Restricted Closed Shell Hartree Fock Roothaan Matrix Method Applied to Helium Atom using Mathematica
Abstract
Slater type orbitals were used to construct the overlap and the Hamiltonian core matrices; we also found the values of the bi-electron repulsion integrals. The Hartree Fock Roothaan approximation process starts with setting an initial guess value for the elements of the density matrix; with these matrices we constructed the initial Fock matrix. The Mathematica software was used to program the matrix diagonalization process from the overlap and Hamiltonian core matrices and to make the recursion loop of the density matrix. Finally we obtained a value for the ground state energy of helium.
References
Brenner, S. C., & Scott, R. (2008). The mathematical theory of finite element methods (Vol. 15). Springer.
Bukowski, R., Sadlej, J., Jeziorski, B., Jankowski, P., Szalewicz, K., Kucharski, S. A., ... & Rice, B. M. (1999). Intermolecular potential of carbon dioxide dimer from symmetry-adapted perturbation theory. The Journal of chemical physics, 110(8), 3785-3803.
Carey, G. F., & Oden, J. T. (1981). Finite elements. 1. An introduction. Prentice-Hall.
Hartree, D. R. (1957). The calculation of atomic structures (pp. 25-25). New York: J. Wiley.
Levine, I. N. (2000). Quantum chemistry (Vol. 5). Upper Saddle River, NJ: Prentice Hall.
Reddy, J. N. (2004). Nonlinear finite element analysis. Oxford University Press, New York.
Szabo, A. (1996). Modern Quantum Chemistry: Introduction To Advanced Electronic Structure Theory Author: Attila Szabo, Neil S. Ostlund, Publ.
Thomée, V. (1990). Finite difference methods for linear parabolic equations. Handbook of numerical analysis., 1, 5.
This work is licensed under a Creative Commons Attribution 4.0 International License.
The copyright for all articles belongs to the authors. All other copyright is held by the journal.