Nonorthogonality corrections in the method of correlated basis functions

✍ Scribed by Eugene Feenberg

• Publisher: Elsevier Science
• Year: 1973
• Tongue: English
• Weight: 472 KB
• Volume: 81
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1016/0003-4916(73)90483-1

✦ Synopsis

A set of normalized linearly independent basis functions @I) 0, ,..., Q5 ,... generates matrix representatives 2' and Jfr of the Hamiltonian operator and the identity. An orthonormal basis #, , & ,..., 6, ,... generated by a Lijwdin transformation is characterized by the distance in Hilbert space between 4, and @, . The choice of positive definite M1la minimizes these distances and maximizes the diagonal elements of Ml/\*. Again for positive definite M/lr'le and a finite basis, 1 Q j p for all positive and negative integral values of n except n = -1 and ( p for n = -1).
Sufficient conditions are determined which permit the application of the binomial theorem to the evaluation of the transform of Z. Approximate formulas for the energy eigenvalues through third order in nondiagonal matrix elements are presented in a compact form containing characteristic nonorthogonality corrections depending on the exterior or interior location of the matrix element in the perturbation formulas.