Generalized symmetric Rayleigh-Ritz procedure applied to the closed-shell Hartree-Fock problem

Harold H. Wadleigh, Irina V. Ionova, Emily A. Carter

Research output: Contribution to journalArticlepeer-review


We present the Generalized Symmetric Rayleigh-Ritz (GSRR) procedure for finding approximate eigenfunctions and corresponding eigenvalues for a linear operator, L, in a finite function space, {φi}Ni = 1. GSRR is derived by minimizing the residual in the norm induced by an inner product, (· , ·), under the constraint that the resulting eigenfunctions be mutually orthogonal with respect to another inner product, (· , ·)a. When L is the closed-shell Fock operator, f, GSRR is a generalization of the Roothaan equations. We apply this method to f with (· , ·) defined by a grid, {rk}Mk = 1, and (· , ·)a defined by analytic integration, noting that a grid-defined (· , ·) lends itself to faster operator evaluation (scaling as MN2) and effective parallelization. When a grid is used, GSRR scales as pseudospectral methods do; however, it is in the spirit of conventional spectral methods (e.g., GSRR does not use an inverse transform).

Original languageEnglish (US)
Pages (from-to)4152-4164
Number of pages13
JournalJournal of Chemical Physics
Issue number9
StatePublished - Mar 1 1999
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy
  • Physical and Theoretical Chemistry


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