Vibrational Spectroscopy, 5 (1993) 125-128 Elsevier Science Publishers B.V., Amsterdam

125

Vapour-liquid frequency shift of the CH stretching vibration of chloroform and intermolecular potentials

Katalin T&h and Gabor Jan&

Central Research Institute for Physics, Atomic Energy Research Instihrte, P.O. Box 49, H-1525 Budapest (Hungary)

(Received 3rd September 1992)

Intermolecular potential functions employed in molecular dynamics simulations and Monte Carlo calculations of liquid chloroform were tested with respect to their suitability for describing the experimentally observed vapour-liquid shifts of vibrational frequency and anharmonicity of the CH stretching vibration of chloroform. The model calculations showed that Coulombic interactions play an important role- in governing the frequency shift on condensation, hence the correct charge distribution is of fundamental importance.

Keywordc Infrared spectrometry; Anharmonicity; Chloroform; Intermolecular potentials; Vapour-liquid frequency shifts

Interpretation of the effect of condensation or pressure applied in the liquid phase on the inter- nal vibrational frequencies has excited consider- able interest among experimental and theoretical investigators since the late 1950s (e.g., [l-5]). Recently, model calculations were made [6] to explore the vapour-liquid frequency shift of CH stretching vibrations (v,) of different haloforms caused by intermolecular interactions arising in the liquid phase. The differences -in sign and magnitude of the shift of the ycrr and their an- harmonicity on condensation were interpreted in terms of the differences in the intermolecular interactions and in the size of the haloform molecules.

For liquid chloroform there are several inter- molecular potential sets available in the literature 17-111. These were used in molecular dynamics (MD) and Monte Carlo (MC) simulations and the results obtained were in satisfactory agreement

Correspondence to: K Toth, Central Research Institute for Physics, Atomic Energy Research Institute, P.O. Box 49, H-1525 Budapest (Hungary).

with the experimentally observed structural and dynamic properties of liquid chloroform.

According to spectroscopic data the frequency of the vcH of CHCI, decreases on condensation (red shift) by 14 cm-’ [12]. The anharmonicity constant (Xl in the liquid phase cannot be ob- tained directly from spectroscopic data alone be- cause of the poor precision of the experimental frequency values of the overtone and combina- tion transitions. However, by combining high-pre- cision experimental data on the vapour pressure differences between CHCl, and CDCI, with reli- able spectroscopic results it was possible to calcu- late X in the liquid phase and it was concluded that the anharmonicity constant of the vcH vibra- tion of CHCI, decreases on condensation (by 2.5%) [13];

The aim of this work was to compare the different intermolecular potentials available in the literature with respect to their ability to pre- dict the vapour-liquid shifts of ycH and the an- harmonicity constant X, of chloroform by using the model calculation method described in detail previously [6]. It will be seen that this method, in

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126 K T&h and G. Jan&/Vi. Spectrosc. 5 (1993) 125428

spite of its simplicity, is suitable for testing the “quality” of intermolecular potentials in this re- spect.

Finally, the fundamental frequency (v) can be obtained by using the relation v = w + 2X.

RESULTS AND DISCUSSION

METHOD OF CALCULATION

The C-H vibration in chloroform can be treated as a diatomic oscillator [6], which can be described by the Morse function in the vapour phase. In the liquid phase the CH oscillator inter- acts with its surroundings, and since the vcH vapour-liquid frequency shift arises mainly from the H - - * Cl interactions [6] only these are con- sidered in the calculations. The potential energy of the C-H bond in the condensed phase (V&r1 is the sum of intramolecular (Morse VM) and inter- molecular (Lennard-Jones V, and Coulomb V,> interaction energies. The parameters of inter- molecular potential functions are available from the literature and relate to the rigid five-site model of chloroform (see below). In our method the equilibrium CH bond distance in the liquid phase (ri) is calculated from the first derivative of V,, with respect to r. From the higher deriva- tives of V,, the quadratic (k), cubic (g) and quartic (j) force constants are obtained in inter- nal coordinates. The following equations, which describe the force constants in the liquid phase, result from the additivity of the potential func- tions:

fk=$k,+f,&,+k,), l-1

R

(1)

g =gM + c (gLl +gC)i (2) i=l

i=jM+ i (jLT+jc)i (3) i=l

where n is the number of interacting H - - - Cl pairs. Note that in the vapour phase k = k,, g=g, and j=jM. Then the force constants are rewritten in terms of dimensionless normal coor- dinates to obtain o, k, and k, through which the anbarmonicity constant can be expressed:

