Density functional theory study of structural and

Journal of Molecular Modeling (2017) 23:356 https://doi.org/10.1007/s00894-017-3522-6

ORIGINAL PAPER

Density functional theory study of structural and electronic properties of trans and cis structures of thiothixene as a nano-drug Akram Noori Tahneh 1 & Samaneh Bagheri Novir 1 & Ebrahim Balali 1 Received: 14 July 2017 / Accepted: 6 November 2017 # Springer-Verlag GmbH Germany, part of Springer Nature 2017

Abstract The geometrical structure, electronic and optical properties, electronic absorption spectra, vibrational frequencies, natural charge distribution, MEP analysis and thermodynamic properties of the trans and cis structures of the drug thiothixene were investigated using density functional theory (DFT) and time-dependent DFT (TDDFT) methods with the B3LYP hybrid functional and 6– 311 + G(d,p) basis set. The results of the calculations demonstrate that the cis structure of thiothixene has appropriate quantum properties that can act as an active medicine. The relative energies of trans and cis structures of thiothixene shows that the cis structure is more stable than the trans structure, with a small energy difference. TDDFT calculations show that the cis structure of thiothixene has the best absorption properties. The calculated NLO properties show that the NLO properties of the cis structure of thiothixene are higher than the trans structure, and the fact that the chemical hardness of the cis structure is lower than that of the trans structure that indicates that the reactivity and charge transfer of the cis isomer of thiothixene is higher than that of trans thiothixene. The molecular electrostatic potential (MEP) maps of both structures of thiothixene demonstrate that the oxygen atoms of the molecule are appropriate areas for electrophilic reactions. The vibrational frequencies of the two conformations of thiothixene demonstrate that both structures of thiothixene have almost similar modes of vibrations. The calculated thermodynamic parameters show that these quantities increase with enhancing temperature due to the enhancement of molecular vibrational intensities with temperature.

Keywords Thiothixene . Schizophrenia . DFT . TDDFT . Absorption spectra

Introduction Thiothixene, which has the IUPAC name of N,N-dimethyl-O- [3-(4-methyl-1-piperaziny1)pro-pylidene]thioxanthene-2-sulfonamide, and trades under the name Navane, is a low-dose antipsychotic drug that is categorized in the group of thioxanthene drugs [1, 2]. Medicines in the thioxanthene group are strong tricyclic psychotherapeutic drugs used in the treatment of schizophrenia, organic psychoses, idiopathic psychotic diseases, and other neuropsychiatric illnesses [3–5]. Thioxanthene medications can be used in other fields, as it had sedative,

* Samaneh Bagheri Novir [email protected]; [email protected] 1

Department of Pharmaceutical Chemistry, Faculty of Pharmaceutical Chemistry, Pharmaceutical Sciences Branch, Islamic Azad University, Tehran, Iran

antihistamine, antinausea, and antiemetic effects, and can be used as a general anesthetic [3, 4]. Thiothixene is used in the therapy of several psychoses, such as schizophrenia, schizoaffective disorder, delirium, mania, bipolar disorder, dementia with agitation and in behavioral disturbances. Thiothixene is used as hydrochloric thiothixene (HT), which can usually be taken orally as doses of 5– 15 mg, or injected intramuscularly as minor doses of 4– 8 mg every 8–12 h [6–9]. The chemical structure of thiothixene consists of a thioxanthene ring (Fig. 1). As shown in Fig. 1, a side chain is attached to the thioxanthene ring by a C = C double bond; the existence of this C = C double bond in the geometry structures of thiothixene means that there are two trans (E) and cis (Z) isomers of thiothixene, the cisisomer of which is the pharmacologically active compound while the trans-isomer is almost inactive. Investigation of thioxanthene derivatives shows that the cis-isomers of these drugs are usually more active

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Computational methods

Trans-Thiothixene

Cis-Thiothixene

Fig. 1 Molecular structure of trans- and cis-thiothixene

biologically than the trans-isomers [1, 4, 10, 11]. The possibility of trans(E)/cis(Z) isomerization around the C = C double bond in thiothixene can disturb its biological properties [12]. Molecular structural modifications that can change the biological activity of drugs can be a consequence of irradiation of biologically active molecules with ultraviolet–visible light [4, 12, 13]. Quantum chemical approaches can be a suitable method when considering and correlating the molecular geometries of drugs and their pharmacological activities. Several experimental and theoretical investigations on the molecular and spectroscopic properties of antidepressant and antipsychotic drugs have been carried out previously [14–18]. Thiothixene have been studied experimentally previously by numerous authors. Articles include: Separation and quantitation of cis- and trans-thiothixene in human plasma by high performance liquid chromatography by Bogbma [1], Improved high-performance liquid chromatographic method for the quantitation of cis-thiothixene in plasma samples using trans-thiothixene as internal standard by Narasimhachari et al. [10], Bupropion and thiothixene versus placebo and thiothixene in the treatment of depression in schizophrenia by Dufresne et al. [19], Thiothixene in the management of delirium: a case series by Leung et al. [7], Injectable long-term control-released in situ gels of hydrochloric thiothixene for the treatment of schizophrenia: preparation, in vitro and in vivo evaluation by Hongzhuo et al. [6]. But, thiothixene medication has not been studied by computational methods, until now. In this study, both trans and cis configurations of thiothixene were investigated with computational methods for evaluation of computed parameters of the trans and cis structures of thiothixene. Also, the description and correlation between the pharmacological activities of trans- and cis-isomers of thiothixene and their calculated quantum parameters, can be estimated by quantum chemical methods. The main objective of this study was to consider the molecular structure, thermodynamic parameters, nonlinear optical (NLO) properties (such as polarizability and hyperpolarizability, electronic absorption spectra and other molecular properties) using density functional theory (DFT) and time-dependent DFT (TDDFT) methods.

