190

Chapter – VI

Structural and vibrational studies of 1, 5-dimethoxynaphthalene:

A spectroscopic approach

182

CHAPTER VI

STRUCTURAL AND VIBRATIONAL STUDIES OF 1,5-

DIMETHOXYNAPHTHALENE : A SPECTROSCOPIC

APPROACH

ABSTRACT

In this work, we reported a combined experimental and theoretical

study on molecular structure, vibrational spectra and NBO analysis of

1,5-dimethoxynaphthalene. The optimized molecular structure, atomic

charges, vibrational frequencies and natural bond orbital analysis of

1,5-dimethoxynaphthalene have been studied by performing DFT/B3LYP/6-

31G(d,p) level of theory. The FTIR, FT-Raman spectra were recorded in the

region 4000-400 cm-1

and 3500-50 cm-1

respectively. The scaled

wavenumbers are compared with the experimental values. The difference

between the observed and scaled wavenumber values of most of the

fundamentals is very small. The formation of hydrogen bond was investigated

in terms of the charge density by the NBO calculations. Besides, molecular

electrostatic potential (MEP), frontier molecular orbitals (FMO) analysis were

investigated using theoretical calculations.

183

CHAPTER VI

STRUCTURAL AND VIBRATIONAL STUDIES OF 1,5-

DIMETHOXYNAPHTHALENE : A SPECTROSCOPIC

APPROACH

6.1. INTRODUCTION

Naphthalene is the simplest and the most important member of this

class of arenas, in which two benzene rings are fused in ortho positions.

Naphthalene, a benzenoid polycyclic aromatic hydrocarbon (PAH), is found

in both middle and heavy oil fractions at crude oil and is obtained by

fractional crystallization. The naphthalene and its derivatives are the most

important class of organic compounds. Because of their spectroscopic

properties and chemical significance, naphthalene and its derivatives were

studied extensively by spectroscopic and theoretical methods. Naphthalene

has been identified as new range of potent antimicrobials effective against

wide range of human pathogens. It is also used in the production of dye and

plastics. Several naphthalene containing drugs are available, such as

nafacillin, naftifine, tolnaftate, terbinafine, etc. which play a vital role in the

control of microbial infection. It is widely recognized that polycyclic aromatic

hydrocarbons and their metabolites are among the most toxic, carcinogenic

and mutagenic atmospheric contaminants [1-4]. Naphthalene and its

184

derivatives are widely used as the chemical intermediate, wetting agent in

many industrial applications, to study heat transfer with mass sublimation in

engineering field, household fumigants such as mothballs, fumigant

pesticides. Exposure to large amounts of naphthalene may damage or destroy

red blood cells and cause confusion, nausea, vomiting, diarrhea, blood in the

urine, jaundice [5]. PAHs can be produced from both natural and human

activities as a result of incomplete combustion or pyrolysis, and there is a

clear evidence of the presence of PAHs in many astronomical objects [6-8].

Recent research showed that the protonated cations of naphthalene are the

source of part of the spectrum of the unidentified interstellar bands (UIBs)

[9]. Naphthalene and alkylated naphthalenes are semi-volatile, present in the

atmosphere mostly in the gas phase [10]. Diesel fuel contains PAHs including

methylnaphthalene and dimethylnaphthalenes [11, 12]. Especially,

naphthalene was studied because of its technological applications in a vast

amount of industrial process [13].

The molecule 1,5-dimethoxynaphthalene is a compound having two

methoxy groups are substituted to naphthalene ring system. There are

positional isomers differing by the location of the methoxy group. The

different positions provide various chemical structures which offer important

roles to each characteristic. Librando and Alparone [14, 15] investigated

methyl naphthalene isomers based on quantum mechanical approach and the

electronic polarizability of dimethylnaphthalenes. Srivastava and Singh [16]

185

investigated the infrared and Raman spectrum of Naphthalene and its cation.

Das et al. [17] reported the infrared spectra of dimethylnaphthalenes in the

gas phase. The vibrational analysis using DFT method of naphthoic acid, 2-

naphthoic acid, bromo naphthoic acid, 1-naphthaldehyde, 1,5-

dinitronaphthalene and 1-hydroxynaphthalene have been extensively studied

and analyzed [13, 18, 19]. Krishnakumar et al. [20] reported the vibrational

assignments in 1-naphthyl acetic acid. Recently, Nagabalasubramanian et al.

reported a scaled quantum mechanical vibrational analysis on 1,5-

methylnaphthalene using FTIR and FT-Raman spectra [21]. Molecular

structure, anharmonic vibrational frequencies and NBO analysis of

naphthalene acetic acid by DFT calculations were carried out by Kavitha et al.

[22]. Xavier et al. [23] investigated the 1-methoxynapthalene by using

Wilson’s F-G matrix method.

Most recently, Govindarajan et al. [24] investigated the FTIR and

FT-Raman spectra of 1-methoxynapthalene. In this work, structural

parameters, vibrational assignments, electronic absorption and frontier

molecular orbital energies were calculated for 1-methoxynapthalene.

Nagabalasubramanian et al. [25] studied the FTIR, FT-Raman, ab initio and

DFT structural, vibrational frequency and HOMO–LUMO analysis of

1-naphthaleneacetic acid methyl ester. Potential energy surface scan, mulliken

atomic charges and thermodynamic properties were also carried out for 1-

naphthaleneacetic acid methyl ester. Shoba et al. [26, 27] reported the FTIR

186

and FT-Raman vibrational analysis, ab initio HF and DFT analysis of

isocyanic acid 1-naphthyl ester and 2,3-naphthalenediol. Here, geometrical

parameters, vibrational assignments, thermodynamic properties, HOMO-

LUMO analysis and UV-Vis spectra analysis were made for isocyanic acid 1-

naphthyl ester and 2,3-naphthalenediol.

Spectroscopic (FTIR and FT Raman) analysis and vibrational study on

2, 3-dimethyl naphthalene were made by Prabhu et al. [28]. Molecular

structure, polarizability, hyperpolarizability analysis and spectroscopic

characterization of 1-(chloromethyl)-2-methylnaphthalene were carried out by

Nagabalasubramanian et al. [29]. Ostojić and Ðorđević [30] studied the ab

initio and density functional study of barrier heights for methyl group torsion

and conformational deformability in 1, 4, 6-trimethylnaphthalene.

