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TRANSCRIPT
Spectroscopic (FT-IR, FT-Raman, UV–vis), Fukui function,
NLO, NBO, NPA and Thermodynamic properties of L-
Alaninium oxalate by ab initio and DFT method.
G.Ramachandran*
*Department of Physics, P.U.M .School, Vasur-632514, Tamilnadu, India.
*corresponding author: [email protected] (Dr.G.Ramchandran)
ABSTRACT
The Fourier Transform Infrared and Raman spectra of the L-Alaninium oxalate have
been recorded and analyzed. The fundamental vibrational wave numbers intensities of
vibrational bands and optimized geometrical parameters of the compound were evaluated using
DFT(B3LYP) method with 6-31+G(d,p) basis set The stable geometry of the compound was
determined from the potential energy surface scan. Complete vibrational assignments and
Natural Bond Orbital (NBO) analysis for the title compound were carried out. The assignments
of the vibrational spectra were carried out with the help of normal co-ordinate analysis (NCA)
following the Scaled Quantum Mechanical Force Field (SQMFF) methodology. The molecule
orbital contributions were studied by using the total (TDOS), partial (PDOS), and overlap
population (OPDOS) density of states. UV–visible spectrum of the compound was recorded and
the electronic properties, such as HOMO and LUMO energies were performed by time-
dependent DFT (TD-DFT) approach. Mulliken population analyses on atomic charges were also
calculated. Besides, molecular electrostatic potential (MEP) and thermodynamic properties
were performed.
Keywords: L-Alaninium oxalate; FTIR; FT-Raman; DFT; HOMO; LUMO;
1. Introduction
L –Alaninium oxalate organic single crystal possess unique opto-electronic
properties and its molecules have delocalized electron namely, conjugated electron system
exhibit various photo responses such as photoconductive, photo catalytic behavior [1,2].The
organic materials with intermolecular charge transfer have second order non liner optical effects
[3].The title compound is asymmetric carbon atom and non-Centro symmetric space group,
which make them optically active. It zwitterionic in nature has large hyperpolarizability and non-
linear optical effect [4]. In the recent years, amino acid complexes have received much attention
because they proved to be useful in nonlinear optical application. In particular, optically active
amino acids display specific features of interest such as molecular chirality, wide transparency
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range in the visible and UV spectral region and zwitterionic nature of the molecule, which favors
crystal hardness [5-9].
Recently density functional theory (DFT) has emerged as a powerful tool for analyzing
vibrational spectra of fairly large molecules. The application of DFT to chemical systems has
received much attention because of faster convergence in time than traditional quantum
mechanical correlation methods [10-13]. Literature survey reveals that so far there is no
complete theoretical study for the title compound LAO. In this study, we set out experimental
and theoretical investigation of the conformation, vibrational and electronic transitions of LAO.
In the
ground state theoretical geometrical parameters, IR, Raman and UV spectra, HOMO and LUMO
energies of title molecule were calculated by using Gaussian 03W program. Detailed
interpretations of the vibrational spectra of the LAO have been made on the basis of the
calculated potential energy distribution (PED). The experimental results (IR, Raman and UV
spectra) were supported by the computed results, comparing with experimental characterization
data; vibrational wavenumbers and absorption wavelength values are in fairly good agreement
with the experimental results. The stable position of LAO with respect to alipatic compound was
obtained by performing the potential energy surface (PES) scan with B3LYP/6-31+G(d,p) level
of theory. The redistribution of electron density (ED) in various bonding, antibonding orbitals
and E(2) energies have been calculated by natural bond orbital (NBO) analysis to give clear
evidence of stabilization originating from the hyper conjugation of various intra- molecular
interactions. By analyzing the total (TDOS), partial (PDOS), and overlap population (OPDOS)
density of states, the molecular orbital compositions and their contributions to the chemical
bonding were studied. The study of HOMO, LUMO analysis has been used to elucidate
information regarding charge transfer within the molecule. Moreover, the Mulliken population
analyses of the title compound have been calculated and the calculated results have been
reported. The experimental and theoretical results supported each other, and the calculations are
valuable for providing a reliable insight into the vibrational spectra and molecular properties.
2. Experimental details
Colorless crystals of LAO were grown by slow evaporation technique by dissolving L-
Alanine with the aqueous solution of oxalic acid in the stoichiometric ratio 1:1 colorless,
transparent crystals of LAO were obtained within two weeks. Repeated crystallization yielded
good quality crystals. The photograph of the grown crystal of LAO is shown in Fig.1.
The powder X-ray diffraction (XRD) measurements were carried out with Cu Kα radiation
using a Siemens D 500 X-ray diffractometer equipped with a rotating anode scanning (0.01 step
in 2θ) over the angular range 10-70˚ at room temperature generating X-ray by 45 kV and 30 mA
power settings. Monochromatic X-ray of λ=1.5418A˚ Kα1 line from a Cu target were made to
fall on the prepared samples. The diffraction pattern was obtained by varying the scattering angle
2θ from 10˚ to 70˚ in step size of 0.02.
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The FTIR spectrum of the compound is recorded in Bruker IFS 66V spectrometer in the
range of 4000–400 cm-1. The spectral resolution is ± 2 cm-1. The FT- Raman spectrum of LAO is
also recorded in the same instrument with FRA 106 Raman module equipped with Nd: YAG
laser source operating at 1.064 lm line widths with 200mW power. The spectrum is recorded in
the range of 4000–100 cm-1 with scanning speed of 30 cm-1 min-1 of spectral width 2 cm-1. The
frequencies of all sharp bands are accurate to •± 1 cm-1. The ultraviolet absorption spectrum of
sample solved in water was examined in the range 100–1000 nm by using Cary 5E UV–Vis NIR
recording spectrometer. All the spectral measurements were carried out at Indian Institute of
Technology, Chennai, India.
3. Computational details
The molecular structure optimization of the title compound and corresponding energy
and vibrational harmonic frequencies were calculated using the DFT with Becke-3-Lee–Yang–
Parr (B3LYP) combined with standard 6-31+G(d,p) basis set using GAUSSIAN 03W program
package without any constraint on the geometry [14]. Geometries have been optimized with full
relaxation on the potential energy surfaces at B3LYP/6-31+G(d,p) basis set. The optimized
geometrical parameters, energy, fundamental vibrational frequencies, IR intensity, Raman
activity and the atomic charges were calculated theoretically using GAUSSIAN 03W package.
The Cartesian representation of the theoretical force constants have been computed at optimized
geometry by assuming C1 point group symmetry. Scaling of force field was performed according
to SQM procedure [15,16] using selective scaling in the natural internal coordinate
representation [17,18]. Transformations of the force field and the subsequent normal coordinate
analysis including the least square refinement of the scaling factors, calculation of the potential
energy distribution (PED) and the prediction of IR and Raman intensities were done on a PC
with the MOLVIB program(VersionV7.0-G77) written by Sundius [19,20]. The symmetry of the
molecule was also helpful in making vibrational assignments. The symmetries of the vibrational
modes were determined by using the standard procedure [21] of decomposing the traces of the
symmetry operation into the irreducible representations. The symmetry analysis for the
vibrational modes of LAO is presented in detail in order to describe the basis for the
assignments. By combining the result of the GAUSSVIEW program [22] with symmetry
considerations, vibrational frequency assignments were made with a high degree of confidence.
There is always some ambiguity in designing internal coordinates. However, the defined
coordinates form complete set and matches quite well with the motions observed using the
GAUSSVIEW program. UV–Vis spectra, electronic transitions, vertical excitation energies,
absorbance and oscillator strengths were computed with the Time-Dependent DFT (TD-DFT)
method. The electronic properties such as HOMO and LUMO energies were determined by TD-
DFT approach. To calculate functional group contributions to the molecular orbitals, the total
density of states (TDOS or DOS) the partial density of states (PDOS) and overlap population
density of states (OPDOS) spectra were prepared by using the program Gauss Sum 2.2[23]. The
PDOS and OPDOS spectra were created by convoluting the molecular orbital information with
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Gaussian curves of unit height and a FWHM (Full Width at Half Maximum) of 0.3 eV. The
contribution of a group to a molecular orbital was calculated by using Mulliken population
analysis.
3.1 The prediction of Raman intensities
The Raman scattering activities (Si) calculated with the GAUSSIAN 03W program were
subsequently converted to relative Raman intensities (Ii) using Raint program [24] by the
following relationship derived from the basic theory of Raman scattering [25]. 4
0( )
[1 exp( )
i i
ii
f v v sIi
hcvv
kT
In the above formula 0 is the laser exciting frequency in cm-1 (in this work, we have used the
excitation wave number ν0 = 9398.5 cm-1, which corresponds to the wavelength of 1064 nm of a
Nd:YAG laser), νi is the vibrational wave number of the ith normal mode (cm-1) and Si is the
Raman scattering activity of the normal mode νi, f (is the constant equal to 10-12) is the suitably
chosen common normalization factor for all peak intensities. h, k, c and T are Planck constant,
Boltzmann constant, speed of light and temperature in Kelvin, respectively.
4. Result and Discussion
4.1 Characterization details of X-ray diffraction analysis
The experimental powder X-ray diffraction pattern of LAO crystal is shown in
Fig.2. Efforts were made to record the powder XRD pattern of the L –Alaninium oxalate crystal
and index them. Obtained unit cell parameters of L- Alanine oxalate compared with L-Alanine
and oxalic acid is shown in Table 1. The calculated Lattice parameter had been determined as a =
5.6304 Å; b = 7.2353 Å; c = 19.597 Å; υ=798.3 Å3 [26]. Which confirm the formation of the title
compound in orthorhombic crystal system.
