Computation of density gradient quantum similarity integrals is analyzed, while comparing such integrals with overlap density quantum similarity measures. Gradient quantum similarity corresponds to another kind of numerical similarity assessment between a pair of molecular frames, which contrarily to the usual up to date quantum similarity definitions are not measures, that is: strictly positive definite integrals. As the density gradient quantum similarity integrals are defined as scalar products of three real functions, they appear to possess a richer structure than the corresponding positive definite density overlap quantum similarity measures, while preserving the overall similarity trends, when the molecular frames are relatively moved in three dimensional space. Numerical results within the atomic shell approximation (ASA) framework are presented as simple examples showing the new performances of the gradient density quantum similarity.

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