Govindarajan and Karabacak have reported the FTIR, FT-Raman and UV

spectral investigation, computed frequency estimation analysis and electronic

structure calculations on 1-nitronaphthalene [31]. To the best of our

knowledge, neither quantum chemical calculation, nor the vibrational spectra

of 1, 5-dimethoxynaphthalene have been reported. Therefore, the present

work aims to provide a complete description on the molecular geometry,

molecular vibrations and electronic features of the 1,5-dimethoxynaphthalene

molecule.

187

6.2. EXPERIMENTAL DETAILS

The compound 1,5-dimethoxynaphthalene was purchased from Sigma-

Aldrich Chemical Company with a stated purity greater than 98% and it was

used as such without further purification. The FTIR spectrum of the sample was

carried out between 4000 cm-1

and 400 cm-1

on an IFS 66V spectrometer using

the KBr pellet technique. The room temperature, FT-Raman spectrum was

recorded using a Thermo Electron Corporation model Nexus 670

spectrophotometer equipped with FT-Raman module accessory. The 1064 nm

line of an Nd-YAG laser was used as excitation wavelength in the region of

3500-50 cm-1

. The spectral resolution was set to 4 cm-1

in a back scattering

mode. A liquid nitrogen cooled Ge detector was used to collect 50 scans for a

good Raman spectrum. The laser output was kept at 150 mW for the solid

samples. The experimental FTIR and FT-Raman spectra along with the

theoretically predicted IR and Raman spectra using DFT/B3LYP/6-31G(d,p) level

of calculations are shown in Figs. 6.1 and 6.2.

6.3. COMPUTATIONAL DETAILS

In the present study, the density functional theory (DFT/B3LYP) at the

6-31G(d,p) basis set level was adopted to calculate the optimized parameters

and vibrational wavenumbers of the normal modes of the title molecule. All

the theoretical calculations were performed using the Gaussian 03W program

package [32] with the default convergence criteria, without any constraint on

the geometry [33]. The equilibrium geometry corresponding to the true

188

Tra

nsm

itta

nce

(%

) T

ransm

itta

nce

(%

)

B 3 L Y P / 6 - 3 1 G ( d , p )

4000 500

E x p e r i m e n t a l

4 0 0 0 3 5 0 0 3 0 0 0 2 5 0 0 2 0 0 0 1 5 0 0 1 0 0 0 5 0 0

W a v e n u m b e r ( c m -1

)

Fig. 6.1: Comparison of experimental and theoretical (B3LYP/6-31G(d,p))

FTIR spectra for 1,5-dimethoxynaphthalene

189

W a v e n u m b e r ( c m - 1

)

Ram

an I

nte

nsi

ty (

arb u

nit

s)

Ram

an I

nte

nsi

ty (

arb u

nit

s)

B3LYP/6-31G(d,p)

4000 500

E x p e r i m e n t a l

3 5 0 0 3 0 0 0 2 5 0 0 2 0 0 0 1 5 0 0 1 0 0 0 5 0 0

Wavenumber (cm-1

)

Fig. 6.2: Comparison of experimental and theoretical (B3LYP/6-31G(d,p)) FT-

Raman spectra for 1,5-dimethoxynaphthalene

190

i

minimum on the potential energy surface (PES) was effectively obtained by

solving self-consistent field equation. The vibrational spectra of the 1,5-

dimethoxynaphthalene were obtained by taking the second derivative the

energy, computed analytically. The optimized structural parameters were used

in the vibrational frequency calculations at DFT levels to characterize all

stationary points as minima using the GAUSSVIEW animation program [34].

Vibrational frequencies were computed at DFT level which had reliable one-

to-one correspondence to experimental IR and Raman frequencies [35]. The

vibrational assignments of the normal modes were made on the basis of the

TED calculated by using the VEDA 4 program [36]. Subsequent total energy

distribution (TED) to each observed frequencies, predicts well the purity of the

fundamental modes and shows the reliability and accuracy of the spectral

analysis. In the present study, we have used the following scaling factor of

0.9608 for B3LYP/6-31G (d, p) method [37]. A comparison of the frequencies

calculated with the experimental values revealed that the 6-31G (d, p) basis set

result shows very good agreement with the experimental observations.

6.4. PREDICTION OF RAMAN INTENSITIES

The Raman activities (SRa) calculated with Gaussian 03 program [32]

converted to relative Raman intensities (IRa) using the following relationship

derived from the intensity theory of Raman scattering [38, 39]

f (v − v ) 4

S I = o i i

v i [1 − exp( − hcv i / kt )]

………. (6.1)

191

where, ν0 is the laser exciting wavenumber in cm-1

(in this work, we have used

the excitation wavenumber ν0 = 9398.5 cm-1

, which corresponds to the

wavelength of 1064 nm of a Nd-YAG laser), νi the vibrational wavenumber

of the ith

normal mode (cm-1

) where as Si is the Raman scattering activity of

the normal mode νi. f (is a constant equal to 10-12

) is a suitably chosen

common normalization factor for all peak intensities. h, k, c and T are Planck

and Boltzmann constants, speed of light and temperature in Kelvin,

respectively. The calculated Raman and IR intensities were used to convolute

each predicted vibrational mode with a Lorentzian line shape with a full width

at half maximum (FWHM=10 cm-1

) to produce simulated spectra.

6.5. RESULTS AND DISCUSSION

6.5.1. Molecular geometry

The most relevant structural parameters, bond lengths, bond angles and

dihedral angles of 1,5-dimethoxynaphthalene determined by Density

functional theoretical calculations with 6-31G(d,p) basis set are given in

Table 6.1. Geometry optimizations were carried out, without any symmetry

constraints; including polarization functions to correctly take into account

intramolecular H-bonding in the molecule. The atom numbering of

1,5-dimethoxynaphthalene molecule used in this paper is reported in Fig. 6.3.

