AuthorKozlowski, Pawel Michal.
Committee ChairAdamowicz, Ludwik
MetadataShow full item record
PublisherThe University of Arizona.
RightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
AbstractGeneral formalism for the application of explicitly correlated Gaussian-type basis functions for nonadiabatic calculations on many-body systems is presented. In this approach the motions of all particles (electrons and nuclei) are correlated at the same time. The energy associated with the external degrees of freedom, i.e., the motion of the center-of-mass, is eliminated in an effective way from the total energy of the system. Methodology for construction of the many-body nonadiabatic wave function and algorithms for evaluation of the multicenter and multiparticle integrals involving explicity correlated Gaussian cluster functions are derived and computationally implemented. Then analytical derivation of multi-center and multi-particle integrals for explicitly correlated Cartesian Gaussian-type cluster functions is demonstrated. The evaluation method is based on application of raising operators which transform spherical cluster Gaussian functions into Cartesian Gaussian functions. Next, the Newton-Raphson procedure for optimization of the non-linear parameters (Gaussian exponents) appearing in the Gaussian-type cluster functions is developed. The procedure employs the first and second analytical derivatives of the variational functional with respect to the Gaussian exponents. The computational implementation of Newton-Raphson optimization procedure is described and some numerical calculations are presented. Finally, the methodology for generating higher nonadiabatic rotational states is presented.