Dyall Hamiltonian

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,

are the orbital energies of the involved orbitals, and

These operators commute with

, 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.

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