New methods for ab initio quantum mechanical calculations in molecular and crystalline systems

• Main Author: Langlois, Jean-Marc
• Format: Others
• Language: en
• Published: 1994
• Online Access: https://thesis.library.caltech.edu/4780/1/Langlois_jm_1994.pdf; Langlois, Jean-Marc (1994) New methods for ab initio quantum mechanical calculations in molecular and crystalline systems. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/j75s-5f43. https://resolver.caltech.edu/CaltechETD:etd-12042007-081615 <https://resolver.caltech.edu/CaltechETD:etd-12042007-081615>

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. This thesis deals with the development of new methods for doing ab initio quantum mechanical calculations of electronic wavefunctions of large molecules and crystalline systems with the emphasis on inclusion of electronic correlation or many body effects using generalized valence-bond (GVB) wavefunctions. Chapters 1 and 2 describe two necessary steps for using the generalized valence-bond (GVB) formalism in large molecular systems. In Chapter 1 a fast method for generating GVB trial wavefunctions is described. The method is based on piecewise atomic and diatomic localization and makes possible calculations with large numbers of GVB pairs. The efficacy of the method is illustrated by application to several cases including GVB wavefunctions with up to 26 pairs. In Chapter 2 the pseudospectral (PS) method for self-consistent-field calculations is applied to the GVB formalism. In the GVB perfect pairing approximation, the PS method is shown to reduce the scaling cost of the calculation from [...] to [...], where N is the number of basis functions. This makes possible the calculation of GVB wavefunctions for large molecular systems. Chapter 3 describes a density-functional method for calculations on crystalline systems using Gaussian type orbitals. Accurate and efficient strategies were developed for computing both the Hamiltonian matrix elements and the Coulomb field. The Hamiltonian matrix elements are computed by decomposing the multicenter numerical integrations into single-center integrations via a projection technique and the Coulomb field is evaluated analytically using a dual-space approach based on the Ewald method. The self-consistent field is obtained by a fast conjugate gradient method which uses both first and second derivative information and an efficient preconditioning strategy. Illustrative calculations are performed on two allotropes of carbon: diamond and [...] crystals.