ELSEVIER

16May 1997

Chemical Physics Letters 270 (1997) 103-107

CHEMICAL PHYSICS LETTERS

Modelling trapping sites of (HF)2 in argon clusters

B.L. Grigorenko, A.V. Nemukhin Department of Chemistry, Moscow State University, Moscow 119899, Russian Federation

Received 12 January 1997; in fmal form I0 March 1997

Abstract

Molecular dynamics simulations have been performed for (HF)2. A r62 heteroclusters to compare the structural and dynamical properties of (HF) 2 in different argon environments. Several minimum energy arrangements which mimic different trapping sites of (HF) 2 in argon related to the matrix isolation and cluster adsorption experimental conditions have been analysed. The potential energy surface of the system has been constructed as a superposition of diatomics-in-molecules potentials for all A r - H - F triangles, the Quack-Suhm SQSBDE potential for (HF) 2 and pairwise A r - A r interaction potentials. Of special interest is a comparison of the configuration in the centre of argon shells and those on the surface of argon clusters. Argon-induced vibrational shifts in (HF) 2 with respect to the naked hydrogen fluoride dimer have been computed for each trapping site. The experimental difference in the H - F stretch frequency shifts for (HF) 2 in the matrix and on the surface of argon clusters is precisely reproduced.

1. Introduction

Understanding the properties of molecules in vari- ous environments is important in a wide range of problems related to the description of guest-host systems. Among those, estimates of matrix shifts, i.e. shifts in molecular parameters due to surrounding matrix atoms benefit an interpretation of the spectral features of matrix-isolated species. Simulations of finite-size prototype systems are important for study- ing solute-solvent interactions on a microscopic level. Even chemically inert solvent media such as rare-gas atoms can influence the electronic interac- tions within the solute, modifying the potential en- ergy surfaces (PES) and other properties associated with PES, in particular, equilibrium geometry param- eters and vibrational frequencies. In addition to tradi- tional matrix isolation experiments, the vibrational

spectroscopy of size-selected clusters is becoming a new powerful experimental tool for direct investiga- tions of guest-host interactions [1,2]. As in matrix isolation, in these cases a molecule can be trapped at different sites which complicates the interpretation of experimental findings.

On the theoretical side, modelling the properties of trapped molecules or molecular complexes in different sites formed by the shells of environmental (matrix) atoms presents a complicated problem, first of all because of the numerous difficulties in com- puting and analysing the PES of weakly interacting species as well as the difficulties in describing the dynamical behaviour of a molecule inside the cages. Unlike studies of atomic guests, not many attempts have been undertaken to model different trapping conditions for molecular species. Simulations of vi- brational spectra of difluoroethane in various argon

0009-2614/97/$17.00 Copyright © 1997 Elsevier Science B.V. All fights reserved. PH S0009-261 4(97)00343-6

104 B.L. Grigorenko, A.V. Nemukhin / Chemical Physics Letters 270 (1997) 103-107

sites have been carried out by Giinthard et al. [3]. Site effects in the spectra of simple molecules inside argon shells have been studied by Schurath et al. [4], and by Fraenkel and Hass [5,6], as well as in our work [7]. In all these applications the potential sur- faces describing guest-host interactions have been approximated by sums of pair potentials. We believe that many-body contributions to the PES are impor- tant in performing simulations of solvent effects. In our studies of rare gas-molecule van der Waals complexes these contributions to the PES have been taken into account with the help of diatomics-in- molecules (DIM) theory [8-10].

Recently, we discussed the theoretical vibrational spectrum of (HF) z in low-temperature argon matri- ces [10]. The main feature of that study was to add the computed argon-induced shifts in (HF) 2 to the known frequencies of the gas-phase complex (HF) 2 in order to predict the spectral bands of the dimer in the matrix. A comparison of the computed and ex- perimental band positions showed that this procedure could lead to fairly promising results. The trapping site of (HF) z inside the 62-atomic argon cluster consisted of 15 surrounding argon atoms located at distances less than 5 ,~ from any of the (HF) 2 atoms. The potential energy surface for the (HF) 2 - Ar n sys- tem in Ref. [10] was constructed as a sum of contri- butions from all A r - H - F triangles which in turn were computed with the help of the diatomics-in- molecules (DIM) technique [8], the point-charge model potential for (HF) 2 and pairwise Ar -Ar inter- actions [11].

The motivation for the present study is twofold. First, we intend to use the techniques described in our previous work [10] to model different trapping sites of the HF dimer in argon clusters in order to compare the results to the experimental data both in matrix [12,13] and in cluster adsorption [14] spec- troscopy. Second, we refine the procedure described before [10] by applying much more reliable potential energy surface of (HF) 2, namely, the Quack-Suhm analytical six-dimensional potential [15] calibrated by the results of ab initio calculations and experi- mental spectral data. An improvement of the DIM- based A r - H - F potential, particularly suitable for the description of the (HF) 2 vibrations is also suggested.