All quantum chemical calculations in this work were completed with the Gamess package [20]. The trans and cis geometries of thiothixene were optimized with DFT [21] using Becke’s three-parameter hybrid function (B3) and the LeeYang-Parr nonlocal correlation function (B3LYP) and 6– 311 + G(d,p) basis set [22–24]. The 6–311 + G(d,p) basis set was applied with the aim of achieving more exact results by applying a triple split valence basis set as well as the polarization functions [(d,p) or (**)], which adds p functions to hydrogen atoms, in addition to the d functions on heavy atom and diffuse function (+) which adds diffuse functions to the heavy atoms. Vibrational frequency calculations at the same level have been used on the optimized structures to confirm that the optimized structures reached to a stationary point with minimum energy and to estimate thermodynamic parameters and NLO properties such as polarizability and hyperpolarizability. Absorption spectra, excitation energies, maximum absorbances (λmax) and oscillator strengths ( f ) of two isomers of thiothixene were calculated with the linear response time-dependent DFT (LR-TDDFT) method at B3LYP/6–311 + G(d,p) level of theory for the lowest 30 singlet–singlet transitions based on optimized ground state structures. The solving of the Casida equations was used to calculate the excitation energies and oscillator strengths [25–28]. The extinction coefficient was obtained from the computed oscillator strengths with a proper full width at half maximum, Δ1/2 as: "
2 2 2 # ω −ω fI 8 exp 2:773 I 2 εðωÞ ¼ 2:174  10 ∑ ð1Þ Δ Δ1=2 I 1=2 where ωI and fI are the excitation frequencies and the oscillator strengths, respectively. In TDDFT calculations, the relaxed one-particle difference density matrix allowed calculation of the first-order parameters [25, 26, 29, 30]. Natural bond orbital (NBO) calculations of two structures of thiothixene, and also the reactive sites of this compound, as estimated by their molecular electrostatic potential (MEP), were calculated by the B3LYP/6–311 + G(d,p) method. All calculations were performed in both the gas and solvent phase. To consider each solvent molecule as a separate molecule would mean that the computational cost of modeling a solvent-mediated chemical reaction would grow excessively high. Modeling the solvent as a polarizable continuum, rather than distinct molecules, makes ab initio computation practicable [25, 26, 31]. Because of its suitable treatment of the long-range electrostatic effects of solvents (polarization effects), the polarized continuum model (PCM) [31, 32] is often used. In the PCM model, the solvent is defined by a structureless dielectric medium, and the solute is limited in a cavity constituted by some overlapping spheres centered on atoms. Among recent

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progress accessible in the continuum model, the conductorlike PCM (CPCM) model [33–35], which is one of the most popular and fastest of such models, was used in this work. In the CPCM model, the surface charge density was found by supposing that the surrounding medium is a conductor with an infinite dielectric constant, and is renormalized by a scaling function to provide an exact charge density for the real medium with a finite dielectric constant. As the solvent in this work, water can form hydrogen bonds with the electronegative atoms of thiothixene. In this case, the CPCM model is not sufficient and may lead to inexact results. Therefore, we applied a generalized continuum model, (implicit–explicit method), which, in this method, augmented the solute molecule through a few solvent molecules and the results are treated via CPCM [26]. We used this method, adding five water molecules to the high electronegative sites. The results of these calculations were analyzed and displayed with the molecular visualization program [36].

Results and discussion Geometrical structures The ground-state geometries of both trans and cis conformations of thiothixene were optimized using the B3LYP/6– 311 + G(d,p) method in the gas phase and water solvent. Frequency calculations at the same level in the gas and solvent phases showed that the optimized structures of thiothixene are at the stationary point without any imaginary frequency. Therefore, the optimized structures of thiothixene are the most optimization, and were justified through no imaginary frequency and total energy values of the structures, as shown in the next section. The geometries of two conformations of thiothixene in the gas and solvent phases are presented in Fig. 2. Thiothixene has C1 point group symmetry. In the optimized structures, it is clear that the piperazine ring is located far from the main structure due to steric effects. Optimized geometric parameters, such as the selected bond lengths, bond angles, and dihedral angles of the two structures are recorded in Table 1. The results in Table 1 show that, for both isomers of these molecules, the S1–O3, S1–O4, N7–C29 and N7–C30 bond lengths, and also the S3–O1–S4 and C22–S1–N7 bond angles in the solvent phase show relatively higher changes compared to those in the gas phase. This can be attributed to hydrogen bonding between the solvent and S, O and N electronegative atoms, while the other water molecules exhibited no notable changes to bond lengths and bond angles. In the CPCM model, the short-range interactions between solute and solvent were ignored. So, the optimized parameters in the solvent phase by assuming solvent as a conductor-like PCM are not totally exact, but this model can nevertheless lead to comprehensive and acceptable results.

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All the CC lengths in the two phenyl rings are between the distance of a single bond and a double bond, showing that resonance bonds exist in the rings of the cis and trans structures of this compound. The aromaticity of the benzene rings is distorted from the hexagonal structure of the benzene because of the substitutions, as is obvious from the difference in bond length between C18–C21 and C24–C27, which is 0.016 Å and 0.014 Å in the trans and cis structures, respectively. The difference in bond angle between C18–C21–C26 and C21–C18–C24 is 3.4 and 3.3 in the trans and cis structures, respectively. Also, the difference in bond angle between C17–C19–C23 and C19–C17–C20 is 2.9 and 3.2 in the trans and cis structures, respectively. Calculations show that, in both trans and cis isomers of the molecule, the C18–C21, C18– C24, C21–C26 and C17–C19 bond lengths, are slightly larger than the other CC bond lengths of the phenyl rings. The S2– C19 and S2–C21 bond lengths in the middle ring are longer than the other bond lengths in this ring. The S1–N7 and S1– C22 bond lengths are larger than the CN and CC bond lengths in the molecule. The C8–N5, C10–N6, N6–C11, and C9–N5 bond lengths are longer than the CC bond lengths in the ring. From the results of Table 1, the C17–C16–C15 bond angle of the trans structure is slightly smaller than that of the cis structure, and the C18–C16–C15 bond angle in the trans structure is slightly larger than that of the cis structure. The other bond lengths and bond angles in the cis and trans structures are practically identical. The calculated dihedral angles C18– C16–C15–C13, C17–C16–C15–C13, C20–C22–S1–O3, C20–C22–S1–O4, C25–C22–S1–O3 and C25–C22–S1–O4 in solvent phase, corresponding to the trans and cis structures, are −1.9, 175.7, 25.4, 155.8, −155.5, −25.1 and 175.7, −1.86, 151.1, −20.1, 29.3, 159.5, respectively. It can been observed that the dihedral angles are considerably affected by the isomerization of thiothixene from trans to cis structures. The changing of dihedral angles around the C = C double bond as a result of the isomerization somewhat explains the pharmaceutical use of cis-thiothixene.

