Molecular point symmetry and the phase of the electronic wave function: Tools for the prediction of critical points of potential energy surfaces

By combining a well-known theorem of Longuet-Higgins on the phase changes of electronic wave functions along loops encircling a conical intersection of potential surfaces, and a recently proven “vertical symmetry theorem” on the relative distributions of point symmetry groups and potential surface critical points in configuration space, a new result is obtained, suitable for the prediction of the presence of a critical point within a domain of configurations.     

Non-empirical SCF MO studies on the protonation of biopolymer constituents

Proton affinities of a large number of tautomeric adenine and guanine structures have been calculated using theab initio Hartree-Fock-Roothaan SCF method. For guanine, and to a lesser extent for adenine, it is likely that several protonated forms may co-exist in acidic solutions. Protonation at the free adenine and guanine positions in DNA may introduce effective acceptor levels between the energy bands of the polymer that may cause fundamental changes in the conduction properties of DNA.     

Proof of the Fukui conjecture via resolution of singularities and related methods. V

The present article is a direct continuation of part IV of this series. The Local Analyticity Proposition (LAP1), which admits a proof via resolution of singularities is a major key to proving the Fukui conjecture via resolution of singularities and related methods. By LAP1, the essential part of the mechanism of the “asymptotic linearity phenomena” is extracted and is elucidated by using tools from the theory of algebraic and analytic curves. Here in the present article, we complete the proof of the LAP1 by using fundamental tools developed in parts III and IV of this series, thus completing the proof of the Fukui conjecture via resolution of singularities and related methods. This series of articles I-V establishes, for the first time, a new linkage between (i) the mathematical field of resolution of singularities and (ii) the chemical field of additivity problems tackled and solved in a unifying manner via the repeat space theory (RST), which is the central theory in the First and Second Generation Fukui Project. A new development called the Matrix Art Program in the Second Generation Fukui Project has also been expounded with a graphical representation of energy band curves of a carbon nanotube.     

The topology of catchment regions of potential energy hypersurfaces

A simple proof is presented for a fundamental topological property of catchment regions of potential energy hypersurfaces: each catchment region C(λ,i), representing a chemical species and its conformational range on the potential energy hypersurface, is simply k-connected for each dimension k=1,2,…3N−6−λ, where λ is the index of the catchment region. The consequences of this property on the structure of the fundamental group of reaction mechanisms (the one-dimensional homotopy group of reaction paths) is discussed. Received: 8 July 1998 / Accepted: 6 October 1998 / Published online: 23 February 1999     

A proof of the metric properties of the symmetric scaling-nesting dissimilarity measure and related symmetry deficiency measures

The scaling-nesting similarity measures were proposed earlier for an intuitively simple shape comparison of molecular “bodies” enclosed by isodensity surfaces. Similarity measures have extended utility and provide rigorous comparisons which can be treated by well-known mathematical techniques if they fulfill the conditions for a metric. Here, a proof is presented showing that the symmetric scaling-nesting dissimilarity measure is indeed a proper metric. Some additional features, relevant to the newly proven properties of these similarity measures, are discussed. © 1997 John Wiley & Sons, Inc.