4.2 Optimized geometry
The Optimized molecular structure of LAO with an atom numbering scheme adopted in
the computation is shown in the Fig.3. The optimized geometric parameters (bond lengths, bond
angles) of the title molecule are presented in Table 2. DFT calculations predict the self-consistent
field (SCF) energy of LAO as -702.1 Hartrees. The lowering of bond angles C(1)-C(3)-C(4)
to109.44˚ and H(16)-C(4)-H(8) to 109.46˚ (normally 120˚) is due to the charge transfer from the
oxalate anion to the alaninium cation which enhances the optical nonlinearity of the molecule.
The important geometrics such as C(1)-O(5) and C(1)-O(6) bond distances 1.21 and 1.31Ǻ and
C(3)-C(1)-O(5) and C(3)-C(1)-O(6) bond angles 120˚ and 120˚ respectively of one amino acid
residue suggest the presence of deprotonated carboxylate group. The H(17)….O(9) distance of
3.4134Ǻ is an increase strong C-H-O hydrogen boding and this length is significantly shorter
than the vandar Waals separation between the O atom and H atom [27]. Computed values show
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that the bond length of N(2)-H(13) and N(2)-H(14) are 1.02Ǻ and 1.02Ǻ respectively. The same
value in N-H distance in the NH3 group indicated the existence N-H…..O hydrogen bonding.
Detail description of vibrational modes can be given by means of normal
coordinate analysis (NCA). For this purpose the full set of 57 standard internal coordinates for
LAO are define as given in Table 3. From these, a non-redundant set of local symmetry
coordinates were constructed by suitable linear combinations of internal coordinated following
the recommendations for Forgrasi et al. [28, 29] are summarized in Table 4. The theoretically
calculated DFT force field were transformed to this latter set of vibrational coordinates and used
in all subsequent calculations.
4.2. Vibrational band assignments
According to the theoretical calculations, LAO has a structure of C1 point group
symmetry. The molecule has 21 atoms and 57 modes of fundamental vibrations. We have taken
recourse to the calculation and visualization of contribution of internal coordinates in each
normal mode by Gaussian package [14] and chemcraft program. The harmonic vibrational
frequencies calculated for the title compound at B3LYP levels using 6-31+G(d,p) along with the
observed FT-IR and FTR frequencies for various modes of vibrations are presented in Table 5.
Some bands found in the predicted FT-IR and FTR spectra were not observed in the
experimental spectra of LAO. Therefore, a linearity between the experimental and scaled
calculated wave numbers for DFT method of LAO can be estimated by plotting the calculated
versus experimental wave numbers as shown in Fig.4. The correlation coefficients (R2) for
experimental and observed wave numbers computed from the DFT method were found to be
0.964. It can be noted from the R2 values that the theoretical prediction is in good agreement
with the experimental wave numbers. Also Fig.4 reveals the overestimation of the calculated
vibrational modes due to neglect of anharmonicity in real system. Inclusion of electron
correlation in DFT to a certain extent makes the frequency values smaller in comparison with the
HF frequency data. For the plots of simulated IR and Raman spectra, pure Lorentzian band
shapes were used with a bandwidth of 40 cm-1. Figs.5 and 6 shows a comparative representation
of theoretical and experimental FT-IR and FTRaman spectra, respectively.
4.2.1 O-H vibrations
The O-H group gives rise to three vibrations (stretching, inplane bending and out-of-
plane bending vibrations). The O-H group vibrations are likely to be the most sensitive to the
environment, so they show pronounced shifts in the spectra of the hydrogen bonded species. The
hydroxyl stretching vibrations are generally [30] observed in the region around 3500 cm-1. In the
case of the unsubstituted phenols it has been shown that the frequency of O-H stretching
vibration in the gas phase is 3657 cm-1 [31]. Similarly in our case a FT-IR band at 3450 cm-1 is
assigned to O-H stretching vibrations. A comparison of this band with that of the computed by
B3LYP/6-31+G(d,p) method (mode no. 57) at 3622 cm-1 show positive deviation of ~60 cm-1,
this may be due to the presence of strong intermolecular hydrogen bonding. The O-H in-plane
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bending vibration in phenols, in general lies in the region 1150-1250 cm-1 and is not much
affected due to hydrogen bonding unlike to stretching and out-of-plane bending frequencies [30].
The medium strong band in FT-IR spectrum at 1250 cm-1 is assigned to O-H inplane bending
vibration for both the O-H groups in the ring. The theoretically computed value (mode no.36) at
1196 cm-1 by B3LYP/6-31+G(d,p) method (Table 5) show very good agreement with recorded
spectrum. The O-H out-of-plane bending mode for the free molecule lies below 300 cm-1 and it
is beyond the infrared spectral range of the present investigation. However, for the associated
molecule [32], the O-H out-of-plane bending mode lies in the region 517-710 cm-1 in both
intermolecular and intramolecular associations, the frequency is at a higher value than in free O-
H. The band at 490 cm-1 by B3LYP/6-31+G(d,p) method (mode no. 17) show excellent
correlation with recorded FTIR and FT-Raman bands at 490 cm-1 and 470 cm-1 respectively, but
this mode is a mixed mode as shown in Table 5.
4.2.2 N-H vibrations
The scaled -NH2 asymmetric and symmetric stretches in the range 3319-3236 cm-1 is in
agreement with experimental value of 3166-3126 cm-1. The PED of this mode is contributing
96% for asymmetric and 99% for symmetric stretching mode. The computed -NH2 scissoring
vibration at 1538 cm-1 is in excellent agreement with expected characteristic value 1600 cm-1
[33,34]. This is also very good agreement with recorded FT-IR value of 1495 cm-1. The C-NH2
out-of-plane and in-plane bending vibrations at 391 cm-1, is also in good agreement with the
assignment in the experimental data. The NH2 wagging computed at 463 cm-1 is missing in both
FT-IR and FT-Raman spectra.
4.2.3 Methyl group vibrations
The CH stretching in CH occurs at lower frequencies than those of the aliphatic
compound (3000–2800 cm-1) [35]. In the present work, CH3 asymmetric stretching is found at
2980 cm-1 in FT-IR and 2933 cm-1 in Raman spectrum. The CH symmetric stretching is found at
2932 cm-1 in FT-Raman. For methyl substituted aliphatic derivatives the symmetric bending
deformations and rocking modes normally appear around 1465–1440 cm-1 and 1040–990 cm-1
respectively [36]. In the present investigation a strong peak at 1440 cm-1 in FT-IR is assigned to
symmetric bending deformation. The in-plane rocking mode appears around 1420 cm-1 in
Raman. The out-of-plane rocking modes are observed around 1180 cm-1 in FT-Raman spectrum.
All these frequencies are shifted towards the maximum. This implies, the methyl vibrations are
favored by the presence of NH2 in the ring. These observations agree well with the earlier work
[37,38]. Also all the above observed frequencies coincide very well with the calculated
frequencies. The in-plane and out-of-plane bending vibrations lie around 410 cm-1 in FT-IR and
380 cm-1 in FT-Raman. CH torsional mode is expected around 50-100 cm-1 in FT-Raman
spectrum. The observed wavenumber (in FTRaman) at 80 cm-1 (mode no.8) is assigned to CH3
torsional mode, shows good agreement with computed wavenumber at 70 cm-1 by B3LYP
method.
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4.2.4 C=O and C-O vibrations
The band observed in the region 1700–1800 cm-1 is usually the most characteristic
feature of carboxylic group. This band is due to the C-O stretching vibration. Also Koczon et al.
[39] observed the range of 1800–1500 cm-1, the C-C and C=O are group stretching vibrations.
The C=O stretching vibration of the LAO is observed at 1740 and 1590cm-1 in FT-IR and 1700
and 1600 cm-1 in FT-Raman spectrum and these wavenumbers are good coherent with empirical
values. Also this mode is observed at 1703 and 1682 cm-1 in FT-IR and FT-Raman spectrum by
Swislocka et al. [40]. The C=O and C-O vibrations also show fairly good coherent in literature
[41].
4.2.5 C-N vibrations
The identification of C-N vibration is a very difficult task, as mixing of several
bands is possible in this region. In this study, the bands of moderate intensity found at 1360cm-1
in FTIR spectra and 1365 cm-1 in FTRaman spectra, respectively, maybe due to interaction
between C-N stretching and N-H bending of C-N-H group [42]. Hence, they are assigned to
asymmetric and symmetric bending vibrations, respectively. The band observed at 1300 cm-1 in
FTIR spectrum is due to C-N-H bending vibration. These are in good agreement with the
computed values. Silverstein et al. [43] assigned C-N stretching absorption in the region 1342–
1266 cm-1.In this study, the band identified at 1270 cm-1 in FTRaman spectrum is assigned to C-
N stretching vibration. The theoretical scaled wave numbers at 410 and 402 cm-1 for the C-C-N
asymmetric and symmetric deformation vibration with PED 35 and 34%, respectively, which fall
in FTRaman spectrum at 410 and 402 cm-1(mode nos. 16 and 15) are in good agreement with the
experimental value. Puviarasan et al. [44] assigned frequencies at 300 and 213 cm-1 in FTRaman
spectrum, which have been assigned to in-plane and out-of-plane bending of C-N-C vibrations.
