Despite the widespread acceptance of the relevance of the nodes of one-body electronic wave functions (atomic or molecular orbitals) in determining chemical properties, relatively little is known about the corresponding nodes of many-body wave functions. As an alternative to mapping the nodal surfaces present in the ground states of many-electron systems, we have focused instead on the structural domains implied by these surfaces. In the spirit of Monte Carlo techniques, the nodal hypervolumes of a series of atomic N-body Hartree-Fock level electronic wave functions have been mapped using a random-walk simulation in 3N dimensional configuration space. The basic structural elements of the domain of atomic or molecular wave functions are identified as nodal regions (continuous volumes of the same sign) and permutational cells (identical building blocks). Our algorithm determines both the relationships among nodal regions or cells (topology) as well as the geometric properties within each structural domain. Our results indicate that ground-state Hartree-Fock wave functions generally consist of four equivalent nodal regions (two positive and two negative), each constructed from one or more permutational cells. We have developed an operational method to distinguish otherwise identical permutational cells. The limitations and most probable sources of error associated with this numerical method are discussed as are directions for future research.

The potential energy surfaces of four cyclic alkanes have been examined using molecular mechanics, semiempirical, and ab initio methods to determine if they produce mutually consistent results and investigate the source of any errors between the methods. The C5 -CR cyclic alkanes were chosen since these structures present a finite set of conformations and transition-state geometries and are still within the computational time and memory limits of the quantum mechanical approaches. We also examined several conformations of 1 ,Z-dideoxyribose to determine the effect of heteroatoms on the results for the 5-membered ring. The molecular mechanics and ab initio calculations are consistent in the relative energies and geometries determined for the conformers of all ring systems. While the semiempirical calculations yielded geometries consistent with the other methods (except for 5-membered rings), the relative energies often deviated substantially. A decomposition analysis of the semiempirical and molecular mechanics energies revealed that the disparities are mainly due to errors in the 1-center energies of the semiempirical calculations. The 2-center bonding and nonbonding energies followed reasonable trends for the conformers. The core-repulsion function, however, is suspected of producing anomalies. A minimum in the attractive Gaussian of this term at 2.1 A for H-H interactions partly explains the propensity of the 5-membered rings to optimize to near planarity (decreasing 12-diaxial hydrogen distances to 2.3 A) and the underestimation of the relative energy of the boat structure of cyclohexane.

The recently reported Random Incremental Pulse Search (RIPS) technique has been used to probe the conformational energy surface of cyclononane. The stochastic method permits searching of the potential energy surface for all minimum-energy conformations. The search located all previously reported structures together with three additional conformations that were not found by earlier, primitive searching techniques. Two of these structures are high-energy skew forms, and the third is a low-energy conformer that should contribute significantly to the overall equilibrium set of cyclononane conformations.The global minimum has been found to be the D3 symmetrical twist chair-boat (TBC) form in accordance with previous studies. The newly discovered low-energy structure, which lies only 2.2 kcal/mol above the global minimum, has been designated twist chair-twist chair (TCTC). The two higher energy conformers are skewed chair-chair (SCC) and skewed boat-boat (SBB) forms that are 5.7 kcal/mol and 10.4 kcal/mol above the global minimum, respectively. The seven reported conformations were reanalyzed quantum mechanically AM^), and a comparison between MM2 and AM1 results is presented.

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