Induced dipole cluster functions

The dipole moment induced in a molecule, or in a group of molecules, is a finite range function of the intermolecular separations, R, which falls off faster than R-3 for R —> oo. Van Kranendonk has argued that, therefore, it is possible to expand the above equation in a series of cluster functions [400, 402]. If ft( 1 n) designates the dipole moment induced in the cluster of molecules 1 n when these are present alone in the given volume V, cluster functions 1/(1 n) can be defined according to... 

The U functions have the property of being zero unless all of the molecules 1 n are close together, within the range of the induced dipole moments. We may solve these equations for the U functions in terms of the p functions. When the solutions U are substituted in the right-hand sides of the above equations, an identity results which represents the cluster development of the /i(l N). Specifically, the /i(12) represent the dipoles induced in pairs and /i(123) the dipole induced in three-body complexes. 

To the extent that the dipole induced in a cluster of atoms may be represented by a sum of pair dipoles induced in dissimilar atoms, i and i, fiu, = ft(Rw), we may write for the total dipole ft = Xw Mu - The summation is over all atoms i and all atoms i. The dipole correlation function can then be written as a sum of three parts (Poll 1980),... 

When attempting to treat ensembles of molecules it is essential to be able to represent the intermolecular interactions, at least beyond some cut-off distance, by pre-determined functions of distance so that high level quantum mechanical calculations do not have to be extended to larger and larger clusters. Masia et a/.88 have addressed the question of how the interaction of a water or carbon tetrachloride molecule interacting with a point charge can be represented. They monitor the molecular dipole as a function of the charge-molecule distance for various orientations of the molecule as calculated by ab initio methods. They find that the most satisfactory method is to represent the molecule by a small number of induced point dipoles with different orientations. In the case of water the ab initio induced dipoles are reproduced at all distances. 

Li et alP reported a theoretical study of the structure and interaction-induced dipole moment, mean polarizability and mean first hyperpolarizability of the NH3-HCl-(H20)n (n = 0 ) clusters. They relied on B3LYP calculations with large standard basis sets aug-cc-pVDZ, aug-cc-pVDZ-fBF (aug-cc-pVDZ augmented with suitable placed bond functions), aug-cc-pVTZ, d-aug-cc-pVDZ and t-aug-cc-pVDZ. The authors have reached important conclusion on the magnitude of electric properties. For the non-hydrated complex NH3-HCI the first hyperpolarizability, calculated with the d-aug-cc-pVDZ basis, is jS = — 3.35 e ao Eh while the respective result for NH3-HCI-H2O is 413.52 and increases to 886.41 for NH3-HC1-(H20)4. 

The letter m represents the position coordinate Rm of atom m. Here, /i(l,l ) is the dipole moment induced in the dissimilar pair 1,1 in total isolation from other atoms, etc. The U functions have the cluster property of being zero unless all the molecules appearing in the argument are interacting at close enough range so that their spectral contributions are significant. The function U2 represents the dipole moment induced in the pair of... 

Computer simulation of molecular dynamics is concerned with solving numerically the simultaneous equations of motion for a few hundred atoms or molecules that interact via specified potentials. One thus obtains the coordinates and velocities of the ensemble as a function of time that describe the structure and correlations of the sample. If a model of the induced polarizabilities is adopted, the spectral lineshapes can be obtained, often with certain quantum corrections [425,426]. One primary concern is, of course, to account as accurately as possible for the pairwise interactions so that by carefully comparing the calculated with the measured band shapes, new information concerning the effects of irreducible contributions of inter-molecular potential and cluster polarizabilities can be identified eventually. Pioneering work has pointed out significant effects of irreducible long-range forces of the Axilrod-Teller triple-dipole type [10]. Very recently, on the basis of combined computer simulation and experimental CILS studies, claims have been made that irreducible three-body contributions are observable, for example, in dense krypton [221]. 

A version of Coupled Cluster theory for use in the calculation of linear response functions (LRCCSD) has been developed by Piecuch et a/.135 and applied to the case of ammonia where the dipole and parallel polarizablity has been calculated as a function of the symmetric stretch and inversion internal coordinates. Coriani et a/.136 have also used CCSD response theory to calculate the electric-field-gradient induced birefringence in H2, N2, C2H2 and CH4. 

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