The theoretically computed values of C-N-C deformations also fall at 291 and 219 cm (mode
Nos 12 and 9), and are found to be in good agreement with the experimental data. The PED
corresponding to this vibration is 61%. The band observed at 508 cm-1 in FTIR spectrum which
has been assigned to N-C-C bending vibration is also in good agreement with the theoretical
value (mode No. 18).
4.2.6 C-H stretching modes
The hetero aromatic structure shows the presence of C-H stretching vibration in the
region 3100–3000 cm-1, which is the characteristic region for the ready identification of C-H
stretching vibrations [45]. In this region, the nature of the substituents does not make any
appreciable change [46]. Gunasekaran et al. [47] have reported the presence of C-H stretching
vibrations in the region 3100–3000 cm-1 for asymmetric stretching and 2990–2850 cm-1for
symmetric stretching. In this molecule, the FTIR band at 3059 cm-1and FTRaman band at 3050
cm-1 represent asymmetric stretching vibration. The FTIR and FTRaman bands at 2980 cm-1 and
2933 cm-1 represent C-H symmetric stretching vibrations. The scaled vibrations calculated at
3029 cm-1 ,and 3013cm-1 by B3LYP/6-31+G(d,p) method (mode Nos 52, and 51) which are
listed in Table 5. correspond to asymmetric and symmetric stretching mode of CH units with the
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PED contribution of 98 and 95%, respectively. The bands corresponding to in-plane and out-of-
plane bending and deformation vibrations of CH group are presented in Table 5. The
experimental frequencies at 1063 cm-1 in FTIR spectra and at 1040 cm-1 in FTRaman spectra and
frequencies at 1063 cm-1 in FTIR spectra [48] which have been assigned to C-CH asymmetric
and symmetric bending vibrations, respectively, are compared with the theoretically calculated
values. The bands observed at 820 and 790 cm-1 in FTIR spectrum and at 814 cm in FTRaman
spectrum, respectively, have been assigned to asymmetric and symmetric N-CH deformation,
and in Raman
spectrum[49] the band observed at 754 cm-1 has been assigned to N-CH deformation. These
assigned frequencies coincide well with the theoretically computed values (mode Nos 28–25).
The wave number calculated by the B3LYP/6-31+G(d,p) method for the C-C-CH deformation
mode at 323 cm-1 is identified at 320 cm-1(mode No. 13) in the FTRaman spectrum [49], and is
found to be in good agreement with the experimental data with the contribution of 48% PED.
5. UV–vis spectra analysis
In the UV–vis region with high extinction coefficients, all molecules allow strong π-π*
and σ-σ* transition [50]. In an attempt to understand the nature of electronic transitions in terms
of their energies and oscillator strengths, time-dependent DFT (TD-DFT) calculations involve
configuration interaction between the singly excited electronic states are conducted. The
calculated excitation energies, oscillator strength (f) and wavelength (λ) and spectral assignments
are given in Table 6. The major contributions of the transitions are designated with the aid of
SWizard program [51]. The theoretical absorption wavelengths (in gas phase and solvent) are
compared in Table 6. Due to the Frank–Condon principle, the maximum absorption peak (λmax)
in an UV–visible spectrum corresponds to vertical excitation. TD-DFT calculations predict three
transitions in the UV–vis region for LAO molecule. The strong transitions at 2.67 eV (463 nm)
with an oscillator strength f = 0.5622 in gas phase, at 3.07 eV (402 nm) with an oscillator
strength f = 0.0007 in water solvent are assigned to n-π* transition. The experimental and
theoretical UV–Vis spectrum of LAO is shown in Fig. 7. In view of calculated absorption
spectra, the maximum absorption wavelength corresponds to the electronic transition from the
HOMO to LUMO with 100% contribution. The other wavelength, excitation energies, oscillator
strength and calculated counterparts with major contributions can be seen in Table 6. The
frontier molecular orbitals, HOMO and LUMO and frontier orbital gap helps to exemplify the
chemical reactivity and kinetic stability of the molecules [52]. The HOMO is the orbital that
primarily actsas an electron donor and the LUMO is the orbital that largely acts as the electron
acceptor. In order to evaluate the energetic behavior of the title compound, we carried out
calculations in gas and in solvent (water). HOMO and LUMO energies of HOMO-1, HOMO
(first excited state), lumo (ground state), HOMO-1 and their orbital energy gaps are calculated
by TD-DFT/B3LYP/6-31+G(d,p) in solvent (water) and Gas phase are presented in Table 6. The
3D plots of the frontier orbitals namely ground state (HOMO), HOMO+1 and first excited state
(LUMO), LUMO+1 are ∆E= -0.12061 eV ∆E= -0.26233 eV shown in Fig. 8. The positive phase
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is blue and the negative one is red. It can be seen from the plots that the HOMO levels are spread
over the amino and carboxylate group expect the methyl group and H atoms. The LUMO of first
excited state is almost uniformly distributed over the molecule expect the H atoms, methyl atoms
and CH atoms. The energy gap of HOMO–LUMO explains the eventual charge transfer
interaction within the molecule, which influences the biological activity of the molecule.
Furthermore, in going from the gas phase to the solvent phase, the increasing value of the energy
gap and molecule becomes more stable. This electronic absorption corresponds that is mainly
described by one electron excitation from the highest occupied molecular or orbital (LUMO).
The energy difference between HOMO and LUMO orbital is a critical parameter in determining
molecular electrical transport properties because it is a measure of electron conductivity,
calculated by B3LYP/6-31+G(d,p) method is -0.12061 eV for the title molecule. The computed
energy values of LAO by B3LYP/6-31+G(d,p) method is presented in Table 7. The observed
transition from HOMO to LUMO is π – π*. Moreover lower in the HOMO and LUMO energy
gap explains the eventual charge transfer interactions taking place within the molecule.
5.1 Total, partial, and overlap population density-of-states
In the boundary region, neighboring orbitals may show quasi degenerate energy levels. In
such cases, consideration of only the HOMO and LUMO may not yield a realistic description of
the frontier orbitals. For this reason, the total (TDOS), partial (PDOS), and overlap population
(OPDOS or COOP (Crystal Orbital Overlap Population)) density of states [53–55], in terms of
Mulliken population analysis were calculated and created by convoluting the molecular orbital
information with Gaussian curves of unit height and full width at half maximum (FWHM) of 0.3
eV by using the GaussSum 2.2 program [23]. The TDOS, PDOS and OPDOS of the LAO are
plotted in Figs. 9–11, respectively. They provide a pictorial representation of MO (molecule
orbital) compositions and their contributions to chemical bonding. The most important
application of the DOS plots is to demonstrate MO compositions and their contributions to the
chemical bonding through the OPDOS plots which are also referred in the literature as COOP
diagrams. The OPDOS shows the bonding, anti-bonding and nonbonding nature of the
interaction of the two orbitals, atoms or groups. A positive value of the OPDOS indicates a
bonding interaction (because of the positive overlap population), negative value means that there
is an anti-bonding interaction (due to negative overlap population) and zero value indicates
nonbonding interactions [56]. Additionally, the OPDOS diagrams allow us to determine and
compare of the donor– acceptor properties of the ligands and ascertain the bonding, non-
bonding. The calculated total electronic density of states (TDOS) diagrams of the LAO is given
in Fig. 9. The partial density of state plot (PDOS) mainly presents the composition of the
fragment orbitals contributing to the molecular orbitals which is seen from Fig. 10. As seen Fig.
11, HOMO orbitals are localized on the ring and their contributions are about 14%. The LUMO
orbitals are localized on the ring (84%) of the compound. Only based on the percentage shares of
atomic orbitals or molecular fragments in the molecule is difficult to compare groups in terms of
its bonding and anti-bonding properties. Thus the OPDOS diagram is shown in Fig. 11 and some
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of orbitals of energy values of interaction between selected functional groups which are shown
from figures easily, (O–H) atoms (green line) are negative (anti-bonding interaction). As can be
seen from the OPDOS plots for the LAO have anti-bonding character in frontier HOMO and
LUMO molecular orbitals for pyridine and oxygen atoms. Also OPDOS showed bonding
character both HOMO and LUMO.
5.2 Global and local reactivity descriptors
Based on the density functional descriptors, global chemical reactivity descriptors
of the title molecule such as ionization potential (I), electron affinity (A), chemical potential (μ),
electronegativity (χ), global hardness (ƞ), global softness(σ) and global electriphilicity (ω) values
can be described as followed [57]. In simple molecule orbital theory approaches, the HOMO
energy (E HOMO) is related to the ionization potential (I) by Koopman’s theorem and LUMO
energy (ELUMO) has been used to estimate the electron affinity (A) [58].
( )
( )
HOMO
LUMO
Ionizationpotential I E
Electronaffinity A E
The average value of the HOMO and LUMO energy is related to the electronnegativity (χ)
define by Mulliken [71]
( )( )
2
I AElectronegativity
In addition, the HOMO and LUMO energy is related to the hardness (ƞ) and softness (σ) [59].
( )
2
1( )
I AGlobalhardness
Globalsoftness
Parr et al. [60] defined global electriphilicity (ω)
2
( )2
Electriphilicity
Where μ is the chemical potential takes the average value of ionization potential (I) and electron
affinity (A) [61].
