Research Article | Open Access
Quantum Chemical and Spectroscopic Investigations of (Ethyl 4 hydroxy-3-((E)-(pyren-1-ylimino)methyl)benzoate) by DFT Method
In the present work we have reported the optimized ground state geometry, harmonic vibrational frequencies, NMR chemical shifts, NBO analysis, and molecular electrostatic potential surface map of the title compound using DFT/B3LYP/6-311++G(2d, 2p) level of theory. We have compared our calculated results with the experimentally obtained values and found that both are in close agreement with each other. We have used the gauge-invariant atomic orbital (GIAO) approach to calculate the NMR (13C and 1H) chemical shifts using Gaussian 09 package. TD-DFT (time-dependent DFT) approach has been used to simulate the electronic spectra of the title compound in order to account for excited states. Other molecular properties such as HOMO-LUMO energies, NBO analysis, and PED distribution analysis have been studied and reported using DFT/B3LYP/6-311++G(2d, 2p) level of theory.
The title compound chosen for DFT studies to extract different molecular properties has been experimentally synthesized and prepared using 1 amino pyrene and (ethyl 3-formyl-4-hydroxybenzoate) at room temperature for six hours in the presence of dry MeOH . The title compound shows sensing properties for selective detection of niobium ions in mixed aqueous media. In the literature survey we found that there are lot of research articles based upon fluorescent techniques for detection of various metal ions, however literature survey also reveals very few ab initio HF/MP2/DFT calculations of such type of compounds. Fluorescence is a very simple technique and acts as a convenient characterization tool for detection of very small amount (in ppm) of various metal ions in solutions . From application point of view niobium metal is used in various kinds of applications such as superconducting magnets  and biological applications . In interest of such applications the quantum mechanical calculations of the title compound are thoroughly investigated. The aim of this work is to predict the structural, electronic, vibrational, and spectral parameters and other molecular properties of the title compound using DFT approach [5–9].
2. Experimental Details
In this section we have reported short details about the methodology and characterization tools used for the title compound, however we advised the readers to consult  for more details. The chemical structure and fluorescent properties of the title compound are confirmed by single crystal X-ray diffraction, UV spectra, 1H and 13C NMR, and FTIR spectra. 1H and 13C NMR are recorded in chloroform using TMS as internal standard on a Varian Mercury 300 spectrometer operating at 300 MHz for 1H and 75 MHz for 13C. IR spectra are recorded on a Perkin-Elmer PE-983 infrared spectrometer as KBr pellets with absorption reported in cm−1. The ultraviolet absorption spectra were recorded on Shimadzu UV-2450 spectrophotometer. Fluorescent spectra measurements were performed on Agilent Technologies Cary Eclipse fluorescence spectrometer.
3. Computational Details
Using DFT/B3LYP/6-311++G(2d, 2p) level of theory  we have investigated the ground state optimized geometry of the title compound. The molecular geometry is fully optimized using tight convergence criteria along with redundant internal coordinates and Berny’s optimization algorithm. The optimized parameters obtained using DFT approach have been compared with the experimental values and are in close agreement with them. Further we have used the optimized ground state geometry of the title compound to study the different properties like NMR spectra, UV-Vis spectra, MEP surface mapping, PED analysis, and NBO analysis. Using DFT/B3LYP/6-311++G(2d, 2p) level of theory and GAIO (Gauge-Invariant Atomic Orbital) [11, 12] approach we have reported the NMR (13C and 1H) chemical shifts of the title compound and compared them with their experimental counterparts. To study the electronic transitions and excited states we have used the TD-DFT (time-dependent) method available in Gaussian 09 package. HOMO-LUMO energies are also calculated at DFT/B3LYP/6-311++G(2d, 2p) level of theory. Vibrational wavenumbers assignment is done by using VEDA 4 program. MEP surface mapping is investigated to comment upon the reactive nature of the title compound. In order to find out the various interactions between the filled and the vacant orbitals, NBO analysis  of the title compound has been done using NBO 3.1 program available in Gaussian 09 package at DFT/6-311++G(2d, 2p) level of theory. The unoptimized structure of our title compound is presented in Figure 1.
