Basic Roothaan-Hall Equations

Secular Equation

ci|F-εiS|ci = 0

ci: eigenvector; F: Fock matrix; ε>i: eigenvalue; S: overlap matrix. The total electronic energy of the system is given by:

E = 1/2P(H+F),

in which P: density matrix; H: one-electron matrix. The general Fock Matrix element is

Fμνα = Hμν +ΣλΣσ[Pμνα+β <μν|λσ> - Pμνα <μλ|νσ>].

Or, spin-free

Fμν = Hμν +ΣλΣσ[Pμν <μν|λσ> - ½Pμν <μλ|νσ>].

The methods all use a minimum basis set consisting of a maximum of one atomic orbital for each angular quantum number. The normal basis set for any atom consists of one s and three p orbitals (px, py and pz).