( )( )
2
I AChemicalpotential
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The electronic chemical potential is the parameter which describes the escaping tendency
of electrons from an equilibrium system. Thus the frontier molecular orbital analysis also
provided the detailed on chemical stability, chemical hardness and electronegativity of the
molecule in B3LYP/6-31+G(d,p) basis set are presented in Table 7, respectively.
6. NBO analysis
By using the second-order bond–antibond (donor–acceptor) NBO energetic analysis,
insight into the most important delocalization schemes was obtained. The change in electron
density (ED) in the (σ*, π*) antibonding orbitals and E(2) energies have been calculated by
natural bond orbital (NBO) analysis [63] using DFT method to give clear evidence of
stabilization originating from various molecular interactions. The hyperconjugative interaction
energy was deducted from the second-order perturbation approach [63] 2
(2) ij
i j i
j i
FE E q
where qi is the donor orbital occupancy, εi and εj are diagonal element, and F (i, j) is the off
diagonal NBO Fock matrix element. The larger E(2) value the more intensive is the interaction
between electron donors and acceptor, i.e. the more donation tendency from electron donors to
electron acceptors and the greater the extent of conjugation of the whole system [64].
Delocalization of electron density between occupied Lewis’s type (bond or lone pair) NBO
orbital and formally unoccupied (anti bond or Rydberg) non-Lewis NBO orbital corresponds to a
stabilizing donor–acceptor interaction. NBO analysis has been performed on the LAO molecule
at the B3LYP/6-31+G (d,p) level to elucidate, the intra-molecular rehybridization and
delocalization of electron density within the molecule. The strong intramolecular
hyperconjugation interaction of the σ and π electrons of C–C to the anti C–C bond to the ring
leads to stabilization of some part in the ring as evident from Table 8. The intra molecular
hyperconjugative interaction of the (C1–C3) distribute to (C1–O5), (N2–H21) , (C3–C4), (C4-H24)
and (N2-H19) leading to stabilization of 0.83, 1.07,0.54, 2.32 and 0.961 kJ/mol respectively. This
enhanced further conjugate with anti bonding orbital of σ*(C1–C3), (C7–C9), leads to strong
delocalization of 4.70 and 1.14 kJ/mol respectively.
6.1 Natural population analysis
Natural population analysis[65](NPA) data of monomer and tetramer were used to
investigate the changes in charge, which give some insight into the interaction taking place upon
aggregation. For the sake of comparison, the calculated natural charges of LAO are presented in
Table 9. It shows that an atoms C13 has the most electronegative charge of -5.23961and O6 has
the most electropositive charge of 8.80348e. Likewise, C1 and C14 atom has considerable
electro negativity and they are tending to donate an electron. Conversely, the C3,C4 and C9
atoms have considerable electropositive and they are tending to acquire electron. Further, the
natural population analysis showed that 142 electrons in the title molecule are distributed on the
sub shell as follows:
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Core: 35.98980 (99.9717% of 36)
Valence: 105.55477 (99.5800% of 106)
Rydberg: 0.45543 (0.3207% of 142)
7. Fukui function analysis
The Fukui function is among the most basic and commonly used reactivity indicators.
The Fukui function is given as the change in the density function ρ(r) of the molecule as a
consequence of changing the number of electrons N in the molecule, under the constraint of a
constant external potential. The Fukui function is defined as:
rN
rrF
where ρ (r) is the electronic density, N is the number of electrons and r is the external
potential exerted by the nuclease. Fukui functions are introduced, which are advocated as
reactivity descriptors in order to identify the most reactive sites for electrophilic or nucleophilic
reactions within a molecule. The Fukui function indicates the propensity of the electronic density
to deform at a given position upon accepting or donating electrons [66,67]. Also, it is possible to
define the corresponding condensed or atomic Fukui functions on the jth atom site as,
)1()1(2
1
)()1(
)1()(
0
NqNqf
NqNqf
NqNqf
jjj
jjj
jjj
for an electrophilic rf j
, nucleophilic or free radical attack rf j
, on the reference
molecule, respectively. In these equations, qj is the atomic charge (evaluated from Mulliken
population analysis, electrostatic derived charge, etc.) at the jth atomic site in the neutral (N),
anionic (N+1) or cationic (N-1) chemical species. Here, it is important to mention that
independently of the approximations used to calculate the Fukui function, all of them follow the
exact equation:
1drrf
which is important in the use of the Fukui function as an intramolecular reactivity index.
The values of the Fukui function calculated from the NBO charges. The values of Fukui
function analysis obtained by employing MEP and Mulliken charges. The results were obtained
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from the NBO charges. From Table 10 note the presence of negative values of the Fukui
function. Recently it was reported that a negative Fukui function value means that when adding
an electron to the molecule, in some spots, the electron density is reduced; alternatively when
removing an electron from the molecule, in some spots, the electron density is increased.
From the calculated values, the reactivity order for the electrophilic case was C1 > N2 >
C3 > C4 > O5 > O6 > O9 > O10 > O11 > O12> H15> H16> H19 On the other hand, for
nucleophilic attack we can observe C7 > C8 > H13 > H14 > H17 > H18 > H20 > H21. Position
of reactive electrophilic sites and nucleophilic sites are accordance with the total electron density
surface and chemical behavior. If one compares the three kinds of attacks it is possible to
observe that, electrophilic attack is bigger reactivity comparison with the nucleophilic and
radical attack.
8. Molecular electrostatic potential surface
MEP is related to the electronic density and is a very useful descriptor in understanding
sites for electrophilic and nucleophilic reactions as well as hydrogen bonding interactions
[68,69]. The electrostatic potential V(r) is also well suited for analyzing processes based on the
“recognition” of one molecule by another, as in drug-receptor, and enzyme- substrate
interactions, because it is through their potentials that the two species first “see” each other
[70,71]. To predict reactive sites of electrophilic and nucleophilic attacks for the investigated
molecule, MEP at the B3LYP/6-31+G (d,p) optimized geometry was calculated. The negative
(red) regions of MEP were related to electrophilic reactivity and the positive (yellow) regions to
nucleophilic reactivity (Fig. 12). The negative region is localized on the carbon atoms and the
positive region is localized on the nitrogen atom. These results provide information concerning
the region where the compound can interact intermolecularly and bond metallically. Therefore,
Fig.12 confirms the nonexistence of intermolecular interactions within the molecule.
9. Mulliken population analysis
The Mulliken atomic charges are calculated by determining the electron population of
each atom as defined by the basis function [71]. The Mulliken atomic charges of LAO molecule
calculated by B3LYP/6-31+G(d,p) basis set. Calculation of effective atomic charges plays an
important role in the application of quantum chemical calculations to molecular systems. Our
interest here is in the comparison of different methods to describe the electron distribution in
LAO as broadly as possible, and assess the sensitivity, the calculated charges to changes in (i)
the choice of the basis set; (ii) the choice of the quantum mechanical method. Mulliken charges,
calculated the electron population of each atom defined in the basic functions. The Mulliken
charges calculated at different levels and at same basis set are listed in Table 11. The results can,
however, better represent in graphical form as given Fig. 13. The charges depending on basis set
are changed due to polarizability. The H20 and H21 atoms have more positive charges at
B3LYP/6-31+G(d,p). This is due to the presence of electronegative oxygen atom; the hydrogen
atoms attract the positive charge from the oxygen atoms The C1,C7 and C8 atoms by B3LYP
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method is more negative charges than the other atoms due to electron accepting substitutions at
that position in LAO. The result suggests that the atoms bonded to O atom and all H atoms are
electron acceptor and the charge transfer takes place from O to H in LAO.
10. First order hyperpolarizability
In discussing nonlinear optical properties, the polarization of the molecule by an external
radiation field is often approximated as the creation of an induced dipole moment by an external
electric field. Under the weak polarization condition, we can use a Taylor series expansion in the
electric field components to demonstrate the dipolar interaction with the external radiation
electric field. The first order hyperpolarizability (β0) and related properties (α, β0 and ∆α) of
LAO are calculated based on the finite-field approach. In the presence of an applied electric
field, the energy to a system is a function of the electric field. The first-order hyperpolarizability
is a third rank tensor that can be described by a 3 3 3 matrix. The 27 components from the
3D matrix can be reduced to 10 components due to the Kleinman symmetry [72]. The
components of β are the coefficients in the Taylor series expansion of the energy in the external
electric field. When the electric field is weak and homogeneous, this expansion becomes.
0 1 1......
2 6E E F F F F F F
where E0 is the energy of the unperturbed molecules, Fα is the field of the origin μα, ααβ and βαβγ
are the components of dipole moment, polarizabiltiy and the first-order hyperpolarizability
respectively. The total static dipole moment μ, the mean polarizability α0, the anisotropy of the
polarizability ∆α and the mean first hyperpolarizability β0, using the x, y and z components are
followed: 1
2 2 2 2( )x y z
03
xx yy zz
1 1
2 2 22 22 ( ) ( ) 6xx yy yy xx xx
yyzxxzzzzz
yzzxxyyyyy
xzzxyyxxxx
zyx
and
2
1
222
0 )(
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The calculated hyperpolarizability values of LAO are given in Table 12. The value of
second order optical susceptibility χ2 in a given depends on the molecular hyperpolarizability β,
the number of chromophores and the degree of non-centro symmetry. The computed first-order
hyperpolarizability, βtotal of the LAO molecules is .,..106129.3 30 use which that of urea is 10
times.