4. Results and Discussion
4.1. Molecular Geometry
We have used the DFT/B3LYP/6-311++G(2d, 2p) level of theory available in Gaussian 09 program to investigate the ground state geometry of the title compound. The geometry is fully optimized with tight convergence criteria and the structure is local minima on the PES. On comparison with the experimentally obtained parameters one can conclude that our calculation is successful, as the difference between calculated and experimental bond lengths, bond angles is of few Å. Figure 2 represents the stable conformation of the title compound using DFT calculations. The selected calculated bond lengths and angles (Å) for the title compound along with their corresponding experimental values are listed in Table 1.
|: Bond lengths (in Angstrom); : Angles (in Degrees).|
Correlation between  the calculated and the experimental parameters of bond lengths and bond parameters for the title compound are shown in Figure 3. Bond length and bond angles correlation values are 0.9802 and 0.9921, respectively.
4.2. Chemical Shifts
NMR spectroscopy is considered as a valuable tool for the structural and functional characterization of molecules. 1H and 13C NMR chemical shifts of the title compound are investigated using DFT/B3LYP/6-311++G(2d, 2p) level of theory with GIAO (gauge-invariant atomic orbital) approach in DMSO. The calculated 1H and 13C NMR chemical shifts of the title compound together with the corresponding experimental values are shown in Tables 2 and 3 as values relative to tetramethylsilane. The 1H NMR spectra of the title compound in DMSO show a triplet peak in the range from 1.36 to 1.40 ppm for C–CH3 and quartet peak in the range from 4.32 to 4.38 ppm for O–CH2. Corresponding calculated values are in the range from 1.31 to 1.46 ppm and 4.27 to 4.32 ppm, respectively. Aromatic protons in pyrene appeared in the range from 8.04 to 8.48 ppm with calculated values ranging from 8.32 to 9.03 ppm. Aromatic protons in substituted benzene showed a singlet peak at 8.66 ppm and doublet at 8.50 ppm and 7.16 ppm. Corresponding calculated values are 8.66 ppm, 8.50 ppm, and 7.44 ppm, respectively. Proton of Schiff base shows a singlet peak at 9.37 ppm while calculated value is at 9.34 ppm. The 13C NMR spectra of the title compound in DMSO showed a peak at 14.44 ppm for C–CH3 (calculated value as 13.48 ppm), at 60.99 ppm for O–CH2 (calculated value as 60.56 ppm), at 165.88 ppm for C=O (calculated value as 180.00 ppm), and at 162.81 ppm for C=N (calculated value as 169.94 ppm). Aromatic carbons of pyrene and substituted benzene showed peaks in the range from 115.67 to 165.12 ppm while calculated values are in the range from 121.53 to 175.80 ppm. We have also reported the hydrogen and carbon NMR chemical shifts by IGAIM and CGST methods using B3LYP/6-311++G(2d, 2p) basis sets . From the comparison table we can conclude that theoretical values for carbon and hydrogen NMR chemical shifts calculated by GIAO method are in close agreement as compared to other CGCST and IGAIM methods. Linear correlation coefficients for linear regression analysis of theoretical and experimental values of 1H and 13C NMR chemical shifts using GIAO method are found to be 0.9959 and 0.9958 respectively.
4.3. Frontier Molecular Orbitals
Analysis of the HOMO-LUMO band gap helps us in understanding many molecular properties of a molecule like chemical reactivity, UV-Vis spectra, and stability of the molecule  along with optical and electrical properties. Chemical reactivity of a molecule can be determined from the HOMO-LUMO band gap. A small band gap implies low kinetic stability of the molecule. HOMO-LUMO separation is a result of significant degree of intermolecular charge transfer from the electron donor groups to the electron acceptor groups through conjugated paths. Energy gap between HOMO and LUMO has also been used to prove the bioactivity from intramolecular charge transfer (ICT). We have reported the HOMO-LUMO analysis of the title compound using DFT/B3LYP/6-311++G(2d, 2p) level of theory . In our analysis we found that the title compound has a total of 986 orbitals out of which 103 are occupied and the remaining 883 are virtual orbitals. The orbitals numbered as 103 and 104 account for HOMO and LUMO orbitals. The HOMO-LUMO energies of the title compound have also been calculated using ab initio calculations and are found to be −5.63 electron volts and −2.50 electron volts, respectively. The HOMO-LUMO for the title compound has been shown in Figure 4 and the gap is found to be 3.13 electron volts. The HOMO LUMO distribution is mostly localized on the rings which show that they are type orbitals. transition implies an ED transfer between rings transition. From this value of band gap we can predict that the title compound can be used for organic solar cell applications, title compound has high kinetic susceptibility and low chemical reactivity. Using HOMO and LUMO energies along with equations as which is electronegativity, as chemical hardness with as chemical softness has been calculated for the title compound. The terms and are equivalent to and and are referred to as ionization potential and electron affinity, respectively. In addition to HOMO/LUMO energies the HOMO−1/LUMO+1 energies of the title compound have been calculated using B3LYP/6-311++G(2d, 2p) level of theory and are found to be −5.61 eV and −2.41 eV, respectively. Electron donating and electron withdrawing ability of the title compound are expresses in terms of , and and come out to be 4.065, 1.565, and 0.3194 .
