Theoretical modeling of infrared spectra of benzoic acid and its deuterated derivative

Article abstract of DOI:10.1016/j.molstruc.2004.03.024

Theoretical simulation of the ν_s stretching band is presented for benzoic acid and its OD derivative at 300 K. The simulation takes into account an adiabatic coupling between the high-frequency O-H(D) stretching and the low-frequency intermolec

Full text of DOI:10.1016/j.molstruc.2004.03.024

Journal of Molecular Structure 700 (2004) 39–48
www.elsevier.com/locate/molstruc
Theoretical modeling of infrared spectra of benzoic acid
and its deuterated derivative
a
Marek Boczar , Krzysztof Szczeponek , Marek J. W o´ jcik , Czesława Paluszkiewicz
a
a,
b
*
a
Faculty of Chemistry, Jagiellonian University, 30-060 Krak o´ w, Ingardena 3, Poland
b
Regional Laboratory, Jagiellonian University, 30-060 Krak o´ w, Ingardena 3, Poland
Received 24 October 2003; revised 21 February 2004; accepted 2 March 2004
Abstract
Theoretical simulation of the n stretching band is presented for benzoic acid and its OD derivative at 300 K. The simulation takes into
s
account an adiabatic coupling between the high-frequency O–H(D) stretching and the low-frequency intermolecular O· · ·O stretching
modes, linear and quadratic distortions of the potential energy for the low-frequency vibrations in the excited state of the O–H(D) stretching
vibration, resonance interaction between the two hydrogen bonds in the dimer, and Fermi resonance between the fundamental n OH(D)
stretching and the overtone of the d O–H(D) bending vibrations.
Infrared, far-infarared, Raman and low-frequency Raman spectra of the polycrystalline benzoic acid and its deuterated form have been
cm a el ca us ul ar te i do .n Ts .he geometry and experimental frequencies are compared with the results of our B3LYP/6-311þþG** and B3LYP/cc-pVTZ
q 2004 Elsevier B.V. All rights reserved.
Keywords: Benzoic acid; Hydrogen bond; Vibrational spectra; Ab initio calculations
5
2h
1
. Introduction
are monoclinic, space group is P2 =c ¼ C and Z ¼ 4:
1
There are two centrosymmetric hydrogen bonded dimers in
˚
each unit cell, linked 2.645 A long hydrogen bonds.
˚
All other intermolecular distances are over 3 A, and
Vibrational spectra of hydrogen bonded dimers have
been a subject of numerous experimental and theretical
papers [1–13]. There have been also numerous studies of
Fermi resonance in hydrogen bonded complexes and
crystals [14–24]. In this paper, we present infrared and
Raman spectra of polycrystalline benzoic acid and its OD
derivative. We, also, compare the experimental frequencies
with the results of our ab initio B3LYP/6-311þþG** and
B3LYP/cc-pVTZ calculations. The theoretical model was
used to simulate O–H(D) stretching bands. Recent infrared
spectra of hydrogen bonded benzoic acid crystals have been
studied experimentally and interpreted theoretically
within so-called ‘strong coupling’ model by Flakus et al.
correspond to normal van der Waals interactions. The
˚
˚
˚
identity periods are: a ¼ 5:25 A, b ¼ 5:14 A, c ¼ 21:9 A
and b ¼ 978: The closest contact between O of one dimer
˚
and O another dimer is 3.65 A, related by a translation b
[29–32].
An anharmonic coupling between the high frequency
X–H stretching and low frequency intermolecular hydro-
gen bond vibrations, described by Mar e´ chal and
Witkowski [2] is an important mechanism shaping fine
structure of n bands in hydrogen-bonded systems. The
s
most important mechanism influencing the fine structure
of vibratonal spectra of hydrogen bonded system is Fermi
resonance. The theoretical model of this mechanism was
published by Witkowski and W o´ jcik [15] and W o´ jcik
[
10,25–28].
At room temperature benzoic acid is a crystal (its melting
points is at 395 K). System which draws our attention in the
present paper is benzoic acid dimer. Benzoic acid crystals
[16]. In this paper, we present a theoretical interpretation
of the fine structure of the n stretching band of benzoic
s
*
Corresponding author. Tel.: þ48-12-632-5392; fax: þ48-12-634-0515.
E-mail address: wojcik@chemia.uj.edu.pl (M.J. W o´ jcik).
acid and its deuterated derivative. For simulation of the
fine structure we used an adiabatic coupling between
0022-2860/$ - see front matter q 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.molstruc.2004.03.024

40
M. Boczar et al. / Journal of Molecular Structure 700 (2004) 39–48
the high-frequency O–H(D) stretching and the low-
frequency intermolecular O· · ·O stretching modes, linear
and quadratic distortions of the potential energies for
these modes in the excited state of the O–H(D) stretching
vibration, resonance interaction between the two hydrogen
bonds in the dimer, and Fermi resonance between the
fundamental n OH(D) stretching and the overtone of the
dO–H(D) bending vibrations.
in the Department of Materials Chemistry, Uppsala
University in Sweden.