11. Thermodynamic Parameters
The standard statistical thermodynamic functions at B3LYP/6.31+G(d,p) level heat
capacity (C0p,m), entropy (S0
m) and enthalpy (Hm0) for the title compound are obtained from the
theoretical wavenumbers (Table13), which shows that these thermodynamic functions are
increasing with temperature ranging from 100 to 1000 K due to the fact that the molecular
vibrational intensities increase with temperature [73]. The correlation equations between heat
capacity, entropy, enthalpy changes and temperatures are built-in by quadratic formulas. The
fitting factors (R2) for these thermodynamic properties are 1.0000, 1.0000 and 1.0000
respectively. The corresponding fitting equations are as follow and the correlation graphs of
those are represented in Figure. 14.
These equations could be used for the further studies on the title compound. They can be
used to compute the other thermodynamic energies according to relationships of thermodynamic
functions and estimate directions of chemical reactions according to the second law of
thermodynamics in thermo chemical field. It is to notice that all thermodynamic calculations are
done in gas phase only and they cannot be used in liquid phase.
12. Conclusion
The organic NLO material from the amino acid family, viz L-Alaninium oxalate (LAO)
was grown by slow evaporation method. From the XRD analysis of the grown crystal, lattice
parameters were calculated. They are in good agreement with reported values. Optimized
geometry of the molecules shows the existence of C-H…O carbon bonding in the molecule.
Assignments of the vibrational bands have been done. The molecular geometry, HOMO and
LUMO energy and thermo-dynamical properties in the ground state have also been calculated.
The lowering of the HOMO-LUMO energy gap value suggests the possibility of intermolecular
charge transfer in the molecule making it a suitable NLO active compound. The correlations
between the statistical thermodynamic and temperature were also obtained. It is seen that the
heat capacities, entropies and enthalpies increase with increase temperature of molecule.
0 4 2 2
,
0 4 2 2
0 4 2 2
71.96 0.346 0.001 10 ( 1.0000)
276.9 1.602 0.003 10 ( 1.0000)
0.064 0.067 0.0001 10 ( 1.0000)
p m
m
m
C T T R
S T T R
H T T R
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Figure 1. Numbering system adopted in the molecular structure of DMPABA.
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Figure.2. Observed and stimulated FT-IR spectra of 2-(2,3-dimethylphenyl)aminobenzoic acid.
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Figure.3. Observed and stimulated FT-Raman spectra of 2-(2,3-dimethylphenyl) aminobenzoic
acid.
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Figure 4 The selected frontier molecular orbitals of 2-(2,3-dimethylphenyl)aminobenzoic acid
with the energy gaps..
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Figure 5 The calculated TDOS diagrams of 2-(2,3-dimethylphenyl)amino benzoic acid.
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‘
Figure 6 The calculated PDOS diagrams of 2-(2,3-dimethylphenyl)amino benzoic acid.
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Figure 7 The calculated OPDOS (or COOP) diagrams of 2-(2,3-dimethylphenyl)amino
benzoic acid.
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Figure 8 Comparative Mulliken 3D plot by B3LYP/6-31G(d,p) and B3LYP/6-
311++G(d,p) levels of 2-[(2,3-dimethylphenyl)amino]benzoic acid.
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Figure 9 Electrostatic potential 3D map and 2D contour map for 2-[(2,3
dimethylphenyl)amino]benzoic acid.
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Figure 10 Correlation graph between Heat Capacity and Temperature in the title compound at
B3LYP/6-311++G(d,p) and B3LYP/6-31G(d,p) method.
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Figure 11 Correlation graph between Entropy and Temperature in the title compound at
B3LYP/6-311++G(d,p) and B3LYP/6-31G(d,p) method.
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Figure 12 Correlation graph between Enthalpy and Temperature in the title compound at
B3LYP/6-311++G(d,p) and B3LYP/6-31G(d,p) method.
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Table 1 Geometrical parameters optimized in 2-[(2,3-dimethylphenyl)amino]benzoic acid bond length (A˚ ), bond angle (◦).
Parameters
Bond lengths(Ǻ) Bond angles(0)
B3LYP/
6-311++G(d,p)
B3LYP/
6-31G(d,p)
Expa Parameters
B3LYP/
6-311++G(d,p)
B3LYP/
6-31G(d,p)
Expa
C1-C2 1.48 1.48 1.35 C2-C1-O8 125.5 125.4 125.5
C1-O8 1.21 1.22 1.21 C2-C1-O9 114.9 115.1 114.9
C1-O9 1.38 1.37 1.34 C1-C2-C3 126.1 126.2 126.2
C2-C3 1.43 1.43 1.34 C1-C2-C7 114.5 114.4 114.4
C2-C7 1.41 1.41 1.34 O8-C1-O9 119.6 119.5 119.6
C3-C4 1.41 1.42 1.34 C1-O9-H23 106.2 105.3 105.7
C3-N10 1.38 1.38 1.27 C1-C9-H24 107.2 106.9 107.2
C4-C5 1.38 1.39 1.34 C3-C2-C7 119.3 119.3 119.3
C4-H19 1.08 1.08 1.10 C2-C3-C4 117.4 117.5 117.4
C5-C6 1.40 1.40 1.34 C2-C3-N10 122.4 122.1 122.2
C5-H20 1.09 1.09 1.10 C2-C7-C6 122.2 122.1 122.2
C6-C7 1.38 1.38 1.34 C2-C7-H22 117.1 116.8 116.2
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C6-H21 1.08 1.09 1.10 C4-C3-N10 120.1 120.4 120.3
C7-H22 1.08 1.08 1.10 C3-C4-C5 121.6 121.5 121.6
O9-H23 0.97 0.97 0.97 C3-C4-H19 118.8 118.7 118.8
N10-C11 1.42 1.42 1.27 C3-N10-C11 127.3 127.8 127.7
N10-H24 1.01 1.01 1.05 C3-N10-H24 115.8 115.3 115.5
C11-C12 1.41 1.41 1.34 C5-C4-H19 119.6 119.7 119.6
C11-C16 1.40 1.40 1.34 C4-C5-C6 121.0 121.0 121.0
C12-C13 1.41 1.41 1.34 C4-C5-H20 118.9 118.9 118.6
C12-C18 1.51 1.51 1.50 C6-C5-H20 120.1 120.1 120.1
C13-C14 1.40 1.40 1.34 C5-C6-C7 118.5 118.5 118.4
C13-C17 1.51 1.51 1.50 C5-C6-H21 120.9 120.9 120.9
C14-C15 1.39 1.39 1.34 C7-C6-H21 120.6 120.6 120.7
C14-H25 1.09 1.09 1.10 C6-C7-C22 120.8 121.0 120.9
C15-C16 1.39 1.39 1.34 H23-O9-H24 146.0 147.6 146.9
C15-H26 1.08 1.09 1.10 C11-N10-H24 116.7 116.4 116.5
C16-H27 1.08 1.08 1.10 N10-C11-C12 119.1 118.7 118.9
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C17-H28 1.09 1.09 1.11 N10-C11-C16 120.2 120.8 120.6
C17-H29 1.10 1.10 1.11 N10-H24-H9 132.5 133.4 133.2
C17-H30 1.09 1.10 1.11 C12-C11-C16 120.6 120.4 120.4
C18-H31 1.09 1.09 1.11 C11-C12-C13 118.9 119.0 119.0
C18-H32 1.09 1.09 1.11 C11-C12-C18 120.3 120.0 120.3
C18-H33 1.10 1.10 1.11 C11-C16-C15 120.0 120.0 120.1
O9-H24 1.90 1.89 1.89 C11-C16-H27 119.4 119.4 119.4
C13-C2-C18 120.8 121.0 120.8
C12-C13-C14 119.6 119.7 119.6
C12-C13-C17 120.9 120.9 120.9
C12-C18-H31 111.1 111.0 111.1
C12-C18-H32 111.6 111.7 111.6
C12-C18-H33 111.7 112.0 111.7
C14-C13-C17 119.5 119.4 119.5
C13-C14-C15 121.0 120.9 120.9
C13-C14-H25 119.3 119.2 119.3
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C13-C17-H28 110.7 110.8 10.7
C13-C17-H29 111.8 111.9 111.8
C13-C17-H30 111.8 111.9 111.8
C15-C14-H25 119.7 119.9 119.8
C14-C15-C16 119.9 120.0 119.9
C14-C15-H16 120.2 120.2 120.2
C16-C15-H26 119.9 119.8 119.9
C15-C16-H27 120.6 120.5 120.5
H28-C17-H29 107.6 107.5 107.5
H28-C17-H30 107.8 107.7 107.8
H29-C17-H30 107.0 106.8 107.0
H31-C18-H32 108.0 107.9 107.9
H31-C18-H33 107.4 107.3 107.4
H32-C18-H33 106.8 106.7 106.8
Notes: Bond lengths are in Ǻ, bond angles are in degrees. a X ray data taken from Ref. Mihaela M Pop, et al., 2002.
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Table 2 Definition of internal coordinates of 2-[(2,3-dimethylphenyl)amino]benzoic acid.
