### Abstract

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, {φ_{i}}^{N} _{i = 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, {r_{k}}^{M} _{k = 1}, and (· , ·)_{a} defined by analytic integration, noting that a grid-defined (· , ·) lends itself to faster operator evaluation (scaling as MN^{2}) 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 language | English (US) |
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Pages (from-to) | 4152-4164 |

Number of pages | 13 |

Journal | Journal of Chemical Physics |

Volume | 110 |

Issue number | 9 |

DOIs | |

State | Published - Mar 1 1999 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry

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## Cite this

*Journal of Chemical Physics*,

*110*(9), 4152-4164. https://doi.org/10.1063/1.478299