3. Theoretical model
The theoretical model of Fermi resonace in infrared
spectra of hydrogen bonded carboxylic acid dimer, which
we are going to use, has been first developed by W o´ jcik
[16]. We used an extended version of this model, modified
to encompass an adiabatic coupling between the high
frequency O–H(D) stretching and low frequency hydrogen
bond stretching vibrations, linear and quadratic distortions
of the potential energies for these modes in the excited state
of the O–H(D) stretching vibration, resonance interaction
between the two hydrogen bonds in a dimer, and Fermi
resonance interaction between the fundamental nOH(D)
stretching and the overtone of the dO–H(D) bending
vibrations.
2
. Methods
Policrystalline benzoic acid, which has been used in this
investigation, was purchased from the Aldrich Chemical
Corporation. The purity was 99%.
Infrared spectra of benzoic acid and deuterated benzoic
acid (benzoic acid-D) presented in this paper were recorded
on an Equinox 55 Brucker Fourier transform spectrometer.
The samples were ground with KBr and pressed.
2
1
Fig. 1 present geometry of the benzoic acid dimer
optimized at the B3LYP/cc-pVTZ level. In this case the two
hydrogen bonds of this dimer are related by the
symmetry operation C2 corresponding to the two-fold
symmetry axis.
The resolution of spectra was 2 cm in the range from
4
2
1
00 to 4000 cm . Far-infrared spectrum of polycrystalline
2
1
benzoic acid in the range from 50 to 450 cm was recorded
on a FTS Biorad 60 V spectrometer in the Regional
Laboratory of Physico–Chemical Analyses and Structural
Research in Krak o´ w. The samples were mixtured with
polyethylene and pressed. The resolution of spectra in this
The vibrational hamiltonian, H, can be written as:
H ¼ TðQ Þ þ TðQ Þ þ h þ hs;2 þ hb;1 þ hb;2
1
2
s;1
2
1
region was 2 cm
.
0
0
0
þ V
þ V
þ V
;
ð1Þ
1
;ah
2;ah
res
Raman spectra of benzoic acid were recorded on a
Renishaw 2000 Micro Raman System. Samples were
excited by a near-infrared diode laser generating light of
wavelength 785 nm (30 mW) and Argon-Ion laser generat-
ing light of wavelenght 514 nm (50 mW). The resolution
where TðQ Þ is the kinetic energy operator of the low-
i
frequency vibration; Q ði ¼ 1; 2Þ are the coordinates of the
i
two low frequency intermolecular O· · ·O stretching modes,
denote n ; h ¼ Tðq Þ þ Vðq ; Q Þ is the vibrational
s
s;i
s;i
s;i
i
2
1
was 2 cm
.
Deuteration of the carboxylic group was done by
hamiltonians of the high frequency ns vibrations;
q ði ¼ 1; 2Þ are the coordinates of the high frequency
s;i
´
dissolving the sample in D O (purchased from IBJ Swierk,
2
O–H stretching vibrations, in the first and second hydrogen
bond; hb;i ¼ Tðq Þ þ Vðq Þ is the vibrational hamiltonians
9
9.1% purity) then heating under a flux condensor, filtering
b;i
b;i
and drying. The sample was deposite above zeolite-A.
The geometry of benzoic acid was optimized and the
vibrational frequencies were computed using the
GAUSSIAN 98 programs [33] at the B3LYP/6-311þþG**
and B3LYP/cc-pVTZ levels. Computations were carried out
of the high frequency n vibrations; q ði ¼ 1; 2Þ are the
b
b;i
coordinates of the in plane bending vibrations in the first or
second hydrogen bond; V ðq ; q Þ is the anharmonic
0
i;ah s;i b;i
coupling terms between the hydrogen bond stretching
0
and bending vibrations; V ðq ; q Þ is the resonance
i;res s;1 s;2
Fig. 1. Geometry of the benzoic acid dimer, optimized at the B3LYP/cc-pVTZ level.

M. Boczar et al. / Journal of Molecular Structure 700 (2004) 39–48
41
interaction potential between the two equivalent hydrogen
bonds; V is the potential energy. We neglect interactions of
n and n vibrations with the other vibrations of the system.
The energies 1 ðQ Þ of the high-frequency hydrogen
s;i
i
stretching vibration of individual hydrogen bonds deter-
mine the effective potential governing the low-frequency
hydrogen bond vibrations. Those potentials are assumed
harmonic and to have the same force constant in the upper
and lower states of the hydrogen bond stretching
vibrations:
s
s
Fermi resonance is considered between the fundamental
vibration n and the first overtone of the bending mode n :
s
b
With a suitable change of the anharmonic coupling
parameter the in plane bending can be replaced by any
other vibration of the system. We do not consider any
coupling between the n and n vibrations.
b
s
1
1
1
2
i
þ
2
i
2
i
In the first exciting state of O–H stretching vibrations,
þ
1s;i ¼ 2 KQ ;
1
¼ R þ LQ þ 2 DKQ þ KQ ;
s;i
i
2
the total vibrational wavefunction, Cj
0
; has the form:
ð5Þ
þ
þ
þ
1 s;1 b;1 s;2 b;2
C
0
¼ a x x x x þ b x x x x
j
1
s;1 b;1 s;2 b;2
where R is vertical excitation energy; L the linear distortion
parameter, DK the quadratic distortion parameter, K the
quadratic force constant.