In Section 2 we describe technical details of our simulation procedure including the construction of

the PES. The results of simulations and comparison to the experimental data are given in Section 3 along with the conclusions.

2. Details of calculations

The potential for (HF) 2 • Ar n is written as a sum of contributions from Ari-(HF) ~, (i = 1 . . . . . n, a = 1,2), Ari-Ar j, (i, j = 1 . . . . . n) interactions and of the (HF) 2 six-dimensional potential:

2

V = ~ ~ V(Ar/(HF),~) + ~ V ( A r i A r j ) o t= l i = 1 i< j

+ V((HF)2 ) . (1)

For the Ar-Ar interaction potential we have used the pairwise representation of Aziz-Chen type [11]. The surface of the HF dimer is modelled by the Quack- Suhm SQSBDE analytical function [15]. The Ar -HF potential which is primarily responsible for the inter- action of the embedded dimer with environmental atoms has been constructed before [8] on the base of the DIM scheme [16] with a balanced treatment of neutral and ionic contributions. It has been shown that the parameters of this potential can be adjusted so that the vibrational red-shifts in the HF molecule attached to size-selected argon clusters as well as in the argon matrix are in excellent agreement with the experimental data. The key step in describing the A r - H - F interaction was to generalise a pairwise a tom-atom potential scheme in such a way that many-body contributions were taken into account. According to our approach [8] the interaction energy of Ar -HF is computed as follows

V(Ar-HF) = [ V(ArF, ?~) cos 2 ~b + V(ArF, [ I )

× sin 2 ~0 + V(ArH)] cos 2/3

+ [ V ( A r F - ) + V(ArH÷)] sin z/3.

(2)

Here V(ArF, Z) and V(ArF, I1) refer to the 2Z and 2FI potentials of ArF, V(ArH) to the 2~ potential of ArH, and V(ArF-) and V(ArH +) to the potentials of ionic species ~ ArF- and t~ ArH+, respectively, is the angle between the H - F and F - A r directions, and the parameter /3 describes the mixing neutral

B.L. Grigorenko, A.V. Nemukhin / Chemical Physics Letters 270 (1997) 103-107 105

H I •

0.920~/~ Hb Ff

Fig. ]. Geometry of the (HF) 2 complex; distances (in ~) and angles (in degrees) correspond to the equilibrium configuration of the SQSBDE surface [15].

and ionic diatomic states. Unlike our previous appli- cations of the A r - H F diatomics-in-molecules poten- tial for modelling the behaviour of the HF dimer in argon shells [10], we introduce here two slightly different mixing parameter functions ~f and fib for the free (Hf-Ff) and bound ( H b - H b) monomer units (see Fig. 1, which shows the geometry of (HF) 2) and the corresponding notation). The reason for such a modification is that according to ab initio calcula- tions [17] the ionicities of the H f - F f and H b - H b fragments are not precisely the same, with the bound unit being slightly more ionic. Therefore, the mixing parameter fl which reflects the weight of ionic con- tributions to the electronic structure of H - F should be greater for A r - H b - F b than for A r - H f - F f trian- gles. We have considerably improved the description of the vibrational matrix shifts of high frequency modes in (HF) 2 when introducing such a modifica- tion. To be more specific, we can reproduce pre- cisely the experimental vibrational shifts for H b-F b and H f - F f modes for the trapping site modelling the matrix, i.e. S1 as described below. These depen- dences of the mixing parameters for the free and bound units, namely, /3f = 21 + 4rHrFf and fib = 18

O Q ~ Q O ® O ~ OO

o ®o o Q @

@ @

Fig. 3. Calculated minimum energy structure of the $2 site for the dimer adsorbed by the argon surface: (left) the view of the (HF)2.Ar62 cluster, (centre and fight) projections of the (HF) 2- Ar H cluster.

Jr" 8rHbFb (here the H - F distances are in ,~), have been used for all other sites.

To create the initial trapping site of (HF) 2 inside the Ar matrix denoted here as S l, we started from 62 atomic fragments of the fcc argon lattice with an inner vacancy filled by the dimer. After geometry relaxation leading to the minimum energy configura- tion we arrived at the structure shown in Fig. 2 (left panel). Other trapping sites positioned entirely inside the argon shells cannot be excluded from considera- tion since the number of local minima for such a flexible system should be fairly large; nevertheless, in all our attempts to reach the energy minimum starting from different arrangements we arrived at pictures similar to those shown in Fig. 2.

