Axilrod-Teller correction

The trouble is that, without saying so, we have assumed that only molecule A feels the effects of other molecules. But we know better. Each molecule polarizes its neighbor, if only a little bit, and that affects how the neighbor molecule will then interact with the next one. The Axilrod-Teller correction estimates the effect of this indirect interaction by applying third-order perturbation theory to the dispersion energy of three spherical molecules. In Section 10.1 we see how second-order perturbation theory predicts the attraction between two polarizable particles. It takes third-order terms to treat the effect of a third particle, and the derivation is lengthy, so let s just jump to the result this time ... 

I SAMPLE CALCULATION I Axilrod-Teller Correction. We will compute the Axilrod-Teller correction in kj moP for three argon atoms positioned at the points of an equilateral triangle with sides of length using the values (from... 

The Axilrod-Teller correction extends the dispersion interaction to three particles. 

The effect of the Axilrod-Teller term (also known as the triple-dipole correction) is to make the interaction energy more negative when three molecules are linear but to weaken it when the molecules form an equilateral triangle. This is because the linear arrangement enhances the correlations of the motions of the electrons, whereas the equilateral arrangement reduces it. 

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]. 

One of the third-order energy terms represents a correction to the dispersion energy. The correction, as shown by Axilrod and Teller, has a three-body character. The part connected to the interaction of three distant instantaneous dipoles on A. B and C reads as... 

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