þ
þ
;
þ a x x x x þ b x x x x
ð2Þ
2
s;1 b;1 s;2 b;2
2 s;1 b;1 s;2 b;2
Introducing dimensionless quantities:
where x ðq ; Q Þ are the eigenfunctions of the hamiltonians
s;i s;i
i
h ; x ðq Þ the eigenfunctions of the hamiltonians
s;i
b;i b;i
h ; a ðQÞ; b ðQÞ the wavefunctions of the hydrogen–bond
1=2
1=2
b;i
i
i
q ¼ Q ðMV="Þ ; p ¼ P =ð"MVÞ
;
i
i
i
i
vibrations n ; not determined yet. Superscript ‘ þ ’ – marks
s
3
1=2
0
ah
b ¼ L=ð"MV Þ ; V ¼ V ="V; r ¼ R="V;
ð6Þ
the excited state of n and of the first overtone of n :
s
ah
b
0
þ
2
0
res
Applying the procedure of Longuet–Higgins [38] to the
Schr o¨ dinger equation with hamiltonian (1) and the wave-
function (2), enables to find the a ðQÞ; b ðQÞ functions and
r ¼ 1 ="V; dk ¼ DK=MV ; V ¼ V ="V;
b;i
res
i
i
the total vibrational energy. With the crude adiabatic
where V is the angular frequency for n vibration and M is
s
2
approximation assumed for the n and n vibrations the
s
reduced mass for n vibration ðK ¼ MV Þ: We can re-write
b
s
eff
effective hamiltonian H for the low-frequency vibration
ns takes the four-dimensional matrix form:
the hamiltonian (3) in a compact form, using the two
orthogonal sets of Dirac matrices s and r:
2
6
ꢂ
3
7
þ
TðQ Þ þ TðQ Þ þ 1 ðQ Þ
1
2
s;1
1
ꢃ
6
6
0
0
V ;
res
7
7
þ1 ðQ Þ þ 1 þ 1b;2
;
V ;
ah
0
s;2
2
b;1
6
6
6
7
7
7
ꢂ
0
V ;
ah
TðQ Þ þ TðQ Þ þ 1 ðQ Þ
þ1 ðQ Þ þ 1 þ 1b;2
6
6
1
2
s;1
1
7
7
ꢃ
6
6
6
6
6
þ
b;1
7
7
7
7
7
;
0;
0
s;2
2
eff
H
¼
ꢂ
;
0
V
;
0;
TðQ Þ þ TðQ Þ þ 1 ðQ Þ
res
1
2
s;1
1
6
7
6
6
ꢃ
7
þ
0
7
þ1 ðQ Þ þ 1 þ 1b;2
;
V
6
6
s;2
2
b;1
ah
7
7
ꢂ
6
6
4
0
7
0;
0;
V ;
ah
TðQ Þ þ TðQ Þ þ 1 ðQ Þ 7
1
2
s;1
1
5
ꢃ
þ
b;2
þ1 ðQ Þ þ 1 þ 1
s;2
2
b;1
ð3Þ
where 1 ðQ Þ are eigenvalues of the hamiltonians h ; 1
s;i
i
s;i b;i
1
1
0
ah
eff
2
2
2
2
the eigenvalues of the hamiltonians h ; V the matrix
H = ꢀh V ¼ 2 ðp1 þ q1Þ1 þ ðp2 þ q2Þ1
b;i
2
ꢀ
ꢀ
ꢁ
element of the anharmonic coupling between excited states
0
1
1
1
2
2
of n and n ; V the vibrational analogue of the exchange
s
þ 4 bq1 þ bq2 þ dkq1 þ dkq2 ð1 þ s3Þ
b
res
0
2
1
2
1
0
integral. The V and V are defined as:
res
ꢁ
ah
1
2
1
2
2
þ 4 bq 2 bq þ dkq 2 dkq ð1 þ s Þr3
1
2
3
2
2
0
þ
þ
b;2 qs;qb ;
s;1 b;1 s;2
1
1
V
¼ kx x x xb;2lV1;ahlx x x x
l
0
ah
s;1 b;1 s;2
þ 2 M s þ V s þ V ð1 þ s Þr
3
ah
1
res
3
1
þ
þ
2
¼
kx x x xb;2lV2;ahlx x x x
l
ð4Þ
s;1 b;1 s;2
s;1 b;1 s;2 b;2 qs;qb
1
0
0
þ
þ
þ 2 ðr þ r Þ1
ð7Þ
V
¼ kx x x x lV lx x x xb;2 qs;qb :
s;1 b;1 s;2 b;2 res s;1 b;1 s;2
l
res

42
M. Boczar et al. / Journal of Molecular Structure 700 (2004) 39–48
0
þ
0
are given by Eq. (2) and the
wavefunctions c ; in the adiabatic approximation, have the
The dimensionless parameter M means the difference
The wavefunctions cj
between the vertical excitation energy r of the hydrogen
bond stretching vibration (to the first excited state) and the
excitation energy to the first overtone of the proton bending
j
form:
ðjÞ
0
þ
0
vibration r ð1 ¼ 0; 1 ¼ r Þ: For exact Fermi resonace
b;i
Cj ¼ a0 xs;1xb;1xs;2xb;2:
ð12Þ
b;i
0
M ¼ 0: 1 is the unit matrix. The four-dimensional Dirac
Neglecting the dependence of the dipole moment m on
the coordinates Q of the low frequency hydrogen bond
vibrations we obtain the intensity given as a combination of
matrices have the following forms:
2
3
2
3
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
6
6
6
6
7
7
6
6
7
7
ðjÞ
the Franck-Condon integrals between the wavefunctions a
and the wavefunctions a^ and b : The intensity is given
by following equation:
0 7
6 0 21
0 7
0
0
0
ðj Þ
ðj Þ
7
6
7
s1 ¼
r1 ¼
; s ¼
;
6
7
3
6
7
^
6
4
1 7
6 0
0
0
0 7
5
4
5
0
0
21
0
2
ðjÞ
ðj Þ
2
ð8Þ
Ijj0 , lm0sl {lka l1 ^ C2la ll
2
3
2
3
0
^
ꢀ
ꢁ
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2j ꢀh V
2
ðjÞ
ðj Þ
2
6
6
7
7
6
6
7
7
þ d lka l1 ^ C lb ll }exp
;
ð13Þ
0
2
^
6
1 7
6 0
0 7
kT
6
7
6
7
; r ¼
:
6
6
4
7
0 7
5
3
6
7
6 0
4
21 0 7
where:
5
0
0
0
21
þ
s;1 b;1 s;2 b;2 qs;qb
m0s ¼ kxs;1xb;1x x lmlx x x x
l
s;2 b;2
In the hamiltonians (3) and (7) we have neglected the
resonance interaction between the two hydrogen bonds
involving the overtone states of the bending n vibrations.