Energy levels The EHOMO, ELUMO, HOMO–LUMO gap (HLG, ELUMO − EHOMO), total molecular energies and the relative energies calculated with the B3LYP/6–311 + G(d,p) method, for trans and cis isomers of thiothixene are listed in Table 2. In the presence of water as solvent, the HOMO and the LUMO energy level of the cis structures decreased by about 0.003 eV and 0.020 eV, respectively, and the HOMO and the LUMO energy level of the trans structure increased by about 0.001 eV and 0.017 eV, respectively. The computed HOMO energy levels of the trans and cis structures in the gas phase (solvent) are located at −6.089 eV and −6.084 eV (−6.088 eV and −6.087 eV), and their corresponding LUMO energy levels are located at −1.653 and −1.669 eV (−1.636

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Fig. 2 Optimized molecular structure of trans-thiothixene and cis-thiothixene at B3LYP/6– 311 + G(d,p) level of theory in both gas and solvent phases (implicit–explicit method)

Trans (gas)

Trans (solvent)

Cis (gas)

Cis (solvent)

and −1.689 eV), respectively. In the presence of both gas and solvent phases, the HOMO energy levels of the trans structure of thiothixene are lower than the HOMO energy level of cis structure, while the LUMO energy levels of the trans structure are higher than those of the cis structures. Therefore, the HLG of the trans structure of thiothixene is larger than the HLG of the cis structure. The relative energies of the structures in both gas and solvent phase show that the cis structure of thiothixene has slightly lower energy level than the trans structure, by 0.003 eV and 0.010 eV, in the gas phase and water phase, respectively. Accordingly, the relative energy in the solvent phase is higher than that in the gas phase. This means that the relative stability of the cis structure compared to the trans structure in the solvent phase is more than in the gas phase. Because of small relative energies, especially very small relative energy in the gas phase, we cannot conclude with certainty that the cis structure is more stable than the trans structure. Since the cis structure of thiothixene is known as an active drug, the lower energy level of the cis structure of this

drug compared to the trans structure may be a good candidate to explain the better activity of the cis structure of thiothixene, but this cannot be determined with certainty. Therefore, the C15–C16 double bond in the structure of this drug is the internal barrier in going from a cis to a trans conformation. Other parameters that justify the better activity of the cis structure are discussed in the next section.

Electronic absorption spectra The electronic absorption spectra of the trans and cis structures of thiothixene were calculated with the TDDFT method at B3LYP/6–311 + G(d,p) level of theory in the gas phase and water phase based on the optimized ground state geometries of the compound. The excitation energies, maximum wavelengths (λmax), oscillator strengths ( f ), main transition and electronic transition configurations of trans and cis isomers of thiothixene in both gas and solvent phases are gathered in Table 3, and the UV-vis absorption spectra of both isomers of

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Table 1 Selected bond lengths (in Å), bond angles (in degree) and dihedral angles (in degree) of trans and cis structures of thiothixene at the B3LYP/6– 311 + G(d,p) level of theory Parameters

Thiothixene Trans Gas / water

Thiothixene Cis Gas / water

Thiothixene

Trans Gas / water

Cis Gas / water

Bond lengths S2-C21 1.784 / 1.786 S2-C19 1.777 / 1.778 C18-C21 1.406 / 1.406 C18-C24 1.402 / 1.403 C21-C26 1.396 / 1.397

1.784 / 1.786 1.777 / 1.778 1.404 / 1.404 1.401 / 1.402 1.396 / 1.397

Bond angles C19-S2-C21 C17-C16-C18 C16-C15-C13 C17-C16-C15 C18-C16-C15

99.9 / 100.1 115.4 / 115.4 129.0 / 128.6 119.8 / 119.8 124.7 / 124.7

99.9 /100.0 115.4 / 115.4 128.8 / 129.1 124.3 / 124.4 120.1 / 120.1

C24-C27 C27-C28 C28-C26 C18-C16 C16-C17 C17-C19 C17-C20 C19-C23 C23-C25 C25-C22 C20-C22 S1-C22 S1-O3 S1-O4 S1-N7 N7-C30 N7-C29 C16-C15

1.390 / 1.391 1.394 / 1.395 1.390 / 1.391 1.484 / 1.484 1.486 / 1.486 1.407 / 1.408 1.399 / 1.399 1.398 / 1.398 1.388 / 1.388 1.395 / 1.396 1.391 / 1.392 1.802 / 1.796 1.459 / 1.476 1.459 / 1.477 1.688 / 1.680 1.464 / 1.479 1.465 / 1.479 1.347 / 1.347

1.390 / 1.391 1.394 / 1.395 1.390 / 1.391 1.486 / 1.487 1.484 / 1.485 1.408 / 1.408 1.400 / 1.400 1.398 / 1.398 1.388 / 1.388 1.395 / 1.396 1.391 / 1.392 1.803 / 1.798 1.459 / 1.477 1.460 / 1.478 1.686 / 1.680 1.464 / 1.478 1.464 / 1.477 1.347 / 1.347

C15-C13-C12 C13-C12-N5 C12-N5-C9 C12-N5-C8 N5-C9-C11 C9-C11-N6 C11-N6-C10 N6-C10-C8 N5-C8-C10 C11-N6-C14 C10-N6-C14 C22-S1-N7 C22-S1-O3 C22-S1-O4 O3-S1-N7 O4-S1-N7 S1-N7-C29 S1-N7-C30

111.2 / 111.1 113.1 / 113.2 112.1 / 111.4 113.1 / 112.9 110.7 / 110.9 110.6 / 110.7 110.4 / 110.1 110.7 / 110.9 110.8 / 110.8 112.2 / 111.8 112.2 / 111.8 107.4 / 108.9 107.2 / 107.7 107.3 / 107.7 105.9 / 106.2 106.0 / 106.3 116.8 / 116.2 116.7 / 116.1

111.2 / 111.0 113.1 / 113.2 111.9 / 111.4 113.1 / 113.0 110.7 / 110.8 110.7 / 110.8 110.4 / 110.1 110.7 / 110.9 110.8 / 110.8 112.2 / 111.8 112.2 / 111.8 107.8 / 109.6 106.9 / 107.5 107.2 / 107.6 105.9 / 106.1 106.0 / 106.3 117.1 / 116.4 116.9 / 116.4

