Algebraic modifications to second quantization for non-Hermitian complex scaled hamiltonians with application to a quadratically convergent multiconfigurational self-consistent field method

Abstract

The algebraic structure for creation and annihilation operators defined on orthogonal orbitals is generalized to permit easy development of bound-state techniques involving the use of non-Hermitian Hamiltonians arising from the use of complex-scaling or complex-absorbing potentials in the treatment of electron scattering resonances. These extensions are made possible by an orthogonal transformation of complex biorthogonal orbitals and states as opposed to the customary unitary transformation of real orthogonal orbitals and states and preserve all other formal and numerical simplicities of existing bound-state methods. The ease of application is demonstrated by deriving the modified equations for implementation of a quadratically convergent multiconfigurational self-consistent field (MCSCF) method for complex-scaled Hamiltonians but the generalizations are equally applicable for the extension of other techniques such as single and multireference coupled cluster (CC) and many-body perturbation theory (MBPT) methods for their use in the treatment of resonances. This extends the domain of applicability of MCSCF, CC, MBPT, and methods based on MCSCF states to an accurate treatment of resonances while still using L² real basis sets. Modification of all other bound-state methods and codes should be similarly straightforward.