To the best of our knowledge the experimental data on the geometric structure

of the title molecule is not available till now in the literature. Due to this

192

Table 6.1: Calculated optimized parameter values of the 1, 5-dimethoxynaphthalene

[Bond length in (Å), angles in (º)]

Bond length B3LYP Bond angle B3LYP Dihedral angle B3LYP

C1-C2 1.381 C5-C6-C7 120.8 C10-C1-C2-C3 0.0 C1-C10 1.433 C5-C6-O11 114.8 C10-C1-C2-H15 -180.0

C1-O13 1.366 C7-C6-O11 124.4 O13-C1-C2-C3 -180.0

C2-C3 1.415 C6-C7-C8 119.9 O13-C1-C2-H15 0.0

C2-H15 1.083 C6-C7-H18 120.9 C2-C1-C10-C5 0.0

C3-C4 1.374 C8-C7-H18 119.2 C2-C1-C10-C9 180.0

C3-16 1.086 C7-C8-C9 121.3 O13-C1-C10-C5 180.0

C4-C5 1.420 C7-C8-H19 118.7 O13-C1-C10-C9 0.0

C4-H17 1.083 C9-C8-H19 120.0 C2-C1-O13-C14 0.0

C5-C6 1.433 C8-C9-C10 119.8 C10-C1-O13-C14 180.0

C5-C10 1.428 C8-C9-H20 121.1 C1-C2-C3-C4 0.0

C6-C7 1.381 C10-C9-H20 119.1 C1-C2-C3-H16 180.0

C6-O11 1.366 C1-C10-C5 118.1 H15-C2-C3-C4 -180.0

C7-C8 1.415 C1-C10-C9 121.8 H15-C2-C3-H16 0.0

C7-H18 1.083 C5-C10-C9 120.1 C2-C3-C4-C5 0.0

C8-C9 1.374 C6-O11-C12 118.3 C2-C3-C4-H17 180.0

C8-H19 1.086 O11-C12-H21 106.1 H16-C3-C4-C5 180.0

C9-C10 1.420 O11-C12-H22 111.6 H16-C3-C4-H17 0.0

C9-H20 1.083 O11-C12-H23 111.6 C3-C4-C5-C6 -180.0

O11-C12 1.418 H21-C12-H22 109.3 C3-C4-C5-C10 0.0

C12-H21 1.091 H21-C12-H23 109.3 H17-C4-C5-C6 0.0

C12-H22 1.098 H22-C12-H23 109.0 H17-C4-C5-C10 -180.0

C12-H23 1.098 C1-O13-C14 118.3 C4-C5-C6-C7 180.0

O13-C14 1.418 O13-C14-H24 106.1 C4-C5-C6-O11 0.0

C14-H24 1.091 O13-C14-H25 111.6 C10-C5-C6-C7 0.0

C14-H25 1.098 O13-C14-H26 111.6 C10-C5-C6-O11 180.0

C14-H26 1.098 H24-C14-H25 109.3 C4-C5-C10-C1 0.0

Bond angle H24-C14-H26 109.3 C4-C5-C10-C9 -180.0

C2-C1-C10 120.8 H25-C14-H26 109.0 C6-C5-C10-C1 -180.0

C2-C1-O13 124.4 Dihedral angle C6-C5-C10-C9 0.0

C10-C1-O13 114.8 C7-C8-C9-H20 180.0 C5-C6-C7-C8 0.0

C1-C2-C3 119.9 H19-C8-C9-C10 180.0 C5-C6-C7-H18 180.0

C1-C2-H15 120.9 H19-C8-C9-H20 0.0 O11-C6-C7-C8 -180.0

C3-C2-H15 119.2 C8-C9-C10-C1 -180.0 O11-C6-C7-H18 0.0

C2-C3-C4 121.3 C8-C9-C10-C5 0.0 C5-C6-O11-C12 180.0

C2-C3-H16 118.7 H20-C9-C10-C1 0.0 C7-C6-O11-C12 0.0

C4-C3-H16 120.0 H20-C9-C10-C5 180.0 C6-C7-C8-C9 0.0

C3-C4-C5 119.8 C6-O11-C12-H21 -180.0 C6-C7-C8-H19 -180.0

C3-C4-H17 121.1 C6-O11-C12-H22 61.1 H18-C7-C8-C9 -180.0

C5-C4-H17 119.1 C1-O13-C14-H25 61.1 H18-C7-C8-19 0.0

C4-C5-C6 121.8 C1-O13-C14-H26 -61.1 C7-C8-C9-C10 0.0

C4-C5-C10 120.1 C6-O11-C12-H23 -61.1 C6-C5-C10 118.1 C1-O13-C14-H24 -180.0

193

Fig. 6.3: Optimized Molecular structure and atomic numbering of

1, 5-dimethoxynaphthalene

194

inadequacy, our optimized structural parameters are not compared with the

experimental data. The molecular structure of 1, 5-dimethoxynaphthalene

belongs to C1 point group symmetry. An account of bond length, bond angles

and dihedral angles the left part of the naphthalene ring almost reproduced the

right part as like as a mirror image, it is evident from the Fig. 6.3 and Table

6.1. The title compound was planar, as indicated by C6-C5-O11-C12 and

C10-C1-O13-C14 torsional angles of 180.0° and 180.0° respectively. The

methyl C-H bond distances longer than the aromatic C-H bond distances. An

interesting fact that occur both the methoxy group, among the three methyl C-

H bonds, one bond in the ring of the molecule is shorter than the other two

non-planar C-H bonds by angle 0.087Å. As it is evident from the bond

lengths of C1–C2 and C2–C10 is 1.381 and 1.430 Å, show slight deviation

when compared with C10–C9 and C9–C8 of 1.420 and 1.374 Å, and

symmetry of naphthalene ring is distorted, yielding ring angles smaller and

larger than the normal value of 120° exactly at the substitution as shown in

Table 6.1. The C2–C1–C10 angle is 120.8° and C8–C9–C10 angle is 119.8°.

There is an elongation calculated in the C-O bond length when it connected

with methyl group carbon atom than the ring carbon which has the values of

1.418 and 1.366 Å respectively.

6.5.2. Vibrational assignments

The observed (FTIR and FT-Raman) wavenumbers, calculated IR and

Raman intensities and assigned wavenumbers of vibrational modes calculated at

195

the B3LYP level using basis set 6-31G(d,p) along with their TED of 1,5-

dimethoxynaphthalene are depicted in Table 6.2. The vibrational spectrum is

mainly determined by the modes of the free molecule observed at higher

wavenumbers together with the lattice modes in the low wavenumbers region.

The aim of the vibrational analysis is to find vibrational modes connected with

specific molecular structures of calculated compound. The comparison of

experimental and theoretical FTIR and FT-Raman spectra are shown in Figs.

6.1 and 6.2. The DFT method predicts vibrational spectra with high accuracy

and is applicable to a large number of compounds, except for the cases where

the effect of dispersion forces is significant. Precise vibrational frequency

assignment for aromatic and other conjugated system is necessary for

characterization of compound. It should be noted that the calculations were

made for a free molecule in vacuum, while experiments were performed for

solid samples. With the assumed structural model, the molecule belongs to C1

point group symmetry and has 26 atoms with 72 normal modes of vibrations. In

order to facilitate assignment of the observed peaks, we have analyzed the

vibrational wavenumbers and compared our calculated values with the

experimental results.