2
and d is the ratio of the intensities of the bending overtone
to the fundamental stretching vibrations.
b
To obtain formula (13) from (11) we have used
symmetrical form of the eigenfunctions of the hamil-
tonian (7):
Applying the symmetry operator C , we can reduce the
2
four-dimensional hamiltonian (7) to the two-dimensional
þ
þ
2
2
hamiltonians h and h . The hamiltonians h and h are
given by the formulas:
2
0
3
ðj Þ
a
b
ꢀ
ꢁ
^
6
6
6
7
7
7
1
1
1
2
1
^
2
1
2
1
2
2
2
2
2
1
0
ðj Þ
h ¼ ðp þ q Þ1 þ ðp þ q Þ1 þ
bq þ 2 dkq
1
1
2
2
6
6
6
6
4
^
7
7
7
7
5
ꢀ
ꢁ
ð14Þ
0
1
1
ðj Þ
2
1
0
^
^
C a
2
þ
bq þ 2 dkq þ M g
^
1
3
2
0
ðj Þ
C b
2
1
1
^
0
þ V g ^ V ð1 þ g ÞC þ ðr þ r Þ1
ah
1
res
3
2
2
2
derived from the eigenfunctions of the two-dimensional
hamiltonians (9):
ð9Þ
where g are the two-dimensional Pauli matrices:
i
2
3
0
ðj Þ
"
#
" 1
#
a
b
^
0
1
1
0
0
4
5
ð15Þ
0
g1 ¼
; g ¼
:
ð10Þ
ðj Þ
3
^
0
21
^
The eigenenergies of the hamiltonians h (9) and
The hamiltonians (9) describe the two low-frequency
vibrations which are coupled through the high-frequency
motions. The two mechanisms, i.e. Fermi resonance and
exchange resonance interaction, which are not in general
separable, contribute to the spectra, which are irregular and
no longer exhibit Franck-Condon type progressions.
The IR intensities of the transitions from the ground state
to the excited state of the hydrogen bond stretching
vibrations are given by the formula:
eigenfunctions a^ and b^ (15) have been calculated
numerically by expanding the eigenfunctions into series
of harmonic oscillators and diagonalising the resulting
energy matrices.
0
The parameters b; dk; Vres and M of the hamiltonians (9)
can be evaluated from the succesive moments M of the
infrared band. These moments are defined as:
k
X
þ
k
I
0
ðEj
0
2 E Þ
ꢀ 2j ꢀh V
ꢁ
j;j0 jj
j
M ¼
X
;
ð16Þ
þ
2
k
Ijj
0
, lkC lmlC
0
ll exp
;
ð11Þ
Ijj
0
j
j
0
j;j
kT
þ
where c is the jth wavefunctions of the ground vibrational
where E are the eigenenergies of the ground state; E
j
0
the
j
j
þ
0
state of the n and n vibrations; c the j th wavefunctions
j
0
eigenenergies of the excited state.
The first and second transition moments describe the
s
b
of the excited vibrational state, m the dipole moment of the
dimer.
centre of gravity of the spectrum v and its theoretical
0

M. Boczar et al. / Journal of Molecular Structure 700 (2004) 39–48
43
half-widths Dv:
Table 1
Optimized geometries of benzoic acid dimer by the B3LYP/6-311þþG**
2
1
1=2
v ¼ M
Dv ¼ ðM 2 M Þ
:
ð17Þ
and B3LYP/cc-pVTZ methods
0
1
2
Assuming, as previously, that the intensity of transitions
to the overtone states is negligible compared to the
fundamental transitions and applying formula (13) we
obtain from (16) and (17):
Calculated
Experimental
B3LYP/
a
6
-31G**
B3LYP/
B3LYP/
6
-311þþG** cc-pVTZ
˚
Bond lengths (A)
v ¼ r 2 V
0
res
0
b
2.64 ; 2.629 ; 2.633
c
d
O
1
· · ·O
2
0
2.663
1.663
1.000
1.230
1.323
1.486
1.400
1.391
1.395
1.395
1.390
1.400
1.082
1.084
1.084
1.084
1.083
2.638
1.635
1.003
1.229
1.318
1.485
1.396
1.388
1.391
1.392
1.386
1.396
1.080
1.082
1.082
1.082
1.080
2.625
1.617
1.006
1.237
1.320
1.487
1.402
1.393
1.397
1.397
1.392
1.402
1.084
1.086
1.086
1.086
1.084
ꢄ
ꢀ
ꢁ
ꢅ
c
ð18Þ
O –H
1
1.64
1
=2
1
1
1
2
1
2
2
2
ah
c
Dv ¼
b þ dk coth ð ꢀh V=2kTÞ þ V
O
2
–H
0.988
2
b
1.24 ; 1.268 ; 1.263
c
d
d
C
C
C
C
1
1
2
2
–O
–O
1
b
1.29 ; 1.275 ; 1.275
c
2
We see that the anharmonic term Vah increases the width
of the spectrum but does not influence its position, whereas
the exchange interaction, described by the parameter Vres;
shifts the centre of gravity but does not change the width.
