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Application of error‐ranked singular value decomposition for the determination of potential‐derived atomic‐centered point charges
Author(s) -
Tan Jeffrey S.,
Boerrigter Stephan X. M.,
Scaringe Raymond P.,
Morris Kenneth R.
Publication year - 2008
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.21101
Subject(s) - singular value decomposition , charge (physics) , set (abstract data type) , singular value , mathematics , point (geometry) , basis set , value (mathematics) , measure (data warehouse) , basis (linear algebra) , eigenvalues and eigenvectors , algorithm , chemistry , physics , quantum mechanics , computer science , molecule , statistics , geometry , data mining , programming language
The present work provides a detailed investigation on the use of singular value decomposition (SVD) to solve the linear least‐squares problem (LLS) for the purposes of obtaining potential‐derived atom‐centered point charges (PD charges) from the ab initio molecular electrostatic potential ( V QM ). Given the SVD of any PD charge calculation LLS problem, it was concluded that (1) all singular vectors are not necessary to obtain the optimal set of PD charges and (2) the most effective set of singular vectors do not necessarily correspond to those with the largest singular values. It is shown that the efficient use of singular vectors can provide statistically well‐defined PD charges when compared with conventional PD charge calculation methods without sacrificing the agreement with V QM . As can be expected, the methodology outlined here is independent of the algorithm for sampling V QM as well as the basis set used to calculate V QM . An algorithm is provided to select the best set of singular vectors used for optimal PD charge calculations. To minimize the subjective comparisons of different PD charge sets, we also provide an objective criterion for determining if two sets of PD charges are significantly different from one another. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2009