4.4. MEP Surface Mapping
We have reported and plotted the MEP surface mapping, alpha density, and total density of the title compound using Gaussian 09 program. The molecular electrostatic potential surface along with Alpha density and total density for the title compound is represented in Figure 5.
MEP surface mapping is useful in understanding hydrogen bonding interactions as well as sites for electrophilic and nucleophilic attacks [19, 20]. The MEP surface provides us with net electrostatic effect caused due to total charge distribution. It can be considered as a fruitful quantity to understand the various molecular properties like hydrogen bonding and reactivity. It also provides a useful tool to know the relative polarity of the molecule . Portion of the molecule which has –ve electrostatic potential will be susceptible to electrophilic attack. The surface is color coded as per the electrostatic potential (red is more electron rich area and blue is more electron poor area.). The total electron density plot of the title compound shows a uniform distribution. The order in the increase of the electrostatic potential as per color code will follow as red < orange < yellow < green < blue . At last we conclude that the investigated molecule has several sites for electrophilic as well as nucleophilic attacks as shown in MEP surface mapping.
4.5. UV-Vis Studies and Electronic Properties
To find the electronic absorption spectrum including singlet and triplet states of the title compound the calculations were performed on fully optimized ground state geometry using DFT/B3LYP/6-31++G(2d, 2p) level of theory. THF is used as a solvent to simulate the electronic absorption. Figure 6 represents the computed electronic spectra of the title compound. The electronic spectra are recorded within a range of 200 nm–800 nm. Using TDDFT theory the oscillator strength along with excitation energy for the triplet and the singlet states has also been calculated. The different values for excitation energy along with oscillator strength as well as CI expansion coefficients are listed in Table 4. For the title compound the maximum absorption value obtained using TD-DFT/B3LYP/6-311++G(2d, 2p) basis set are 485 nm, 332 nm, and 285 nm, respectively, with THF as solvent in CPCM model. Corresponding experimental values as reported are 383 nm and 258 nm, respectively. The calculated band at 485 nm is intense and accounts for a type of transition. absorption band in the calculated spectrum indicates a transition and is close to experimentally calculated values.
4.6. Vibrational Spectra
In the present study we have reported the molecular vibrations of the title compound by means of FTIR spectroscopy. Our title compound is asymmetric top with C1-symmetry and is characterized by 141 normal modes of vibration. We have used DFT/B3LYP/6-311++G(2d, 2p)  method to investigate the normal modes of vibration of our title compound. The main reason for selecting this computational scheme is that it reproduces experimental frequencies with high accuracy and the same can be predicted from the comparison of the calculated values with the experimental ones. The calculated and experimental FTIR spectra of the title compound are shown in Figure 6. On comparison we found that the calculated values using the above method are found to be in close agreement with the experimental values. Calculated C–H stretching vibrations of aromatic rings appeared in the wavenumber range 2800–3200 cm−1. The same has been confirmed with the experimental IR where the wavenumber range for aromatic rings ranges from 3000 to 3200 cm−1. The bands observed in the wavenumber range from 3250 to 2850 cm−1 in the calculated IR spectra of the title compound are assigned to the alkyl C–H stretching vibrations and the same is confirmed with the experimental values. C=O (ester) stretching vibrations are predicted at 1649 cm−1 while for the same functional group experimental values are at 1711 cm−1. C=N (Schiff base) stretching vibrations are predicted at 1611 cm−1, while experimental values are at 1610 cm−1. We have also analyzed and reported our modes of vibrations in terms of PED. PED analysis is done by using VEDA 4 program . This program generally uses the Gaussian output file in formatted checkpoint form as its input files for PED analysis. These input files contain information about orientation of coordinates, force constants (F-matrix), and frequencies with atom displacement matrix. The information on F-matrix must start form the line “Force Constants in Cartesian coordinates” (Figure 7).
