Journal of Molecular Liquids, 45 (1990) 71-76
Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
71
INFRARED SPECTRA OF HC1, HBr AND HI DISSOLVED IN LIQUID XENON
J. Perez 1, S. Velasco2, J. A. White 2 and A. Calvo Hern~ndez 2
1Departamento de Fisica Fundamental y Experimental, Universidad de La
Laguna, 38002 Tenerife (Spain)
2Departamento de Fisica Aplicada. Universidad de Salamanca. 37008 Salamanca
(Spain)
ABSTRACT
A theoretical calculation of the fundamental vibration-rotation spectra of
HC1, HBr and HI in liquid Xe is presented. The main characteristics of these
spectra (essentially the existence of the P, Q, and R branches) are explained from
the decomposition of the rotational motion of the diatomic as a quasi-free
rotational motion and a rotational diffusion motion . The used spectral theory
involves only a reduced set of statistical parameters concerning the diatomic and
the diatomic-liquid medium interaction: the mean square of the interaction, its
correlation time, the vibrational dephasing time, the rotational diffusion constant
and the fraction of molecules executing rotational diffusion motion. By
comparison between theoretical and experimental spectra, the behavior of the
statistical parameters with the rotational constant of the diatomic molecules is
also discussed.
INTRODUCTION
The infrared spectra of small polar diatomic molecules immersed in
non-polar liquids is an usual method to obtain information about the interaction
and dynamic behaviour of molecular systems. In most cases, the fundamental
vibration-rotation band of those systems exhibits a central peak, Q branch, in
contrast with the depression observed in the gas phase spectrum, and two more or
less prominent shoulders (P and R branches), where fine rotational structure is
frequently absent.
A spectral theory for the study of the infrared (0-1) band of dilute solutions
of diatomic polar molecules in non polar liquids, has been recently developed
(ref. 1). This spectral theory is based on the decomposition of the rotational
motion of the diatomic molecule into two limiting cases, according to the model
developed by Bratos and coworkers (ref .2): quasi-free rotation motion, which
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© 1990 Elsevier Science Publishers B.V.
72
gives account of the P and R branches and part of the Q branch (as overlapping of
the P and R components), and rotational diffusion motion, which is mainly
significant in the Q branch region.
The purpose of this paper is to apply the above spectral theory to study the
fundamental band of the infrared spectra of HC1, HBr, and HI in liquid Xe at the
fixed temperature of 165 K. From comparison between the theoretical and the
experimental results of Goldring et al. (ref. 3) quantitative values for the
parameters involved in the theory are obtained as function of the different
solutes.
MODEL AND SPECTRAL THEORY
We are interested in the study of the vibration-rotation absorption bands of
a dilute solution of diatomic polar molecules in a non polar liquid solvent.
According to Bratos' model (ref. 2), the infrared fundamental band can be written
as a sum of two contributions associated with the two limit cases of the rotational
motion of the diatomic molecule: quasi-free rotation and rotational diffusion. The
fraction ~ of molecules executing rotational diffusion plays the role of a weight
between the two above mentioned contributions.
The quasi-free rotation contribution is analyzed by means of a quantum
rigid rotor-harmonic oscillator (System S) weakly interacting with a thermal bath
(System B) making use of the non markovian TTOC (total time ordering
cumulant) approach. In this formalism, the absorption coefficient is written as a
sum of basic non-lorentzian resonances located near the rotovibrational
frequencies of the diatomic molecule (secular contribution), and a term due to the
overlapping effect a m o n g them (interference contribution). The molecular
interaction between the diatomic and the solvent is represented by an average
directing intermolecular field (DIF) acting on the dipole moment of the diatomic
molecule (ref. 4). The time evolution of the DIF is described by a Gaussian random
process, which allows us to calculate the autocorrelation function of the
interaction system-bath in a time exponential form involving two statistical
parameters: the mean square of the interaction ~,2 and its correlation time t c .
73
The rotational diffusion contribution is calculated as the convolution of the
pure vibrational spectrum, considered as an Ornstein-Uhlenbeck stochastic
process (ref. 5), with the rotational diffusion spectrum described by the Debye
model (ref. 6). The rotational diffusion contribution is then a lorentzian line with
halfwith r" = (2tv)'l+ 2D r, being t v the vibrational dephasing time, and D r the
rotational diffusion constant.
NUMERICAL ANALYSIS AND DISCUSSION
The spectral theory developed in ref. 1 allows us to obtain the theoretical
infrared spectrum in terms of a set of parameters regarding the diatomic molecule
(these parameters are summarized in Table 1 for HCI, HBr and HI) and the above
mentioned ~2, tc ' ~ and I" statistical parameters. Besides, the experimental
frequency of the Q branch ( 2852 cm "1 for HCI, 2530 cm "1 for HBr and 2213 cm-1 for
HI) and the solution temperature ( 165 K ) are required.
The values of the ~2, tc ' ~ and F parameters obtained by fitting the calculated
and the experimental spectra of Goldring et al. (ref. 3) are depicted in Table 2.
From this table we briefly discuss some observed features. Firstly, t c decreases
monotonically with
the rotational
constant of the diatomic molecule B
TABLE 1
Molecular parameters used in the calculations: Rotational constant, B; permanent
dipole moment, ~o; first derivative of the dipole moment respect to the
vibrational coordinate, (~p./Ox) o
; reduced mass, m; and vibration rotation
coupling constant, (ze .
