Basis set quality. II. Information theoretic appraisal of various s‐ orbitals

Abstract

The expectation values ( r k ) ( -2 s k 5 4 , k = lo), values of the charge density p ( r ) at selected points, and coefficients in the MacLaurin expansion of p ( r ) are used to test the quality of 71 orbital basis sets used for the atomic helium Hartree-Fock problem. These tests in position space are complementary to the momentum space tests previously carried out [Int. J. Quantum Chem. 21, 419 (1982)l. Information theoretic measures with respect to either or both position and momentum space properties are subsequently defined and the orbitals are ranked accordingly. These measures indicate that, for a given orbital, momentum space properties are more poorly predicted than position space ones. Moreover an improvement in the virial ratio does not necessarily lead to a more balanced orbital with respect to position and momentum space properties. Basis sets containing Slater-type orbitals are again found to be rather accurate. The exponentially damped rational function is confirmed to be the outstanding two-parameter unconventional orbital.

The quality of s‐orbitals determined by least‐squares fitting and constrained variational methods

“…The energies, descriptions, sources, J({e}), and J({E, AR, A P } ) values are listed in Tables I-VI for each of the 94 orbitals under consideration except in the case of the cusp functions of Table I, where J ( { E , A R } ) is given instead of J({E,AR,AP}) because the latter is undefined [2]. The numbering of the 71 orbitals considered in our earlier studies is the same as in those papers [ 1,2].…”

“…Moreover, an information theoretic quality assessment technique [3] was used [2] to rank the various basis sets according to their ability to produce accurate approximations to the Hartree-Fock limit values of various combinations of properties. In those studies [ I , 21, our main objectives were to determine (1) whether any of the many nonconventional basis sets tested were more useful than the usual Slater-type orbitals (STO'S) and Gaussian-type orbitals (GTO'S) and (2) to what extent accuracy in position space was coupled to accuracy in mornentum space.…”

“…In previous papers [ 1,2] we calculated a wide range of momentum and position space properties in order to test the quality of 71 orbital basis sets that had been used for the atomic helium Hartree-Fock problem. Moreover, an information theoretic quality assessment technique [3] was used [2] to rank the various basis sets according to their ability to produce accurate approximations to the Hartree-Fock limit values of various combinations of properties.…”

Completeness profiles of one-electron basis sets

“…Furthermore, some workers focused their attention on the asymptotic behaviour (4), or concentrated on calculations of chemical shifts (5) and spin densities (6, 7), while others studied momentum space properties (8). Some recent investigations used information theory to examine the quality of one-electron basis sets (9)(10)(11)(12). In contrast, the object of this work is to present a simple visual representation of the completeness of atomic orbital basis sets at different regions of space as tested by a scanning orbital (13).…”

Substituent effects in alkynes and cyanides: a momentum density perspective

“…Hence all partial waves displayed in this paper were obtained via analytic formulae. It is worth noting that S T 0 basis sets provide a reasonable balance between accuracy in position space and accuracy in momentum space (10).…”