The formulas (18) can also be generalized for the case of
non-negligible intensity of transitions to the overtone
bending vibrations:
b
1.48 ; 1.484
d
–C
–C
1
3
4
5
6
7
2
c
1.39; 1.390
b
1.42 ; 1.387
d
d
c
d
c
3
C –C
b
1.36 ; 1.379
C
C
C
C
C
C
C
C
4
5
6
7
3
4
5
6
–C
–C
–C
–C
b
1.37 ; 1.384
b
1.41 ; 1.401
b
1.39 ; 1.392
b
–H
–H
–H
–H
3
4
5
6
7
0.79
b
0.96
2
v ¼ r 2 V þ 2dV cosw þ uðd Þ;
ð19Þ
b
0
res
ah
0.91
ꢄ
ꢀ
ꢁ
b
0.96
1
1
2
2
b
Dv ¼
b þ dk coth ð ꢀh V=2kTÞ:
7
C –H
0.79
2
2
ꢅ
1=2
Bond angles (8)
2
0
2
0
0
O
1
H
1
O
2
0
177.14
126.84
110.27
123.26
114.50
122.24
121.40
119.90
118.70
119.86
120.02
120.15
119.98
120.02
119.48
120.66
119.85
120.07
119.91
119.94
120.09
119.93
121.12
118.86
178.73
124.79
110.50
123.44
114.59
121.97
121.42
119.82
118.76
119.91
120.07
120.13
119.97
120.08
119.46
120.63
119.84
120.07
119.92
119.95
120.09
119.94
121.10
118.82
þV 2 2dV M cosw þ uðd Þ
ah
ah
C
C
1
1
O
O
1
H
H
O
1
124.63
110.41
123.72
114.62
121.66
121.68
119.95
118.73
119.84
120.08
120.17
119.97
119.99
119.36
120.80
119.84
120.08
119.91
119.92
120.10
119.93
121.29
118.72
2
1
1
2
2
1
3
7
1
4
5
6
7
2
where w is the angle between the transition dipole moments
to these states.
b
122 ; 123.2
d
O
1
C
b
118 ; 119.9
c
O C C
2
1
b
122 ; 120.2
d
c
d
c
d
c
d
c
d
C
C
C
C
C
2
1
3
7
2
C
1
2
2
2
3
O
b
122 ; 118.0
C
C
C
C
C
C
C
C
b
119 ; 119.9
4
. Results and discussion
b
119 ; 118.8
b
118 ; 120.1
b
123 ; 119.9
Fig. 1 presents the geometry of the benzoic acid dimer
C C C
3
4
5
6
2
4
5
6
7
3
b
118 ; 120.3
optimized at the B3LYP/cc-pVTZ level. Optimized
geometries, calculated at the B3LYP/cc-pVTZ and
B3LYP/6-311þþG** levels, are summarized in Table 1
and compared with the experimental data. This table
contains also results of Alcolea Palafox et al. [34] ab initio
B3LYP/6-31G** frequencies calculation for the benzoic
acid dimer. The calculated values reproduce reasonably
well the experimental bond lengths and angles. The largest
differences are observed for the bonds which involve the
hydrogen atoms. The agreement between the calculated and
the experimental angles is slightly worse than for the bond
lengths. The largest discrepancies are for the angles which
involve the oxygen atoms, both in the carboxylic and ester
groups. On the base on our calculations we can conclude
that optimization at the B3LYP/cc-pVTZ level gives better
resuls.
C
C
C
C
H
C
C
C
C
C
C
C
b
122 ; 119.7
b
120 ; 119.8
H
3
4
4
5
5
6
6
7
7
2
3 3
C C
C C H
4
3
4 4
H C C
4 5
C C H
H
5
C
5
C
H
5 6
C C
6 6
H C C
C C H
6
7
H
7
C
7
C
a
b
c
d
Ref. [34].
Ref. [29].
Ref. [30].
Ref. [31].
The experimental far-infrared spectrum of the polycrys-
contains also results of our ab initio B3LYP/cc-pVTZ and
B3LYP/6-311þþG** frequencies calculations for the
benzoic acid dimer. To compensate for partial neglect of
electron correlation [39], the calculated frequencies were
uniformly scaled by a factor of 0.9754 and 0.9786 for
B3LYP/6-311þþG** and B3LYP/cc-pVTZ, respectively.