6.5.2.1. C-H vibrations

The aromatic C-H stretching vibrations are normally found between

3100 and 3000 cm−1

due to aromatic C-H stretching vibrations [40-43]. The

wavenumbers calculated in the range 3107-3062 cm-1

by B3LYP

196

FTIR FT-

Unscaled Scale Raman

3360vs 3234 3107 3207w 3233 3107

3127s 308 2s 3224 3098

3224 3098

3055s 3187 3062

3187 3062

2984s 300 8s 3147 3024

3147 3024

2941s 2960w 3077 2957

2937w 3077 2957

2880w 3016 2898

2851w 2835w 3015 2897

1611w 1678 1612

1597w 1583vs 1649 1585

1541w 1638 1574

1495w 1562 1501

1470w 1466w 1522 1463

1519 1460

1453w 1512 1453

1446w 1504 1445

1504 1445

1497 1438

1414vs 1484 1426

1460 1403

1391w 1386vs 1447 1390

1344m 1420 1365

1321w 1383 1329

1274s 1301 1250

1244vs 1295 1244

1249 1200

1173m 1225 1177

1216 1168

1208 1160

1149w 1204 1157

1138vs 1186 1139

1179 1133

1102w 1179 1133

1080m 1124 1080

Table 6.2: Comparison of the experimental and calculated vibrational spectra

and proposed assignments of 1, 5-dimethoxynaphthalene

Mode Experimental

wavenumbers/cm-1

Theoretical wavenumbers/cm-1/

B3LYP/6-31G(d,p)

Vibrational assignments

nos.

d aIIR

bIRA with TED (≥10%)

1 0.00 69.22 υCH(93)

2 13.12 0 υCH(91) 3 27.95 0 υCH(93) 4 0.00 61.97 υCH(91) 5 0.00 65.87 υCH(92) 6 30.30 0 υCH(92) 7 0.00 69.84 υCH(91) 8 46.97 0 υCH(91) 9 82.93 0 υCH(98)

10 0.00 42.95 υCH(88) 11 0.00 100.01 υCH(81) 12 130.46 0 υCH(90) 13 0.00 16.24 υCC(62)+δCCC(11) 14 83.43 0 υCC(61) 15 0.00 127.5 υCC(64) 16 131.98 0 υCC(33) 17 0.00 34.85 ρHCH(49) 18 74.69 0 γCHOH(11) 19 0.00 39.02 υCC(15)+γCHOH(14)+υOC(11) 20 10.59 0.02 γCHOH(13) 21 0.00 81.88 γCHOH(13) 22 11.64 0 γCHOH(20) 23 0.00 6.43 γCHOH(27) 24 0.00 118.84 ηHCCC(57)+ ρHCH(31) 25 268.72 0 ηHCCC(38)+ ρHCH(43) 26 0.00 474.6 υCC(72) 27 7.68 0 υCC(19) 28 302.43 0 υOC(30) 29 0.00 4.7 υOC(49)+γCHOH(14) 30 33.94 0 υCC(53) 31 0.00 12.92 γCOCH(29) 32 34.36 0 γCHOH(32)+υCC(12) 33 0.00 27.49 γCHOH(26) 34 13.30 0 υCC(16)+γCHOH(11) 35 0.00 23.07 υCC(11) 36 1.66 0 γCHOH(85) 37 0.00 21.72 γCHOH(85) 38 203.20 0 υOC(57)

39 1112 1068 0.00 31.18 υCC(23)+υOC(18)

197

FTIR

Table 6.2 (Contd.): Comparison of the experimental and calculated vibrational

Spectra and proposed assignments of 1, 5-dimethoxynaphthalene

Mode Experimental

wavenumbers/cm-1

Theoretical wavenumbers/cm-1/

B3LYP/6-31G(d,p)

Vibrational assignments

nos. FT-

Raman Unscaled Scaled

aIIR

bIRA with TED (≥10%)

40 1040vs 1093 1050 58.39 0 υCC(57) 41 1055 1013 0.00 17.45 υOC(72) 42 963w 970 932 0.00 3.86 ηHCCC(81) 43 931w 969 931 1.28 0 ηHCCC(64) 44 862s 853m 891 856 16.16 0 υOC(25)+δCCC(12)+υCC(11) 45 880 845 0.00 15.37 ηHCCC(71) 46 879 844 1.93 0 ηHCCO(65)+ηHCCC(10) 47 839s 870 836 0.00 26.67 υCC(31) 48 825 793 0.00 9.23 ηCCCC(43)+ηHCCC(22) 49 793 762 89.27 0 ηHCCO(18)+ηHCCC(52) 50 754s 790 759 13.08 0 δCCC(70) 51 712s 741 712 0.00 24.2 ηHCCC(49)+ηCCCC(18) 52 685s 695 668 0.00 119.38 υCC(44) 53 655vs 686 659 3.33 0 ηCCCC(76) 54 611 587 18.92 0 δCOC(77) 55 602 578 1.06 0 ηCCCC(79) 56 535m 546 524 0.00 35.9 δCCC(26)+υCC(13) 57 534 513 0.00 23.09 ηCCCC(83) 58 524 503 6.54 0 δCCC(61) 59 478m 478 460 0.00 9.05 δCCC(60)+υCC(11) 60 456w 478 459 0.00 59.55 ηCCCC(58) 61 334s 357 343 1.72 0 δCCC(62) 62

63

335

315

322 0.00

303 0.00

175.46 δCOC(46)+υCC(11)+δCCC(11) ηCCCO(42)+ηHCOC(23)+ηCCCC

0 (10)

64 265w 281 270 0.00 8.2 ηHCOC(75)+ηCCCC(11) 65 256 246 0.00 50.85 δCOC(85) 66 223m 254 244 0.28 0 ηHCOC(62)+ηCCCO(22) 67 208 200 0.00 98.9 ηCCCC(51)+ηHCOC(22) 68 183 176 0.13 0 ηCCCC(53) 69 145w 173 166 4.04 0 δCOC(80) 70 118 114 7.52 0 ηCCCO(72) 71 96vs 95 91 0.00 30.45 ηCCOC(89)

72 61 59 3.85 0 ηCCCC(70) ν-stretching; δ-in-plane-bending; γ-out-of-plane bending; η-torsion; ρ-rocking; w-weak; s-strong;

vs-very strong; m-medium, aIIR-IR Intensity (Kmmol

−1);

bIRa-Raman intensity (Arb units) (intensity

normalized to 100%).

