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Dyall Hamiltonian

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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.

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