C15-C13 C13-C12 C12-N5 N5-C8 C8-C10 C10-N6 N6-C11 C11-C9 C9-N5 N6-C14

1.500 / 1.500 1.539 / 1.538 1.460 / 1.463 1.463 / 1.466 1.525 / 1.525 1.459 / 1.463 1.460 / 1.463 1.525 / 1.524 1.463 / 1.466 1.454 / 1.458

1.500 / 1.500 1.538 / 1.538 1.461 / 1.463 1.464 / 1.466 1.525 / 1.525 1.459 / 1.462 1.459 / 1.463 1.524 / 1.524 1.464 / 1.466 1.454 / 1.458

C29-N7-C30 C18-C21-C26 C24-C27-C28 C21-C18-C24 C17-C19-C23 C20-C22-C25 C19-C17-C20 O3-S1-O4

114.7 / 113.7 120.9 / 121.1 119.9 / 119.9 117.8 / 117.7 120.8 / 121.0 121.1 / 121.3 118.1 / 118.1 122.1 / 119.6

114.8 / 113.8 120.9 / 121.2 119.9 / 119.9 118.0 / 117.9 120.9 / 121.1 121.1 / 121.3 118.0 / 117.9 122.1/ 119.6

Table 2 EHOMO (eV), ELUMO (eV), HLG (eV), total energy (eV) and relative energy ΔE = E cis − E trans (eV) of trans and cis structures of thiothixene with B3LYP/6–311 + G(d,p) method in the gas and water phases

Thiothixene Gas Trans Cis Water Trans Cis

Trans Gas / water

Cis Gas / water

Dihedral angles C26-C21-S2-C19 C21-S2-C19-C23 C21-C18-C16-C15 C18-C16-C15-C13 C19-C17-C16-C15

−148.7 / -148.9 149.8 / 150.5 136.2 / 136.6 −2.1 / -1.9 −136.3 / -136.3

150.1 / 150.1 −148.5 /−148.5 −135.9 /−136.5 175.1 /175.7 135.6 /136.3

C17-C16-C15-C13 C13-C12-N5-C8 C13-C12-N5-C9 C8-C10-N6-C14 C9-C11-N6-C14 C17-C20-C22-S1 C23-C25-C22-S1 C20-C22-S1-O3 C20-C22-S1-O4 C25-C22-S1-O3 C25-C22-S1-O4 C22-S1-N7-C30 C22-S1-N7-C29

175.4 / 175.7 75.5 / 72.1 −159.3 / -163.7 −176.9 / -178.2 176.8 / 178.1 178.2 / 177.9 179.8 / -179.9 23.3 / 25.4 156.1 / 155.8 −156.7 / -155.5 −23.9 / -25.1 70.3 / 68.5 −70.9 / -69.3

−2.00/−1.866 74.8 /72.6 −160.3 /−163.2 −177.1/−178.2 176.8 /178.1 −178.8/−178.9 −178.8/−179.1 −155.5/151.1 −23.0/−20.1 24.1/29.3 156.6/159.5 70.1 /69.9 −72.1/−68.9

EHOMO

ELUMO

HLG

Total energy

Relative energy ΔE = E cis–E trans

−6.089 −6.084

−1.653 −1.669

4.436 4.415

−54,567.326 −54,567.329

−0.003

−6.088 −6.087

−1.636 −1.689

4.452 4.398

−54,567.848 −54,567.858

−0.010

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Table 3 Calculated excitation energies, maximum wavelengths (λmax) (nm), oscillator strengths ( f ), main transition and electronic transition configurations of trans and cis structures of thiothixene, with the TDDFT-B3LYP/6–311 + G(d,p) method

Thiothixene

Gas Trans Cis Water Trans Cis a

Excitation energies

λmax

f

Main transition (electronic transition configurations)

5.3716 5.3604

230.82 231.30

0.146 0.175

H-3 → L + 2 (27.05%) H-3 → L + 2 (31.39%)

5.2985 5.2805

234.12 234.80

0.308 0.386

H-3 → L + 2 (34.17%) H-3 → L + 2 (41.55%)

Experimentala

228 229

Ref. [1]

thiothixene in the two phases with a Gaussian line broadening of 0.333 eV, are plotted with Grace 5.1.23 software [37] and presented in Fig. 3. The maximum absorption wavelengths (λmax) of trans and cis structures of thiothixene in the gas phase are observed at 230.82 nm with an oscillator strength f = 0.141 ,and at 231.30 nm with an oscillator strength f = 0.175, respectively. TDDFT calculations of this compound in the solvent phase were also carried out with the CPCM model. The λmax of trans and cis isomers of this molecule in water were observed at 234.12 nm with an oscillator strength

f = 0.308 ,and 234.80 nm with an oscillator strength f = 0.386, respectively. The results shown in Table 3 and Fig. 3 reveal that the presence of water as solvent shifts the absorption bands of the trans and cis structure of thiothixene toward longer wavelengths and larger oscillator strengths. Because, with increasing solvent polarity, the energy of the excited state is lowered more than that of the ground state, the λmax of both structures of thiothixene have a slight red-shift by solvent effects [38]. The electronic absorption spectra show that the maximum absorption wavelengths are associated with the

Fig. 3 Electronic absorption spectra of trans- and cis-thiothixene in the gas phase and solvent with time-dependent density functional theory (TDDFT) method using B3LYP/6–311 + G(d,p) level of theory