We have repeated our PED analysis few hundred times to achieve maximum value of PED contributions. In PED interpretation each fundamental normal mode coordinate is expressed in terms of internal mode coordinates which is a combination of stretchings, bendings, or torsions. This transformation basically results in the nondiagonality of the force constant matrix, which means that PED contributions of different modes are mutually related to each other by nondiagonal terms. Further we explain how this procedure works as a normal mode coordinate is replaced by an internal set of coordinates and PEDs are calculated. A parameter EPm is used to express the maximum PEDs and is basically considered as optimization of the PED analysis. If our title compound consists of a large number of modes, then it will result in an increase of optimization time. Theoretically calculated and experimental wavenumbers (available) are summarized in Table 5. Detailed vibrational assignments, IR intensities, and computed wavenumbers along with the percentage of PED are given in Table 5. The spectra were analyzed in terms of the PED contributions by using the VEDA program.
|, , , and denote the stretching, bending, torsion, and out ( ABCD means the angle between the AD vector and the BCD plane) modes. Indices notation: s: symmetric; as: asymmetric; A: aliphatic; ring 1: C1-C2-C3-C4-C5-C6; ring 2: C15-C16-C17-C18-C19-C20; ring 3: C21-C22-C23-C24-C16-C17; ring 4: C17-C18-C24-C25-C26-C27; ring 5: C23-C24-C25-C28-C29-C30.|
4.6.1. Ring, C=O and C=N Vibrations
The C–H stretching vibrations in the range 2800–3200 cm−1 are for aromatic compounds. From the PED analysis we found that C–H stretching vibrations for ring 1 are assigned at 3183 cm−1. This mode is very pure mode as its PED analysis is about 99%. The values observed in the range (3158–3224) cm−1 are assigned to the stretching vibrations of methyl hydrogen’s while their experimentally obtained counterparts are at 3200 cm−1 and 3118 cm−1, respectively. The percentage of PED calculated for these modes by VEDA 4 program varies from 92 to 99% indicating that they are pure modes. C–N modes of vibrations are assigned on the basis of PED calculations. In the PED analysis we found that C–N modes of vibrations are at 1407 and 1387 cm−1 respectively, however these modes are not pure modes and are mixed with C–C stretching modes, while experimentally observed value is at 1611 cm−1. On the basis of PED analysis the wavenumbers at 1648, 1643, 1675, 1554, and 1526 cm−1 are assigned to C=O stretching modes, however again these modes are not pure modes and are mixed with other modes of vibrations. Experimentally obtained values for C=O stretching modes is at 1649 cm−1. The PED analysis for various modes of the title compound along with their percentage values are summarized in Table 5.
4.7. NBO Analysis
In order to understand the hyper conjugation as well as delocalization of the title compound we have investigated the natural bond orbital analysis of the title compound using NBO 3.1 program implemented in Gaussian 09 package . We have used DFT/B3LYP/6-311++G(2d, 2p) level of theory in order to understand different kind of interactions between the filled and the vacant orbitals. We can investigate both intra- and intermolecular interactions using NBO analysis. In addition to this NBO analysis is also useful for understanding charge transfer conjugative interactions in different compounds. Using DFT/B3LYP/6-311++G(2d, 2p) level of theory the second-order perturbation theory analysis of Fock matrix in NBO basis  for title compound is listed in Table 6. For each donor and acceptor the stabilization energy associated with the delocalization is determined as Large value shows the intensive interaction between electron-donors and electron-acceptors groups and greater extent of conjugation of the whole system. The possible intensive interactions are also listed in Table 6. The second-order perturbation theory analysis of Fock matrix in NBO basis shows strong intramolecular hyper conjugative interactions of electrons. From Table 6 we can see that the intramolecular hyper conjugative interactions are formed by the orbital overlap between oxygen, nitrogen, and carbon-carbon bond orbitals. This orbital overlapping is responsible for ICT causing stabilization of the system under study. From the analysis of Table 6 we found that the strong intramolecular hyper conjugative interaction is of C7–O9 from n2 (C7–O9)which increases ED (0.10070 e) that weakens the respective bonds leading to stabilization of 32.78 kcal mol−1. Similarly another strong intramolecular hyper conjugative interaction of C7–O8 from n2(C7–O8) increases ED (0.28565 e) that weakens the respective bonds leading to stabilization of 46.67 kcal mol−1. We have also found another strong intramolecular hyper conjugative interaction of C21–C22 from n1 (C21–C22) which increases ED (0.18831 e) that also weakens the respective bonds leading to stabilization of 46.88 kcal mol−1. We predicted one more strong intramolecular hyper conjugative interaction of C21–C22 from n1(C21–C22) which increases ED (0.18831 e) that weakens the respective bonds leading to stabilization of 46.88 kcal mol−1, as well as strong intramolecular hyper conjugative interaction of C24–C25 from n1(C24–C25) which increases ED (0.46625 e) that weakens the respective bonds leading to stabilization of 71.49 kcal mol−1. These interactions are observed as an increase in electron density (ED) in C–C antibonding orbitals that weakens the respective bonds.
