Evenhyphen;tempered atomic orbitals. III. Economic deployment of Gaussian primitives in expanding atomic SCF orbitals

摘要

Expansion of atomic selfhyphen;consistenthyphen;field orbitals in terms of Gaussianhyphen;type primitive AO's calls for the most economic deployment and efficient use of all available basis functions to avoid computational waste. In evenhyphen;tempered representations maximal use of all primitives in representing all SCFAO's is ensured. Here, the optimal number of primitives perindividualSCFAO, consistent with a giventotalnumber of primitives is investigated. Maximal effectiveness is found to occur when the following conditions prevail: (1) The number of primitives per SCFAO is approximately the same for all SCFAO's, sayx; (2) the number of primitives needed to express the set of SCFAO's with angularhyphen;momentum quantum numberlin atom A is approximately given byNl(A) equals;xaplus;byl(A) whereaandbare constants andyl(A) is the number of different SCFAO's with quantum numberlin atom A. Thus the efficiency rapidly increases withyl(A). Explicit results and optimal expansions based on 3ndash;14 primitives are discussed for all atoms up to krypton. The achieved systematization permits the unambiguous selection of economic evenhyphen;tempered expansions for molecular calculations.