198

method is assigned to C-H stretching vibrations. A strong band appeared at

3127 and 3055 cm-1

in FTIR spectrum and at 3082 cm-1

in FT-Raman

spectrum are assigned to C-H ring stretching vibrations. As evident from the

TED column, they are pure stretching vibrations almost contributing to above

90%. The C-C-H in-plane ring bending vibrations are normally occurred as a

number of strong to weak intensity bands in the region 1300-1000 cm-1

[44].

In the present case, the C-H in-plane bending vibrations of the present

compound are computed in the range 1390-932 cm-1

by B3LYP method. The

wavenumbers observed at 1391 cm-1

in FTIR spectrum and at

1386 cm-1

in FT-Raman spectrum showed excellent agreement with predicted

wavenumbers 1390 cm-1

. Substitution patterns on the ring can be judged from

the out-of-plane bending of the ring C–H bonds in the region 960–675 cm−1

and these bands are highly informative [45]. The C-H out-of-plane bending

vibrations are normally observed in the region 1000–809 cm−1

[44, 46-49].

The C-H out-of-plane bending vibrations are observed in FTIR spectrum at

963, 931, 862 and 712 cm-1

and FT-Raman at 853 cm-1

. The experimental and

theoretical (1013-712 cm-1

by B3LYP method) out-of-plane bending

vibrational wavenumbers are found to be well within their characteristic

region.

6.5.2.2. -OCH3 group vibrations

Electronic effects such as back-donation and induction, mainly caused

by the presence of oxygen atom adjacent to CH3 group, can shift the position

199

of CH stretching and bending modes [50-53]. Methyl group vibrations are

generally referred to as electron-donating substituent in the aromatic rings

system, the antisymmetric C-H stretching mode of CH3 is expected around

2980 cm-1

and CH3 symmetric stretching is expected at 2870 cm-1

[54, 55].

For the assignments of CH3 group one can expect that nine fundamentals can

be associated to each CH3 group, namely the symmetrical stretching in CH3

(CH3 symmetric stretch) and asymmetrical stretching (CH3 asymmetric

stretch), in-plane stretching modes (i.e. in-plane hydrogen stretching mode),

the symmetrical (CH3 symmetric deform) and asymmetrical (CH3 asymmetric

deform) deformation modes, the in-plane rocking (CH3 ipr), out-of-plane

rocking (CH3 opr) and twisting (tCH3) bending modes. For the methyl group

compound [56], the asymmetric stretching mode appears in the range 2825-

2870 cm−1

, lower in magnitude compared to its value in CH3 (compounds)

(2860-2935 cm−1

) whereas the asymmetric stretching modes for both the type

of compounds lie in the same region 2925-2985 cm−1

. The weak bands

observed at 2984, 2941 cm−1

in FTIR spectrum and at 3008, 2960 and 2937

cm−1

in FT-Raman spectrum could be attributed to CH3 asymmetric stretching

vibrations. The same vibrations are computed at 3024, 2957 cm−1

by B3LYP

method show good agreement with experimental observations. The bands

observed at 2880 cm−1

in FTIR spectrum and at 2851 cm-1

in FT-Raman

spectrum could be attributed to CH3 symmetric stretching vibration. The

theoretically computed value for symmetric stretching vibration at 2898 cm−1

200

and 2897 cm−1

by B3LYP method show excellent agreement with

experimental observation.

For methyl substituted benzene derivatives, the antisymmetric and

symmetric deformation vibrations of methyl group normally appear in the

region 1465–1440 cm−1

and 1390–1370 cm−1

, respectively [57-59] while the

rocking mode appear in the 990-1050 cm−1

predicted by the DFT calculation,

the series of bands appearing in the 1400-1500 cm−1

region are mainly due to

the methyl deformation coupling with the ring C-C-H bending and C-C

stretching motions, to different extents and in different ways. In the case of

title molecule, the bands observed at 1470 and 1466 cm−1

in FTIR and FT-

Raman spectrum respectively correspond to CH3 deformation and correlated

with the calculated wavenumbers at 1463cm−1

by B3LYP method.

6.5.2.3. Ring vibrations

Naphthalene ring stretching vibrations are expected in the region 1620-

1390 cm-1

. Naphthalene ring vibrations are found to make a major

contribution in the IR and Raman spectra [60, 61]. The wavenumbers

observed in FTIR spectrum at 1611, 1597, 1541, 1495, 1344 and 1321 cm-1

and in FT-Raman spectrum at 1583 and 1453 cm-1

are assigned to C-C

stretching vibrations. The theoretically predicted harmonic wavenumbers at

1612, 1585, 1574, 1501, 1453, 1365 and 1329 cm-1

(mode nos. 13-16, 19,

26-27) by B3LYP/6-31G(d,p) level show a good agreement with experimental

data. These vibrations are mixed up with C-H in-plane bending vibrations as

201

shown in Table 6.2. The TED corresponds to these vibrations are mixed

modes as evident from Table 6.2.

6.5.2.4. C-O-C vibrations

The (O-C) and (C-O) stretching vibrations have already been reported

by Druzbicki et al. [62] and Dolega et al. [63] at ~1270 cm-1

and ~1040 cm-1

.

In the present study, the observed stretching bands are observed at 1274 and

1244 cm-1

in FTIR and 1080 cm-1

in FT-Raman. And then we have calculated

the ν (O-Cnaphthalene) frequency in methoxynaphthalene group is at 1250

and 1244 cm-1

. On the otherhand, the stretching vibrations of the ν (Cmethyl-O)

band assigned at 1080 and 1014 cm-1

. The TED corresponds to these

vibrations are mixed modes as evident from Table 6.2.

6.5.3. NBO analysis

NBO analysis has been performed on the molecule 1,5-

dimethoxynaphthalene at the DFT/B3LYP/6-31G(d,p) level in order to elucidate

the intramolecular, rehybridizaion and delocalization of electron density within

the molecule. Natural bond orbital analysis provides an efficient method for

studying intra-and intermolecular bonding and interaction among bonds, and

also provides a convenient basis for investigating charge transfer or

conjugative interaction in molecular systems [64]. The larger E(2) value, the

more intensive is the interaction between electron donors and electron

acceptors, i.e., the more donating tendency from electron donors to electron

acceptors and the greater the extent of conjugation of the whole system.

