Desenvolupament computacional de la semblança molecular
quàntica
P. Constans. Desenvolupament computacional de la semblança molecular
quàntica. Published online February 2002, TDC@T,
NDLTD.
Abstract
The present Doctoral Thesis, entitled Computational Development of Quantum Molecular
Similarity, fundamentally deals on the calculation of similarity measures arising
from the comparison of electron density functions.
The first chapter, Quantum Similarity, is introductory. Electron probability
functions are described, emphasizing their significance in Quantum Mechanics, and
their mathematical constrains.
In the chapter Models of molecular electron densities, original procedures to fit
electron densities to 1s Gaussian expansions are presented. Mathematical constrains
attached to probability distribution functions are explicitly considered, in the
procedure named Atomic Shell Approximation (ASA). This procedure, implemented in the
computer program ASAC, uses an initial, nearly complete functional space, from where
functions or shells are variationally selected, according to the non-negativity
requirements. The quality of these model densities and the accuracy of the derived
similarity measures are extensively verified. The ASA model is also extended to
dynamic distributions, presumably a more physical representation of free molecule
and ligand electron densities. The ASA procedure, explicitly consistent with the
N-representability conditions, is adapted to the direct determination of hydrogenoid
electron densities, in a context of the Density Functional Theory.
The chapter Global Maximization of the Similarity Function describes original
algorithms to determine the maximum overlap of two molecular electron densities.
Similarity measures are identified with the maximum overlap in order to measure the
distances among molecules, independently on the reference framework where they are
defined. Starting from the known global solution attached to hypothetical,
infinitely compacted molecular electron densities, one proposes three levels of
approach for an efficient scanning and global maximization of the non-deformed
similarity function. Parametrazing overlap integrals through Lorentzian-like
functions is also proposed to speed up computations. In the practice of
structure-activity relationships, the presented advances provide an efficient
implementation of quantitative similarity measures, and, moreover, provide a new,
completely automatic methodology for molecular superposition and alignments.
The chapter Similarities of atoms in molecules describes an algorithm for the
comparison of Bader atoms. The accurate similarity measures obtained provide a
rigorous quantification of the degree of transferability of atoms and functional
groups.
Finally, in the chapter Similarities among crystalline structures, it is proposed a
similarity definition for the comparison of crystalline structures regarding the
concept of softness. This concept emerges from the BCS theory of superconductivity.
It appears related to the influence of electron-phonon interactions in the
transition temperatures to the superconducting state. The application of this
methodology in analyzing BEDT-TTF salts reveals a structural correlation among
superconductors and non-superconductors, according to pointed hypothesis regarding
the influence of some intermolecular interactions.
The present Thesis concludes listing the ASAC code, implementation of the ASA
algorithm, together with a chapter containing bibliographic references.
Keywords
Atomic Shell Approximation, molecular alignments, structural similarity, electron
density.
PDF reprint, by chapters:
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Preface & Table of Contents
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Introduction
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Quantum Similarity
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Electron Density Models
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Global Maximization of the Similarity function
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Similarities among Atoms in Molecules
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Similarities among Crystal Structures
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Conclusions
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Appendix
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References
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