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HOMO-3 → LUMO + 2 transitions. The HOMO-3 and LUMO + 2 frontier MOs of the trans and cis structures of thiothixene in the solvent phase (shown in Fig. 4) show that, for this molecule, the frontier MOs are usually composed of p atomic orbitals. Thus, these electronic transitions correspond to π → π*. These results are in good qualitative agreement with the experimental results [1] shown in Table 3. The experimental values of maximum absorptions of trans and cis structures of thiothixene in methanol have been reported at 228 nm and 229 nm, respectively [1]. The experimental UV spectra of cis structure of thiothixene [39] is in qualitative agreement with the computational results. We cannot achieve the exact quantitative results from the TDDFT calculations, because of the small difference between TDDFT calculations and experimental results due to the difference between the DFT exchange and correlation function and the computational model of solvent effects [40–42]. From Table 3 and Fig. 3., we can conclude that the absorption bands and oscillator strengths of the cis structure of thiothixene are higher than those of the trans structure, meaning that the absorption peak intensity of the cis structure is higher than that of the trans structure. Subsequently, the cis structure of thiothixene shows the best absorption properties, i.e., red shifted absorption bands, higher oscillator strength

and broader absorption spectra, while the trans structure shows smaller absorption bands and lower oscillator strength. The improved properties of the cis structure of thiothixene can be attributed to the better properties of cis-thiothixene as a medicine. Since thiothixene absorbs only UV light, the λmaxs of this molecule are outwith the range of UVA, i.e., UVB and UVC, and the λmax of cis-thiothixene is slightly larger than trans-thiothixene, the improved absorption properties of cis-thiothixene do not cause any greater phototoxicity of this structure. Therefore, drugs that absorb UV light, especially out of the range of UVA, are not recognized as important phototoxicity drugs [43, 44].

NLO properties and other molecular properties The total static dipole moment (μ), mean polarizability (α), anisotropy of polarizability (Δα) and first order hyperpolarizability (β) are among the NLO properties of the molecule that were investigated in this study. Dipole moment, which can be applied as a descriptor to demonstrate the charge transfer within a molecule, is an important parameter of major significance in structural chemistry [45–47]. Polarizabilities and hyperpolarizabilities are quantities by which the induced dipole moment of a molecule characterizes

Fig. 4 Highest occupied molecular orbital (HOMO)-3 and lowest unoccupied molecular orbital (LUMO) + 2 plots of transand cis-thiothixene computed at B3LYP/6–311 + G(d,p) level in the solvent phase

LUMO+2 Trans- Thiothixen

LUMO+2 Cis- Thiothixene

HOMO-3 Trans- Thiothixene

HOMO-3 Cis- Thiothixene

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the reaction of a molecule in an applied electric field [45, 46, 48]. However, as the polarizability and hyperpolarizability values of the output file are presented as atomic units (a.u.), they have been converted to electronic units (esu) (α; 1 a.u. = 1.48176 *10–25 esu, β; 1 a.u. = 8.63993 * 10−33 esu) [46]. In order to investigate the relationships among NLO properties, HLG and chemical reactivity descriptors such as electronegativity (χ), chemical hardness (η) and softness (σ), chemical potential (ρ) and electrophilicity index (ω) of the molecule, these parameters have been subjected to Koopman’s theorem [49–51]. DFT is as a popular method with which to characterize the chemical reactivity and selectivity of a molecule, on the basis of global parameters such as electronegativity, chemical hardness (η), chemical softness and chemical potential; these quantities are useful in clarification of the thermodynamic properties of chemical reactivity. The chemical potential of a system is defined as the first order derivative of total energy (E) of a system with respect to the number of electrons (N) at fixed external potential, V(r), and the chemical hardness is defined as the second order derivative of E with respect to the N2. These global quantities, as well as the polarizability values, have been used as proper quantities for the explanation of chemical reactivity of a molecule [48, 52]. Electronegativity (χ) is a measure of the power of an atom or a group of atoms to attract electrons and can be achieved from the HOMO and LUMO energy level as the Eq. 2. It has also been termed Mulliken’s absolute electronegativity [46, 48, 52, 53]: 1 χ≈− ðEHOMO þ E LUMO Þ 2

ð2Þ

The stability and reactivity of a molecule is related to η, which is a measure of the resistance of a system to charge transfer [46, 48]. This quantity can be computed from this equation: η¼

1 1 ½IP−EA≈ ½E LUMO −EHOMO  2 2

ð3Þ

The electrophilicity index (ω) determines the stabilization energy of the systems when it becomes saturated by electrons, and can be calculated from the electronegativity and chemical hardness using the equation [46, 54, 56]: ω¼

χ2 2η

All the above quantities for both trans and cis structures of thiothixene in the gas and solvent phases were computed with the B3LYP/6–311 + G(d,p) method and are presented in Table 4. According to the results in Table 4, dipole moments μ, polarizability α, anisotropy of polarizability Δα and the total first-order hyperpolarizability βtot of the cis-thiothixene are all higher than those of trans-thiothixene in both gas and solvent phases, and the values of μ, α, and βtot in the solvent phase are higher than those in the gas phase. The higher dipole moment, polarizability, and hyperpolarizability shows that the cis structure of thiothixene has better NLO properties than the trans isomer; a molecule with a higher dipole moment has stronger intermolecular interactions [46]. The calculated dipole moments for the trans and cis structures of thiothixene are 5.5091 Debye and 5.8157 Debye in the gas phase and 7.3580 Debye and 7.8611 Debye in the solvent phase, respectively. These values show that the cis structure of thiothixene molecule has stronger intermolecular interactions than the trans structure. The calculated polarizability, anisotropy of the polarizability and first hyperpolarizability of transthiothixene in the gas phase (solvent phase) is 0.525*10−22 (0.730*10 −22) esu, 0.161*10−22 (0.142*10 −22) esu and 0.027*10−28 (0.088*10−28) esu, respectively. Also, the values of α, Δα and βtot of cis-thiothixene in the gas phase (solvent phase) are 0.529*10−22 (0.731*10−22) esu, 0.185*10−22 Table 4 Calculated dipole moment μ (Debye), isotropic polarizability α, anisotropy of polarizability Δα, total first-order hyperpolarizability βtot, chemical hardness η and softness σ (eV), electronegativity (χ), Chemical potential (ρ) and electrophilicity index (ω) values of trans and cis structures of thiothixene, with the B3LYP/6–311 + G(d,p) method Thiothixene

where, on the basis of Koopman’s theorem IP ≈ EHOMO and EA ≈ ELUMO which IP is ionization potential and EA is electron affinity [46, 48, 52]. The chemical softness (σ), which can be computed from the inverse of hardness, characterizes the capacity of a molecule to accept electrons, and measures the ease of charge transfer. Softness is related to polarizability, with soft molecules having high polarizability and hard molecules having low polarizability [46, 52, 54]. The evasion affinity of an electron from equilibrium is called the electronic chemical potential (ρ), and is the negative of the Mulliken’s absolute electronegativity [54, 55].