In order to model trapping sites corresponding to the dimer lying on the surface of the argon clusters we withdrew the (HF) 2 moiety from its location in S 1 and moved it arbitrarily to the border of the At62 cluster. Then the geometry of the (HF)2. At62 sys- tem was adjusted in order to reach energy minima.

Fig. 2. Calculated minimum energy structure of the site modelling the matrix (SI): (left) the view of the (HF)~.Ar6z cluster, (centre and fight) projections of the (HF)2 .Ar aS) cluster.

0 0

@

Fig. 4. Calculated minimum energy structure of the $3 site for the dimer adsorbed by the argon surface: (left) the view of the (HF)2-Ar62 cluster, (centre and right) projections of the (HF) 2 . Arn] cluster.

106 B.L. Grigorenko, A.V. Nemukhin / Chemical Physics Letters 270 (1997) 103-107

®+ d®,+ <+ ®

Fig. 5. Calculated minimum energy structure of the $4 site for the dimer adsorbed by the argon surface: (left) the view of the (HF) 2 -Ar62 cluster, (centre and right) projections of the (HF) 2 • Arl4 cluster.

The usual simulated annealing technique was used to facilitate the search of the stationary points on the multidimensional PES which may be interpreted as different trapping sites. Several of them are demon- strated in Fig. 3 ($2), Fig. 4 ($3), Fig. 5 ($4).

For each specific geometry configuration, molecu- lar dynamics (MD) simulations at temperatures of 5 -10 K were performed. The classical equations of motion were solved for about 50 ps, using the Gear predictor-corrector algorithm with an integration step of 0.5 fs. The power spectra obtained as the Fourier transforms of velocity-velocity autocorrelation func- tions gave the picture of vibrational spectra.

3. Results and discussion

One of the main goals of our investigation is the spectroscopic characterization of different trapping sites. Therefore we concentrate much of our attention on comparing the matrix shifts of the H - F stretch vibrations in (HF) 2 in various argon environments with respect to the free dimer. It should be noted that the changes in the geometry parameters of the dimer due to the argon surroundings compared to its free state are almost negligible, as discussed in Ref. [ 10].

Figs. 2 -5 picture the structures of heteroclusters corresponding to minima on the (HF) 2 • Ar62 poten- tial energy surface. They show a general view of the

Table 1 Experimental frequencies of the stretch vibrations Ip|(HfFf) and ~2(HbFb) of (HF) 2 in cm- n

Gas-phase Argon matrix Argon clusters [18] [12,13] [14]

v l (Hf -F f stretch) 3931 3896 - v2(Hb-F b stretch) 3868 3826 3832

entire system (HF) 2 • Ar62 (left panels) and two pro- jections of subsystems composed of the hydrogen fluoride dimer with the immediate argon atoms (central and right panels).

The 'matrix ' site S1 (Fig. 2) is essentially the same as shown in our previous study [10], which, in particular, means that the refinement of the (HF) 2 potential does not lead to dramatic changes in the site geometries. Configurations on the surface of argon clusters ($2, $3, $4) although possessing close energies (however, higher than that of $1) look remarkably different from each other. Configuration $2 may be viewed as a derivative of $1 as is clearly seen from a comparison of the central and right panels of Figs. 2 and 3. The hydrogen bonded monomer fragment H b-F b is located entirely inside the argon cage while the free fragment H f-El points out of the cluster. Shells of the surrounding argon atoms in S1 and $2 look similar. Unlike $2, the configuration $3 corresponds to the case when the free monomer unit Hf-Ff is trapped inside the cage and the bound fragment H b--Fb is located practically on the surface. The best way to characterize the $4 site is to notice that in this case the hydrogen fluo- ride dimer is located in the layer next to the surface shell. In all these configurations one can easily rec- ognize the familiar pentagonal pyramids composed of argon atoms which are typical of the icosahedral structure of free argon clusters.

Table 1 contains sets of experimental frequencies of stretch vibrations (vj , /.-'2 ) in (HF) 2 referring to the gas-phase [18], to the matrix-isolated species

Table 2 Theoretical harmonic frequencies in c m - t of (HF)2 [ 15] and of (HF) 2 At62 obtained in this work

(HF) z Ar62(HF) 2 Ar62(HF)2 Ar62(HF) 2 Ar62(HF) 2 S1 $2 $3 S4

vt(Hr-F f stretch) 4100 4065 4069 4067 4068 v2(H r F t , stretch) 4048 4006 4012 40 11 4013

B.L. Grigorenko, A.V. Nemukhin / Chemical Physics Letters 270 (1997) 103-107

Table 3 Shifts in frequencies (in c m - ' ) for vl(HrF f) and v2(HbFb) of (HF) 2 in different argon environments