X = $k, - lSk,2/4o (4)

In the MD and MC studies the chloroform molecule is represented by a rigid five-site model with force centres located on the atoms. In three cases [7-91 standard Lennard-Jones [12,61 and Coulomb potential functions are employed to de- scribe the pair interactions. The potential used by Biihm and Ahhichs [lo] in their MD simulation is of another type (exp - 6 - 11, the parameters of which were derived partly from an abinitio calcu- lation and partly from a fitting procedure to the experimental second virial coefficient data. Jor- gensen et al. [ll] used a so-called four-site OPLS (optimized potentials for liquid simulations) model in their fluid simulation calculation. In this model each atoms has an interaction site, except the CH group, which is considered as a united atom centred on the carbon.

The Lennard-Jones parameters are collected in Table 1 and the partial charges and the calcu- lated dipole moments are listed in Table 2. The parameters (~uci and cHCL can be obtained by the usual combining rule am-, = (urrrr + a&/2 and E -(E HCI - HH~CIa)1/2. Note that in contrast with the other potential functions the carbon atom in the Biihrn and Ahlrichs’s potential carries a large negative partial charge. The dipole moment of the models is higher than the gas-phase value (1.01 D) 1141 as the effective pair potentials have

TABLE 1

Leonard-Jones potential parameters for different chloroform models

Site (i) qi (lOI erg) Uii (Al

DHK’I E[8l,KKL I91 DH[71 EN,KKL[91

C 70.7 70.4 3.40 3.2 Cl 208.1 241.6 3.44 3.5 H 13.8 18.5 2.2 2.75

JBC [ll] JBC [ll]

CH 55.6 3.80 Cl 208.6 3.47

K Tdh and G. Jan&/ VI. Spectrosc. 5 (1993) 125-128

TABLE 2

Partial charges (in elementaty charges) and the calculated dipole moment (~1 for different chloroform models

Model qH 9c ei qc!H p 0)

DH 171 - E[8j -

0.082 0.179 0.087 1.10 0.131 0.056 - 0.063 1.17

KKL [91 0.100 0.320 -0.140 1.60 BA [lo] 0.393 - 0,687 0.098 1.33 JBC [ll] - 0.140 0.420 1.07

been devised to include many-body interactions in the liquid phase.

The model calculations were carried out on two different geometrical arrangements of chlo- roform molecules. The first molecular arrange- ment (see inset in Fig. 1) reflects the structural picture of liquid chloroform drawn by Kovacs et al. [9] according to which the coordination num- ber obtained by the integration of the H-Cl ra- dial distribution function (g,_,) down to its first minimum is 1.0. Therefore, there is only one nearest neighbour Cl atom of the H o,f the central molecule at a distance of about 3.2 A. The stag- gered configuration (inset iu Fig. 2) corresponds

AX hi’)

,a4

.a2

.-CL2

--0.4

-6

-lo i

\ ./ \ .A ‘I “..,_,,/

/.’

Fig. 1. Vapour-liquid shift of vibrational frequency and an- harmonicity constant of the CH stretching vibration of chloro- form versus intermolecular H. . . Cl distance (s). Av ( = vliq.- vsas) and AX ( = Xriq,- Xgas) were obtained for the molecular arrangement shown in the inset by using different intermolec- ular potentials: - , DH [71; ------, E [8]; and .-.-., KKL 191.

I i\ 5 Cl?. ‘.