No(i) Symbol Type Definitiona
Stretching
1-15 Ri C-C C1-C2,C2-C3,C2-C7,C3-C4,C4-C5,C5-C6,C6-C7,C11-C12,C11-C16,C12-C13,C12-C18,C13-C14,C13-C17,C14-C15,
C15-C16
16-18 Ri C-H C4-H19,C5-H20,C6-H21,C7-H22,C14-H25,C15-H26,C16-H27,C17-H28,C17-H29,C17-H30,C18-H31,C18-H32,C18-H33
29-30 Ri C-O C1-O8,C1-O9
31 Ri C-N C3-N10
32-33 Ri O-H O9-H23,O9-H24
34 Ri N-C C10-C11
35 Ri N-H N10-H24
In-plane bending
36-41 γi Ring1 C3-C2-C7,C2-C3-C4,C2-C7-C6,C3-C4-C5,C4-C5-C6,C5-C6-C7
42-47 γi Ring2 C12-C11-C16,C11-C12-C13,C11-C16-C15,C12-C13-C14,C13-C14-C15,C14-C15-C16
48-66 γi C-C-H C2-C7-H22,C3-C4-C19,C5-C4-H19,C4-C5-H20,C6-C5-H20,C5-C6-H21,C7-C6-H21,C6-C7-H22,C11-C16-H27,
C12-C18-H31,C12-C18-H32,C12-C18-H33,C13-C14-H25,C13-C17-H28,C13-C17-H29,C13-C17-H30,C15-C14-H25,
C16-C15-H26,C15-C16-H27
67-68 γi C-C-O C2-C1-O8,C2-C1-O9
69 γi O-C-O O8-C1-O9
70-71 γi C-O-H C1-O9-H23,C1-O9-H24
72-73 γi C-C-C C1-C2-C3,C1-C2-C7
74-77 γi C-C-N C2-C3-N10,C4-C3-N10,N10-C11-C12,N10-C11-C16
78 γi C-N-C C3-N10-C11
79-80 γi C-N-H C3-N10-H24,C11-N10-H24
Out-of-plane bending
81-87 ρi H-C-C H22-C7-C6-C2,H21-C6-C5-C7,H20-C5-C4-C6,H19-C4-C3-C8,H25-C14-C13-C15,H26-C15-C14-C16,
H27-C16-C15-C11
88 ρi O-C-O C2-C1-O8-O9
89-90 ρi C-H-H C18-H33-H32-H31,C17-H29-H30-H28
91 ρi H-N-C H24-N10-C3-C11
Torsion
92-95 τi Ring1 C2-C1-C4-C5,C3-C4-C5-C6,C4-C5-C6-C7,C5-C6-C7-C2,C6-C7-C2-C3,C7-C2-C3-C4
96-100 τi Ring2 C11-C12-C13-C14,C12-C13-C14-15,C13-C14-C15-C16,C14-C15-C16-C11,C15-C16-C11-C12,C16-C11-C12-C13
101-102 τi C-N-C C3-N10-C11-C12,C3-N10-C11-C12
103-104 τi CH3 C17-H28-H29-H30,C18-H31-H32-H33
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105-106 τi C-C-N C2-C3-N10-C11,C4-C3-N10-C11
107 τi H-N-C H24-N10-C11-C12
108 τi C-CO2 C2-C1-O8-O9
aFor numbering of atom refer Fig. 1.
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Table 3 Definition of local symmetry coordinates of 2-[(2,3-dimethylphenyl)amino]benzoic acid.
No.(i) Symbola Definitionb
1-15 ν CC R1,R2,R3,R4,R5,R6,R7,R8,R9,R10,R11,R12,R13,R14,R15
16-28 ν CH R16,R17,R18,R19,R20,R21,R22,R23,R24,R25,R26,R27,R28
29-30 ν (CO2ss) R29+R30/√2,R31+R32/√2
31 ν CN R33
32-33 ν OH R34,R35
34 ν NC R36
35 ν NH R37
36 β trig1 (γ38-γ39+γ40-γ41+γ42-γ43)/ √6
37 β asym1 (-γ38-γ39+2γ40-γ41-γ42-2γ43)/ √12
38 β sym1 (γ38-γ39+γ41-γ42)/ √2
39 β trig2 (γ44-γ45+γ46-γ47+γ48-γ49)/ √6
40 β asym1 (-γ44-γ45+2γ46-γ47-γ48-2γ49)/ √12
41 β sym1 (γ44-γ45+γ47-γ48)/ √2
42-51 β CCH (γ50-γ51)/ √2, (γ52-γ53)/ √2, (γ54-γ55)/ √2, (γ56-γ57)/ √2, (γ58-γ59)/ √2, (γ60-γ61)/ √2,
(γ62-γ63)/ √2, (γ64-γ65)/ √2, (γ66-γ67)/ √2, (γ68-γ69)/ √2
52-54 β CCO (γ70-γ71)/ √2, (γ72-γ73)/ √2, (γ74-γ75)/ √2, (γ76-γ77)/ √2
55 β CO2rock (γ78-γ79)/ √2
56 β CO2sic (2γ80-γ81-γ82/ √6)
57 ω CCC ρ 83, ρ 84
58-61 ω CCN ω85, ω86, ω87, ω88
62 ω CNC ω89
63-65 ω CNH ω90, ω91, ω92
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Abbreviations: ν, stretching; β, in plane bending; ω, out of plane bending; τ, torsion.
aThese symbols are used for description of the normal modes by PED in Table 4.
bThe internal coordinates used here are defined in table given in Table 2.
Table 4 The experimental FT-IR, FT-Raman and calculated frequencies using B3LYP/6.31G(p,d),B3LYP/6-311++G(d,p) force
field along with their relative intensities, probable assignments and potential energy distribution (PED) of 2-[(2,3-
dimethylphenyl)amino]benzoic acid.
Modes
Experimental
Wave numbers (cm-1) Calculated frequencies(cm)
Assignments(PED)a
FT-IR FT-Raman
B3LYP/
6-31G(d,p)
B3LYP/
6-311++G(d,p)
Unscaled Scaled Unscaled Scaled
1 3640(s) 3641(w) 3764 3636 3765 3640 ν OH (100)
2 - 3470(vw) 3596 3474 3597 3478 ν OH (100)
3 - - 3208 3099 3206 3100 ν CH3(99)
4 - 3091(m) 3204 3095 3203 3097 ν CH3(98)
5 - - 3193 3084 3192 3087 ν CH3(95)
6 - - 3188 3080 3188 3083 ν CH3(90)
7 - - 3177 3069 3176 3071 ν CH3(89)
8 - - 3166 3058 3166 3062 ν CH3(85)
9 - - 3160 3053 3161 3057 ν CH3(80)
10 - - 3118 3012 3117 3014 ν CH3(75)
11 3000(vs) 3003(w) 3105 2999 3104 3002 ν CH3(66)
12 2993(m) - 3081 2976 3081 2979 ν CH3(54)
13 - - 3066 2962 3066 2965 ν CH(96)
14 - - 3021 2918 3020 2920 ν CH(96)
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15 - - 3011 2909 3010 2911 ν CH(96)
16 1725(ms) - 1788 1727 1769 1711 C=O(85)
17 1598(ms) - 1652 1596 1648 1594 ν CC(73),ν COO(12)
18 - - 1641 1585 1637 1583 ν CC(70),ν COO(12)
19 - - 1623 1568 1620 1567 β CCH(32),ν CC(26)
20 - - 1622 1567 1617 1564 ν CC(18),ν CCC(16)
21 - - 1559 1506 1554 1503 NH3ass(70)
22 - - 1513 1462 1512 1462 ν CC(90),ν CH(18),ν CO(10)
23 - - 1507 1456 1506 1456 ν CC(85),ν CH(15),ν CO(10)
24 - - 1502 1451 1499 1450 ν CC(80),ν CH(12),ν CO(10)
25 - - 1499 1448 1496 1447 ν CC(75),ν CH(10),ν CO(10)
26 - 1442(w) 1493 1442 1491 1442 δ CC(70),δ CH(08),δ CO(10)
27 1430(s) - 1483 1433 1481 1432 δ CC(65),δ CO(18),δ CH(10)
28 - - 1478 1428 1476 1427 ν CC(40),β CCO(18),β CCC(18),
29 - - 1455 1405 1453 1405 β CCO(15),ν CC(35),β CCH(23)
30 - 1377(s) 1421 1373 1420 1373 δ C-O(65),ν OH(18),ν CC(14)
31 - - 1412 1364 1410 1363 ν CC(75),ν CO(16),ν CH(10)
32 - - 1371 1324 1366 1321 ν CC(69),ν CO(18),ν CH(10)
33 1300(vs) - 1347 1301 1345 1301 ν CC(65),ν CO(15),ν CH(10)
34 1280(vs) 1282(vw) 1320 1275 1319 1275 ν CC(75),ν CO(15),ν CH(10)
35 - - 1309 1264 1306 1263 ν CO2(22),ν CC(21),β CCH(14),ν HOC(10)
36 - - 1304 1259 1299 1256 ν CC(49),β CCC(17),β CCH(11),β CCO(10)
37 - - 1273 1230 1272 1230 β CCH(23),ν CC(21),ν C0(11)
38 - - 1253 1210 1252 1211 ν CC(17),β CO(27),β CCH(13),ν CO(10)
39 1170(vs) - 1205 1164 1204 1164 δ CH(60),γ OH(22),γ CC(11)
