Structural analysis of certain linear operators representing chemical network systems via the existence and uniqueness theorems of spectral resolution. VI*

The present Part VI of this series of articles provides a mathematical and methodical link between (i) fundamental methodology in the repeat space theory (RST), which is referred to as the approach via the aspect of form and general topology and which has universal unifying power to handle additivity problems of molecules that have many identical moieties, and (ii) frontier electron theory of reactivity indices. Using theoretical tools required to link (i) and (ii), we establish a theorem from which the Generalized Alpha Existence Theorem (a theorem essential in the RST and proved in the previous Part V) directly follows. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem 84: 389–400, 2001     

Molecular Shape Analysis of a Maillard Reaction Intermediate

Abstract

The Maillard (browning) reaction involving the polycondensation of sugars and amino acids is believed to be an important abiotic pathway for humic substance formation in nature. However, a major drawback is that the Maillard reaction is extremely slow at temperatures encountered under normal environmental conditions. In order to elucidate some details of this process molecular shape analysis was applied to investigate the initial reaction between D-glucose and glycine to form the Amadori compound fructosylglycine which is an intermediate product in the Maillard reaction. The structure of the Amadori compound was optimized at a quantum mechanical level and its ground state electron energy calculated. Molecular Iso-Density Contours (MIDCO's), electron density contour surfaces of constant electron density, were constructed for D-glucose, glycine and fructosylglycine in order to study the steric conditions for the reaction. The calculations indicate that the Amadori compound and water on one hand and the separate entities D-glucose and glycine on the other hand are very similiar to each other in terms of their ground state energy. This agrees with the experimental observation that the reaction between D-glucose and glycine to form the Amadori compound is slow.     

Energy relations between small and large unit cell boron–nitrogen polymer analogues of spiral graphite and nanoneedle structures

Based on a comparison of nuclear charges combined with a convexity property of Hamiltonians, and employing nuclear charge transformations representing a limited case of the Universal Molecule Model, simple electronic energy relations are obtained for the unit cells of polymeric boron–nitrogen analogues of carbon-based nanoneedles and spiral graphite structures.     

Charge-conserving electron density averaging for a set of nuclear configurations

The Löwdin-Inverse Löwdin Transformation (LILT) technique combined with the Diophantine Density Matrix Purification (DDMP) method is suggested for a charge-preserving density averaging approach for a range of nuclear configurations.     

Metric Properties of Factor Space of Molecular Shapes

Molecular shape equivalence classes defined with respect to equivalence of geometrical and topological properties are represented by logical models. Consequently, the factor space of molecular shapes is provided by a metric useful in shape comparisons.     

Shape‐similarity relations based on topological resolution

Shape‐similarities of electron density clouds of molecules provide important clues concerning chemical and physical properties, including information about their reactivities in biochemical systems. The concept of topological resolution is used for quantifying molecular similarities: within a hierarchy of finer and cruder topologies, the crudest topology that already provides discrimination between two objects (such as two fuzzy electron density clouds) is used to define a measure of their similarities. The finer this topology, the more similar the two objects. This approach, the method of topological resolution‐based similarity measures (TRBSM), can be combined with a geometrically motivated resolution‐based similarity measure (RBSM) within a metric space. Some of the relations between these two approaches are discussed in this contribution, with special emphasis on applications to electron densities. This revised version was published online in July 2006 with corrections to the Cover Date.