107

Exp. Ar matrix [12,13] Ar62(HF)2 SI Exp. Ar clusters [14] Ar62(HF) 2 $2 Ar62(HF) 2 $3 Ar62(HF)2 $4

Avt(Hf-F f) - 3 5 - 3 5 - - 31 - 3 3 - 3 2 A v2(Hb-F b ) - 4 2 - 4 2 - 3 6 - 3 6 - 3 7 - 3 5

[12,13] and to the species trapped by the surface of argon clusters [14]. In Table 2 we show the calcu- lated harmonic frequencies of naked (HF) 2 obtained with the given PES [30] and reproduced by our molecular dynamics simulations and the frequencies assigned to the H - F stretch vibrations in the (HF) 2 • Ar n clusters for the geometries sketched in Figs. 2-5. Table 3 shows the computed shifts in the H - F stretch vibrations together with the matrix and clus- ter adsorption experimental data.

As was mentioned before, we could adjust mixing parameters of the A r - H - F diatomics-in-molecules PES in such a way that the experimental matrix shifts are completely reproduced (cf. Columns 2 and 3 of Table 3). With these fixed parameters the model precisely reproduces the experimental vibrational shift of the H b-F b mode for the cluster absorption experiments (cf. Columns 4 and 5 of Table 3). This is a remarkable conclusion which demonstrates a predictive power of the present model.

Another important conclusion is also seen from the data of Table 3; namely, in spite of the drastic differences in geometries of sites $2, $3 and $4 clearly noticeable in Figs. 3-5 , the differences in computed vibrational shifts are not greater than 2 cm - j . Therefore, according to our simulations such a quantity (2 cm - l ) gives an estimate of the broad- ening or splitting of the spectral bands in matrices due to so-called site effects.

The last two paragraphs constitute the most im- portant results of this study. We do not discuss here the behaviour of low-frequency modes since the model is calibrated only for high frequency stretch vibrations, and the predictions for intermolecular degrees of freedom are less reliable with the present formulation.

Acknowledgements

The authors are grateful to Dr. M. Suhm for sending us the FORTRAN codes of the SQSBDE

potential of (HF) 2 and his comments on this work. Valuable stimulating discussions with Dr. A. Vigasin and Dr. F. Huisken are greatly acknowledged. This work is partly supported by the Russian Foundation of Basic Research (Project No. 96-03-34255).

References

[1] T.E. Gough, M. Mengel, P.A. Rowntree, G. Scoles, J. Chem. Phys. 83 (1985) 4958.

[2] F. Huisken, M. Stemmler, J. Chem. Phys. 98 (1993) 7680. [3] R. Gunde, H.J. Keller, T.-K. Ha, H.H. Giinthard, J. Phys.

Chem. 95 (1991) 2802. [4] M. Winter, K. Seranski, U. Schurath, Chem. Phys. 159

(1992) 235. [5] R. Fraenkel, Y. Hass, Chem. Phys. Lett. 220 (1994) 77. [6] R. Fraenkel, Y. Hass, J. Chem. Phys. 100 (1994) 4324. [7] A.V. Nemukhin, B.L. Grigorenko, Chem. Phys. Lett. 233

(1995) 627. [8] B.L. Grigorenko, A.V. Nemukhin, V.A. Apkarian, J. Chem.

Phys 104 (1996) 5510. [9] B.L. Grigorenko, A.V. Nemukhin, A.A. Buchachenko, N.F.

Stepanov, S.Ya. Umanskii, J. Chem. Phys. 106 (1997) No. 10.

[10] A.V. Nemukhin, B.L. Grigorenko, A.V. Savin, Chem. Phys. Lett. 250 (1996) 226.

[11] R.A. Aziz, H.H. Chert, J. Chem. Phys. 67 (1977) 5719. [12] L. Andrews, G.L. Johnson, J. Phys. Chem. 88 (1984) 425. [13] L. Andrews, S.R. Davis, R.D. Hunt, Mol. Phys. 77 (1992)

993. [14] A. Kulcke, lnfrarot und Ramanspektroskopie an kleinen

wasserstoffbruckenbundenen Molekulclustern, Thesis, Max- Planck-lnstitut Fir Stri~mungsforschung, G~ttingen (1994).

[15] M. Quack, M.A. Suhm, J. Chem. Phys. 95 (1991) 28. [16] J.C. Tully, in: Modem Theoretical Chemistry, VoL 7A.

Semiempirieal Methods of Electronic Structure Calculation, G.A. Segal (Ed.), Plenum Press, New York, ch. 6.

[17] A.V. Nemukhin, Russ. J. Phys. Chem. 66 (1992) 4. [18] A.S. Pine, W.J. Lafferty, B.J. Howard, J. Chem. Phys. 81

(1984) 2939.