 – C23) 0.24140 17.24 0.30 0.065 πœ‹* (C8 – C9) 0.47400 18.48 0.28 0.067 πœ‹* (C11 – C15) 0.40135 21.06 0.27 0.069 πœ‹(C14 – C16) 1.77190 πœ‹* (O5 – N7) 0.60349 16.48 0.17 0.052 πœ‹* (C8 – C9) 0.47400 13.55 0.30 0.061 πœ‹* (C10 – C12) 0.44633 12.99 0.31 0.060 πœ‹(C18 – C21) 1.68756 πœ‹* (C10 – C12) 0.44633 18.62 0.28 0.067 πœ‹* (C20 – C22) 0.27301 18.46 0.29 0.066 πœ‹(C20 – C22) 1.69812 πœ‹* (C10 – C12) 0.44633 18.47 0.29 0.067 πœ‹* (C18 – C21) 0.27488 18.77 0.29 0.067 πœ‹*(C8 - C9) 0.47400 πœ‹* (C10 – C12) 0.44633 16.36 0.28 0.061 πœ‹* (C11 – C15) 0.40135 23.40 0.26 0.070 πœ‹* (C13 – C17) 0.36737 18.20 0.28 0.064 πœ‹*(C10 – C12) 0.44633 236.16 0.01 0.074 πœ‹*(C14 – C16) 0.22748 134.76 0.02 0.072 πœ‹*(C11 – C15) 0.40135 πœ‹*(C13 – C17) 0.36737 276.35 0.01 0.084 πœ‹*(C13 – C17) 0.36737 πœ‹*(O4 – C23) 0.24140 112.33 0.01 0.063 a E(2) means energy of hyper conjugative interaction (stabilization energy). b Energy difference between donor (i) and acceptor ( j) NBO orbitals. c F(i,j) is the Fock matrix element between i and j NBO orbitals. Bhawani Dutt Joshi / BIBECHANA 14 (2017) 86-97 : RCOST p.90 (Online Publication: Dec., 2016) Table 2: Comparison between NBO and Mullikan charges (esu) of AA II. Atom No NBO charges Mulliken charges Atom No NBO charges Mulliken charges 1 O -0.541 -0.364 2 O -0.523 -0.339 3 O -0.688 -0.064 14 C 0.108 0.067 4 O -0.595 -0.333 15 C 0.269 0.189 5 O -0.367 -0.245 16 C -0.147 0.172 6 O -0.384 -0.271 17 C -0.201 0.122 7 N 0.522 0.156 18 C -0.180 0.080 8 C -0.061 -0.045 19 C 0.318 0.429 9 C -0.032 0.103 20 C -0.165 0.032 10 C -0.026 0.016 21 C -0.179 0.014 11 C 0.298 0.078 22 C -0.189 0.027 12 C -0.054 -0.084 23 C 0.820 0.328 13 C -0.124 -0.067 Fig. 2: Correlation between NBO and Mulliken charges. 3.2 Chemical Reactivity 3.2 (a) Global Reactivity Descriptors Electrophilicity and hardness are two important molecular properties, which are useful for interpreting and understanding the stability and reactivity of molecular system [17]. According to the Hohenberg and Kohn (HK), theorems [7], the energy of the basic state of an electronic system is a functional of electron density. On the basis of Koopman’s theorem [17], global reactivity descriptors: electronegativity (Ο‡), Bhawani Dutt Joshi / BIBECHANA 14 (2017) 86-97 : RCOST p.91 (Online Publication: Dec., 2016) chemical potential (ΞΌ), global hardness (Ξ·), global softness (S) and global electrophilicity index (Ο‰) were calculated using the energies of frontier molecular orbitals EHOMO, ELUMO and given by relations (1) - (5) [18-20]. Ο‡ = βˆ’ 1 2 [ 𝐸𝐻𝑂𝑀𝑂 + πΈπΏπ‘ˆπ‘€π‘‚] (1) ΞΌ = βˆ’ Ο‡ = 1 2 [ 𝐸𝐻𝑂𝑀𝑂 + πΈπΏπ‘ˆπ‘€π‘‚] (2) Ξ· = 1 2 [πΈπΏπ‘ˆπ‘€π‘‚ βˆ’ 𝐸𝐻𝑂𝑀𝑂] (3) S = 1 2 Ξ· (4) Ο‰ = ΞΌ2 2Ξ· (5) βˆ†π‘π‘šπ‘Žπ‘₯ = βˆ’ ΞΌ Ξ· (6) According to Parr et al., electrophilicity index (Ο‰), a positive and finite quantity, is a global reactivity index similar to the chemical hardness (a measure of the resistance