System
B (cm"1)
HC1
HBr
HI
10.59
8.40
5.50
~o (D)
(Op,/0x)o ( D~ "1)
1.08
0.81
0.38
0.88
0.47
-0.05
m (a.m.u)
0.95
0.98
0.99
cxe (cm"1)
0.30
0.23
0.17
74
TABLE 2
Adjustable parameters for different diatomic molecules obtained by fitting the
calculated and the experimental spectra. The tilde denoted reduced units (2nBc for
frequencies and Bhc for energies).
System
HC1
HBr
HI
"~2
70
95
115
'~c
~
0.18
0.17
0.16
1.25
1.43
2.00
0.05
0.13
0.10
while ~2 grows when B decreases. The same behaviour of k 2 and t c with B has
also been observed in a non-Markovian study of the far infrared spectrum for the
HF, HC1 and DCI dissolved in liquid SF6 at T=273 K reported in ref. 7 (it must be
noted that if we neglect the vibration-rotation coupling the quasi-free rotation
contribution can be calculated by the simple translation of the pure rotational far
infrared spectrum if the emission rotational lines are considered). As happens for
~2, it is observed that the halfwidth F increases when the rotational constant of
the diatomic molecule decreases. F is related with the vibrational dephasing time
and the rotational diffusion constant [F -- (2tv)'l + 2D r ]. However, no solid
conclusions can be achieved for t v and D r from the only knowledge of F. The
parameter ~ changes as the relative height of the Q and R branches. Note that the
relative height of the Q and R branches presents an intriguing behaviour with B,
being the highest height for the HBr spectrum and attaning its minimum value
for the HC1 spectrum.
The theoretical infrared spectrum, cz'(c0), is calculated from eqs. (2.3), (3.9)
and (4.14) of ref. 1 for parameters in Tables 1 and 2. Figures 1 and 2 show cz'(0~)for
HC1, HBr and HI dissolved in liquid Xe at T -- 165
K
.
In these figures the
75
e x p e r i m e n t a l spectra of G o l d r i n g et al. are also plotted. In all cases, the numerical
values are n o r m a l i z e d to the unity.
F r o m these f i g u r e s it is f o u n d t h a t all r e p o r t e d i n f r a r e d a b s o r p t i o n
coefficients are d e v o i d of r e s o l v e d r o t a t i o n a l structure. O t h e r w i s e , r o t a t i o n a l
structure has been o b s e r v e d for the s a m e solvent in the case of H F at T = 250 K
(ref. 8). This feature can be explained because the spacing of the rotational lines for
the H F system (B = 20. 5 cm -1) is greater than the spacing for HCI ( B = 10.59 cm "1 ),
HBr ( B = 8.4 cm "1 ) a n d HI ( B = 6.5 cm "1 ) r o t a t i o n a l lines. Besides, for
t e m p e r a t u r e s higher than the here considered, n u m e r o u s resolved fine rotational
structure in the P branch w i n g was also observed in the HC1-Xe solution at T = 234
K (ref. 8). So, w e note that in the infrared spectra of different d i a t o m i c molecules
dissolved in the same s o l v e n t , both the t e m p e r a t u r e of the solution as well as the
r o t a t i o n a l c o n s t a n t of the d i a t o m i c are r e l e v a n t s in the a p p e a r a n c e of fine
rotational structure.
|
I
!
I
"
I
1'
HC
%"
3
v
0.5
0.5
--*
I
I
2800
FREQUENCY,~(cm -I )
1-
2400
2600
FREQUENCY,
~ (cm -I)
Fig. 1. F u n d a m e n t a l v i b r a t i o n - r o t a t i o n b a n d s p e c t r a of HCI a n d HBr in
liquid Xe at 165 K . Experimental (0eeeeeee) a n d theoretical (
) profiles w i t h
p a r a m e t e r s from Table 2 .
76
1'
Fig. 2. Fundamental vibration
rotation band spectrum of HI in
liquid Xe at 165 K . Experimental
(0eoooe) and theoretical (
.)
profiles with parameters from
Table 2.
I
Hl-Xe~,em
Z
:;
0.5
.
:
O-
.
.•Z /
,
I
2200
2
3'0
0
FREQUENCY, ~(Cm-1)
In summary, the fundamental band spectra of HC1, HBr and HI dissolved in
liquid Xe at T=165 K has been studied. Althoughsmall discrepancies are observed
in the separation of the P and R branches for the HI-Xe system, the spectral theory
describes quite well the main characteristics of the experimental spectra (i.e., the P,
Q and R branches) in function of a reduced set of parameters concerning both the
interaction and relaxation of diatomic molecules in liquid Xe.
ACKNOWLEDGEMENT
The present work has been partially supported by CICYT of Spain under
Grant No PB85-0316.
REFERENCES
1 J. P4rez, D. Luis, A. Calvo Hern~ndez and S. Velasco, J. Chem. Phys. In press.
2 S. Bratos, J. Rios and Y. Guissani, J. Chem. Pys., 52 (1970) 439-452.
3 H. Goldring, J. Kwok and G. W. Robinson, J. Chem. Phys., 43 (1965) 3220-3228.
4 P. N. M. Hoang and L. Bonamy, J. Chem. Phys., 67 (1977) 4431-4440.
5 W. Horstheme and R. Lefever, Noise-Induced transitions, Springer Verlag,
Berlin, 1984.
6 C. H. Wang, Spectroscopy of condensed media, Academic press, N. York, 1985.
7 A. Calvo Hern~ndez, S. Velasco, J. P4rez, J. G~4mez and J. A. White, Mol. Phys.,
65 (1988) 1001-1006.
8 M.A. Bernikov, M.O. Bulanin and K.G. Tokhadze, J. Mol. Liquids, 32 (1986)
25-39