Energies, Polarizabilities, and Forces of Interacting Molecules at Long or Intermediate Range
Abstract
Collisioninduced molecular phenomena are widely researched subjects. In complement with other research, deriving new results to understand the nature and effects of the interaction between molecules at long or intermediate range is the main goal of this thesis. By applying RayleighSchrodinger perturbation theory, we have obtained the molecular interaction energy to second order in terms of nonlocal polarizability densities. The derivation also includes the effects of an applied field. The nonlocal polarizability density alpha (r; r^', omega) plays a central role in this research. The polarizability density is a linearresponse tensor that determines the electronic polarization induced at point r in a molecule, by an external electric field of frequency omega, acting at r^ '. When a nuclear position in the molecule shifts infinitesimally, we find that the change in alpha(r; r^', omega) is connected to the same hyperpolarizability beta_{alphabetagamma }(r; r^', omega, r^{' '}, 0) that describes the electronic charge distribution's response to external fields, i.e.: partialalpha_{ betagamma}(omega)/partial R ^{I}_alpha=int dr dr^' dr^ {''} beta _{betagammadelta}(r; r^', omega, r^{''}, 0) Z^{rm I} T_{deltaalpha}(r ^{''}, R^{rm I}). This is a generalization of the relationship between partialalpha_{beta gamma}(0)/partial R^{I} _alpha and beta_ {betagammadelta}(r; r^', r^ {''}).. Due to establishment of the relationships between partialalpha_{ betagamma}/partial R^{I }_alpha and beta _{betagammadelta}, we have obtained new analytical results for the forces acting on nuclei in a molecule. For the first time, we have proven the equivalence of forces from interaction energy calculations and those obtained via the Hellmann Feynman theorem, order by order. We are also able to separate forces on nuclei in one of the interacting molecules (A) into those due to its "own" electrons vs. forces due to the charge distribution of the collision partner, B. By taking the long range limit of the new analytical results for forces acting on nuclei in a molecule, we express the electrical shielding effects in interacting molecules through nonlocal polarizability and hyperpolarizability densities. Intermolecular fields are screened via the same tensors that describe shielding of external fields. An explicit expression for the momentum distribution of a particle in a onedimensional box is also included in this thesis. It is a result from my work as a teaching assistant for the graduate course in quantum chemistry for several terms. The result corrects misconceptions about the momentum distribution in several quantum chemistry textbooks.
 Publication:

Ph.D. Thesis
 Pub Date:
 1992
 Bibcode:
 1992PhDT.......262L
 Keywords:

 LONG RANGE LIMIT;
 SHIELDING TENSOR;
 Chemistry: Physical; Physics: Molecular; Physics: Atomic