|(2) means stabilization energy.|
bEnergy difference between the donor and acceptor NBO orbitals.
is the Fock matrix element between and NBO orbitals.
Using DFT/B3LYP/6-311++G(2d, 2p) level of theory a detailed study of molecular structure, NMR chemical shifts, electronic properties, MEP surface mapping, NBO analysis, and vibrational and PED analysis of the title compound has been investigated and reported. On comparison with experimentally obtained parameters by one of coauthors of this paper we found that both of them are in agreement with each other. HOMO-LUMO analysis of the title compound shows that the electron charge distribution is mainly concentrated over the rings and there may be a charge transfer through system which accounts for bioactivity of the molecule. The title compound has also large band gap as reported in HOMO-LUMO analysis which accounts for its future applications as a useful material in solar cell devices. Molecular electrostatic surface maps give an idea about the chemical reactivity of the title compound. Our overall simulated results for different molecular properties of the title compound are obtained for the first time and we hope that they are helpful in the synthesis and design of new applications.
Conflict of Interests
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors thank Indian Institute of technology Mandi for providing the infrastructure required for computational studies as well MHRD scholarships. The authors also want to thank Dr. C. P. Parameswaran for allowing them to use some of the experimental data for comparison with simulated results along with useful and fruitful discussions for the completion of the paper.
- A. K. Gupta, A. Dhir, and C. P. Pradeep, “A fluorescence 'turn-on' chemodosimeter for selective detection of Nb5+ ions in mixed aqueous media,” Dalton Transactions, vol. 42, no. 36, pp. 12819–12823, 2013.
- J. R. Lakowicz, Topics in Fluorescence Spectroscopy. Volume 4: Probe Design and Chemical Sensing, Plenum Press, New York, NY, USA, 1994.
- J. L. H. Lindenhovius, E. M. Hornsveld, A. den Ouden, W. A. J. Wessel, and H. H. J. ten Kate, “Powder-in-tube (PIT) Nb3Sn conductors for high-field magnets,” IEEE Transactions on Applied Superconductivity, vol. 10, no. 1, pp. 975–978, 2000.
- D. Touati, “Iron and oxidative stress in bacteria,” Archives of Biochemistry and Biophysics, vol. 373, no. 1, pp. 1–6, 2000.
- B. Çatikkaş, E. Aktan, and Z. Seferoǧlu, “DFT, FT-Raman, FTIR, NMR, and UV-Vis studies of a hetarylazo indole dye,” International Journal of Quantum Chemistry, vol. 113, no. 5, pp. 683–689, 2013.
- A. Raj, Y. Sheena Mary, C. Yohannan Panicker, H. T. Varghese, and K. Raju, “IR, Raman, SERS and computational study of 2-(benzylsulfanyl)-3,5-dinitrobenzoic acid,” Spectrochimica Acta A: Molecular and Biomolecular Spectroscopy, vol. 113, pp. 28–36, 2013.
- V. Chiş, S. Filip, V. Miclǎuş et al., “Vibrational spectroscopy and theoretical studies on 2,4- dinitrophenylhydrazine,” Journal of Molecular Structure, vol. 744–747, pp. 363–368, 2005.
- M. Kumru, V. Küçük, and P. Akyürek, “Vibrational spectra of quinoline-4-carbaldehyde: combined experimental and theoretical studies,” Spectrochimica Acta A: Molecular and Bimolecular Spectroscopy, vol. 113, pp. 72–79, 2013.
- R. J. Xavier and P. Dinesh, “Conformational stability, vibrational spectra, HOMO-LUMO and NBO analysis of 1,3,4-thiadiazolidine-2,5-dithione with experimental (FT-IR and FT-Raman) techniques and scaled quantum mechanical calculations,” Spectrochimica Acta A: Molecular and Biomolecular Spectroscopy, vol. 113, pp. 171–181, 2013.
