Ab initio calculations on sulfur-containing compounds. I. Uniform quality basis sets for sulfur: Total energies and geometries of H2S

Uniform quality basis sets (UQ-NG ; N=3, 4, 5), with s = p and s ≠ p, and a 6-31 G^* basis set have been optimized for the sulfur atom. These uniform quality basis sets in their uncontracted and contracted forms were used, together with other basis sets reported in the literature (a total of 40 basis sets), to study their accuracy in predicting the bond length and bond angle of H₂S.     

Level set topologies and convexity relations for hamiltonians with linear parameters

Level sets of the expectation value functional of hamiltonians depending on linear parameters are convex over a subset of the space spanned by these parameters. When the parameters enter the hamiltonian through a positive definite perturbation term, then properties of convex polyhedra in the parameter space lead to energy inequalities which may be utilized in perturbation theory.     

Dimension Concepts and Reduced Dimensions in Toxicological QShAR Databases as Tools for Data Quality Assessment

The dimensions of databases can be defined based on a variety of concepts, ranging from the standard tools of principal component analysis to context-biased approaches. The effective dimensions of databases, in particular the effective dimensions involving continua such as electron density data, provide a set of important tools for database comparisons and for the evaluation of some aspects of database quality. The problems associated with database comparisons and database mergers, such as those occurring in the process of database unification in the actual merger of two pharmaceutical companies, provide challenging tasks and opportunities for data science. Some of the tools for effective dimension reduction and dimension expansion are reviewed in the context of database quality control and conditions for database compatibility are presented. A common misconception affecting data sampling techniques for data quality evaluation is discussed and methods for circumventing the associated sampling errors are described.     

The Holographic Principle for Latent Molecular Properties

All information about all latent molecular properties, not exhibited by a given molecular structure but reproducibly exhibited by the same molecule in a different state or having a different conformation, is fully encoded in any nonzero volume of the non-degenerate ground state electron density.     

A note on a non-empirical molecular orbital study of some cytosine and thymine tautomers

The relative stabilities of a series of cytosine and thymine tautomers have been investigated by means of non-empirical (ab initio) LCAO-MO-SCF Hartree-Fock-Roothaan calculations employing a small contracted Gaussian basis set (STO-3G) in all cases. The relative stabilities of the various tautomeric forms agree in general with the results of earlier empirical and semi-empirical calculations on these molecules. In particular, the “enol forms” of cytosine and thymine, within the isolated molecule approximation inherent in these MO calculations, are predicted to possess greater stability than the forms commonly assigned to these molecules in aqueous solution and found in the solid state by X-ray crystallographic studies.     

Cell-shedding transformations,equivalence relations,and similarity measures for square-cell configurations

A family of related techniques for the reduction of square-cell configurations (“animals”) to simpler ones by cell-shedding processes provide physically motivated, novel approaches for shape characterization and similarity criteria as well as similarity measures based on equivalence relations. The two main algorithms, cs_k, k = 1, 2, involve the simultaneous “shedding” of all cells having precisely k sides exposed on the periphery of the animal; the shedding steps are repeated as long as the resulting structure is an animal. Since the termination criteria of these two algorithms are different, they can be combined sequentially into composite algorithms, leading to various alternative shape characterizations and equivalence relations. The third main algorithm, cs₃₂, involves incomplete elimination of peripheral cells of a given type, thus retaining some additional local shape features inherited from the original animal. Following the introduction of these transformations, some of their properties are derived and several examples are discussed. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 62 : 353–361, 1997