A spectroscopic study of the dynamical state of orientation of diatomic polar molecules in liquid non-polar solvents

CHEMICAL

PHYSICS

LETTERS

1 (1966)

526-528.

NORTH-

HOLLAND

STUDY OF THE DYNAMICAL A SPECTROSCOPIC OF DIATOMIC POLAR MOLECULES IN LIQUID

PUBLISHING

A calculation is

presented.

The

of the absorption agreement

with

profile

15 December

of a polar

experimental

diatomic

data

suggests

January 1968 . . .’

Aerfzienne,

1967

molecule to

consider

orientation of a dissolved simple molecule in a liquid is not able to be tion, nor by a libration. but is intermediate between these two limiting

In a previous paper [l] we described a theoretical approach to the spectral line shape in liquid systems and we applied it to the calculation of the vibration-rotation spectrum of a diatomic polar molecule dissolved in a non-polar solvent. In this paper we will extend these considerations to the far infrared spectrum where only orientational degrees of freedom are concerned and we will deduce certain conclusions about the dynamical state of the orientation of the dissolved moiecules in such liquid solvents. It has been shown [2] that diatomic polar molecules exhibit in the dissolved state, a continuous absorption in the far infrared. This absorption appears as a broad band extending, for HCl dissolved in CCl4, between 35 and 250 cm-l. No rotational structure appears in this band which possesses only a single maximum near 150 cm-l. Sp’ectra of similar mixtures in the same spectral region (HF in cyclohexane, DC1 in CC14 and cyclohexane [2], HCl in liquid argon [3]) show the same characteristics. The purpose of this letter is to give a quantitive theoretical account of this far infrared spectrum, starting from the same considerations as for the calculations already published [l]. In that model it was supposed that the solute diatomic polar molecule was trapped in a potent&l well due to the presence of the liquid solvent molecules. The directing action of the solvent on the polar molecules, for a given position of its mass center with respect to the cell center, was taken into account [II) by introducing the orientating potential averaged on the positions of the solvent molecules [V(0) = p-C, of eq. (1) of ref. [l]], and the fluctuation AV(6) of the true coupling po-

~ AMSTERDAM

STATE OF ORIENTATION NON-POLAR SOLVENTS

D. ROBERT and L. GALATRY Groupe de Physique MoL&ulaire, Laborafoire de Specfmscopie FaculfI des Scfences. 25. Besancon, France Received

COMPANY

dissolved that

the

in a non-polar dynamical

solvent

state

of

represented by a perturbed rotacases.

tential around this last value [5]. Moreover, the quantum averages, involved in the trace operation leading to the spectral properties, were calculated with the set of wave functions *jM for the solute molecules derived from a Hamiltonian which explicitely included the V(6) coupling potential. The fluctuation AV(6) was then introduced as a broadening agent. We can therefore apply eq. (2) * of ref. [l], to the vibrathe far infrared spectrum by replacin tioral transition matrix element (01 p lgl} by the dipole intensity n itself, by putting wl0 = 0 and by taking into account the effect of the induced emission through the multiplicative factor [l - exp (-BEj p~v,jl~)]. If, in the first stage, the dissipative character of the fluctuations of the directing field is neglected (AV(0) = 0), one obtains a set of infinitely narrow lines (fig. 1). In the low frequency regions this pattern exhibits a strong modification with respect to the unperturbed spectral scheme (equally spaced lines) while for higher frequencies where the perturbing action of the solvent is comparatively smaller, it reproduces this familiar aspect, the similarity becoming more evident as the frequency increases. If, now: the directing field fluctuations due to the molecular motions in the liquid are taken into account (A V( 6) # 0), this leads to a theoretical profile (fig. 2) which exhibits the main features of the corresponding experimental spectrum: absence of rotational structure and appearance of a * In eq. (2) of ref. [l] a factor 2 has been omitted before the square module of the sin 8 cos 40matrix eiement. 526

DYNAMICAL

STATE

OF ORIENTATION

OF DIATOMIC

POLAR

MOLECULES

: : I

:

_____,__fAjL

t

1 I 8

1, Integrated

A&O

!Ajl=i

I

Fig.

a0 AMam-l

Aj

. . . . . . . . . . . .._....

:

-__i_._

:

Aj -

I

IA&I

2

kM?=C$l

1

and position of spectral components computed in the set of distorted HCI in liquid CC14, in the pure rotation region. at T = 3000K.

40“-.-‘-.-__._._-.I_.---.-..--_

.

. . . -..---...--.-...-..--

. .

.

.

. . .

. .

.

.

. . .

.

. . . . . . . . .

. . .

_.__

.

.

527

.._.._......._

_____..___

_.__..

wave functions

__________..__

W (cm-l) 200 Fig. 2. Far infrared absorption coefficient, by concentration unit, in the pure rotation band of HCl dissolved in : experimental profile from ref. [2]. liquid CC14 at T = 300*K. : profile drawn from cakxdated absorp;ion at o frequencies (x) (eq. (2) of ref. [l) modified as indicated in the text); this profile is obtained as the sum cf cal= 1, AM= 0, Aj = 1, AM= ‘1) and induced culated initially allowed and strongly perturbed absorption B(r){ ----}(Aj absorption B(i) ( . . . . f(Aj=O. AM= -1. Aj=2. AM= 0.51).

100

D. ROBERT

528

single. maximum in agreement with that of the experimental absorption band (near 150 cm-l). As shown in fig. 2 this theoretical profile was obtained by adding contributions related to the various Aj = 1, AM = 0, *l ‘(allowed but perturbed) transitions and Aj = 2, AM = 0, 4, Aj = 0, AM= -1 (induced) transitions. It may be seen that the band intensity is mainly due to transitions of the first class. Contributions from Raman-like transitions are weak. The numerical values cbtained by the present theory for the absorption coefficient seem lower than the available experimental data [2]. However it is necessary to mention the unaccuracy of absolute intensity and concentration measurements and, on the other hand, the possibility of a supplementary absorption arising from translational transitions, in connection with a non resonant

induced absorption

in EC!! [S]. This study strongly suggests that, although the liquid band roughly corresponds to the envelop of unperturbed

rotational

lines,

one should not con-

clude that, in the liquid phase, the molecules rotate nearly freely. Indeed the present agreement

and L. GALATRY

between experimental and theoretical shapes was obtained by introducing the highly distorted wave functions $‘*i,f which cannot be related to any sort of classic al! weakly perturbed rotational motion. On the other band, it may be shown that the average field strength is generally too low to transform the orientational state into pure libration. It seems therefore that this type of problem cannot be handled by any type of perturbation method but rather that it requires ,.sstematic use of computer facilities, as was done in this work.

References [l] D.Robert and L.Galatry. (1967) 399. [Z] P.Daka and G.M.Barrow.

2137.

Chem.

Phys.

Letters

J. Chem. Phys.

1

43 (1965)

[3] P. Marteau and H. Vu. private communication. [4] D-Robert, Thsse de Doctorat d’Etat. Besancon (1967). [5] L.Bonamy. D.Robert and L.Galatry. J. Mol. Struct. 1 (1967) 91. [6] L.Galatry, Compt. Rend. 260 (1965) 2159.