of a system to transfer charge), and chemical potential. This new reactivity index measures the stabilization in energy when the system acquires an additional electronic charge (βˆ†N) from the environment up to saturation. The direction of the charge transfer is completely determined by the electronic chemical potential of the molecule because an electrophile is a chemical species capable of accepting electrons from the environments. Therefore its energy must decrease upon accepting electronic charge and its electronic chemical potential must be negative. The energies of frontier energy levels (EHOMO, ELUMO), energy band gap (Ξ”E), electronegativity (Ο‡) that representing the tendency of atoms or molecules to attract electrons; chemical potential (ΞΌ), global hardness (Ξ·), global softness (S), global electrophilicity index (Ο‰), and additional electronic charge (Ξ”N) for AA II are listed in the Table 3. The calculated high value of electrofilicity index (Ο‰) shows that the molecule behaves as a strong electrophile. Table 3: Calculated EHOMO, ELUMO, energy band gap (Ξ”E), electronegativity (Ο‡), chemical potential (ΞΌ), global hardness (Ξ·), global softness (s), global electrophilicity index (Ο‰) and additional electronic charge (Ξ”Nmax) (in eV) for AA II , using B3LYP/6-31G (d,p). EHOMO ELUMO βˆ†E ΞΌ Ξ· S Ο‰ βˆ†Nmax -6.113904 - 2.396963 3.716941 -4.267835 1.858471 0.269038 4.900378 2.296299 3.2 (b) Local Reactivity Descriptors Using Hirshfeld population analysis of neutral, cation and anion state of molecule, Fukui functions (π‘“π‘˜ +, π‘“π‘˜ βˆ’, π‘“π‘˜ 0) [20, 21], are calculated at same calculation method B3LYP/6-31 G (d,p) using following relations (7-9): π‘“π‘˜ + = [q(N+1) – q(N)] for nucleophilic attack (7) π‘“π‘˜ βˆ’ = [q(N) – q(N-1)] for electrophilic attack (8) π‘“π‘˜ 0 = Β½[q(N+1) –q(N-1)] for radical attack (9) where N, N-1 and N+1 are total electrons present in neutral, cation and anion state of molecule, respectively. Local softnesses (π‘ π‘˜ +, π‘ π‘˜ βˆ’, π‘ π‘˜ 0) and local electrophilicity indices (Ο‰π‘˜ +, Ο‰π‘˜ βˆ’, Ο‰π‘˜ 0), also used to describe the reactivity of atoms in molecule, are calculated using the following equations (10) and (11): π‘ π‘˜ + = Sπ‘“π‘˜ +, π‘ π‘˜ βˆ’ = Sπ‘“π‘˜ βˆ’, π‘ π‘˜ 0 = Sπ‘“π‘˜ 0 (10) Ο‰π‘˜ + = Ο‰π‘“π‘˜ +, Ο‰π‘˜ βˆ’ = Ο‰π‘“π‘˜ βˆ’, Ο‰π‘˜ 0 = Ο‰π‘“π‘˜ 0 (11) where +, βˆ’, 0 signs show nucleophilic, electrophilic and radical attack, respectively. Bhawani Dutt Joshi / BIBECHANA 14 (2017) 86-97 : RCOST p.92 (Online Publication: Dec., 2016) Table 4: Hirshfelf atomic charges (in esu), Fukui functions (π‘“π‘˜ +, π‘“π‘˜ βˆ’); Local softness (π‘ π‘˜ +, π‘ π‘˜ βˆ’); and local electrophilicity indices (Ο‰π‘˜ +, Ο‰π‘˜ βˆ’); in eV for atomic sites of AA II, using Hirshfeld population analysis at B3LYP/6-31G (d,p) level. Atom no. Hirshfeld atomic charges Fukui functions Local softness Local electrophilicity indices qN