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

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  1. ^ 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.