The log derivative version of Kohn's variational principle is used as a setting for a new numerical approach to quantum scattering problems. In particular, a new radial basis set is devised which is both (a) ideally suited to the log derivative boundary value problem, and (b) directly amenable to a
The equivalence of the log derivative Kohn principle with the R-matrix method
โ Scribed by Hans-Dieter Meyer
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 272 KB
- Volume
- 223
- Category
- Article
- ISSN
- 0009-2614
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โฆ Synopsis
The log derivative version of Kohn's variational principle, as discussed by Manolopoulos and Wyatt in 1988, is shown to be equivalent to the R-matrix method. Both methods yield identical S matrices when the same basis set is adopted. The working equations of both methods appear to be quite different at first glance, but we show that even here the relationship is much closer than one might have expected.
๐ SIMILAR VOLUMES
The convergence of the S matrix for the renormalized Numerov method, the original log-derivative method, and. one recent version of this method is studied. A single-and a two-channel problem are analyzed and the percent relative errors for the S matrix and transition probabilities are calculated.
A method is proposed for reducing the complexity of scattering calculations carried out using the Kohn variational principle. The technique is based upon the use of a pointwise representation for the L2 part of the basis set and eliminates the need to explicitly evaluate any integrals involving such
The first application of the Gaussian very fast multipole method (GvFMM) to the calculation of molecular energy second derivatives of Kohn-Sham (KS) density functional theory (DFT) is reported. The GvFMM is used both in the solution of the coupled-perturbed KS (CPKS) equations and in the calculation