- #1

twist.1995

- 9

- 1

Hello, dear scientists and forum users.

I have recently finished programming the restricted closed-shell and unrestricted Hartree-Fock matrix equations. They seem to work fine for small diatomic molecules. However, I cannot understand the restricted open-shell theory that was firstly published by Roothaan. Particularly, in his equations, he separates the matrices according to "SPECIES" and calls them supervectors or supermatrices. Could someone explain how I can 1) multiply supermatrices by normal matrices, 2) Normalize the overlap matrix to the half of the number of open-shell or closed-shell electrons 3) Understand the difference between ROHF, RHF and UHF.

Also, I am wondering in if it is possible to compute the excited states and energies using HF method. Thanks.

See the figure below (extracted from Roothaan's paper, Ref: C. J. Roothaan. 1960. Self-Consistent Field Theory for Open Shells of Electronic Systems. Review of Modern Physics: 32, 2.)

I have recently finished programming the restricted closed-shell and unrestricted Hartree-Fock matrix equations. They seem to work fine for small diatomic molecules. However, I cannot understand the restricted open-shell theory that was firstly published by Roothaan. Particularly, in his equations, he separates the matrices according to "SPECIES" and calls them supervectors or supermatrices. Could someone explain how I can 1) multiply supermatrices by normal matrices, 2) Normalize the overlap matrix to the half of the number of open-shell or closed-shell electrons 3) Understand the difference between ROHF, RHF and UHF.

Also, I am wondering in if it is possible to compute the excited states and energies using HF method. Thanks.

See the figure below (extracted from Roothaan's paper, Ref: C. J. Roothaan. 1960. Self-Consistent Field Theory for Open Shells of Electronic Systems. Review of Modern Physics: 32, 2.)