Quantum molecular similarity measures (QMSM) and the atomic shell approximation (ASA)

Molecular Quantum Similarity: Theory and Applications

“…In a first approach, Constans and Carbó -Dorca used a positive restricted fitting technique. 87 In other implementations, [88][89][90][91][92][93] we can use a fairly simple idea for assuring that the constraints of Eq. [52] are obeyed.…”

Toward a global maximization of the molecular similarity function: Superposition of two molecules

“…ASA densities provide accurate enough values, not only in self-similarities, but also in all the similarity function domain. 7,8 In Table VII the number of compatible functions or shells for each molecular density is also reported. EASA densities, due to their definition and construction, yield acceptable self-similarity values but somehow erroneous cross-similarity global maxima.…”

“…8 Global search and local optimization algorithms were implemented, as described in the previous section, in a computer program named ASASim. Speeding techniques, such as parallelization, integer arithmetic in distance evaluation, or dynamic thresholding in integral and derivative computations, have yet to be considered and will be described elsewhere.…”

“…Similar 3 3 pictures comparing ASA similarity functions with the MP2r6᎐311G** ones are published elsewhere. 8 Deviations are lesser and only noticeable in a difference plot. The relevant information of the QMSM function for simple cases consisting of linear molecules is manifested, once the molecules are aligned, by translating one of them along the internuclear axis.…”

“…rate values for the similarity integral 2 as extensively analyzed in previous works. 7,8 The partition of the electron density into atomic contributions is also advantageous for the study of molecular fragments. Furthermore, a global search algorithm for the maximization of the overlap density function can be established, providing safeguards to unbiased and reproducible molecular alignments.…”