The thesis is devoted to the quantum-mechanical analysis of the decomposition of electrostatic component of intermolecular interaction energy into the
contributions localized in accordance with the graph of the covalent bonds of a molecule. Molecular dynamic simulations in combination with quantum mechanics methods (DFT, 2nd-order Möller-Plesset perturbation theory, atoms in molecules electron charge density topology analysis method (QTAIM), symmetry-adapted perturbation theory (SAPT), as well as LPO and CLPO orbital localization methods developed in this thesis) were used to investigate the decomposition of one-electron molecular properties of biomolecules into the localized contributions. The conformational dependence of the covalent bonding descriptors obtainable from one-particle density matrix was studied. The values of bond orders for pairs of covalently bonded atoms in different conformers were obtained by Natielo-Medrano, NPA-Weiberg, and Mayer methods in model DNA constituents. Using the method of molecular electrostatic potential approximation, the dependence of atomic charges of canonical 2'-deoxygribonucleotides was investigated. The modification of the principal component regression method was developed to obtain atomic charges from such the observable properties of molecules as the spatial structures and dipole moments of their conformers. The problem of approximating the reduced one-particle density matrix, initially given in the basis of orthonormal functions, by a diagonal part of its expansion over the localized orbitals is formulated, and numerical algorithm as well as its software implementation for finding the localized orbitals (LPOs) as a solution of the formulated problem are created. Modification of the LPO algorithm based on the new conditions for orbitals occupancy and ionicity is developed and implemented in software package JANPA for obtaining the CLPO localized orbitals. These localized orbitals are shown to mimic the electron pairs of the covalent bonds and single-atomic lone pairs, well-known in the classical Lewis model of molecular electronic structure. Basing on the developed methods, a new procedure for finding the covalently bonded atoms and determining their integer-valued bond order
from a reduced one-particle density matrix of the molecule is proposed. It is shown that the distribution of the lengths of detected covalent bonds gets close to the normal one after removing the bonds which can be considered as conjugate. In this case, for all bonds their average lengths agree with the corresponding experimental values within one standard deviation. The covalent radii corresponding to single, double and triple bonds were found for atoms of chemical elements H, B, C, N, O, F, Si, P, S, Cl, Ge, As, Se, Br solely from the first-principle data. A new model is proposed for approximating the charge density of a molecule by the sum of the point charges located on atomic nuclei and equal to NPA charges, and of the following localized electronic components, neutralized by the appropriate fraction of nuclear charge – electron pairs of atoms and covalent bonds.