The scaling factor has been determined as the slope of
2
1
talline benzoic acid in the range 50–450 cm
standard infrared spectrum in the range 400–4000 cm
recorded by us, are presented in Fig. 2. Fig. 3 presents a far-
and its
2
1
,
2
1
Raman spectrum in the range 50–400 cm and Raman
1
2
spectrum in the range 400–4000 cm . The experimental IR
and Raman frequencies are shown in Table 2. This table

44
M. Boczar et al. / Journal of Molecular Structure 700 (2004) 39–48
2
1
The calculated frequencies are 419 and 413 cm
in
B3LYP/cc-pVTZ and B3LYP/6-311þþG**, respectively.
In our theoretical calculations we used these two
experimental Raman frequencies n , 114 and 420 cm
2
1
,
s
for the intermolecular O· · ·O stretching vibrations. The
coupling between the O–H(D) stretching and the inter-
molecular O· · ·O modes produces bandshapes of the main ns
bands as presented in Figs. 4–5. We were unable to
reproduce the observed infrared bandshapes of the O–H(D)
stretching vibrations in benzoic acid using in our model
other low-frequency modes.
To determine the optimum parameters we performed a
series of calculations of the n stretching band to minimize
s
the square root deviation between the experimental and
theoretical spectra. All parameters which were determined
in minimization procedure were increased by 0.01.
Fig. 2. Far-infrared spectra (a) and infrared spectra (b) of the polycrystalline
benzoic acid.
The theoretical spectra of benzoic acid and its deuterated
derivative are shown and compared with the experimental
ones in Figs. 4 and 5. The values of the optimized
the correlation diagram for experimental versus computed
frequencies. We used the MOLEKEL program [37] to visualize
the amplitudes of the normal modes. The corespondence
between the experimental and calculated frequencies was
based on the comparison of frequencies and intensities and
on the assignment of calculated normal modes. The
differences between the calculated and experimental
frequencies are due to anharmonicity, intermolecular
interactions, correlation effects and the limited basis set.
2
parameters are given in Table 3. d denotes the ratio of
the intensities of the bending overtone to the fundamental
stretching vibrations. The theoretical spectra are shown as d
functions and as bandshapes calculated with Gaussian
functions of the half-width. For benzoic acid-H the positions
and the fine structure of the theoretical n bands agree well
s
with the experimental spectrum (Fig. 4). The positions of
the major bands are well reproduced, but the calculated
intensities are too small. The theoretical bandshape is
underestimated. As showed by Flakus [10], bandshapes of
the spectra of C H COOH and C D COOH are different.
The experimental n stretching bands of benzoic acid and
s
its O–D derivative are shown in Figs. 4–5. All spectra
exhibit fine structure. To explain the fine structure we
applied a theoretical model presented in the preceding
section. The intermolecular O· · ·O stretching vibration
observed in the far-Raman spectrum has a frequency
6
5
6 5
In Table 4 we showed the calculated total atomic charges
in the benzoic acid. The calculated partial charges of the
hydrogen atom H are equal 0.168 e and 0.128 e, and of the
2
1
3
1
mode are 119 and 114 cm
14 cm (Table 2). The calculated frequencies for this
2
1
oxygen atom O are equal 20.393 e and 20.282 e, in
2
in B3LYP/cc-pVTZ and
B3LYP/6-311þþG** and B3LYP/cc-pVTZ, respectively.
B3LYP/6-311þþG**, respectively. There is another mode
The calculated bond lenght O · · ·H is equal 2.426 and
2
3
involving intermolecular hydrogen bond stretching
observed in the far-Raman spectrum at 420 cm
˚
2
1
2.424 A, in B3LYP/6-311þþG** and B3LYP/cc-pVTZ,
.
respectively. The O · · ·H bond lenght is slighty shorter than
2
3
˚
hydrogen bond O· · ·O lenght, equal 2.64 A. This might
probably be the source of another resonance mechanism
between the fundamental nOH(D) stretching and the
dC–H(D) bending vibrations.The effect of deuteration
(
Fig. 5) is reproduced correctly. In all cases the ns
bandshapes are formed as a result of the complex
mechanism of coupling between the O–H(D) stretching
vibration and the hydrogen bond stretching intermolecular
O· · ·O vibrations, with linear and quadratic distortions of the
potential energies for these modes in the excited state. This
coupling involves resonance interaction between the two
hydrogen bonds and Fermi resonance between the O–H(D)
stretching and the overtone of the O–H(D) bending
vibrations, all acting at the same time.
The ratios of b and dk parameters used in our
calculation of the n bands in benzoic acid-H and benzoic
s
Fig. 3. Far-Raman spectra (a) and Raman spectra (b) of the polycrystalline
benzoic acid. Samples were excited by light of wavelenght (a) 785 nm and
acid-D are: b1H=b1D ø 1:83; b2H=b2D ø 1:60; dk1H=dk1D
ø
(b) 514 nm.
1:25; dk2H=dk2D ø 1:30: The harmonic value of these

M. Boczar et al. / Journal of Molecular Structure 700 (2004) 39–48
45
Table 2
Observed and calculated vibrational frequencies for benzoic acid dimer ðn; stretching; d; in-plane bending; g; out-of-plane bending; t; torsion)
21
21
No.
Sym.
