Comparison of the errors observed in computing the volume of 2 Slater functions as a function of separation using various recurence levels of Becke's fuzzy voronoi switching function.

Quadrature.pdf (version 02/10/2008) (13 pages)
This document introduces members of the lab to numerical quadrature and the related software within our group library. A greater emphasis is placed on understanding the concepts required for its practical application than providing a generic overview. The discussion of one-dimensional integration primarly focuses on Gauss-Laguerre quadrature and its usage in computing the integral of a three-dimensional spherical function. This particular example is chosen due to the natural transition to angular quadrature and extension to the integration of arbitrary three-dimensional functions; however, the concepts discussed with the Gauss-Laguerre example are easily applied to Gauss-Hermite quadrature, for example, and its application to anharmonic oscillator problems. Multicenter molecular quadrature is discussed with emphasis on understanding the conceptual problem of double counting integrands and the associated requirement of spatial partition functions. This document has not been completed, and I don't see myself trying to complete it in the near future.

The error of a three dimensional Taylor series expansion (centered about x=10) in representating the electrostatic potential of a point charge located at the origin. The Taylor expansion uses all harmonics up to order L=8.

Electrostatics.pdf (version 02/10/2008) (15 pages)
This document demonstrates that the Laplace expansion of the Coulomb operator is equivalent to a three-dimensional Taylor series expansion. In doing so, the addition theorems of the regular and irregular solid harmonics are derived. These properties are then used to develop expressions for the Coulomb interaction between charges densities described by point multipoles and Gaussian multipoles. Linear-scaling evaluation of the Coulomb energy via the fast multipole method is discussed. This document is fairly complete and likely won't contain major additions.

(Partial) Explanation of the ROHF formalism.

DFT.pdf (version 04/10/2008) (26 pages)
This document is under active development and lacks an abstract.

1. Introduction
2. Hartree-Fock theory
   1. The electronic problem
   2. The Roothaan-Hall equations
   3. Integration of the spin-coordinates
   4. The generalized eigenvalue problem
   5. The RHF/UHF SCF procedure
   6. Convergence criteria and acceleration
   7. High-spin restricted open-shell Hartree-Fock
3. Density functional theory
   1. The Hohenberg-Kohn theorems
   2. The uniform electron gas
   3. The Kohn-Sham method
   4. Spin-polarized density functionals
      1. Slater-Dirac and Xalpha exchange functionals
      2. VWN correlation functional
      3. PW92 correlation functional
      4. PBE exchange functional
      5. PBE correlation functional
      6. OPTX exchange functional
      7. LYP correlation functional
      8. HCTH/n exchange and correlation functionals

HSERILib.pdf (version 03/11/2008) (12 pages)
This manuscript is a modified version of the documentation I had written for a library which computed the electron repulsion integrals based on the work of Hamilton and Schaefer. No attempt is made herein at deriving the recurrence relationships, but if the reader is familiar with several important papers on the subject, then the notation and description of the algorithm will be reasonably clear. It is not the intent of this document to be a authoritative introduction to Gaussian integral evaluation; however, the explanations in notation, and particularly the appendices, will compliment the literature.