Atomic Shell Approximation: Electron Density Fitting Algorithm Restricting Coefficients to Positive Values

Abstract

Expressing molecular electron densities as linear combinations of Guassian 15 spherical functions extends accurate computations of ab initio quantum molecular similarity measures to large systems. These approximate least squares fitted functions lose the density of probability statistical meaning since some coefficients might be negative. A new algorithm using positive coefficients only and thus providing an electron density picture as a superposition of atomic shells is presented.

Quantum similarity of isosteres coordinate versus momentum space and influence of alignment

“…In the TGSA algorithm molecules are aligned on the common atomic dyads and triads and the best alignment is chosen based on the best fit. At the end of the algorithm the overlap and Coulomb rQSM are computed using the atomic shell approximation (ASA) [23][24][25] to build approximate electron densities. In this approximation, the molecular density is expressed as a sum of atomic densities located in the same locations in space as the molecule.…”

Alternative Kullback−Leibler Information Entropy for Enantiomers

“…or aligning the molecules so that the resulting molecular similarity is maximized (QSSA 43,44,45,46,47 ). It deserves mentioning that for a true distance, one can demand internal consistency over a molecular set 46 .…”

Average replicated T-matrix approximation: valence band of non-crystalline metallic alloys

“…Finally, the conclusion of this section is that we have got a new method of calculating DoS of a disordered multi-component system founded on equations (18) and (19). The data required by this method are the partial structure factors and quantitative composition of the system under consideration, the single-site potentials in self-consistent field approximation of every component and finally the Green function of reference system.…”

“…In (26), we treat the atomic electron densities ρ (at) α (r) within the atomic shell approximation [18] via Gaussian-type decomposition…”

“…Turning back to ARTA equations (18,19) and reminding that we assume the reference system to be the free electron gas, the next equation for DoS can be got in a way similar to the one we used before in [19,20] DoS(E) = (2E)…”