0 n *Y” 4-

2-

3

-2-

-4-

-6-

-a-

-lO-

-12-

\ i .a i / \ ,’ 0’ ‘\ .0. . .._.M

127

Fig. 2. Vapour-liquid shift of vibrational frequency and an- harmonicity constant of the CH stretching vibration of chloro- form versus intermolecular H . . . Cl distance (~1. Av ( = vrs.- vsas) and AX ( = X,,- X,) were obtained for the molecular arrangement shown in the inset by using different intermolec- ular potentials: -, DH [7]; - - - - - -, E [81; and .-._. , KKL 191.

to the result obtained from an MD simulation by Dietz and Heinzinger [7], who found three neigh- bouring chlorin: atoms up to the first minimum distance of 4 A. Both plausible models can be considered as only a simplification of the real arrangement of molecules in the liquid [15].

The values for AV (= “lis.- vsaS) and AX (= Xrrg.- XBBs) are plotted against the intermolecular Cl - - * H distance (s) in Figs. 1 and 2 for the two molecular orientations. The lines correspond to the calculations carried out by using the potential parameters of Dietz and Heinzinger (DH) [7], Evans (E) 181 and Kovacs et al. (KKL) [9].

From Fig. 1 it can be seen that the calculated frequency shifts have the same sign as that ob- served over fairly wide range of S. Thus, using the DH potential parameters, the calculated fre- quency shift is to the red from s = 3.0 A, whereas the corresponding s values for the E and IUU potentials are larger. The zero and the minimum points of the Av and AX vs. s are at almost the same distances for the E and KKL potentials, which is plausible as the Lermard-Jones parame- ters are the same in both instances. However, the

128

magnitudes of Av and AX are different because the partial charges on the atoms are significantly larger in the KKL than in the E potential, which results in a larger shift for the KKL potential. It was found that the major part (96%) of the H... Cl interaction energy arises from electro- static interactions whereas only a small part comes from the Lennard-Jones contribution (4%). It should be mentioned that the opposite behaviour was observed for the chloroform-chloroform in- teractions, as the Coulomb contributions to the interaction energies are less than 7% of that from the Lennard-Jones term [9].

The decrease in the anharmonicity constant of the CH stretching vibration on condensation (AX > 0 since X < 01 is also adequately described by the three potentials, although the quantitative agreement between the experimental value (AX = 1.6 cm-’ [13]) and the calculation is in need of improvement. It is clear from comparison of Figs. 1 and 2 that the molecular arrangement corre- sponding to the staggered configuration of chlo- roform molecules gives Av values which are closer to the experimental values (- 14 cm-‘). This improvement is due to the fact that in this in- stance the number of nearest neighbour chlorine atoms interacting with the CH oscillator is larger.

As pointed out in a previous paper [6], a blue shift occurs in the repulsive range of the inter- molecular interactions and this shift extends even to the attractive range (the cross-over in the vibrational frequency shift occurs between the inflection and the minimum point of the inter- molecular interaction function). Therefore, the BGhm and Ahlrichs’s potential [lo] is not ex- pected to give a red shift as the two terms approx- imating the first-order SCB interaction are posi- tive in the case of H - - - Cl interaction (note that both H and Cl carry positive partial charges), and only the higher order, dispersion and polarization contribution can bring about a red shift. The fact that the Bijhm and Ahhichs’s potential is not capable of reproducing even the sign of AvcH can be considered as a deficiency of this poten- tial.

There is another type of difficulty with Jor- gensen’s potential: as it treats the C-H group as a united atom it is not possible to consider sepa-

K T&h and G. Jancsb/ Vii. Spectrosc. 5 (1993) 125-128

rately the interaction between the hydrogen atoms and its surroundings or, consequently, the change in the CH stretching frequency.

It can thus be seen that there is reasonable agreement between the available observed data on vapour-liquid frequency and anharmonic con- stant shifts of the CH stretching vibration of chloroform and the values calculated from the DH, E and KKL potentials in spite of the fact that in the last instance the dipole moment in the liquid phase seems to be unrealistically high. Even though our model calculation might be consid- ered crude, the method described here can cer- tainly be used to test the “quality” of the various intermolecular potentials employed in MD and MC simulations in such simple examples as liquid chloroform.

Financial support from the Hungarian Re- search Fund under grant OTKA-1846 is grate- fully acknowledged.

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