202

Delocalization of electron density between occupied Lewis-type (bond or lone

pair) NBO orbitals and formally unoccupied (antibond or Rydgberg) non-

Lewis NBO orbitals correspond to a stabilizing donor-acceptor interaction.

The second-order Fock matrix was carried out to evaluate the donor-acceptor

interactions in the NBO analysis [65]. The interactions result is a loss of

occupancy from the localized NBO of the idealized Lewis structure into an

empty non-Lewis orbital. For each donor (i) and acceptor (j), the stabilization

energy E(2) associated with the delocalization i→j is estimated as

E (2) = ΔEij

= qi

F (i , j )2

ε −ε

…….. (6.2) j i

Where qi is the donor orbital occupancy, εi and εj are diagonal elements and

F(i, j) is the off diagonal NBO Fock matrix element.

The intramolecular interaction are formed by the orbital overlap between ζ(C-

C) and ζ*C-C); π(C-C) and π*(C-C) bond orbital which results intramolecular

charge transfer (ICT) causing stabilization of the system. The strong

intramolecular hyperconjugation interaction of the ζ and π electrons of C-C

and C-H to anti C-C, C-H and C-O bond in the ring leads to stabilization of

some part of the ring as evident from Table 6.3. Particularly in the

naphthalene ring system, the intramolecular hyperconjugative interaction of

the π(C5-C10) conjugate with antibonding orbital of [π*(C1-C2), π*(C6-C7)]

and [π*(C3-C4), π*(C8-C9)] which leads to charge delocalization of 18.97

and 15.88 kJ/mol respectively.

203

Table 6.3: Second order perturbation theory analysis of Fock matrix in NBO basis

for 1, 5-dimethoxynaphthalene

Donor (i) ED (i)(e) Acceptor (j) ED E(2) KJ E(j)-E(i) F(i,j)

(j)(e) mol-1

a.u a.u

π*(C3-C4) 0.265 18.68 0.31 0.068

π(C1-C2) 1.739 π

*(C5-C10) 0.469 13.72 0.3 0.06

π*(C1-C2) 0.330 15.53 0.28 0.06

π(C3-C4) 1.756 π

*(C5-C10) 0.469 16.81 0.29 0.066

π*(C1-C2) 0.330 18.97 0.27 0.065

π*(C3-C4) 0.265 15.88 0.28 0.062

π(C5-C10) 1.585

π*(C6-C7) 0.330 18.97 0.27 0.065

π*(C8-C9) 0.265 15.88 0.28 0.062

π*(C5-C10) 0.469 13.72 0.3 0.06

π(C6-C7) 1.739 π

*(C8-C9) 0.265 18.68 0.31 0.068

π*(C5-C10) 0.469 16.81 0.29 0.066

π(C8-C9) 1.756 π

*(C6-C7) 0.330 15.53 0.28 0.06

ζ(C2-C3) 1.975 ζ*(C1-O13) 0.028 5.21 1.04 0.066

ζ(C2-H15) 1.978 ζ*(C1-C10) 0.029 4.55 1.06 0.062

ζ(C4-H17) 1.980 ζ*(C2-C3) 0.016 4.06 1.07 0.059

ζ*(C5-C10) 0.030 4.26 1.06 0.06

LP(2)O11 1.840 π*(C6-C7) 0.330 31.12 0.35 0.097

LP(2)O13 1.840 π*(C1-C2) 0.330 31.12 0.35 0.097

π*(C1-C2) 0.330 π

*(C3-C4) 0.265 172.2 0.01 0.076

π*(C6-C7) 0.330 π

*(C8-C9) 0.265 172.2 0.01 0.076

ED means Electron Density

dE(2) means energy of hyper conjugative interactions

eEnergy difference between donor and acceptor i and j NBO orbitals

fF(i,j) is the Fock matrix element between i and j NBO orbitals

204

On the otherhand, Among the title molecule, a strong intramolecular

hyperconjugative interaction of π-electrons with the greater energy

contributions from C1-C2 → C3-C4(18.68 kJmol−1

), C5-C10(13.72 kJmol−1

);

C3-C4 → C1-C2 (15.53 kJmol−1

), C5-C10 (16.81 kJmol−1

); C6-C7 → C5-

C10 (13.72 kJmol−1

), C8-C9 (18.68 kJmol−1

); C8-C9 → C5-C10 (16.81

kJmol−1

), C6-C7 (15.53 kJmol−1

) for naphthalene ring of the molecule,

Furthermore, the most interaction energy, related to the resonance in the

molecule, is electron donating from the nO11(2) and nO13(2) to the antibonding

acceptor π*(C6-C7) and π*(C1-C2) leads to moderate stabilization energy of

31.12 kJ/mol respectively. The π*(C6-C7) and π*(C1-C2) of the NBO

conjugated with π*(C8-C9) and π*(C3-C4) resulting to a greater stabilization

energy of 171.2 kJ/mol respectively for the title molecule.

6.5.4. Frontier molecular orbital analysis

The electronic absorption corresponds to the transition from the ground

to the first excited state and is mainly described by one electron excitation

from the highest occupied molecular orbital (HOMO) to the lowest

unoccupied molecular orbital (LUMO). The HOMO represents the ability to

donate an electron, LUMO as an electron acceptor represents the ability to

obtain an electron. Both HOMO and LUMO are the main orbitals that take

part in chemical stability [66]. The energy values of LUMO and HOMO and

their energy gap reflect the chemical activity of the molecule. The decrease in

the HOMO and LUMO energy explains the Intramolecular charge transfer

205

(ICT) interaction taking place within the molecule which is responsible for

the activity of the molecule. The HOMO-LUMO energy separation has served

as a simple measure of kinetic stability. A molecule with a small or no

HOMO-LUMO gap is a chemically reactive [67-69]. Pearson showed that the

HOMO-LUMO gap represents the chemical hardness of the molecule [70,

71]. The HOMO-LUMO energy gap of 1,5-dimethoxynaphthalene was

calculated at the B3LYP/6-31G(d,p) level and their values shown below

reveals that the energy gap reflect the chemical activity of the molecule. The

HOMO is located over the naphthalene part of the molecule, the HOMO →

LUMO transition implies an electron density transfer to oxygen and

conjugated bond of ring system from naphthalene part. Moreover, these

orbital significantly overlap in their position for 1,5-dimethoxynaphthalene.

