42
S. Subashchandrabose et al. / Journal of Molecular Structure 1042 (2013) 37–44
polarizability a0, the anisotropy of polarizability Da and the mean
first hyperpolarizability b0, using the x, y, z components are defined as
calculation gives the wavenumbers 1397, 1397, 1475, 1477 (mode
nos: 75, 76, 79, 80) are assigned to be NACAH in-plane bending
vibration (pyridine ring). While dN11@C12AH13/dN24@C25AH26 is
assigned to harmonic wavenumber 1354/1355 cmꢁ1 (mode nos:
73, 74) respectively. The harmonic frequencies at 620, 650 cmꢁ1
(mode nos: 27, 28) are attributed to dCANAC mode in both pyridine
rings. These assignments are supported by observed bands 1465,
1488, 1342, 618 in FT-IR and 1474, 652 cmꢁ1 in FT-Raman spectra.
1=2
l
¼ ðl2x
þ
þ
ly2
þ
lz2
Þ
ð3Þ
ð4Þ
axx
ayy
3
þ
azz
a0
¼
2
2
2
¼ 2ꢁ1=2½ðaxx
ꢁ
ayyÞ þ ðayy
ꢁ
azzÞ þ ðazz
ꢁ
axxÞ þ 6ða2xy
The harmonic frequencies of mode numbers 48, 49 (964, 964 cmꢁ1
)
D
a
1=2
a2yz
þ
a2xzÞꢄ
ð5Þ
are assigned to CN11@C12AH13/CN24@C25AH26 vibrations, whereas the
þ
frequency 961 cmꢁ1 in FT-IR spectrum supports the mode numbers
48 and 49.
1=2
b0 ¼ ðb2 þ b2 þ b2Þ
ð6Þ
x
y
z
4.3.3. CAC vibrations
Many organic molecules, containing conjugated
p
electrons
In general, the bands around 1600 and 1400 cmꢁ1 in benzene
are assigned to skeletal CAC stretching modes [38]. In this work,
the middle to strong bands are observed at 1576, 1448, 1283,
1094 cmꢁ1 in FT-IR and strong bands observed at 1571,
1452 cmꢁ1 in FT-Raman are assigned to aromatic CAC stretching
vibrations (benzene ring), which are good agreement with theoret-
ically calculated value at 1567–1085 cmꢁ1 (mode nos: 84, 83, 78,
70, 62, 59). These assignments find support from the work of
Fereyduni et al. [29] and are within the frequency intervals given
by Varsanyi [38]. Similarly the frequencies observed in FT-IR
spectrum at 1590, 1535, 1008, 873 cmꢁ1 are assigned to CAC
stretching vibrations for pyridine. The corresponding vibrations
were characterized by large values of molecular first order hyper
polarizabilities and analyzed by means of vibrational spectroscopy
[42–45]. The intra molecular charge transfer from the donor to
acceptor group through a single-double bond conjugated path
can induce large variations on both the molecular dipole moment
and the molecular polarizability making IR and Raman activity
strong at the same time [46].
The total molecular dipole moment (l) and mean first order
hyperpolarizability (b0) are given as 1.714 Debye and
1.117 ꢂ 10ꢁ30 esu, respectively. The total dipole moment of the
title compound is approximately higher and the first order
hyperpolarizability (b0) of the title molecule is three times greater
than that of urea, hence this molecule has considerable NLO
activity. The computation of the molecular polarizability of NBPMB
is shown in Table 2.
appear in the FT-Raman spectrum at 1591, 1527 and 1006 cmꢁ1
.
The computed values in the range 1585–875 cmꢁ1 (mode nos:
86, 85, 82, 81, 76, 75, 52, 43) shows good coherence with experi-
mental data and also in line with literature value [39]. These
assignments are also supported by TED values.
4.5. NBO analysis
The ring (benzene) in-plane deformation vibrations are ascribed
to the FT-IR band at 1094, 618 cmꢁ1 and harmonic bands at 1085,
835 and 620 cmꢁ1 (mode nos: 59, 39, 27). The CACAC out-of-plane
deformations (benzene) are found at 712, 564 cmꢁ1 FT-IR bands
and the harmonic bands at 735, 716, 560 cmꢁ1 (mode nos: 33,
31, 25). Similarly the CACAC in-plane-bending vibrations (pyri-
dine) are attributed to the harmonic bands in the range 657–
437 cmꢁ1 (mode nos: 30, 29, 21, 19) and the FT-IR bands at 670,
499, 426 cmꢁ1. The out-of-plane vibrations due to CACAC (pyri-
dine) are characterized by the harmonic bands at 725, 716, 375
and 248 cmꢁ1 (mode nos: 32, 31, 18, 17, and 12). These assign-
ments are supported by Sundaraganesan et al. [39], Erdog˘du
et al. [34] and Wang et al. [40] for pyridine and benzene rings.
The hyperconjugation may be given as stabilizing effect that
arises from an overlap between an occupied orbital with another
neighboring electron deficient orbital, when these orbitals are
properly orientated. This non-covalent bonding (antibonding)
Table 2
The molecular dipole moment (
l), polarizability (a) and
hyperpolarizability (b0) values of NBPMB.
Parameters
B3LYP/6-31G(d,p)
Dipole moment (l)
lx
ly
lz
l
0.0001
1.7143
ꢁ0.0001
1.7143 Debye
4.4. Hyperpolarizability calculations
Polarizability (a)
axx
axy
ayy
axz
ayz
azz
a
311.07
0.00
299.77
32.03
The first order hyperpolarizabilities (b0, a0 and Da) of NBPMB is
calculated using B3LYP/6-31G(d,p) basis set, based on the
finite-field approach. In the presence of an applied electric field,
the energy of a system is a function of the electric field. First hyper-
polarizability is a third rank tensor that can be described by a
3 ꢂ 3 ꢂ 3 matrix. The 27 components of the 3D matrix can be re-
duced to 10 components due to Kleinman symmetry [41]. It can
be given in the lower tetrahedral format. It is obvious that the
lower part of the 3 ꢂ 3 ꢂ 3 matrix is a tetrahedral. The components
of b are defined as the coefficients in the Taylor series expansion of
the energy in the external electric field. When the external electric
field is weak and homogeneous, this expansion becomes:
ꢁ0.01
109.67
6.47 ꢂ 10–30 esu
Hyperpolarizability (b0)
bxxx
bxxy
bxyy
byyy
bxxz
bxyz
byyz
bxzz
byzz
bzzz
b0
ꢁ0.13
ꢁ837.08
0.07
ꢁ473.04
0.02
ꢁ53.46
0.02
0.00
E ¼ E0 ꢁ laFa ꢁ 1=2aabFaFb ꢁ 1=6ba FaFbFc
ð2Þ
b
c
17.48
0.00
where E0 is the energy of the unperturbed molecules, F is the field at
a
1.1167 ꢂ 10ꢁ30 esu
the origin, and la
moment, polarizability and the first order hyperpolarizabilities
respectively. The total static dipole moment the mean
,
aab, b
are the components of the dipole
a
bc
Standard
value
for
urea
l = 1.3732 Debye,
b0 = 0.3728 ꢂ 10ꢁ30 esu.
l,