Paul G. Mezey

A fast intrinsic localization procedure applicable for ab initio and semiempirical linear combination of atomic orbital wave functions

A new intrinsic localization algorithm is suggested based on a recently developed mathematical measure of localization. No external criteria are used to define a priori bonds, lone pairs, and core orbitals. It is shown that the method similarly to Edmiston–Ruedenberg’s localization prefers the well established chemical concept of σ–π separation, while on the other hand, works as economically as Boys’ procedure. For the application of the new localization algorithm, no additional quantities are to be calculated, the knowledge of atomic overlap intergrals is sufficient. This feature allows a unique formulation of the theory, adaptable for both ab initio and semiempirical methods, even in those cases where the exact form of the atomic basis functions is not defined (like in the EHT and PPP calculations). The implementation of the procedure in already existing program systems is particularly easy. For illustrative examples, we compare the Edmiston–Ruedenberg and Boys localized orbitals with those calculated b...

The holographic electron density theorem and quantum similarity measures

How much information about the complete molecule is present in a part of the molecule? Quantum similarity measures provide comparisons between molecular electron densities based on integration over the whole space. Such integration involves boundaryless electron densities, whereas an early application of the Hohenberg—Kohn theorem to local subsystems of molecules requires these molecules to be confined to bounded, finite regions of the space. However, actual molecules have no boundaries, they are not confined to any finite region of the space. In order to find deterministic relations between local and global, boundaryless electron densities, and to classify the link between quantum similarity measures involving the full space and local subsystems, the unique extension property called the holographic property of subsystems of complete, boundaryless electron densities is established. Any nonzero volume piece of the ground state electron density completely determines the electron density of the complete, bou...

Macromolecular density matrices and electron densities with adjustable nuclear geometries

Based on the additive fuzzy electron density fragmentation principle introduced earlier within theab initio Harttee-Fock quantum chemical computational framework, two new methods are introduced for the construction of geometry-adjustable,ab initio quality macromolecular electron densities. Both methods are designed for the computation ofab initio quality electron densities and other properties for macromolecules of arbitrary reference nuclear geometry, as well as for the rapid computation of approximate electron densities and other molecular properties for nuclear geometries slightly distorted with respect to the reference geometry. This latter feature is expected to improve the description of some of the vibrational and dynamic properties of macromolecules. The first of the two techniques, the Adjustable Local Density Assembler, or ALDA method, generates geometry-adjusted macromoleculer electron densities directly, using Mulliken-Mezey fragment density matrices, basis set information, and nuclear coordinates. The method requires an ALDA fragment electron density matrix database. The second technique, the Adjustable Density Matrix Assembler or ADMA method, is introduced for the generation ofab initio quality approximatedensity matrices for macromolecules. The method assembles Mulliken-Mezey fragment density matrices designed to fulfill a macromoleculer compatibility condition. The ADMA method generates macromoleculer density matrices without requiring the computation of a macromoleculer wavefunction. The ADMA method allows one to apply most of the density matrix techniques of conventional quantum chemistry to macromolecules such as proteins.

Catchment Region Partitioning of Energy Hypersurfaces, I

The space of internal coordinates of a molecular system is partitioned into catchment regions of various critical points of the energy hypersurface. The partitioning is based on an ordering of steepest descent paths into equivalence classes. The properties of these catchment regions and their boundaries are analyzed and the concepts of chemical structure, reaction path and reaction mechanism are discussed within the framework of the Born-Oppenheimer and energy hypersurface approximations. Relations between catchment regions and the chemically important reactive domains of energy hypersurfaces, as well as models for “branching” of reaction mechanisms, caused by instability domainsDμ, μ ≥ 1, are investigated.

Ab initio quality properties for macromolecules using the ADMA approach

We describe new developments of an earlier linear scaling algorithm for ab initio quality macromolecular property calculations based on the adjustable density matrix assembler (ADMA) approach. In this approach, a large molecule is divided into fuzzy fragments, for which quantum chemical calculations can easily be done using moderate‐size “parent molecules” that contain all the local interactions within a selected distance. If greater accuracy is required, a larger distance is chosen. With the present extension of this approximation, properties of the large molecules, like the electron density, the electrostatic potential, dipole moments, partial charges, and the Hartree–Fock energy are calculated. The accuracy of the method is demonstrated with test cases of medium size by comparing the ADMA results with direct quantum chemical calculations.