The atomic orbital compositions of the frontier molecular orbital are sketched

in Fig.6.4.

HOMO energy = -5.0986 eV

LUMO energy = -0.4757 eV

HOMO-LUMO energy gap = 4.6230 eV

206

HOMO Plot

(Ground state)

HOMO Energy = -5.0986 eV

Energy gap = 4.6230 eV

LUMO Energy = -0.4757 eV

LUMO Plot

(First excited state)

Fig. 6.4: The atomic orbital compositions of the frontier molecular orbital for

1, 5-dimethoxynaphthalene

207

6.5.5. Molecular electrostatic potential (MEP)

The molecular electrostatic potential, V(r) is related to the electronic

density and is a very useful descriptor for determining sites for electrophilic

attack and nucleophilic reactions as well as hydrogen bonding interaction [72,

73]. MEP values were calculated using the equation [74]:

V(r) =∑ZA/|RA-r|-∫ρ (r′)/|r

′-r|d

3r

′

……… (6.3)

where, ZA is the charge of nucleus A located at RA, ρ(r’) is the electronic

density function of the molecule, and r’ is the dummy integration variable. To

predict reactive sites for electrophilic and nucleophilic attack for the title

molecule, MEP was calculated at the B3LYP/6-31G (d,p) optimized

geometry. The negative (red) regions of MEP were related to electrophilic

reactivity and the positive (blue) regions to nucleophilic reactivity shown in

Fig. 6.5.

As easily can be seen in figure this molecule has two possible sites for

electrophilic attack over O11 and O13. For the title compound, the maximum

negative electrostatic potential is noted over the oxygen atoms. For possible

nucleophilic reactions the maximum positive region is found on the hydrogen

of the naphthalene ring.

208

Fig. 6.5: Molecular electrostatic potential map of 1, 5-dimethoxynaphthalene

calculated by B3LYP/6-31G (d, p) method

209

6.6. CONCLUSION

In this present study, we have investigated to clarify the characterization

of 1,5-dimethoxynaphthalene by using of computational methods along with the

FTIR and FT-Raman spectra of 1,5-dimethoxynaphthalene. The molecular

geometry and wavenumber have been calculated using DFT/B3LYP with 6-

31G (d, p) basis set and the normal modes are assigned based on TED values.

The equilibrium geometries, atomic charges and harmonic wavenumbers

calculations of 1,5-dimethoxynaphthalene have been carried out for the first time

at DFT level. The vibrational frequencies of the fundamental modes of the

compound have been precisely assigned and analyzed and the theoretical

results were compared with the experimental vibrations. The theoretically

constructed IR and Raman spectra exactly coincide with experimentally

observed counterparts. The NBO result reflects the charge transfer mainly due

to methoxy group. HUMO and LUMO orbitals have been visualized. It has

been conclude that the lowest singlet excited state of the 1,5-

dimethoxynaphthalene molecule is mainly derived from the HOMO →

LUMO (π→π*) electron transition.

210

References

[1]. D. Hoffmann, E.L. Wynder, A.C. Stern (Eds.), Air Pollution, vol. 2,

Academic Press, New York, 1977, pp. 361.

[2]. M. Nordquist, D.R. Thakker, H. Yagi, R.E. Lehr, A.W. Wood, W.

Levin, A.H. Conney, D.M. Jerina, R.S. Bhatnagar (Eds.), Molecular

Basis of Environmental Toxicity, Ann Arbor Science Publisher, Ann

Arbor, MI, 1980, pp. 329.

[3]. R.G. Harvey, Polycyclic Aromatic Hydrocarbons: Chemistry and

Carcinogenicity, Cambridge University Press, Cambridge, UK, 1991.

[4]. S. Motta, C. Federico, S. Saccone, V. Librando, P. Mossesso, Mutat.

Res. 561 (2004) 45.

[5]. J.E. Amoore, E. Hautala, J. Appl. Toxicol. 3 (6) (1983) 272-290.

[6]. J.L. Puget, A. Leger, F. Boulanger, Astron. Astrophys.142 (1985) L19.

[7]. L.J. Allamandola, Top. Curr. Chem. 153 (1990) 1.

[8]. J. Szczepanski, M. Vala, Nature 363 (1993) 699.

[9]. M. Duncan, Astrobiol. Mag. 25 (2008).

[10]. F. Warnia, D. Mackay, Environ. Sci. Technol. 30 (1996) 390.

[11]. P.T. Williams, K.D. Bartle, G.E. Andrews, Fuel 65 (1986) 1150.

[12]. J. Bundt, W. Herbel, H. Steinhart, S. Franke, W. Francke, High

Resolut. Chromatogr. 14 (1991) 91.

[13]. S. Chandra, H. Saleem, N. Sundaraganesan, S. Sebastian, Spectrochim.

Acta A 74 (2009) 704.

[14]. V. Librando, A. Alparone, Environ. Sci. Technol. 41 (2007) 1646.

[15]. V. Librando, A. Alparone, Polycycl. Aromat. Compd. 27 (2007) 65.

[16]. A. Srivastava, V.B. Singh, Ind. J. Pure Appl. Phys. 45 (2007) 714.

[17]. P. Das, E. Arunan, P.K. Das, Vib. Spectrosc. 47 (2008) 1.

[18]. V. Krishnakumar, R. Mathammal, S. Muthunatesan, Spectrochim. Acta

A 70 (2008) 201.

[19]. M. Arivazhagan, V. Krishnakumar, R.R.J. Xavier, G. Ilango, V.

Balachandran, Spectrochim. Acta A 70 (2008) 201.

[20]. V. Krishnakumar, R. Mathammal, S. Muthunatesan, Spectrochim. Acta

A 70 (2008) 210.

[21]. P.B. Nagabalasubramanian, S. Periandy, Spectrochim. Acta A 77

(2010) 1099.

211

[22]. E. Kavitha, N. Sundaraganesan, S. Sebastian, M. Kurt, Spectrochim.

Acta A 77 (2010) 612.

[23]. J. Xavier, V. Balachandran, M. Arivazhagan, G. Ilango, Ind. J. Pure

Appl. Phys. 48 (2010) 245.

[24]. M. Govindarajan, K. Ganasan, S. Periandy, M. Karabacak,

Spectrochim. Acta 79A (2011) 646.

[25]. P.B. Nagabalasubramanian, M. Karabacak, S. Periandy, Spectrochim.

Acta 82A (2011) 169.

