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Toward a compact description of molecular electron densities
Author(s) -
Chodkiewicz Michał L.,
Howard Siân T.,
Woźniak Krzysztof
Publication year - 2004
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.20002
Subject(s) - electron density , orthonormal basis , chemistry , electron , substituent , basis set , density functional theory , computational chemistry , orbital free density functional theory , basis function , molecule , basis (linear algebra) , electron scattering , electron localization function , statistical physics , physics , quantum mechanics , hybrid functional , mathematics , stereochemistry , organic chemistry , geometry
A formalism is presented for the description of the electron density in a molecule or its fragment, using only a small number of parameters. The method is based on statistical analysis of a set of fragment electron densities obtained for a given quantum mechanical subsystem embedded in different environments (e.g., substituent groups, external fields). The electron density is expressed as the sum of its average value in such a subsystem and a linear combination of orthonormal functions expressed on a molecular orbital basis and chosen in such a way that each successive function maximally reduces the residual density. The technique used is functional principal component analysis (FPCA), which seems well suited to the statistical properties of the electron density. In addition to providing an efficient means of parameterizing an electron density, the FPCA also appears to provide the basis of a scheme for systematic analysis of the perturbations in electron density caused by changes of the molecular environment. An example of the application of this method, to the aldehyde fragment of HCOX compounds, is presented. Most of the variation of electron density in this fragment (97%) is described by only four functions. The coefficients of the first function correlate (−0.93) with the resonance substituent constants, and the second one with the induction parameter F (−0.9). This approach appears to have many potential applications: in developing rapid density functional methods for large molecules, in more efficient parameterizations of reconstructed experimental densities (from scattering experiments), and in analyzing substituent effects. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004