pydmqmc.utils.sc1

pydmqmc.utils.sc1(ba, a, r, perms, sys)

Hamiltonian matrix element between singly excited states.

Parameters:

baarray_like

Bitarray for the state.

aint

Index of the occupied orbital to be vacated.

rint

Index of the unoccupied orbital 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, sc2

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 2) [1]:

\[<\Psi_{0}|H|\Psi_{a}^{r}> = <a|h|r> + \sum_{b} <ab|rb> - <ab|br>\]

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

References

[1]

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