A method for accurate electron-atom resonances: The complex-scaled multiconfigurational spin-tensor electron propagator method for the $^2P\, \mbox{Be}^{-}$ shape resonance problem

TL;DR

This paper introduces the CMCSTEP method, combining complex scaling with multiconfigurational spin-tensor electron propagator techniques, to accurately determine electron-atom resonance parameters, demonstrated on the Be- shape resonance.

Contribution

The paper develops and applies the novel CMCSTEP method for the first time to resonance problems, enhancing accuracy in calculating resonance parameters for open-shell, highly correlated systems.

Findings

Resonance parameters for Be- shape resonance closely match previous results.

CMCSTEP achieves high accuracy, within ±0.2 eV of experimental and FCI data.

The method is expected to be reliable for other complex resonance problems.

Abstract

We propose and develop the complex scaled multiconfigurational spin-tensor electron propagator (CMCSTEP) technique for theoretical determination of resonance parameters with electron-atom/molecule systems including open-shell and highly correlated atoms and molecules. The multiconfigurational spin-tensor electron propagator method (MCSTEP) developed and implemented by Yeager his coworkers in real space gives very accurate and reliable ionization potentials and attachment energies. The CMCSTEP method uses a complex scaled multiconfigurational self-consistent field (CMCSCF) state as an initial state along with a dilated Hamiltonian where all of the electronic coordinates are scaled by a complex factor. CMCSCF was developed and applied successfully to resonance problems earlier. We apply the CMCSTEP method to get $^2 P\,\mbox{Be}^{-}$ shape resonance parameters using $14s11p5d$, $14s14p2d$, and $14s14p5d$ basis sets with a $2s2p3d$\,CAS. The obtained value of the resonance parameters are compared to previous results. This is the first time CMCSTEP has been developed and used for a resonance problem. It will be among the most accurate and reliable techniques. Vertical ionization potentials and attachment energies in real space are typically within $\pm 0.2\,eV$ or better of excellent experiments and full configuration interaction calculations with a good basis set. We expect the same sort of agreement in complex space.