𝔖 Bobbio Scriptorium
✦   LIBER   ✦

The generalized eigenvalue problem in quantum chemistry

✍ Scribed by Brian Ford; George Hall

Publisher
Elsevier Science
Year
1974
Tongue
English
Weight
689 KB
Volume
8
Category
Article
ISSN
0010-4655

No coin nor oath required. For personal study only.

✦ Synopsis

The matrix form of the molecular orbital equations is that of a generalized eigenvalue eq~iation, when the basis functions are non-orthogonal. Five algorithms for the reduction of this equation to standardαΊ½igenvalue form are analysed and compared. The behaviour of the algorithms as the overlap matrix becomes sing~ilaris considered in detail and illustrated from the examples of two, three and four functions approaching coalescence. In particular, it is shown that the elements of the density matrix corresponding to the coalescing functions arelarge and almost entirely determined by the coalescence. The resulting effect on the total energy is to produce instability through large cancellations.

πŸ“œ SIMILAR VOLUMES

The scattering problem in quantum mechan
The scattering problem in quantum mechanics as an eigenvalue problem
✍ L.I Ponomarev; I.V Puzynin; T.P Puzynina; L.N Somov πŸ“‚ Article πŸ“… 1978 πŸ› Elsevier Science 🌐 English βš– 641 KB

A method is proposed which allows the scattering problem to reduce to the eigenvalue problem. Unlike the usual method when the scattering phase is extracted from the asymptotits of solution of the Cauchy problem at a given collision energy, in the proposed method the collision energy is obtained fro

Biorthogonal Rational Functions and the
Biorthogonal Rational Functions and the Generalized Eigenvalue Problem
✍ Alexei Zhedanov πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 170 KB

We present some general results concerning so-called biorthogonal polynomials of R II type introduced by M. Ismail and D. Masson. These polynomials give rise to a pair of rational functions which are biorthogonal with respect to a linear functional. It is shown that these rational functions naturall

Wavelet based in eigenvalue problems in
Wavelet based in eigenvalue problems in quantum mechanics
✍ Jason P. Modisette; Peter Nordlander; James L. Kinsey; Bruce R. Johnson πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 799 KB

The use of Daubechies' compact support wavelets in quantum mechanical eigenvalue problems is investigated. It is shown that these orthogonal multiresolution functions provide an efficient basis for systems in which the potentials vary strongly in different regions.