qN+1 qN-1 π‘“π‘˜ + π‘“π‘˜ βˆ’ π‘ π‘˜ + π‘ π‘˜ βˆ’ Ο‰π‘˜ + Ο‰π‘˜ βˆ’ 1 O -0.137056 -0.082403 -0.154852 0.05465 0.01779 0.0147 0.0048 0.2678 0.0872 2 O -0.154125 -0.084260 -0.180316 0.06986 0.02619 0.0188 0.0070 0.3424 0.1283 3 O 0.014549 0.054444 -0.024939 0.03989 0.03948 0.0107 0.0106 0.1955 0.1935 4 O -0.285351 -0.247806 -0.310391 0.03754 0.02504 0.0101 0.0067 0.1840 0.1227 5 O -0.188738 -0.146976 -0.272371 0.04176 0.08363 0.0112 0.0225 0.2046 0.4098 6 O -0.197151 -0.168658 -0.278778 0.02849 0.08162 0.0077 0.0220 0.1396 0.4000 7 N 0.235014 0.239420 0.193255 0.00440 0.04175 0.0012 0.0112 0.0216 0.2046 8 C -0.004447 0.007625 -0.015539 0.01207 0.01109 0.0032 0.0030 0.0592 0.0544 9 C -0.001680 0.024782 -0.005068 0.02646 0.00338 0.0071 0.0009 0.1297 0.0166 10 C 0.002314 0.017857 -0.029614 0.01554 0.03192 0.0042 0.0086 0.0762 0.1565 11 C 0.067660 0.115375 0.035707 0.04771 0.03195 0.0128 0.0086 0.2338 0.1566 12 C -0.003587 0.019794 -0.024961 0.02338 0.02137 0.0063 0.0058 0.1146 0.1047 13 C -0.019426 0.041108 -0.050936 0.06053 0.03151 0.0163 0.0085 0.2966 0.1544 14 C 0.037710 0.073211 -0.007816 0.03550 0.04552 0.0096 0.0122 0.1740 0.2231 15 C 0.060119 0.117917 0.026964 0.05779 0.03315 0.0155 0.0089 0.2832 0.1625 16 C 0.032000 0.105890 -0.068122 0.07389 0.10012 0.0199 0.0269 0.3621 0.4906 17 C 0.027244 0.077415 -0.035180 0.05017 0.06242 0.0135 0.0168 0.2459 0.3059 18 C 0.001778 0.029849 -0.037889 0.02807 0.03966 0.0076 0.0107 0.1376 0.1944 19 C 0.252942 0.342971 0.204487 0.09002 0.04845 0.0242 0.0130 0.4412 0.2374 20 C 0.019442 0.075432 -0.037948 0.05599 0.05739 0.0151 0.0154 0.2744 0.2812 21 C 0.016208 0.092320 -0.075592 0.07611 0.0918 0.0205 0.0247 0.3730 0.4499 22 C 0.014773 0.073505 -0.047009 0.05873 0.06178 0.0158 0.0166 0.2878 0.3028 23 C 0.209756 0.221156 0.196862 0.0114 0.01289 0.0031 0.0035 0.0559 0.0632 Bhawani Dutt Joshi / BIBECHANA 14 (2017) 86-97 : RCOST p.93 (Online Publication: Dec., 2016) 3.3 Thermodynamic Properties Computation of thermodynamic properties of molecules is important for both thermochemistry and chemical equilibrium. Statistical thermodynamics with the two key ideas, Boltzmann distribution and the partition function leads to the derivation of the equations utilized for computing thermochemical data in Gaussian programs. The standard thermodynamic functions: heat capacity (𝐢𝑝,π‘š π‘œ ), entropy (π‘†π‘š π‘œ ) and enthalpy (π»π‘š π‘œ ) together with the total energy, zero point energy, rotational constants, dipole moment were obtained directly from the output of DFT calculation employing 6-311G (d,p) basis set and listed in Tables 5a and b. As observed from the table, the values of 𝐢𝑝,π‘š π‘œ , π‘†π‘š π‘œ and π»π‘š π‘œ increase with the increase of temperature from 100 K to 900 K which is attributed to the enhancement of molecular vibration while the temperature increases. The correlation between temperature and these thermodynamic properties