- C. Lee, W. Yang, and R. G. Parr, “Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density,” Physical Review B, vol. 37, no. 2, pp. 785–789, 1988.
- R. Dltchfield, “Molecular orbital theory of magnetic shielding and magnetic susceptibility,” The Journal of Chemical Physics, vol. 56, no. 11, pp. 5688–5691, 1972.
- K. Wolinski, J. F. Hinton, and P. Pulay, “Efficient implementation of the gauge-independent atomic orbital method for NMR chemical shift calculations,” Journal of the American Chemical Society, vol. 112, no. 23, pp. 8251–8260, 1990.
- E. D. Glendening and A. E. Reed, NBO Version 3.1, TCL, University of Wisconsin, Madison, Wis, USA, 1998.
- M. Izadyar and M. Khavani, “Quantum chemistry aspects of the solvent effects on the ene reaction of 1-Phenyl-1,3,4-triazolin-2,5-dione and 2-methyl-2-butene,” International Journal of Quantum Chemistry, vol. 114, no. 10, pp. 666–674, 2014.
- H. Pir, N. Günay, Ö. Tamer, D. Avci, and Y. Atalay, “Theoretical investigation of 5-(2-Acetoxyethyl)-6-methylpyrimidin-2,4-dione: Conformational study, NBO and NLO analysis, molecular structure and NMR spectra,” Spectrochimica Acta A: Molecular and Biomolecular Spectroscopy, vol. 112, pp. 331–342, 2013.
- Diwaker, “Quantum mechanical and spectroscopic (FT-IR, 13C, 1H NMR and UV) investigations of 2-(5-(4-Chlorophenyl)-3-(pyridin-2-yl)-4,5-dihydropyrazol-1-yl)benzo[d]thiazole by DFT method,” Spectrochimica Acta A: Molecular and Biomolecular Spectroscopy, vol. 128, pp. 819–829, 2014.
- J. Fleming, Frontier Orbitals and Organic Chemical Reactions, John Wiley and Sons, New York, NY, USA, 1981.
- R. G. Pearson, “Absolute electronegativity and hardness correlated with molecular orbital theory,” Proceedings of the National Academy of Sciences, vol. 83, no. 22, pp. 8440–8441, 1986.
- P. Politzer, P. R. Laurence, and K. Jayasuriya, “Molecular electrostatic potentials: an effective tool for the elucidation of biochemical phenomena,” Environmental Health Perspectives, vol. 61, pp. 191–202, 1985.
- A. Pullman, B. Pullman, and R. Lavery, “Molecular electrostatic potential versus field. significance for DNA and its constituents,” Journal of Molecular Structure: THEOCHEM, vol. 93, pp. 85–91, 1983.
- V. D. Vitnik, J. Ž. Vitnik, N. R. Banjac, N. V. Valentić, G. S. Ušćumlić, and I. O. Juranić, “Quantum mechanical and spectroscopic (FT-IR, 13C, 1H NMR and UV) investigations of potent antiepileptic drug 1-(4-chloro-phenyl)-3-phenyl-succinimide,” Spectrochimica Acta A: Molecular and Biomolecular Spectroscopy, vol. 117, pp. 42–53, 2014.
- B. Çatıkkaş, E. Aktan, and Z. Seferoǧlu, “DFT, FT-Raman, FTIR, NMR, and UV-Vis studies of a hetarylazo indole dye,” International Journal of Quantum Chemistry, vol. 113, no. 5, pp. 683–689, 2013.
- M. H. Jamróz, J. C. Dobrowolski, and R. Brzozowski, “Vibrational modes of 2,6-, 2,7-, and 2,3-diisopropylnaphthalene. A DFT study,” Journal of Molecular Structure, vol. 787, no. 1–3, pp. 172–183, 2006.
- Gaussian 09, “Gaussian,” Wallingford CT, 2004.
- N. Günay, H. Pir, D. Avci, and Y. Atalay, “NLO and NBO analysis of Sarcosine-Maleic acid by using HF and B3LYP calculations,” Journal of Chemistry, vol. 2013, Article ID 712130, 16 pages, 2013.
- W. B. Person and J. H. Newton, “Dipole moment derivatives and infrared intensities. I. Polar tensors,” The Journal of Chemical Physics, vol. 61, no. 3, pp. 1040–1049, 1974.
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