Potentials triple dipoles

In 1980s, it was concluded from neutron diffraction data on krypton that the structure of this sytem could not be described adequately with a single two-boby potential. A supplementary contribution to the energy had to be taken into account, which is the triple-dipole three-body correction [104],... 

This section reports the results obtained from two self-consistent schemes that have been extended to deal with the triple-dipole interaction, which reduces to a state-dependent effective pair potential. The pair potential of Aziz and Slaman [106] (AS) is combined with the Axilrod and Teller [108] (AT) triple-dipole potential to describe the interactions in Xe and Kr fluids. Note that other investigations have been performed with ab initio potentials [113, 114]. 

If the structure is decided by an effective potential ues (r), it was demonstrated in the mean spherical approximation (MSA) that the direct correlation function c(r) should rapidly approach — pMerr (r) for large r (see Section IE). According to Reatto and Tau [131], this relationship, which is asymptotically exact for large distance and low density, holds quite well when the long-range dispersion term of the AS potential, - Cg / r6, and the AT triple-dipole potential, < m3 (r) > (8n/3)vp/r6, are considered, so that the direct correlation function reads... 

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]. 

Explanation of the stability of the cubic crystals on the basis of a two-body potential function was thus unsuccessful. As a next step three-body interactions were considered by several authors. Axilrod summed the triple-dipole interaction, a nonadditive part of the van der Waals attraction, in both the cubic and hexagonal close packings. He concluded The difference in the triple-dipole interaction for the cubic and hexagonal close-packed lattices, although favoring the former structure, is less... 

Figure 1. Axilrod-Teller triple dipole potential for representative triangles formed by three atoms. The angle 6, is that between t,i and r,.

If the potential is anharmonic, the higher terms of the potential energy according to Eq. 2.1-16 are not negligible, the mechanical anharmonicity gives rise to overtones, vibrations with the double, triple, or multiple frequency of the fundamentals. Overtones are also produced by the higher terms of the dipole moment according to Eq. 2.3-1, the electrical anharmonicity. Since both equations may contain mixed terms, combinations of two or more normal vibrations, i.e., sums or differences, are produced. These appear in the spectra, but usually only with small intensity. Also Raman spectra show overtones and combinations due to mechanical and electrical anharmonicities (see below). 

Figure 30. Potential energy curve for the rotational motion of a molecular motor (upper panel). A hindered rotation takes place in a triple potential well. Starting from the bottom of the lowest potential well, the absorption of energy from a control field leads to free rotational motion. The case where a clockwise directional motion is obtained is indicated as (+). For a weaker field, the motion is forced to take place in the counterclockwise direction (—). The lower panel shows the dipole moment entering into the construction of the control field.

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