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

Abstract

Negative-ion resonances are important metastable states that result from the collision between an electron and a neutral target. The course of many chemical processes in nature is often dictated by how an intermediate resonance state falls apart. This article reports on the development of an electron propagator (EP) based on a Hamiltonian H ̂perturbed by a complex absorbing potential (CAP) and a multiconfigurational self-consistent field (MCSCF) initial state to study these resonances. Perturbation of H ̂by a CAP makes the resonances amenable to a bound-state method like MCSCF. Resonances stand out among the non-resonant states as persistent complex eigenvalues of the perturbed H ̂when the strength (η) of the CAP is varied. The MCSCF method gives a reliable and accurate description of the target states, especially when the non-dynamical correlations are dominant. The resonance energies are obtained from the poles of the EP. We propose three variants of our EP depending on how the effect of the CAP is introduced. We find that the computationally most efficient variant is the one in which the reference state of the EP is an unperturbed MCSCF wavefunction and a non-zero CAP is defined only on the virtual orbital subspace of the reference state. The onset of the CAP is carefully optimized in order to minimize the artifacts due to reflections from the CAP. An extrapolation method (based on a Padéapproximant) and a deperturbation method are adopted in order to account for the limitations of finite basis sets used and determine the resonance energy in the limit of η → 0. 2 P Be − , 2 Π g N 2 − , and 2 Π CO − shape resonances are investigated. The position and width of these resonances computed in this study agree well with those reported earlier in the literature.

Negative Ion Resonance States: The Fock-Space Coupled-Cluster Way

“…Most notable attempts were done using smooth CAPS and subsequent Padeá pproximants. 156,157 In this work under review, the results discussed involve box-shaped CAP in the context of FS-MRCC.…”

“…One may also note that the box-type CAP and Voronoi CAP are artificial potentials, which may introduce unphysical perturbation due to their poor finite Gaussian basis sets representations or due to the artificial reflection of outgoing electron density from the edges of the CAP potential. , There have been many attempts to minimize this nonphysical artificial perturbation. Most notable attempts were done using smooth CAPS and subsequent Padé approximants. , In this work under review, the results discussed involve box-shaped CAP in the context of FS-MRCC.…”

Projected Complex Absorbing Potential Multireference Configuration Interaction Approach for Shape and Feshbach Resonances

“…51 There have been some recent implementations of CAP with multireference methods, focusing mostly on multiconfigurational perturbation theory or MCSCF. [50][51][52]59 An earlier implementation combined CAP with MRCI and examined the applicability of the projection scheme. 48,61 That work however did not integrate CAP with a generally available MRCI code, restricting its applicability.…”

“…A small change of 0.01 eV in the position and width is seen at the lowest tolerance setting, which is once again quite minimal. It is worth noting that the energy position and width reported at the lowest tolerance 90 2.53 0.54 CAP-MRCISD 49 2.97 0.65 CAP-FSMRCC 43 2.52 0.39 CAP-EOM-EA-CCSD 42 2.57 0.25 OSM-EOM-EA-CCSD 60 2.52 0.49 CAP-EP-MCSCF 52 3.12 0.31 This further cements the fact that in CAP only the resonance state needs to be accurately represented, unlike the stabilization method, where the final position is strongly dependent on the energy convergence of the pseudocontinuum states. Also, by smartly adjusting the convergence threshold of pseudocontinuum states, one can easily perform the calculation for a higher subspace size and have it converge faster.…”

“…The success of CAP based methods can be attributed to the ease of integration with any available electronic structure method. Methods augmented with CAP include coupled cluster (EOM-CC and FSMRCC), algebraic diagrammatic construction (ADC) schemes, symmetry adapted cluster/configuration interaction (SAC-CI), multireference configuration interaction (MRCI), multireference perturbation theory (XMCQDPT2, XMS-CASPT2), electronic propagator (EP), and density functional theory (DFT). − Several properties such as complex Dyson orbitals and natural transition orbitals, as well as analytic gradients, and algorithms for locating crossing points have also been developed within CAP. − Recent implementation of analytic gradients within the CAP-EOM-CC formalism has enabled computation of optimized structures and exceptional points. − Optimized structures and adiabatic electron affinities have been computed for several polyatomic systems such as formaldehyde, formic acid, and ethylene anions using the CAP-EOM-CC formalism . Recently, CAP-EOM-CC has also been employed to compute minimum energy exceptional points on crossings between resonances and minimum energy crossing points between neutral and anionic surfaces. , The routine application of a variety of CAP augmented methods to compute resonances serves as a testament to their success compared to other non-Hermitian or even Hermitian methods.…”