ð4Þ

Dipole moment μ α (10−22 esu) Δα (10−22 esu) βtot (10−28 esu) Chemical hardness η Chemical softness σ Electronegativity χ Chemical potential ρ Electrophilicity index ω

Gas

Water

Trans

Cis

Trans

Cis

5.5091 0.525 0.161 0.027 2.2176 0.4509 3.8713 −3.8713 3.3790

5.8157 0.529 0.185 0.031 2.2073 0.4530 3.8770 −3.8770 3.4049

7.358 0.730 0.142 0.088 2.2258 0.4493 3.8621 3.8621 3.3506

7.8611 0.731 0.185 0.124 2.1986 0.4584 3.8884 −3.8884 3.4386

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(0.185*10−22) esu and 0.031*10−28 (0.124*10−28) esu, respectively. From these values, we can conclude that the cis structure of thiothixene, which is used as a pharmacologically active molecule, constitute a better NLO molecule than transthiothixene. The chemical hardness of these molecules, which is related to the HLG of these structures, determines the charge transfer and the reactivity of the molecule. Hard molecules with larger HLG will be less reactive than soft molecules with smaller HLG [46, 54, 55, 57]. As observed in Table 4, the chemical hardness of the cis structure of thiothixene, in both gas and solvent phases, is smaller than that of the trans structure. This means that the trans structure of thiothixene is harder than the cis structure, and the chemical softness of the cis structure is higher than the trans structure, meaning that the charge transfer and reactivity of cis-thiothixene are higher than for transthiothixene. As can be seen from the data in Table 4, there is an opposite correlation between polarizabilities values and the chemical hardness (η) of the molecule. The cis structure of thiothixene with the smaller HLG, shows lower chemical hardness (η), higher λmax and larger polarizability and hyperpolarizability than the trans structure. The reduced chemical hardness illustrates that the electron density is more easily influenced and the molecule could be more reactive. The improved polarizabilities facilitate distortion of the electron cloud by an electric field to the acceptor group, and cause the much higher intramolecular charge transfer capability. Subsequently, the lower chemical hardness means higher polarizability and hyperpolarizability [38, 57]. From Table 4, it is clear that the electronegativity of transthiothixene is 3.8713 eV in the gas phase and 3.8621 eV in the solvent. This parameter for cis-thiothixene has been observed to be enhanced from 3.8770 eV to 3.8884 eV from gas to solvent phase. The electrophilicity indices of the trans and cis structures of thiothixene in the gas phase are 3.3790 eV and 3.4049 eV, respectively, and this quantity in the solvent phase is observed to be increased from 3.3506 eV to 3.4386 eV when going from the trans to cis structure of thiothixene. Regarding these parameters, we find that the electronegativity, chemical potential and electrophilicity index of the cis conformation of thiothixene, in both gas and solvent phases, are higher than those of the trans conformation. This means that cis-thiothixene has better reactivity on the basis of these chemical reactivity descriptors.

Natural charge distributions and MEP The natural atomic charges of the trans and cis conformations of thiothixene, calculated with B3LYP/6–311 + G(d,p) method in the gas and solvent phases, are listed in Table 5. In the thiothixene molecule, all hydrogen atoms have positive natural atomic charges, and all the carbon, oxygen, nitrogen atoms have negative atomic charges. The negative atomic charges of

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O and N, which are known as electronegative atoms, are higher than those of the carbon atoms. The O3 and O4 atoms show the highest negative atomic charge, and the S1 atom shows the highest positive atomic charges among all the atoms of the molecule. The result in Table 5 shows that the negative natural atomic charges of all the negative atoms of the molecule, except C15, C17, C19, C20, C23 and C25 atoms, in the water phase are more negative relative to the gas phase. Calculation of MEP is a suitable method with which to determine the three dimensional charge distributions of molecules. This kind of map is very beneficial when characterizing the reactive sites of molecules in both electrophilic and nucleophilic reactions in investigation of biological systems [46, 58]. For characterization of reactive sites of electrophilic and nucleophilic attacks for trans and cis isomers of thiothixene molecule, the MEP was calculated for both isomers of thiothixene at the B3LYP/6–311 + G(d,p) optimized structure with the electron density isosurface of 0.0004 a.u, and is shown in Fig. 5. Usually, the different values of the electrostatic potential are represented by various colors, with the order of potential values as follows: red < orange < yellow < green < blue. The maximum positive region, which is the site chosen for nucleophilic attack, is in blue. The negative areas of MEP are associated with electrophilic reactivity and are specified in red and yellow, with the preferred site for electrophilic attack in red. According to Fig. 5, the color of the trans structure of thiothixene in this map is in the range between −0.05686 a.u. (dark red) and +0.05686 a.u. (dark blue), and, for the cis structure of thiothixene, this range is between −0.05717 a.u. and +0.05717 a.u. The MEP maps of thiothixene molecule show that the negative charges are more concentrated around the oxygen atoms linked to the S1 atom (yellow and red color). Therefore, these regions of the molecule are appropriate areas for electrophilic reactivity, and the red regions of MEP are especially favored sites for electrophilic reactions. Other regions of the molecule are neither dark blue nor dark red, meaning that these regions are almost neutral. The greater electronegativity of the oxygen atoms makes them the most reactive parts for electrophilic reactivity in the molecule [46, 58].

