A physical interpretation of the He-He interaction by partitioning of the associated density matrices

Typescript.Thesis (Ph. D.)--University of Hawaii, 1968.Bibliography: leaves 142-143.vi, 143 l graphs, tablesThe advent of high speed computers allows the quantum chemist to obtain very precise energy calculations by using "good" approximate wavefunctions. These wavefunctions become very complicated which makes the abstraction of much physical information from these wavefunctions quite difficult. Klaus Ruedenberg has devised a method using two functions: the first and second order density matrices, which gives a physical interpretation of atomic interactions based on "good" mathematical wavefunction approximations. In this analysis, the density matrices are partitioned into various fragments which help one to understand atoms and bonds within a molecule, long range coulombic forces short range overlap forces, van der Waals forces, and others. The density matrices have parts containing "atomic" densities and terms containing the interactions between these "atomic" densities. The density matrices are partitioned into four major fragments. The first fragment is promotion energy which causes a rearrangement inside of the separated atom due to these factors: 1) the value of the orbital parameter obtains the same value in the promoted atom state as in the molecule, 2) a hybridization of the atomic orbitals. The quasi-classical energy is the second major fragment. It arises from the electrostatic coulombic interactions between the atoms when they are moved from their separated positions to the internuclear distances being considered. The third major fragment is called the sharing penetration energy and arises from the sharing of electrons between the atoms in the molecule. Interference energy is the fourth major fragment and is the most important part of the partitioning. The interference energy is caused by an interference among the atomic orbitals which causes a rearrangement in the total density without changing its total population. This partitioning scheme has been applied to the helium-helium interaction for several different wavefunction approximations and at many different internuclear distances. The He-He interaction is an interesting system to study because although it does not have a strong attractive force as in a chemical bond, there is an attractive force between the two atoms due to the van der Waals forces. Another aspect that makes this an interesting interaction is the calculations with the lS-2S-2Pσ and 1S-1S' basis sets. The calculations using these basis sets were the most accurate calculations performed over a wide range of internuclear distances. until quite recently, and have a spurious minimum in the van der Waals region as has been shown by the new calculations. It is interesting to study the comparison of the results of the lS-2S-2Pσ and 1S-1S' basis sets and the results of the more accurate calculations by the use of the partitioning method. The application of the partitioning to the helium-helium interaction has given new insight into the theoretical treatment of the interaction and in the applicability of Ruedenberg's theory. This theory is useful in giving a good physical interpretation of the He-He interaction and also seems to be able to predict errors that may be occurring in the wavefunction approximations. The partitioning on this interaction has again shown that the kinetic interference energy is the term which determines if bonding or antibonding occurs and also shown the strong relationship between this and the sharing of e1ectrons