Calculated B3LYP n (cm
)
Experimental n (cm
)
Literature Infrared
2
Approximate description
1
n (cm
)
6-311þþG**
cc-pVTZ
IR
Raman
a
1
2
3
4
5
6
7
8
9
Au
Au
Bg
Bu
Bg
Au
Ag
21
32
23
32
25
‘Butterfly’
a
35
Torsion (‘twist’)
oop monomers rocking
Cogwheel
a
40
69
41
a
59
62
63
80
71
a
62
63
79
t(Ph-COOH) twisting
t(–COOH)
b
85
85
94
a
103
111
168
175
253
276
379
404
405
413
435
437
499
533
616
616
653
662
677
679
690
706
784
784
796
811
845
845
864
937
939
958
975
975
985
986
993
993
106
116
166
183
257
285
383
409
409
419
440
443
503
541
621
621
658
668
692
692
713
712
813
791
804
813
853
853
949
952
952
989
985
984
1002
1002
1001
1002
1028
1029
1081
1081
1127
1130
1162
1162
1176
1177
1288
1296
1317
1320
1327
110
98
110
H-bond shearing
ns(O· · ·O)
g(Ph–COOH)
a
A
A
g
u
114
127
b
146
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
Bg
Ag
g(Ph–COOH)
d(CO· · ·O) þ d(CC)
d(CO· · ·O) þ d(CC)
n(CC) þ d(CC)rings
g(CC)rings
B
u
283
387
413
Bu
Bg
Au
Ag
Au
Bg
Ag
Bu
Ag
Bu
Ag
Bu
Bg
Au
Bg
Au
Bg
Ag
Bu
g(CC)rings
420
n(O· · ·O) þ d(CC)ring
g(CC)rings
b
432
421
g(CC)rings
d(CC)
b
552
619
668
685
708
491
d(CC) þ n(O· · ·O)
617
660
686
712
d(CC)rings
b
615
d(CC)rings
d(CC)rings þ d(COOH) sciss.
d(CC)rings þ d(COOH) sciss.
g(CC)rings þ g(CC)
g(CC)rings þ g(CC)
g(CH)rings þ g(CC)
g(CH)rings þ g(CC)
g(CH)rings þ g(CC)rings
n(CC)rings þ d(COOH) sciss.
n(CC)rings þ d(COOH) sciss.
g(CH)rings þ g(CC)rings
g(CH)rings
b
669
b
687
b
711
796
813
b
806
810
767
b
A
u
813
Au
Bg
Bg
Bg
Au
Au
Bg
Au
Bg
Au
Bu
Ag
Bu
Ag
Ag
Bu
Bu
Ag
Bu
Ag
Bu
Ag
Ag
Bu
Ag
Bu
Ag
b
856
g(CH)rings
g(OH)
g(CH)rings
b
920
936
937
g(CH)rings
g(OH)
b
960
992
g(CH)rings þ g(OH)
g(CH)rings þ g(OH)
g(CH)rings
b
945
974
b
1002
998
g(CH)rings
b
1000
1026
1002
n(CC)rings
n(CC)rings
b
1020
1020
1074
1074
1118
1122
1155
1155
1169
1170
1277
1285
1311
1313
1317
1027
n(CC)rings þ d(CH)
n(CC)rings þ d(CH)
n(CC)rings þ d(CH)
n(CC)rings þ d(CH)
1028
b
1073
1129
1066
b
1027
n(Ph–COOH) þ n(CC)rings þ d(CH)
n(Ph–COOH) þ n(CC)rings þ d(CH)
n(CC)rings þ d(CH)
1135
1158
b
1181
1187
1164
n(CC)rings þ d(CH)
b
1185
n(CC)rings þ d(CH)
1182
1290
n(CC)rings þ d(CH)
b
1316
n(Ph–COOH) þ d(OH) þ d(CH)
n(CC)rings þ d(OH) þ d(CH)
n(CC)rings þ d(OH) þ d(CH)
n(CC)rings þ d(OH) þ d(CH)
n(CC)rings þ d(CH)
b
1275
1294
1322
1323
b
1297
(continued on next page)

46
M. Boczar et al. / Journal of Molecular Structure 700 (2004) 39–48
Table 2 (continued)
21
21
No.
Sym.
Calculated B3LYP n (cm
)
Experimental n (cm
)
Literature Infrared
Approximate description
21
n (cm
)
6
-311þþG**
cc-pVTZ
IR
Raman
b
6
6
6
6
6
6
6
6
6
6
7
7
7
0
1
2
3
4
5
6
7
8
9
0
1
2
Bu
Bu
Ag
Bu
Ag
Ag
Bu
Bg
Ag
Bu
Ag
Ag
Bu
1317
1417
1438
1444
1449
1487
1487
1580
1581
1603
1603
1645
1688
1327
1437
1453
1456
1471
1498
1499
1589
1590
1612
1612
1646
1696
1327
1426
1380
n(CC)rings þ d(CH)
d(OH)
b
1430
1447
d(OH) þ d(CH)
d(CH)
b
1454
1456
d(OH) þ d(CH)
d(CH)
d(CH)
b
1497
1584
1496
b
1590
n(CC)rings þ d(CH)
n(CC)rings þ d(CH)
n(CC)rings
1605
1639
b
1603
1688
3073
1606
n(CC)rings
b
1699
n(CyO) þ d(OH)
n(C ¼ O) þ d(OH)
b
1738
b
2
605
73
74
75
76
77
78
79
80
81
82
83
84
Ag
Bu
Ag
Bu
Ag
Bu
Ag
Bu
Ag
Bu
Bu
Ag
3026
3088
3088
3101
3101
3109
3110
3118
3124
3124
3131
3131
2937
3100
3100
3113
3113
3122
3122
3045
3138
3138
3144
3144
3010
3040
n(OH)
n(CH)rings
n(CH)rings
b
b
b
3041
3068
3012
n(CH)rings
n(CH)rings
n(OH) þ n(CH)rings
3073
n(CH)rings
n(OH)
3012
n(CH)rings
b
b
3079
3098
n(OH) þ n(CH)rings
n(CH)rings
n(CH)rings
RT he fe . c[ a3 l6c ]u. lated frequencies were uniformly scaled by a factor of 0.9754 and 0.9786 for B3LYP/6-311þþG** and B3LYP/cc-pVTZ, respectively.
