Fast, Localized, Orthonormal Virtual Orbitals which Depend Smoothly on Nuclear Coordinates

Document Type

Article

Publication Title

Journal of Chemical Physics

Department

Chemistry

ISSN

0021-9606

Volume

123

Issue

11

DOI

10.1063/1.2033687

First Page

114108-1

Last Page

114108-9

Publication Date

9-1-2005

Abstract

We present here an algorithm for computing stable, well-defined localized orthonormal virtual orbitals which depend smoothly on nuclear coordinates. The algorithm is very fast, limited only by diagonalization of two matrices with dimension the size of the number of virtual orbitals. Furthermore, we require no more than quadratic (in the number of electrons) storage. The basic premise behind our algorithm is that one can decompose any given atomic-orbital (AO) vector space as a minimal basis space (which includes the occupied and valence virtual spaces) and a hard-virtual (HV) space (which includes everything else). The valence virtual space localizes easily with standard methods, while the hard-virtual space is constructed to be atom centered and automatically local. The orbitals presented here may be computed almost as quickly as projecting the AO basis onto the virtual space and are almost as local (according to orbital variance), while our orbitals are orthonormal (rather than redundant and nonorthogonal). We expect this algorithm to find use in local-correlation methods.

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