40 - - 1200 1159 1198 1158 CH3ss(54),ν CO(15),ν CH(10)
41 - - 1194 1153 1193 1154 CH3iop (64),ν CO(15),ν CH(10)
42 1142(vs) - 1187 1146 1185 1146 CH3opd (74),ν CO(15),ν CH(10)
43 1090(vs) 1090(vw) 1127 1089 1125 1088 γ CH(40),γ OH(20),γ CC(11)
44 1074(vs) 1070(vw) 1112 1074 1110 1073 γ CH(73),γ CC(18)
45 - - 1095 1057 1090 1054 γ CH(63),γ CC(18)
46 - - 1085 1048 1083 1047 γ CH(53),γ CC(18)
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47 - - 1067 1031 1066 1031 γ CH(43),γ CC(18)
48 - - 1056 1020 1051 1016 γ CH(33),γ CC(18)
49 - 1000(vs) 1041 1006 1040 1006 δ C-O(75),ν CC(12),ν CH(08)
50 - - 1010 976 1009 976 γ CH(70),δ CC(37),ν CO(13)
51 - - 997 963 998 965 γ CH(60),δ CC(27),ν CO(13)
52 - - 987 953 988 955 γ CH(50),δ CC(17),ν O(13)
53 945(w) 945(vw) 976 943 981 949 γ CH(45),δ CC(17),ν CO(13)
54 905(s) - 936 904 934 903 γ CH(40),δ CC(17),ν CO(13)
55 - - 911 880 914 884 δ CC(68),δ CO(12),δ CH(08)
56 - - 876 846 874 845 δ CC(58),δ CO(22),δ CH(18)
57 829(s) - 857 828 856 828 γ CH(32),γ CO(18),τ CH3(10)
58 - - 824 796 824 797 γ CH(68),γ CO(12),τ CH3(12)
59 - - 805 778 805 778 γ CH(75),γ CH3(15),γ CC(13)
60 - 770(vs) 804 777 804 777 γ CH(65),γ CH3(15),γ CC(13)
61 750(vs) - 776 750 774 748 γ CH(55),γ CH3(15),γ CC(13)
62 - - 763 737 761 736 γ CH(45),γ CH3(15),γ CC(13)
63 - - 739 714 737 713 γ CC(65),γ CH(12),γ CO(10)
64 - - 721 696 719 695 CH3ipr(40),ν CO(15),ν CH(10)
65 - - 715 691 712 689 CH3opr(45),ν CC(15),ν CH(10)
66 - 620(s) 642 620 640 619 γ OH(34),ν CO(15),ν COOH(10)
67 600(vw) - 629 608 628 607 CH3ipr(54),ν CC(15),ν CH(10)
68 - - 589 569 587 568 CH3ipr(30),ν CH(20),ν CO(15)
69 - - 585 565 570 551 CH3opr(20),δ CH(20),δ COO(15)
70 545(ms) - 557 538 552 534 γ OH(67), γ CC(15),γ COOH(10)
71 - - 541 523 530 513 δ CC(45),δ CH(12),δ CO(10)
72 - 510(vw) 528 510 525 508 CH3ipr(48),ν CC(18),ν CH(10)
73 - - 520 502 515 498 CH3ipr(45),ν CC(15),ν CH(10)
74 - - 514 497 513 496 CH3ipr(40),ν CC(15),ν CH(10)
75 - - 499 482 499 483 CH3opr(35),ν CC(15),ν CH(10)
76 - - 471 455 472 456 CH3opr(30),ν CC(15),ν CH(10)
77 - 414(vw) 434 419 432 418 CH3opr(45),ν CC(15),ν CH(10)
78 - - 392 379 390 377 γ CC(42),γ CH(18),γ CO(12)
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79 - 342(w) 356 344 356 344 γ CC(64),γ CO(12),γ CH(8)
80 - - 324 313 324 313 γ CC(45),τ CH3(12)
81 - 285(vw) 299 289 298 288 γ CC(54),γ CH(18),γ CO(12)
82 - - 275 266 274 265 γ CCO(42),γ COC(24),γ CCO(15)
83 - - 245 237 243 235 γ CC(40),γ COC(46),γ CCC(13)
84 - - 223 215 221 214 γ CCC(31),γ COC(36),γ CCC(13)
85 - - 189 183 187 181 δ CC(46),γ OH(22)
86 - - 165 159 166 161 γ COC(27),ν CCC(32),γ CO2(27)
87 - 135(s) 140 135 140 135 δ CC(65),γ CH(12)
88 120(w) - 128 124 126 122 δ C-O(75),γ CC(12),γ CH(08)
89 - - 85 82 98 95 δ CO(26),γ CCC(23)
90 - 65(vw) 68 66 68 66 δ O(52),γ OH(18),γ CO(12)
91 - - 60 58 55 53 δ C-O(75),γ CC(12),ν CH(08)
92 - 30(vs) 32 31 32 31 δ C-O(38),ν OH(18),τ CH3(10)
93 - 22(s) 26 25 23 22 τ CH3(75)
ν – stretching, δ – in plane, γ – out-plane, w – weak, m – medium, vw – very weak, s – strong, vs – very strong, ass – asymmetric
stretching, ss – symmetric stretching, ipb,β – in –plane bending, opb – out-of-plane bending, ipr – in-plane rocking, opr – out-of-plane
rocking, τ – torsion. aOnly PED contributions≥10% are listed.
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Table 5 The ab initio B3LYP/6-31G(d,p) and B3LYP/6-311++G(d,p) calculated electric
dipole moments (Debye), Dipole moments compound, polarizability (in a.u) ,β components and
βtot (10-30 esu) value of 2-[(2,3-dimethylphenyl)amino]benzoic acid.
Parameters B3LYP/
6-31G(d,p)
B3LYP/
6-311++G(d,p)
µx 2.8858 3.2049
µy -0.2035 -0.0441
µz 0.4001 0.5509
µ 2.9205 3.2522
αxx -110.2431 -112.3185
αyy -95.1216 -96.7523
αzz -107.4862 -108.3726
α -91.6319 -95.1069
βxxx 63.0356 74.0324
βyyy -36.8750 -35.9070
βzzz -6.1133 -5.4846
βxyy -10.3416 -8.8117
βxxy 29.2654 31.9790
βxxz 15.5342 18.5339
βxzz -2.0657 -0.0537
βyzz -8.0808 -6.8662
βyyz -6.5401 -5.8714
β0(esu) 1.408910-30 2.205310-30
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Table 6 Second –order perturbation theory analysis of Fock matrix in NBO basis corresponding to the intramolecular of
the title compound.
Donor NBO(i) EDa(i)/e Acceptor NBO(j) EDa(j)/e E(2)b
(kcalmol-1) E(j)-E(i)c(a.u) F(i,j)d(a.u)
σ (C1-C2) 1.97445 σ*(C1-O8) 0.00321 1.71 1.23 0.041
σ(C1-O8) 1.99366 σ*(C1-C2) 0.00652 2.2 1.45 0.051
σ(C1-O9) 1.99599 σ*(C1-O8) 0.00321 0.86 1.19 0.031
σ(C2-C3) 1.96898 σ*(C2-O7) 0.00028 4.57 1.23 0.067
σ(C2-C7) 1.96504 σ*(C3-C4) 0.00172 2.29 1.17 0.046
σ(C3-C4) 1.97444 σ*(C3-N10) 0.00311 51.05 1.71 0.264
σ(C3-N10) 1.98819 σ*(C6-C7) 0.00025 3.21 0.68 0.042
σ(C4-C5) 1.97678 σ*(C4-H19) 0.00011 1.04 1.14 0.031
σ(C4-H19) 1.97616 σ*(N10-C11) 0.00008 0.62 0.82 0.02
σ(C5-C6) 1.98047 σ* (C11-C16) 0.00004 1.67 0.53 0.027
σ(C5-H20) 1.98041 σ* (C4-C5) 0.00045 0.7 1.06 0.024
σ(C6-C7) 1.97676 σ*(C11-C16) 0.00004 1.88 0.53 0.028
σ(C6-H21) 1.98035 σ*(C16-H27) 0.00004 4.67 0.16 0.025
σ(C7-H22) 1.97663 σ* (C18-H32) 0.00003 1.44 1.58 0.043
σ(O9-H23) 1.98605 σ*(C11-C16) 0.00004 30.67 0.6 0.121
σ(N10-C11) 1.9887 σ*(C12-H30) 0.00002 12.96 3.12 0.18
σ(N10-H24) 1.97901 σ*(C11-C16) 0.00004 111.92 0.2 0.15
σ(C11-C12) 1.96814 σ*(C6-C7) 0.00013 129.4 0.58 0.245
σ(C11-C16) 1.97142 σ*(C17-H30) 0.00002 9.58 3.04 0.153
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Table 7 Accumulation of natural charges and electron population of atoms in core, valance, Rydberg orbitals of
2-[(2,3-dimethylphenyl)amino]benzoic acid.
