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





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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.