Computational Chemistry 4.27 - Self-Consistent Field
Short lecture on the self-consistent field procedure in Hartree-Fock theory.
The self-consistent field procedure produces solutions to the Hartree-Fock-Roothaan equations for the best possible approximate molecular orbitals for a molecule within the Born-Oppenhiemer approximation and Hartree-Fock approximation for a particular choice of atomic orbital basis set and nuclear coordinate configuration. The high-level algorithmic steps for this procedure are as follows:
1) Specify nuclear charges and positions, number of electrons, and choice of basis set.
2) Calculate all overlap, kinetic energy, nuclear attraction, and two-electron integrals.
3) Diagonalize S and obtain the orthogonalization matrix X.
4) Obtain an initial guess density matrix (P).
5) Calculate the two-electron potential matrix G.
6) Calculate the Fock matrix as the sum of the core Hamiltonian and G matrices.
7) Transform the Fock matrix with the X matrix.
8) Diagonalize the Fock matrix to obtain the coefficient matrix (C) and orbital energy matrix (E).
9) Un-transform the C matrix with the X matrix.
10) Obtain the next density matrix from the last C matrix.
11) Determine if the density matrix is converged. If not, go back to step 5.
12) Use the final C matrix to calculate all desired molecular properties.
Notes Slide: https://i.imgur.com/zv22Qm6.png
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