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

The expectation values 〈 r k 〉 (−2 ⩽ k ⩽ 4, k = 10), values of the charge density ρ( r ) at selected points, and coefficients in the MacLaurin expansion of ρ( 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)]. 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.