Vibrational spectra The calculated IR spectra of the trans and cis structures of thiothixene in the solvent phase were obtained through vibrational frequency calculations at the B3LYP/6–311 + G(d,p) level of theory in the solvent phase. The vibrational frequencies with the higher IR intensities of the two isomers of thiothixene are listed in Table 6. The calculated IR spectra of the two structures with a Gaussian line broadening of 40 cm−1 are presented in Fig. 6. The calculated IR spectra of the cis and trans isomers of the molecule and its experimental IR spectra [59] show that calculated results are almost in qualitative

356 Table 5

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Page 10 of 15 Natural atomic charges of trans and cis isomers of thiothixene in the gas and water phases

Thiothixene

Gas

Water

Trans

Cis

Trans

Cis 2.22772 0.33021 −0.94900 −0.94897 −0.57801 −0.57465 −0.73036 −0.18593 −0.18069 −0.18179 −0.18235 −0.15626

S S O O N N N C C C C C C

1 2 3 4 5 6 7 8 9 10 11 12 13

2.22898 0.33707 −0.91649 −0.91553 −0.57205 −0.56546 −0.73096 −0.18218 −0.17416 −0.17869 −0.17621 −0.15258 −0.43097

2.22984 0.33721 −0.91612 −0.91740 −0.57248 −0.56337 −0.73205 −0.18255 −0.17449 −0.17781 −0.17942 −0.15323 −0.43121

2.22733 0.33103 −0.94918 −0.94904 −0.57804 −0.57491 −0.72986 −0.18614 −0.18086 −0.18180 −0.18239 −0.15689 −0.43489

C

14

−0.35273

−0.35263

−0.35814

−0.43565 −0.35816

C C C C C C C C C C C C C C C C H H

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

−0.12615 −0.04936 −0.05837 −0.07572 −0.14464 −0.17538 −0.15510 −0.28313 −0.20452 −0.17713 −0.18780 −0.21071 −0.20241 −0.18874 −0.37015 −0.36997 0.17143 0.19542

−0.12267 −0.06051 −0.05865 −0.06338 −0.14421 −0.17610 −0.15849 −0.28326 −0.20486 −0.17936 −0.18435 −0.20992 −0.20114 −0.19233 −0.36989 −0.36975 0.17244 0.19620

−0.11551 −0.06124 −0.05623 −0.07857 −0.14395 −0.17357 −0.16130 −0.28922 −0.20304 −0.18192 −0.18629 −0.21650 −0.20695 −0.19447 −0.37337 −0.37367 0.17138 0.20375

−0.11047 −0.07385 −0.05575 −0.06613 −0.14319 −0.17453 −0.16526 −0.28878 −0.20244 −0.18493 −0.18337 −0.21611 −0.20598 −0.19872 −0.37289 −0.37319 0.17149 0.20380

H H H H H H H H H H H H H H H

33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

0.19743 0.17084 0.16930 0.19713 0.19718 0.16957 0.16313 0.19678 0.20936 0.21984 0.19298 0.16173 0.19303 0.19428 0.24065

0.19727 0.17218 0.16701 0.19821 0.19782 0.16791 0.16588 0.19691 0.21035 0.21383 0.19356 0.16121 0.19347 0.19837 0.23992

0.20369 0.17066 0.16924 0.20321 0.20325 0.16903 0.17071 0.19861 0.21954 0.21577 0.19611 0.16531 0.19618 0.20406 0.24377

0.20375 0.17079 0.16924 0.20328 0.20320 0.16902 0.17116 0.19892 0.21992 0.21316 0.19617 0.16527 0.19615 0.20520 0.24541

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Table 5 (continued) Thiothixene

Gas Trans

H H H H H H H H H H H H

48 49 50 51 52 53 54 55 56 57 58 59

0.22125 0.21241 0.23724 0.21679 0.21075 0.21076 0.22745 0.20164 0.17762 0.22674 0.17631 0.20220

agreement with the experimental IR spectra. Usually, significant differences have been observed between the experimental and the calculated IR spectra. Because IR spectra are usually obtained from solid samples, the calculations were performed in the solvent phase. Also, differences could be due to the basis set level of theory used to describe the properties.

Water Cis 0.22158 0.21289 0.23734 0.21628 0.21010 0.21049 0.22619 0.20154 0.17956 0.22668 0.17765 0.20174

Trans 0.23281 0.22064 0.24188 0.22548 0.21972 0.22024 0.22236 0.21445 0.19020 0.22223 0.19046 0.21487

Cis 0.23326 0.22149 0.24135 0.22500 0.21915 0.21990 0.22257 0.21443 0.18913 0.22264 0.19022 0.21443

Usually, such differences arise due to differences between the DFT computational model and experimental conditions. This could help clarify some differences observed among the spectra. Also, the obvious vibrational frequencies are almost similar for the trans and cis conformations of thiothixene. The largest IR intensity of the two spectra is associated with the C12– H39, C8–H31 and C9–H34 stretching vibrations, with corresponding frequencies observed at 2915.31 cm −1 and 2915.45 cm−1 for the trans and cis structures, respectively. For the SO2 group, asymmetric stretching vibrations are observed at 1251.59 cm−1 and 1250.95 cm−1, and symmetric stretching vibrations are observed at 1071.15 cm−1 and 1070.02 cm−1 for the trans and cis structures, respectively. For both trans and cis structures of thiothixene, the SN stretching mode is reported in the range 661–929 cm−1. The SO2 bending modes and the SC stretching modes were observed at 573.75 cm−1 and 576.08 cm−1 for trans and cis structures, respectively. Therefore, the variation in the structure of the molecule from trans to cis does not alter the vibrational modes much.

Thermodynamic properties

Fig. 5 Molecular electrostatic potential (MEP) map of a trans-thiothixene and b cis-thiothixene

The thermodynamic parameters of the trans and cis structure of thiothixene, such as total thermal energy (E), zero point vibrational energy, heat capacity (C), entropy (S), enthalpy change (ΔH) and Gibbs energy change (ΔG), were calculated with the frequency calculations at different temperatures from 100 K to 500 K, by the B3LYP/6–311 + G(d,p) method in water solvent, and are listed in Table 7. Thermodynamic quantities can be achieved by the basic equations based on suitable partition function. A minimum geometry of the molecule must

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Fig. 6 Calculated infrared (IR) spectra of a cis-thiothixene and b trans-thiothixene at B3LYP/6– 311 + G(d,p) level in the solvent phase

(a)

Cis-Thiothixene

(b) Trans-Thiothixene

Table 6 Selected vibrational frequencies (cm−1) and assignment for trans- and cis-isomers of thiothixene calculated at the B3LY P/6–311 + G(d,p) level in water Vibrational frequencies (cm −1)

IR intensity

Obvious assignment

Trans 2915.31 1251.59 1071.15 929.66 664.71

469.92 400.75 239.32 125.49 233.30

C12-H39, C8-H31, C9-H34 stretching S1-O3, S1-O4 asymmetric stretching S1-O3, S1-O4 symmetric stretching; C = C stretching and bending and C-H bending S1-N7; N7-C29, N-C30 stretching S1-N7 stretching; N7-C29, N7-C30 bending, stretching and bending over the entire molecule

