Ab initioSCF MO calculations on the reactions of hydroxyl radical with imidazole and monoprotonated imidazole

The addition reactions of hydroxyl radical with imidazole and its protonated form to yield radical adducts have been investigated by ab initio SCF MO methods using STO -3G and 4-31G basis sets. Analogous radical species are of importance in radiation damage to biological systems. Of the possible radical products, the calculations indicate that the allylic species are generally favored energetically over the nonallylic forms. On an energetic basis, the results show that the allylic adducts formed by addition at the C2 and C5 positions are about equally favorable. Although the C5 species is generally identified as the experimentally observed product in aqueous media for both protonated and unprotonated imidazole, some experimental evidence exists indicating the presence of other forms. Our results suggest that this other form is the C2 adduct. The calculations also point to the protonated form of imidazole being less reactive than imidazole, which is in accord with experimental observations.     

Shape groups of the electronic isodensity surfaces for small molecules: Shapes of 10-electron hydrides

An algorithm for a detailed 3-D characterization of the shapes of molecular charge distributions is implemented in the form of a comprehensive package of computer programs, GSHAPE, and applied to a series of 10-electron hydrides to critically evaluate the methodology. Attention is paid to the effects of nuclear geometry and the size of basis on the molecular shape. The characterization is performed by computing a number of topological invariants (“shape groups”) associated with a continuum of molecular surfaces: the complete family of all electronic isodensity contours for the given molecules. These shape groups (the homology groups of truncated surfaces derived from isodensity contours) depend on two continuous parameters: a density value defining the density contour and a reference curvature value, to which the local curvatures of the isodensity contours are compared. The electronic charge distribution is calculated at the ab initio level using basis sets ranging from STO-3G to 6-31G**. No visual inspection is required for the characterization and comparison of shapes of molecular charge densities, as these are done algorithmically by the computer. However, visualization of the results is one option of our program using Application Visualization Software (AVS). For a given molecule, in a given nuclear geometry, the technique provides a 2-D shape map, displaying the distribution of the shape gruops as a function of the local curvature and the level set value (the value of the charge density at the contour). The computer program GSHAPE performs the analysis automatically. This feature makes it potentially useful in the context of computer-aided drug design, where unbiased, automated shape characterization methods are valuable tools. As examples, a variety of 2-D shape maps are discussed. © John Wiley & Sons, Inc.     

Comparison of potential energy maps and molecular shape invariance maps for two-dimensional conformational problems

Summary It is well known that many molecular properties are strongly dependent on internal nuclear arrangements. Two possible, independent approaches can be followed while studying changes in molecular characteristics as functions of the nuclear geometry. These are the analysis of potential energy surfaces and the analysis of molecular shape. In this work, we seek to establish relationships between potential energy maps and shape invariance region maps, where each point of these maps represents a nuclear configuration. The study is performed by analyzing the occurrence and lack of certain symmetries in both types of maps. As illustrative examples, we consider the three structural isomers of the dihydroxybenzene molecule. Potential energy is computed at the STO-3G ab initio level, while the shape is described by the shape group method as applied to fused-sphere van der Waals surfaces. It is shown that the symmetry of the shape invariance maps follows closely, but not exactly, the symmetry of potential energy surfaces. The molecular surface is thus blind to some small changes of the potential (a feature to be expected to hold also for molecular surfaces defined in terms of electronic charge density). Our findings suggest that a crude fused-sphere model may suffice to describe some of the structural changes in molecular surfaces, as well as their relationships to the electronic energy.     

A general formulation of the “quantum chemical le Chatelier principle”

Regularities observed in the variations of calculated energy components, for example, those of electronic and nuclear repulsion energies in the analysis of conformational changes and in studies of the propagation of basis set errors in ab initio calculations, are found to be related to the variational principle and to the boundedness of energy expectation value functionals. These relations are analogous to the le Chatelier principle of equilibrium thermodynamics, and may be formulated as a general “compensation principle” for two sets of general parameters of the molecular total energy functional.     

A global characterization and similarity analysis of two-dimensional potential energy surfaces

Potential energy surfaces can be classified into combinatiorial equivalence classes, based on their partitioning into catchment regions. Two classification theorems are proven: one for reaction spheres and another for reaction tori. A method for constructing all possible equivalence classes of reaction spheres and reaction tori is presented. As illustration of the general results, it is shown that not all the two-dimensional reaction spheres are combinatorially equivalent to polyhedra in the three-dimensional Euclidean space. As examples, several reaction spheres are calculated by using the RHF method at the 3-21G * level, describing the interactions between a series of polyatomic ions and H⁺. The calculations show that the potential energy surface of the CO …?H⁺ interaction, combinatorially equivalent to that of the NO^?₃ …?H⁺ interaction, is not combinatorially equivalent to any polyhedron in 3-space; however, the combinatorially different potential energy surface of the PO …? H⁺ interaction is equivalent to a polyhedron in 3-space. The topological classification scheme is proposed for the study of similarities between various families of chemical reactions.     

Representation of square-cell configurations in the complex plane: Tools for the characterization of molecular monolayers and cross sections of molecular surfaces

Two numerical codes, a complex face vector F and a real face vector D are developed for the characterization of square-cell configurations (lattice animals), used for representing the shapes of molecular monolayers and cross sections of molecular surfaces. The real face vector D represents all the intrinsic properties, size, and shape of the lattice animal. The complex face vector F contains complete information about the size, the shape, and also the placement of the particular lattice animal with respect to the lattice. Based on the properties of the face vectors, a method is developed for the classification of similar animals into equivalence classes. The face vector method is proposed for an algorithmic, nonvisual computer analysis of similarity of shapes of molecular monolayers and planar domains of cross sections of molecular surfaces, approximated by lattice animals.     

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

The present article develops a methodology and a unifying theorem to treat, on an equal footing, mathematical phenomena that were hitherto studied separately in each of the research fields of dynamical systems and quantum chemistry involving the spectral symmetry of alternant hydrocarbons. This article also serves as a foundation of a theoretical framework for the analysis of certain dynamical systems of chemical kinetic equations, which shall be made in the context of operator algebra in Parts II and III of this series of papers. © 1995 John Wiley & Sons, Inc.