Perturbation theory short-range

The perturbation theory described in section Al.5.2,1 fails completely at short range. One reason for the failure is that the multipole expansion breaks down, but this is not a fiindamental limitation because it is feasible to construct a non-expanded , long-range, perturbation theory which does not use the multipole expansion [6], A more profound reason for the failure is that the polarization approximation of zero overlap is no longer valid at short range. 

Lattice vibrations are calculated by applying the second order perturbation theory approach of Varma and Weber , thereby combining first principles short range force constants with the electron-phonon coupling matrix arising from a tight-binding theory. 

In order to determine the phonon dispersion of CuZn and FeaNi we made use of an expanded tight binding theory from Varma and Weber . In the framework of a second order perturbation theory the dynamical matrix splits in two parts. The short range part can be treated by a force constant model, while the T>2 arising from second order perturbation theory is given by... 

Equation (5.15b) is the fundamental assumption underlying London s theory, which is essential both for numerical evaluation and for physical interpretation of the perturbative expressions. Whereas short-range intramolecular interactions in (5.16a) and (5.16b) must be described with properly antisymmetric eigenfunctions satisfying... 

At long range, a perturbation method is the obvious choice for the calculation of intermolecular interactions. At short ranges the standard methods of valence calculation are an equally obvious choice, and quite a lot of work of this kind is being reported. This type of calculation is also being carried out at intermediate distances at which perturbation theories of the type mentioned in Section 2 are also appropriate. 

It has been pointed out by a number of authors (see Cracknell et al., 1995) that the dispersion, electrostatic and induced (polarization) energy terms can be quantitatively accounted for by quantum-mechanical perturbation theory. However, this is not the case for the short-range repulsion. Some evidence suggests an exponential... 

Besides the mentioned aperiodicity problem the treatment of correlation in the ground state of a polymer presents the most formidable problem. If one has a polymer with completely filled valence and conduction bands, one can Fourier transform the delocalized Bloch orbitals into localized Wannier functions and use these (instead of the MO-s of the polymer units) for a quantum chemical treatment of the short range correlation in a subunit taking only excitations in the subunit or between the reference unit and a few neighbouring units. With the aid of the Wannier functions then one can perform a Moeller-Plesset perturbation theory (PX), or for instance, a coupled electron pair approximation (CEPA) (1 ), or a coupled cluster expansion (19) calculation. The long range correlation then can be approximated with the help of the already mentioned electronic polaron model (11). 

We are not going into details of the above groups of procedures and shall limit ourselves to an overview of the main results of ordinary Rayleigh-Schroedinger perturbation theory for long range interactions first, and then of the methods developed in [40,41] to deal with short range interactions. 

Recent calculations by Bems et al. show that also for the He—H2 system the dispersion contribution is small. At long range it is completely dominated by induction, at short range by overlap effects. The calculations of Bems et al. have been performed by the VB approach mentioned above No perturbation theory or multipole expan-... 

Thus perturbation theory calculations currently suffer from the same disadvantage of supermolecule calculations for defining the intermolecular potential between organic molecules at short range. They are so expensive when used to obtain results of reasonable accuracy that are converged with respect to basis set, even for small molecules, that it is impossible to calculate the energies at a sufficient number of points to define the potential energy surface. Calcula-... 

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