101.54

S1-O3, S1-O4 bending; S1-C22 and S2-C19 stretching

544.50 364.17 262.75 130.79 135.29 136.68

C12-H39, C8-H31, C9-H34 stretching S1-O3, S1-O4 asymmetric stretching S1-O3, S1-O4 symmetric stretching; C = C stretching and bending and C-H bending S1-N7; N7-C29, N-C30 stretching S1-N7 stretching; N7-C29, N7-C30 bending, stretching and bending over the entire molecule S1-O3, S1-O4 bending; S1-C22 and S2-C19 stretching

573.75 Cis 2915.45 1250.95 1070.02 927.23 661.11 576.08

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Table 7 Thermodynamic properties at different temperatures of trans and cis structures of thiothixene, at the B3LYP/6–311 + G(d,p) level in the solvent phase Temperature(K) Zero point energy (kcal mol −1)

Total thermal energy (E) (kcal mol −1)

Heat capacity (C) (cal mol−1 K−1)

Entropy (cal mol−1 K−1)

Enthalpy changes (ΔH) (kcal mol −1)

Gibbs energy changes (ΔG) (kcal mol −1)

Trans-thiothixene 100 305.852 200 305.852 273 305.852 298.15 305.852 300 305.852 400 305.852 500 305.852 Cis-thiothixene

308.471 314.646 321.270 323.972 324.180 377.105 353.180

44.500 78.497 103.130 111.769 112.404 145.722 174.848

113.218 156.046 184.702 194.340 195.051 232.543 268.765

308.646 315.019 321.787 324.539 324.751 337.873 345.145

297.325 283.812 271.368 266.601 266.240 244.864 219.774

308.582 314.746 321.365 324.066 324.273 337.196 353.260

44.345 78.424 103.065 111.703 112.339 145.650 174.784

111.657 154.412 183.045 192.678 193.384 230.902 267.070

308.756 315.119 321.883 324.633 324.844 337.964 354.226

297.591 284.239 271.915 267.191 266.833 245.610 220.701

100 200 273 298.15 300 400 500

305.990 305.990 305.990 305.990 305.990 305.990 305.990

be achieved and applied because the vibrational partition functions are related to the frequencies [60, 61]. According to Table 7, the thermodynamic quantities of trans and cis conformations of thiothixene are not very different, and in fact are practically close to each other. Zero point vibrational energies, total thermal energies, enthalpy changes and Gibbs energy changes of cis-thiothixene are a little more than those of trans-thiothixene, which could confirm the relative stability of cis structures compared to the trans structure, while heat capacities and entropies of cis-thiothixene are smaller than those of trans-thiothixene. Since the cis structure of thiothixene can act as an active drug, according to our results, we can conclude that the higher zero point vibrational energy, higher total thermal energy, higher enthalpy change and higher Gibbs energy change are appropriate quantities for a molecule to be used as an active drug. The Gibbs energy change values will help us determine the spontaneity of the reaction. The higher values of Gibbs energy changes of the cis structure of thiothixene show that trans-thiothixene can convert spontaneously to cis-thiothixene. The results in Table 7 show that all thermodynamic parameters, except zero point vibrational energy and Gibbs energy change, increasing with increasing temperature from 100 to 500 K, because the molecular vibrational intensities enhance with temperature but the zero point vibrational energy does not change with temperature [55, 62]. The equations of these thermodynamic properties, which can be obtained from the data in Table 7, can be used to compute the values of every thermodynamic parameter at any temperature, and to calculate

the other thermodynamic energies for further studies of these molecule [55].

Conclusions This work investigated the geometries, electronic properties, electronic absorption spectra, NLO properties, thermodynamic properties, natural charge distribution, MEP analysis and vibrational frequencies of cis and trans structures of the drug thiothixene, have been investigated by DFT methods to compare the trans and cis structures of thiothixene and explain why the cis structure of thiothixene is active as a drug. Geometrical analysis shows that, in the phenyl rings of this molecule, the C–C bonds where substitution groups are attached are longer than the other bond lengths of the phenyl rings, because the hexagonal structures of the phenyl rings are distorted. The calculated energy levels, and the relative energy of trans and cis structures of the molecule, show that the cis structure is more stable than the trans structure, with a small energy difference. The HOMO energy levels of the trans structure of thiothixene are slightly lower than the HOMO energy level of the cis structure, while the LUMO energy levels of the trans structure are higher than those of the cis structure. Therefore, the HLG of the trans structure of thiothixene is larger than the HLG of the cis structure. TDDFT calculations show that the cis structure of thiothixene has the better absorption properties, while the superior properties of the cis structure of thiothixene can be attributed to the

356

better properties of cis-thiothixene as an active medicine. The calculated properties such as dipole moment (μ), the NLO parameters [polarizability (α), anisotropy of polarizability (Δα) and first order hyperpolarizability (β)], electronegativity (χ), chemical hardness (η) and softness (σ), chemical potential (ρ) and electrophilicity index (ω) of the molecule, show that dipole moment and NLO properties of the cis structure of thiothixene are higher than those of the trans structure, which shows that cis-thiothixene has the better NLO properties than trans-thiothixene and has stronger intermolecular interactions. The chemical hardness of the cis structure of thiothixene is lower than the trans structure, and the electronegativity, chemical softness and electrophilicity index of the cis structure of thiothixene are greater than those of the trans structure. This means that the reactivity and charge transfer of the cis isomer of thiothixene is higher than that of the trans isomer. Also, there is an inverse correlation between chemical hardness and polarizability values of the molecule. MEP maps of the molecule reveal that the areas around the oxygen atoms of the molecule are appropriate areas for electrophilic reactions. The vibrational frequencies of the two isomers of thiothixene show that both structures of the molecule have almost the same modes of vibrations, and the highest IR intensity of the two spectra is associated with the C12–H39, C8–H31 and C9– H34 stretching vibrations of the molecule. The computed thermodynamic quantities, such as total thermal energy, heat capacity, entropy and enthalpy change from 100 K to 500 K show that all these thermodynamic quantities increase with increasing temperature. Acknowledgment We would like to thank Dr. Sabzyan for providing us with hardware and software facilities.

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