Heuristic molecular lipophilicity potential (HMLP): A 2D‐QSAR study to LADH of molecular family pyrazole and derivatives

The quantum chemical and structure‐based technique heuristic molecular lipophilicity potential (HMLP) is used in the liver alcohol dehydrogenase (LADH) study of molecular family pyrazole and derivatives. The molecular lipophilic index LM, molecular hydrophilic index HM, lipophilic indices lss, and hydrophilic indices hss of the substitutes (fragments), and atomic lipophilicity indices las are constructed and used in QSAR study. The HMLP indices are correlated with bioactivities of 18 pyrazole derivatives according to the 2D QSAR procedure. The multiple linear regression equation between the bioactivities of pyrazole derivatives and HMLP indices are built using partial least square (PLS) with the optimal statistical quantity (r = 0.987, s = 0.479, F = 47.19). The inhibition mechanism of LADH of the pyrazole derivatives is explained according to the physical meaning of HMLP indices. During the HMLP calculations for the 2D QSAR, the only input parameters are the atomic van der Waals radius without the need to resort to any empirical parameters. Accordingly, HMLP can provide a rigorous theoretical approach with a crystal clear physical meaning for the 2D QSAR.

Quantum similarity measures and Löwdin's transform for approximate density matrices and macromolecular forces

The relations between the general form of Carbos quantum similarity measure and the similarity measure based on the Lowdin transform of approximate density matrices are discussed. These relations provide the basis for the study of macromolecular forces and small deformations of electron densities induced by limited changes of nuclear configurations of both small and large molecules.

Functional Groups in Quantum Chemistry

Publisher Summary A chemical functional group is a collection of nuclei and the associated electron density, which occur with a similar nuclear arrangement and a similar local electron density cloud in many molecules. A functional group is a molecular moiety of a specific stoichiometry that typically undergoes similar chemical reactions in most molecules containing this moiety. In chemistry, especially in organic chemistry, the concept of functional groups is a powerful tool used for the characterization and classification of molecules and their reactions; in fact, the presence of a given functional group in a family of molecules is an expression of chemical similarity. Molecules containing common functional groups often exhibit similar physical properties in addition to their similar chemical properties. This chapter describes the quantum chemical concept of functional groups, following a topological approach, based on the three-dimensional shape of fuzzy molecular bodies and the local shapes of various molecular moieties. This quantum chemical description of functional groups was proposed, based on the topological shape analysis of molecules and on the density domain approach to chemical bonding. Density domains are formal bodies enclosed by molecular isodensity contours; density domains play an important role in molecular shape analysis and serve as the basis of various molecular similarity measures. The proposed quantum chemical model of functional groups also fits within a rather broad, essentially geometrical framework.

Quantum chemistry of macromolecular shape

Some of the new developments in the quantum-chemical study of macromolecular shapes are reviewed, with special emphasis on the additive fuzzy electron density fragmentation methods and on the algebraic-topological shape group analysis of global and local shape features of fuzzy three-dimensional bodies of electron densities of macromolecules. Earlier applications of these methods to actual macromolecules are reviewed, including studies on the anticancer drug taxol, the proteins bovine insulin and HIV protease, and other macromolecules. The results of test calculations establishing the accuracy of these methods are also reviewed. The spherically weighted affine transformation technique is described and proposed for the deformation of electron densities approximating the changes occurring in small conformational displacements of atomic nuclei in macromolecules.

SHAPE GROUP STUDIES OF MOLECULAR SIMILARITY: SHAPE GROUPS AND SHAPE GRAPHS OF MOLECULAR CONTOUR SURFACES

The earlier, symmetry-independent group theoretical characterization of the shapes of three-dimensional molecular functions, such as electrostatic potentials, electronic charge densities, or molecular orbitals, is extended and compared to a new family of shape descriptors. The incidence graphs and shape graphs, defined by the curvature properties of various molecular contour surfaces, provide an easily visualizable, alternative mathematical technique for a computer-based, non-visual evaluation of molecular shape and molecular similarity. The invariance domains of incidence graphs, shape graphs and shape groups within the dynamic shape spaceD provide the mathematical basis for the development of a general method for a dynamic description of molecular shapes.