[26]. D. Shoba, M. Karabacak, S. Periandy, S. Ramalingam, Spectrochim.

Acta 81A (2011) 504.

[27]. D. Shoba, S. Periandy, M. Karabacak, S. Ramalingam, Spectrochim.

Acta 83A (2011) 540.

[28]. T. Prabhu, S. Periandy, S. Mohan, Spectrochim. Acta 78A (2011) 566.

[29]. P.B. Nagabalasubramanian, M. Karabacak, S. Periandy, Spectrochim.

Acta 85A (2012) 43.

[30]. B.D. Ostojić, D.S. Ðorđević, Chem. Phys. Lett. 536 (2012) 19.

[31]. M. Govindarajan, M. Karabacak, Spectrochim. Acta 85A (2012) 251.

[32]. Gaussian 03 program, (Gaussian Inc, Wallingford CT), 2004.

[33]. H.B. Schlegel, J. Comput. Chem. 3 (1982) 214.

[34]. A. Frisch, A.B. Nielson, A.J. Holder, GAUSSVIEW User Manual,

Gaussian Inc, Pittsburgh, PA, 2000.

[35]. V. Krishnakumar, R. Mathammal, S. Muthunatesan, Spectrochim. Acta

70A (2008) 210.

[36]. M.H. Jamroz, Vibrational Enegy Distribution Analysis, VEDA 4

Computer Program, Poland, 2004.

[37]. N. Sundaraganesan, G. Mariappan, S. Manoharan, Spectrochim. Acta

A 87 (2011) 67.

[38]. G. Kereztury, S. Holly, J. Varga, G. Besenyei, A.Y. Wang, J.R. Durig,

Specrochim. Acta 49A (1993) 2007.

[39]. G. Kereztury, in: J.M. Chalmers, P.R. Griffith (Eds.), Raman

Spectroscopy: Theory, in Hand book of Vibrational Spectroscopy, vol.

1, John Wiley & Sons Ltd, New York, 2002.

[40]. V. Krishnakumar, V. Balachandran, T. Chithambarathanu,

Spectrochim. Acta 62A (2005) 918.

[41]. N. Puviarasan, V. Arjunan S. Mohan, Turk. J. Chem. 26 (2002) 323.

212

[42]. G. Varsanyi, Vibrational Spectra of Benzene Derivatives, Academic

Press, New York, 1969.

[43]. V. Krishnakumar, R. John Xavier, Ind. J. Pure Appl. Phys. 41 (2003)

597.

[44]. N. Sundaraganesan, H. Saleem, S. Mohan, M. Ramalingam, V.

Sethuraman, Spectrochim. Acta 62A (2005) 740.

[45]. P.S. Kalsi, Spectroscopy of Organic Compounds, Wiley Eastern

Limited, New Delhi, 1993, pp. 116.

[46]. V. Krishnakumar, N. Prabavathi, Spectrochim. Acta 71A (2008) 449.

[47]. A. Altun, K. Gölcük, M. Kumru, J. Mol. Struct. (Theochem.) 637

(2003) 155.

[48]. Y.X. Sun, Q.L. Hao, Z.X. Yu, W.J. Jiang, L.D. Lu, X. Wang,

Spectrochim. Acta 73A (2009) 892.

[49]. N. Sundaraganesan, B.D. Joshua, T. Radjakoumar, Ind. J. Pure Appl.

Phys. 47 (2009) 248.

[50]. B. Smith, Infrared Spectral Interpretation, A Systematic Approach,

CRC Press, Washington, DC, 1999.

[51]. M. Gussoni, C. Castiglioni, J. Mol. Struct. 521 (2000) 1.

[52]. J. Palomar, J.L.G. De Paz, J. Catalan, Chem. Phys. 246 (1999) 167.

[53]. M. Rumi, G. Zerbi, J. Mol. Struct. 509 (1999) 11.

[54]. D. Sajan, I. Hubert Joe, V. S. Jayakumar, J. Raman Spectrosc. 37

(2005) 508.

[55]. M. Gussoni, C. Castiglioni, M. N. Ramos, M. C. Rui, G. Zerbi, J. Mol.

Struct. 224 (1990) 445.

[56]. D.N. Singh, I.D. Singh, R.A. Yadav, Ind. J. Phys. 76B (3) (2002) 307.

[57]. B. V. Reddy, G. R. Rao, Vib. Spectrosc. 6 (1994) 231.

[58]. J. F. Areanas, I. L. Tocn, J. C. Otero, J. I. Marcos, J. Mol. Struct. 410

(1997) 443.

[59]. D. A. Long, W. O. Jeorge, Spectrochim. Acta 19 (1963) 1777.

[60]. C. Surisseau, P. Marvel, J. Raman Spectrosc. 25 (1994) 447.

[61]. A.J. Barnes, M.A. Majid, M.A. Stuckey, P. Gregory, C.V. Stead,

Spectrochim. Acta 41A (1985) 629.

[62]. Kacper Druzbicki, Edward Mikuli, Miroslawa D Ossowska-Chrusciel,

Vib. Spectrosc. 52 (2010) 54.

[63]. Diana Dolega, Anna Migdal-Mikuli, Janusz Chrusciel J. Mol. Struc.

933 (2009) 30.

213

[64]. M. Snehalatha, C. Ravikumar, I. Hubert Joe, N. Sekar, V.S.

Jayakumar, Spectrochim. Acta A 72 (2009) 654.

[65]. M. Szafran, A. Komasa, E.B. Adamska, J. Mol. Struct. (Theochem.)

827 (2007) 101.

[66]. R.G. Pearson, J. Org. Chem. 54 (1989) 1423.

[67]. J.I. Aihara, Phys. Chem. Chem. Phys. 2 (2000) 3121.

[68]. X. Liu, T.G. Schmalz, D.J. Klein, Chem. Phys. Lett. 188 (1992) 550.

[69]. M.D. Diener, J.M. Alford, Nature (London) 393 (1998) 668.

[70]. R.G. Pearson, Proc. Natl. Acad. Sci. USA 83 (1986) 8440.

[71]. R.G. Pearson, J. Am. Chem. Soc. 110 (1988) 2092.

[72]. E. Scrocco, J. Tomasi, Adv. Quant. Chem. 11 (1978) 115.

[73]. N. Okulik, A.H. Jubert, Internet Electron. J. Mol. Des. 4 (2005) 17.

[74]. P. Politzer, J.S. Murray, Theor. Chem. Acc. 1087 (2002) 134.