Atomsa Charge(e) Natural population(e)
Total(e) Atomsb Charge(e) Natural population(e)
Total(e) Core Valence Rydberg Core Valence Rydberg
C1 0.78358 1.99934 3.17029 0.04679 0.04679 C2 -0.21016 1.99872 4.19403 0.01742 6.21016
C3 0.21773 1.99893 3.76467 0.01867 5.78227 C4 -0.25166 1.99907 4.23599 0.0166 6.25166
C11 0.18654 1.99869 3.79381 0.02096 5.81346 C5 -0.15159 1.99913 4.13518 0.01728 6.15159
H19 0.20898 0.00000 0.78853 0.00249 0.79102 C6 -0.25279 1.99916 4.23316 0.02048 6.25279
H20 0.20953 0.00000 0.78877 0.00171 0.79047 C7 -0.11496 1.99889 4.09883 0.01725 6.11496
H21 0.21200 0.00000 0.78618 0.00182 0.78800 O8 -0.62782 1.99976 6.6144 0.01366 8.62782
H22 0.23995 0.00000 0.75785 0.00220 0.76005 O9 -0.70995 1.99972 6.69736 0.01288 8.70995
H23 0.50614 0.00000 0.48892 0.00494 0.49386 N10 -0.61244 1.99925 5.59549 0.01770 7.61244
H24 0.41859 0.00000 0.57662 0.00478 0.58141 C12 -0.06895 1.99893 4.05434 0.01568 6.06895
H25 0.20169 0.00000 0.79631 0.00200 0.79831 C13 -0.02800 1.99897 4.01390 0.01513 6.02800
H26 0.20607 0.00000 0.79208 0.00185 0.79393 C14 -0.21848 1.99913 4.20128 0.01818 6.21848
H27 0.20003 0.00000 0.79743 0.00254 0.79997 C15 -0.18598 1.99913 4.16874 0.01628 6.18598
H28 0.20951 0.00000 0.78842 0.00207 0.79049 C16 -0.24623 1.99909 4.23086 0.01628 6.24623
H29 0.20918 0.00000 0.78847 0.00234 0.79082 C17 -0.58382 1.99920 4.57509 0.00953 6.58382
H30 0.20918 0.00000 0.78847 0.00234 0.79082 C18 -0.58722 1.99930 4.57969 0.00823 6.58722
H31 0.20645 0.00000 0.79151 0.00203 0.79355
H32 0.21252 0.00000 0.78553 0.00195 0.78748
H33 0.21251 0.00000 0.78553 0.00195 0.78749
a Atoms containing negative charges. b Atoms containing positive charges.
Journal of Information and Computational Science
Volume 9 Issue 8 - 2019
ISSN: 1548-7741
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Table 8 Comparison of HOMO, LUMO energy gaps and related molecular properties of 2-[(2,3-dimethylphenyl)amino]benzoic
acid at B3LYP/6-31G(d,p) and B3LYP/6-311++G(d,p) level of theory.
Molecular Properties Energy
(a.u)
Energy gap
(eV)
Ionization
potential
(I)
Electron
affinity
(A)
Global
hardness
(ƞ)
Electro
negativity
(χ)
Global
softness
(σ)
Chemical
potential
(μ)
Global
electrophilicity
(ω)
B3LYP/6-31G(d,p)
HOMO -0.2044 0.1537 0.2044 0.0507 0.0768 0.1275 13.0070 -0.1275 0.1053
LUMO -0.0507
HOMO -0.2044 0.1854 0.2044 0.0189 0.0927 0.1168 10.7870 -0.1116 0.0668
LUMO+1 -0.0189
HOMO -0.2044 0.1930 0.2044 0.0114 0.0965 0.1280 10.3590 -0.1280 0.0844
LUMO+2 -0.0114
B3LYP/6-311++G(d,p)
HOMO -0.2094 0.1507 0.2094 0.0587 0.0753 0.1340 13.2661 -0.1340 0.1187
LUMO -0.0587
HOMO -0.2094 0.1827 0.2094 0.0267 0.0913 0.1504 10.9469 -0.1504 0.1237
LUMO+1 -0.0267
HOMO -0.2094 0.1909 0.2094 0.0184 0.0954 0.1524 10.4723 -0.1524 0.1215
LUMO+2 -0.0184
Journal of Information and Computational Science
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Table 9 Using Mulliken population analysis: Fukui functions (
kf ,
kf , 0
kf ) for atoms of
2-[(2,3-dimethylphenyl)amino]benzoic acid.
Atoms
Mulliken atomic charges Fukui functions
qN+1 qN qN-1
C1 0.3799 0.7836 0.6658 -0.4037 0.1177 -0.1430
C2 -0.0182 -0.2102 -0.2623 0.1920 0.0521 0.1220
C3 0.0675 0.2177 0.1457 -0.1502 0.0721 -0.0391
C4 -0.0258 -0.2517 -0.2740 0.2259 0.0223 0.1241
C5 -0.1049 -0.1516 -0.3125 0.0467 0.1609 0.1038
C6 0.0074 -0.2528 -0.2567 0.2602 0.0039 0.1320
C7 -0.0769 -0.1150 -0.2094 0.0380 0.0945 0.0663
O8 -0.0268 -0.6278 -0.7537 0.6010 0.1258 0.3634
O9 -0.3572 -0.7100 -0.7631 0.3528 0.0532 0.2030
N10 -0.0220 -0.6124 -0.3458 0.5905 -0.2667 0.1619
C11 0.1057 0.1865 0.1738 -0.0809 0.0127 -0.0341
C12 0.0687 -0.0690 -0.1693 0.1376 0.1003 0.1190
C13 -0.0428 -0.0280 -0.0760 -0.0148 0.0480 0.0166
C14 0.0500 -0.2185 -0.2772 0.2685 0.0587 0.1636
C15 -0.1011 -0.1860 -0.1958 0.0849 0.0098 0.0474
C16 -0.0416 -0.2462 -0.2865 0.2046 0.0402 0.1224
C17 -0.2971 -0.5838 -0.5926 0.2867 0.0088 0.1478
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C18 -0.3021 -0.5872 -0.8683 0.2851 0.2811 0.2831
H19 0.1083 0.2090 0.1802 -0.1007 0.0287 -0.0360
H20 0.1189 0.2095 0.1761 -0.0906 0.0334 -0.0286
H21 0.1166 0.2120 0.1796 -0.0954 0.0324 -0.0315
H22 0.1327 0.2400 0.2182 -0.1073 0.0218 -0.0428
H23 0.2624 0.5061 0.4685 -0.2437 0.0376 -0.1031
H24 0.2168 0.4186 0.4002 -0.2018 0.0184 -0.0917
H25 0.1110 0.2017 0.1818 -0.0907 0.0199 -0.0354
H26 0.1176 0.2061 0.1891 -0.0885 0.0170 -0.0357
H27 0.1063 0.2000 0.2042 -0.0938 -0.0042 -0.0490
H28 0.1137 0.2095 0.1946 -0.0958 0.0149 -0.0405
H29 0.1128 0.2092 0.1939 -0.0964 0.0152 -0.0406
H30 0.1128 0.2092 0.1945 -0.0964 0.0147 -0.0409
H31 0.1042 0.2065 0.1747 -0.1023 0.0318 -0.0352
H32 0.1222 0.2125 0.1640 -0.0903 0.0485 -0.0209
H33 0.1222 0.2125 0.1624 -0.0904 0.0501 -0.0201
Journal of Information and Computational Science
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Table 10 Mulliken’s atomic charge of 2-[(2,3-dimethylphenyl)amino]benzoic acid at
B3LYP/6-311G++(d,p) ,6-31G(d,p)
Atom
No.
Atomic charges(e)
B3LYP/
6-311G++(d,p)
B3LYP/
6-31G(d,p)
C1 -0.8620 0.4620
C2 0.0904 -0.2512
C3 -0.3949 0.2589
C4 0.0643 -0.1246
C5 -0.3511 -0.0776
C6 -0.4199 -0.1011
C7 0.0788 -0.0332
O8 -0.2932 -0.3407
O9 -0.3142 -0.3868
N10 0.1189 -0.5447
C11 -0.2529 0.1348
C12 0.5787 -0.0845
C13 0.3349 -0.1029
C14 -0.5872 -0.0631
C15 -0.4022 -0.0901
C16 0.2068 -0.0671
C17 -0.6265 -0.2671
C18 -0.6443 -0.2626
H19 0.1749 0.1237
H20 0.1710 0.0967
H21 0.1656 0.0928
H22 0.2218 0.1103
H23 0.3399 0.2630
H24 0.3895 0.2542
H25 0.1107 0.0793
H26 0.1690 0.0918
H27 0.1793 0.1114
H28 0.1447 0.1071
H29 0.1581 0.1255
H30 0.1597 0.1221
H31 0.1950 0.1214
H32 0.1411 0.1170
H33 0.1785 0.1249
Journal of Information and Computational Science
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Table 11 Thermodynamic function of 2-[(2,3-dimethylphenyl)amino]benzoic acid at
B3LYP/ 6-311++G(d,p) and B3LYP/6-31G(d,p) methods.
Temperature(K)
Thermodynamic parameter
B3LYP/6-311++G(d,p) B3LYP/6-31G(d,p)
S Cp (G-E)/T S Cp (G-E)/T
100 356.44 113.59 7.44 355.66 113.45 7.43
200 458.53 191.37 22.61 457.48 190.76 22.56
298.15 550.15 273.15 45.4 548.83 272.48 45.29
300 551.85 274.68 45.91 550.52 274.48 45.79
400 641.87 353.39 77.39 640.36 352.74 77.21
500 728.17 420.42 116.19 726.51 419.8 115.94
600 809.83 475.04 161.06 808.06 474.48 160.75
700 886.5 519.4 210.85 884.65 518.89 210.5
800 958.31 555.86 264.67 956.4 555.89 264.27
900 1025.59 586.28 321.82 1023.63 585.89 321.38
1000 1088.73 611.94 381.77 1086.73 611.6 381.29
Journal of Information and Computational Science
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