a
b
Ref. [35].
pffiffi
ratios is close to 2: It should be stressed that our
simulation shows that the coupling between the O–H(D)
and O· · ·O stretching vibrations in benzoic acid gives rise
to important linear and quadratic distortions in the
potentials of the low-frequency O· · ·O stretching
vibrations in the excited states of the O–H(D) vibrations.
The resonance interaction between the two hydrogen
bonds in the benzoic acid-H dimer is large, but in this
case, the Fermi resonance interaction between the
fundamental nOH stretching and the overtone of the
dO–H bending vibrations is small. In the case of benzoic
acid-D the situation is reversed. The resonance interaction
parameter Vres in the benzoic acid-D dimer is small, but
the Fermi resonance interaction parameter Vah is large.
The present model allows to reproduce main features
of the experimental spectra, but it is unable to explain all
Fig. 4. Comparison between the experimental (bold solid line), theoretical
Fig. 5. Comparison between the experimental (bold solid line), theoretical
(
d functions and thin line) n spectra for benzoic acid-H.
s
(d functions and thin line) n spectra for benzoic acid-D.
s

M. Boczar et al. / Journal of Molecular Structure 700 (2004) 39–48
47
Table 3
The theoretical model used for these calculations was
based on the Fermi resonance in the carboxylic acid dimer.
The model was modified to encompass an adiabatic
coupling between the high-frequency O–H(D) stretching
and the low-frequency intramolecular O· · ·O stretching
modes. The linear and quadratic distortions of the potential
energy for the low-frequency vibration in the excited state, a
resonance interaction between the two hydrogen bonds in
the dimer and Fermi resonance between the fundamental
nO–H(D) and the overtone of the dO–H(D) vibrations
was done.
Optimized parameters (the frequencies of the O–H and O–D stretching
2
vibrations were taken as 3012 and 2231 cm , respectively; they represent
1
0
the parameter 1=2ðr þ r Þ in Eq. (9), the frequencies of the O–H and O–D
2
bending vibrations were taken as 1471 and 1088 cm , respectively)
1
Low frequencies (exp.)
Benzoic acid-H Benzoic acid-D
Vres
M
21.10
0.0
20.11
0.0
V
0.1
1.9
ah
2
d
0.2
0.2
2
2
1
1
n1 ¼ 114 cm
n2 ¼ 420 cm
b1
1.280
0.250
0.0016
20.390
0.701
0.200
0.001
20.300
dk1
The calculated spectra are in fairly good agreement with
the experimental ones. The effect of deuteration was well
reproduced by our model calculations. Our results show that
spectra of benzoic acid and its deuterated analogue can be
successfully simulated by our model.
b2
dk
2
21
21
Half-width 100 cm
100 cm
Table 4
Total atomic charges in the benzoic acid dimer
Acknowledgements
Atoms
Calculated charge, e
B3LYP/6-311þþG**
B3LYP/cc-pVTZ
This work was completed when MJW was a JSPS
Visiting Scientist at the Department of Chemistry, Tohoku
University in Seudai, Japan. The hospitality of Professor
Naohiko Mikami is kindly acknowledged. The authors
thank Dr B. Kawałek of the Jagiellonian University for
performing deuteration of benzoic acid.
0
O
O
1
, O
, O
1
20.337
20.393
21.226
2.490
20.385
20.282
0.334
0
2
2
0
C
1
C
2
C
3
C
4
C
5
C
6
C
7
, C
, C
, C
, C
, C
, C
, C
1
0
2
0.001
0
3
20.817
20.010
20.529
0.097
20.109
20.104
20.094
20.108
20.096
0.250
0
4
0
5
0
6
0
References
7
20.745
0.592
0
H
H
H
H
H
H
1
3
4
5
6
7
, H
, H
, H
, H
, H
, H
1
0
0.168
0.128
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0.189
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2
fine details. Further improvements of the model require
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2
[
[
(
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5
. Conclusions
[
[
[
[
[
The ab initio calculated geometries and frequencies
agree well with the experimental ones. The differences
between the calculated and experimental frequencies are
partly due to anharmonicity, to intermolecular interactions,
the correlation effects and the limited basis set.
17] G.S. Denisov, G.K. Tokhadze, Dokl. Phys. Chem. 229 (1994) 117.
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[
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[
19] O. Henry-Rousseau, D. Chamma, Chem. Phys. 229 (1998) 37.
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The experimental Raman frequencies assigned to the
intermolecular O· · ·O stretching vibrations were used in
our calculations of the fine structure of the n stretching
3
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