pydmqmc.utils.sc2

pydmqmc.utils.sc2(a, b, r, s, perms, sys)

Hamiltonian matrix element between doubly excited states.

Parameters:

a, bint

Indices of the occupied orbitals to be vacated.

r, sint

Indices of the unoccupied orbitals to be filled.

permsint

Number of permutations associated with the excitation.

sysIntegral

System object with integral information.

Returns:

float

Hamiltonian matrix element.

See also

sc0, sc1

Other Slater-Condon rules.

pydmqmc.systems.Integral.generate_hamiltonian

Uses this function to generate the Hamiltonian matrix.

Notes

Math from Szabo and Ostlund (Table 2.5, Case 3) [1]:

\[<\Psi_{0}|H|\Psi_{ab}^{rs}> = <ab|rs> - <ab|sr>\]

where \(a\) and \(b\) are occupied orbitals and \(r\) and \(s\) are unoccpied orbitals. Note that this equation is written in physicists’ notation.

The bitarray is not needed as input since the orbitals involved are fully specified by the indices.

References

[1]

Attila Szabo and Neil S. Ostlund, “Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory,” Dover Books on Chemistry, 1996