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.

Type

Date

May, 1997

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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.

**Contents**

- Introduction
- Quantum Similarity
- Electron Density Models
- Global Maximization of the Similarity function
- Similarities among Atoms in Molecules
- Similarities among Crystal Structures
- Conclusions
- Appendix
- References