Applications of optimization to quantum chemistry

The behavior of the geometry optimization of a large set of molecules has been examined. Particular failures and difficulties are noted for some systems and are shown to correspond to certain conditions. In cyclic systems, difficulties which can arise from using Z-matrix coordinates, which necessarily leave one or more bonds undefined, can be eliminated by using natural internal coordinates. The construction and definition of natural internal coordinates is extended to weakly bound systems, and possible definitions for fused polycyclic ring assemblies are discussed. -- 5-Substituted cyclopentadienes were chosen for their relevance to studies of facial selectivity in the Diels-Alder reaction. The central atom of the substituents chosen were of p-block elements, with any remaining valences filled with hydrogen. Basis set effects on the structures were examined, as well as the role of conformation on the various geometric parameters. The relative stabilities of the various conformers and the changes in geometry upon change in conformation are predictable from hyperconjugation arguments. -- The symmetric transition state of the degenerate substituent migration in 5-substituted cyclopentadienes has been studied. The activation barrier to migration was shown to correlate well with a dimensionless 'stretching' parameter. -- Several metal-aquo complexes were studied, including Li⁺, Be²⁺, Mg²⁺, A1³⁺, Sc³⁺, Zn²⁺, Ga³⁺, Cd²⁺, and In³⁺. For Li(H₂O)₅⁺, the character of stationary points can change with different basis sets. The vibrational frequency of the symmetric M-O stretching mode is always underestimated with extended basis sets, but can be improved by explicit inclusion of a second solvation sphere. -- The bimolecular complexes HF...HF, HF...H₂O, HF...NH₃, HF...CO, HF...NN, HF...NCH, and H₂O...H₂O have been studied. A rough correlation exists between the inverse of the hydrogen-bond distance and the bond strength. For HF complexes, the HF bond lengthens in accordance with the strength of the intermolecular interaction. -- The valence tautomerism between benzene oxide and oxepin has been studied. The enthalpies and barriers to tautomerization were very sensitive to basis set and method of correlation. The inversion barriers of the oxepin forms are reported. The effect of simultaneous methyl substitution at the 2 and 7 positions, of protonation, and of the replacement of oxygen with sulfur is examined. Some corrections to photoelectron band assignments are pointed out. The anti selectivity in the Diels-Alder reaction of benzene oxide is determined by a steric effect. -- Several 5,6-disubstituted 1,3-cyclohexadienes were studied. The potential surfaces of monocyclic structures were very basis set dependent, with minima disappearing and reappearing as one progressed to higher levels. A full comparison between experimental and theoretical structural and vibrational properties is made for 1,3-cyclohexadiene. The effect of conformation on the structure of cis-3,5-cyclohexadiene-1,2-diol is studied. The predicted photoelectron spectra are compared with experiment and assignments are made. -- The Z-matrix optimizations involved in the above studies were examined carefully. For 1,3-cyclopentadienes, some optimization problems could be traced to linearization of atoms involved in a bending coordinate, which rendered a corresponding torsion undefined. The transition state of the substituent shift in 1,3-cyclopentadienes, can be found by minimization in the totally symmetric subspace. The optimization of these species took more function evaluations on average than the corresponding reactant. Indications of the inability of Davidon's Optimally Conditioned method to deal with nearly converged structures may be a problem with either the method itself or the quality of the Hessian. For metal-aquo complexes, the symmetry of the species can be used to simplify the search for minima and/or transition states. In many cases, there are no totally symmetric modes corresponding to water librations, in which case the optimization proceeds smoothly. Bimolecular complexes gave optimization problems when symmetry could not be used to remove coordinates corresponding to the relative orientation of the molecules. For the valence tautomerisations, the monocyclic species optimized more quickly than the bicyclic species. The use of linear angles, and the resulting nearly singular Hessian gave problems. Poor Hessian updates for transition state optimization resulted in several failures which were corrected by resetting the Hessian. Many problems are related to both the coordinate system and the poor Hessian guess used for high amplitude modes. Proper internal coordinates in general speed up the optimization