are given in Fig. 3. Table 5(a): Theoretically calculated thermodynamic properties at different temperatures using 6-311G (d,p) basis set. Temperature (K) Enthalpy (kJ/mol) Specific heat (J/mol-K) Entropy (J/mol-K) 100 600.0808 109.4366 349.5692 200 615.3002 195.5655 457.4258 300 639.3226 284.6956 556.9808 400 671.9977 366.7323 652.7906 500 712.2009 434.9499 744.0818 600 758.5195 489.2314 829.8888 700 809.6702 532.1265 909.9358 800 864.6581 566.3607 984.4193 900 922.7266 594.0700 1053.757 The correlation equations are as follows: π»π‘š π‘œ = 583.65002 + 0.10323 T + 3.07745 x10-4T2 (R2 = 0.99952) (12) 𝐢𝑝,π‘š π‘œ = -2.98254 + 1.12581 T – 5.14425 x10-4 T2 (R2 = 0.99957) (13) π‘†π‘š π‘œ = 238.13449 + 1.14381 – 2.63687 x10-4 T2 (R2 = 0.99999) (14) These thermodynamic relations would provide useful information for the study of thermodynamic energies and estimate directions of chemical reactions according to the second law of thermodynamics in thermochemical field. Further, these equations could be utilized in predicting the Gibbs free energy, which would help in the judgment of spontaneity of the reactions. [22]. 3.4 Nonlinear Optical properties (NLO) Nonlinear optics (NLO) deals with the interactions of applied magnetic fields in various materials to generate new magnetic field altered in phase, frequency, amplitude or other physical properties [23]. Some organic substances with πœ‹ electronic system exhibit the largest known nonlinear coefficients and show promise for thin fabrication, allowing the enormous function and cost integrated electronic circuitry. Bhawani Dutt Joshi / BIBECHANA 14 (2017) 86-97 : RCOST p.94 (Online Publication: Dec., 2016) Fig. 3: Correlation between the thermodynamic parameters with the temperature. Table 5(b): Theoretically calculated thermodynamic properties at room temperature using 6-311G (d,p) basis set. Thermodynamic properties DFT (B3LYP) HF Total energy (eV) -30513.38103 -30336.08362 Zero-point energy (kJ/mol) 142.05075 151.82499 Rotational constants (GHz) 0.33647 0.33647 0.27097 0.27097 0.15671 0.15671 Dipole moment (D) 6.2937 6.8561 Entropy (J/mol-K) 555.17088 498.49426 Enthalpy (kJ/mol) 638.80014 673.31022 Specific heat (J/mol-K) 283.07796 256.55586 First hyperpolarizability is a third rank tensor that can be described by a 3Γ—3Γ—3 matrix. The 27 components of the 3D-matrix can be reduced to 10 components due to the Kleinmann symmetry [21]. It can be given in the lower tetrahedral format. It is obvious that the lower part of the 3Γ—3Γ—3 matrix is a tetrahedral. The components of Ξ²0 are defined as the coefficients in the Taylor series expansion of the Bhawani Dutt Joshi / BIBECHANA 14 (2017) 86-97 : RCOST p.95 (Online Publication: Dec., 2016) energy in the external electric field. When the external electric field is weak and homogeneous this expansion becomes: 𝐸 = 𝐸0 βˆ’ μ𝑖𝐹𝑖 βˆ’ 1 2 α𝑖𝑗𝐹𝑖𝐹𝑗 βˆ’ 1 6 Ξ²π‘–π‘—π‘˜πΉπ‘–πΉπ‘—πΉπ‘˜ … .. where 𝐸0 is the energy of the unperturbed molecules, 𝐹𝑖 is the field at the origin and μ𝑖, α𝑖𝑗, Ξ²π‘–π‘—π‘˜ are the components of dipole moment, polarizability, and first hyperpolarizability respectively. The total dipole moment (ΞΌ0), the mean polarizability (|Ξ±0|), the anisotropy of the polarizability (βˆ†Ξ±) and the total first hyperpolarizability (Ξ²0) using x, y, z components are defined as [24]: πœ‡ = (πœ‡π‘₯ 2 + πœ‡π‘¦ 2 + πœ‡π‘§ 2) 1 2⁄ (15) |Ξ±0| = 1 3 (Ξ±π‘₯π‘₯ + α𝑦𝑦 + α𝑧𝑧) (16) βˆ†Ξ± = 2βˆ’1/2 [(Ξ±π‘₯π‘₯ βˆ’ α𝑦𝑦) 2 + (α𝑦𝑦 βˆ’ α𝑧𝑧) 2 + (α𝑧𝑧 βˆ’ Ξ±π‘₯π‘₯)2 + 6Ξ±π‘₯π‘₯ 2 ] 1/2 (17) Ξ²0 = ( Ξ²π‘₯ 2 + β𝑦 2 + Ξ²z 2) 1/2 (18) Where Ξ²π‘₯ = Ξ²π‘₯π‘₯π‘₯ + Ξ²π‘₯𝑦𝑦 + Ξ²π‘₯𝑧𝑧 β𝑦 = β𝑦𝑦𝑦 + Ξ²π‘₯π‘₯𝑦 + β𝑦𝑧𝑧 β𝑧 = β𝑧𝑧𝑧 + Ξ²π‘₯π‘₯𝑧 + β𝑦𝑦𝑧 Since the x, y, z components of |Ξ±0|, βˆ†Ξ± and Ξ²0 of Gaussian 09 output are reported in a atomic mass unit (a.u.), the calculated values have been converted into electrostatic unit (esu) (for |Ξ±0|: 1 a.u. = 0.1482 Γ— 10βˆ’24 esu; for Ξ²0: 1 a.u. = 0.086393 Γ— 10βˆ’31 esu) and listed in the Table 6. The high value of Ξ²0, one of the key factors in an NLO system, supports that the investigated molecule will show good NLO response. Table 6: Dipolemoment (Β΅ Debye), polarizability (Ξ± x10-24esu) and first order hyperpolarizability (Ξ²0 x10-31esu). Dipole moment Polarizability Hyperpolarizability DFT HF DFT HF DFT HF ΞΌπ‘₯ -5.2839 -5.2243 Ξ±π‘₯π‘₯ -119.1408 -118.3740 Ξ²π‘₯π‘₯π‘₯ 27.3548 31.7449 μ𝑦 4.0465 3.7945 α𝑦𝑦 -121.7131 -122.2665 β𝑦𝑦𝑦 53.8593 47.8559 μ𝑧 0.1350 0.2183 α𝑧𝑧 -136.8908 -138.6496 β𝑧𝑧𝑧 5.8486 6.4994 ΞΌ0 6.6567 6.4607 Ξ±π‘₯𝑦 10.6612 12.0501 Ξ²π‘₯𝑦𝑦 -71.5489 -71.1348 Ξ±π‘₯𝑧 -2.7854 -2.4720 Ξ²π‘₯π‘₯𝑦 37.2794 38.8391 α𝑦𝑧 0.7627 0.7135 Ξ²π‘₯π‘₯𝑧 -17.6840 -16.7678 |Ξ±0| -125.9149 -126.4300 Ξ²π‘₯𝑧𝑧 7.6975 8.5779 βˆ†Ξ± 207.6443 206.4903 β𝑦𝑧𝑧 16.6563 18.0840 30.7314 30.5606 β𝑦𝑦𝑧 8.8145 9.7722 Ξ²π‘₯𝑦𝑧 -9.5344 -10.3423 Ξ²0 9.8355 9.4355 4. Conclusion Computational study proves that NBO analysis and NLO properties of the investigated molecule are successfully predicted by the B3LYP/6-311G (d,p) method. The πœ‹ β†’ πœ‹* interactions are responsible for Bhawani Dutt Joshi / BIBECHANA 14 (2017) 86-97 : RCOST p.96 (Online Publication: Dec., 2016) the conjugation of respective πœ‹-bonds within aromatic rings, rings and C=O, NO2 groups, which stabilized the molecule with maximum energy ~ 21.06, 17.24 and 16.48 kcal/mol, respectively. The electron donation related to the resonance interaction in the molecule is mainly confined between the rings and the lone pair groups leading to the maximum energy 168.74 kcal/mol. The calculated high value of electrofilicity index (Ο‰) is in agreement that the molecule behaves as a global electrophile. The compound exhibits strong effective ICT due to the movement of the πœ‹-electron cloud from donor to acceptor and shows second-order nonlinearity. 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