Note

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CIS

Restricts the active space to single-electron excitations for configuration interaction calculations (i.e. Configuration Interaction Singles).

The CIS active space is not useful for improving the Hartree-Fock approximation of ground-state properties such as total energies, forces, vibrational frequencies, and relaxed geometries. This phenomenon is explained by Koopmans’ Theorem [10], which shows that the many-electron Hamiltonian does not couple the Hartree-Fock ground state to singly-excited configurations. An active space must include configurations with at least two-electron excitations to improve ground-state properties (e.g. CISD).

Number of configurations for \(n\) doubly-occupied orbitals and \(m\) empty orbitals

excitation type

# of configs

none (RHF ground state)

\(1\)

1 \(\alpha\) electron

\(m n\)

1 \(\beta\) electron

\(m n\)