Electron–Atom and Electron–Molecule Resonances: Some Theoretical Approaches Using Complex Scaled Multiconfigurational Methods

An Electron Propagator Approach Based on a Multiconfigurational Reference State for the Investigation of Negative-Ion Resonances Using a Complex Absorbing Potential Method

“…The SDs are obtained by distributing a subset of electrons (“active electrons”) in a few chemically relevant CCBON spin orbitals (“active orbitals”). The CCBON property may be expressed in terms of the spin orbitals {ϕ p , ϕ q , ...} as where x indicates all coordinates (spin and spatial) of an electron. − Here and in what follows, the Dirac’s bra and ket notations are to be understood in terms of the complex symmetric scalar product (“c-product”). , When all possible SDs, consistent with the spatial and spin symmetry of the system, are generated by distributing the active electrons in the active orbitals, the SD space is referred to as the complete active space (CAS). The MCSCF with a CAS is termed as CASSCF.…”

“…The energy of a resonance is given by The corresponding Hamiltonian is not Hermitian, but complex symmetric. Due to this symmetry, the left and the right eigenvectors of the Hamiltonian may be chosen to be the same . Thus, the lack of Hermiticity does not pose too great a challenge in adopting the standard bound-state computer codes.…”

“…Thus, the lack of Hermiticity does not pose too great a challenge in adopting the standard bound-state computer codes. Current methods of analytical continuation make use of a complex conjugate biorthonormal (CCBON) basis − for the Hamiltonian and redefine the relevant quantum mechanical inner products in terms of the so-called “c-product” …”

“…The resonances appear as new complex eigenvalues of the complex-scaled Hamiltonian, which are stable with respect to the scaling parameter beyond a critical value of the parameter. The CSM is straightforward in the case of atomic systems because it entails scaling of only one- and two-electron integrals by a complex factor (for example, see refs , , − ). This requires trivial modifications of the existing quantum chemistry codes for atoms.…”

“…The electron propagator (EP) is a reliable tool to determine the electron attachment and detachment energies for a bound-state with high numerical accuracy. − In other words, the EP provides a computationally efficient route to find the energy of an ( N ± 1)-electron state if the N -electron wavefunction is known. This prompted researchers to develop EP-based tools to investigate resonances. ,,,,,,,,,, In this article, we report on the development of an EP-based approach where the reference state (target state) of the EP is a variationally optimized multiconfigurational self-consistent field (MCSCF) − wavefunction. The wavefunction is obtained from an in-house quadratically convergent MCSCF code adapted for a Hamiltonian perturbed by a CAP.…”