This project is funded under the Theoretical and Computational Chemistry program. The work involves questions of fundamental theory of how the energy of a molecular system changes when the positions of the nuclei are varied. The consequences of these changes can be quite subtle but still detectable experimentally, and properties of small clusters of alkali metal atoms are expected to be explained by the theoretical developments to be undertaken. In more detail, earlier work on the implications of conical intersections between Born-Oppenheimer potential energy surfaces is to be extended in several directions. Such intersections produce anomalous sign changes in electronic wave functions when the nuclear coordinates traverse a closed path around the intersection. The past results on the effect of permutation symmetry for three and four identical nuclei are extended to the general case. Professor Mead will study the generalization to phase changes and unitary transformations experienced by electronic wave functions representing Kramers doublets when the nuclear coordinates traverse closed paths, and the analogy with gauge field theories of elementary particles. He will also obtain general functional forms for potential energy surfaces and derivative couplings for various systems. The nonremovable derivative coupling, which cannot be transformed away by going to a diabatic basis, will be further studied, and the question of whether there are specific effects which can be attributed to it will be explored.
