In quantum chemistry, the Dyall Hamiltonian is a modified Hamiltonian with two-electron nature. It can be written as follows:[1]





where labels
,
,
denote core, active and virtual orbitals (see Complete active space) respectively,
and
are the orbital energies of the involved orbitals, and
operators are the spin-traced operators
. These operators commute with
and
, therefore the application of these operators on a spin-pure function produces again a spin-pure function.
The Dyall Hamiltonian behaves like the true Hamiltonian inside the CAS space, having the same eigenvalues and eigenvectors of the true Hamiltonian projected onto the CAS space.
References
- ↑ Dyall, Kenneth G. (March 22, 1995). "The choice of a zeroth‐order Hamiltonian for second‐order perturbation theory with a complete active space self‐consistent‐field reference function". The Journal of Chemical Physics. 102 (12): 4909–4918. Bibcode:1995JChPh.102.4909D. doi:10.1063/1.469539.