ISSN:
1089-7690
Source:
AIP Digital Archive
Topics:
Physics
,
Chemistry and Pharmacology
Notes:
We have analyzed the locality of matrices of the kinetic energy operator in even-tempered Gaussian and Slater-type (STO) bases, as well as in several three-dimensional, one-dimensional, and pseudo-one-dimensional basis sets of orthogonal polynomials and trigonometric functions. We find that the locality of the kinetic energy matrix in Gaussian bases is dependent upon the basis function parameters, while STO bases are found to always produce kinetic energy matrices which are very nearly equal to the matrices of local operators. In addition, it is observed that in the limit of completeness, the locality measure for all of the one-dimensional basis sets appears to converge to a common value. In the case of a basis set of particle on a ring eigenfunctions, an exact value for this limit has been determined analytically. Three-dimensional and l=0 pseudo-one-dimensional basis sets of orthogonal polynomials give kinetic energy matrices that do not behave similarly in the limit of completeness. It is found that all of these basis sets result in kinetic energy matrices which clearly exhibit nonlocal behavior, except for those involving exponentials. Such bases, like the STO bases, appear always to yield kinetic energy matrices that remain nearly local regardless of the basis function parameters and the number of basis functions used. © 1996 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.471322
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