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

Abstract

Anion resonances are formed as metastable intermediates in low-energy electron-induced reactions. Due to the finite lifetimes of resonances, applying standard Hermitian formalism for their characterization presents a vexing problem for computational chemists. Numerous modifications to conventional quantum chemical methods have enabled satisfactory characterization of resonances, but specific issues remain, especially in describing two-particle one-hole (2p–1h) resonances. An accurate description of these resonances and their coupling with single-particle resonances requires a multireference approach. We propose a projected complex absorbing potential (CAP) implementation within the multireference configuration interaction (MRCI) framework to characterize single-particle and 2p–1h resonances. As a first application, we use the projected-CAP-MRCI approach to characterize and benchmark the 2Πg shape resonance in N2 –. We test its performance as a function of the size of the subspace and other parameters, and we compute the complex potential energy surface of the 2Πg shape resonance to show that a smooth curve is obtained. One key benefit of MRCI is that it can describe Feshbach resonances (most common examples of 2p–1h resonances) at the same footing as shape resonances. Therefore, it is uniquely positioned to describe mixing between the different channels. To test these additional capabilities, we compute Feshbach resonances in H2O– and anions of dicyanoethylene isomers. We find that CAP-MRCI can efficiently capture the mixing between the Feshbach and shape resonances in dicyanoethylene isomers, which has significant consequences for their lifetimes.

Recent Advances in the Study of Negative‐Ion Resonances Using Multiconfigurational Propagator and a Complex Absorbing Potential

“…[259,260] Recently, Matsika and co-workers proposed a projected CAP in the framework of MRCI. [261] A comparative study on the performance of the CAP, stabilization and analytic continuation methods was performed by Davis and Sommerfeld. [262]…”

“…Experiment (estimated from experimental data) [63] 2.32 0.41 CAP/CODFT(LSD-XC)/[5s, 4p, 2d] [252] 3.39 0.506 CAP/EOM-CCSD/[5s, 7p, 3d] [222] 2.44 0.39 CAP/EOM-EA-CCSD/aug-cc-pVQZ + 3s3p3d(1st order) [217] 2.478 0.286 CAP/FSMRCC/TZ(7p2d) [246] 2.52 0.39 CAP/MRCI/aug-cc-pVTZ + 3s3p3d(C.M.) [261] 3.06 0.40 CAP/MR-CI/[5s, 3p] + [9p] + 2d [243] 2.97 0.65 CAP/SCF/[5s, 4p, 2d] [252] 3.28 0.395 CAP/static exchange/[5s, 10p, 13d] (1st order) [148] 3.776 1.199 Complex scaling/SCF/[5s, 3p] + 2d + [3p, 2d] + 4p6d [110] 3.19 0.44 Complex scaling/Second-order dilated EP/[4s, 9p] [114] 2.14 0.265 Complex scaling/Third-order biorthogonal dilated EP/[4s, 9p] [189] 2.11 0.18 Complex scaling/MRD-CI/[5s, 3p] + 1d þ 10p [209] 1.38 0.414 Complex scaling/M 1 /[4s, 9p] [176] 2.14 0.27 Complex scaling/M 1 /aug-cc-pVQZ(-f,g) + 3s8p [80] 2.136 0.320 Complex scaling/MCSTEP/aug-cc-pVQZ(-f,g) + 3s8p [80] 2.132 0.318 Many-body optical potential/[5s, 7p, 3d] [321] 2.534 0.536 Stabilization method/MRD-CI/[5s, 3p] + 3p2d þ 4s1p1d(C.M.) [113] 2.62 0.45 Stabilization method/MRCI/6-31G * þ 3p [58] 2.34 0.51 Stabilization method/MPPT(R)/[4s, 3p, 2d, 1f ] + 2s2p7d4g [160] 2.36 0.43 Stabilization method/TDDFT(HFE_PBE)/aug-cc-pVTZ + 3p [163] 3.078 0.54 Stieltjes imaging technique [322] 2.23 0.40 TCAP/MR-CI/[5s, 3p] + 7p3d2f [102] 2.42 0.45 the 1p g orbital may not be involved in the capture of the incident electron, but 2p g and 3p g orbitals may have a strong role in it.…”

“…Recently, CAP was combined with the electron propagator to study the electron attachment process of the metastable states within the framework of second and third order non‐Dyson ADC scheme by Trofimov and co‐workers [259,260] . Recently, Matsika and co‐workers proposed a projected CAP in the framework of MRCI [261] . A comparative study on the performance of the CAP, stabilization and analytic continuation methods was performed by Davis and Sommerfeld [262] …”

Irradiation of Plutonium Tributyl Phosphate Complexes by Ionizing Alpha Particles: A Computational Study

“…The application of complex boundary conditions was extended to the Schrödinger equation, , and then to the time-dependent Schrödinger equation applied on molecular systems to deal with diffuse reactions such as collisions between atoms. , In this context, CAP have been introduced as an alternative to mask functions . By adding a complex component to the system’s Hamiltonian, the electron density is gradually absorbed beyond a threshold distance. ,,− CAPs have been shown to be very effective when coupled with various electronic structures methods such as multiconfigurational methods, − coupled-cluster methods, − Lanczos-based approach, and Electron Attachment Algebraic-Diagrammatic Construction (EA-ADC) method in the study of metastable resonance states for anionic molecular systems. Its applications are extended in the generation of high harmonic generation (HHG) spectra with RT-TD-DFT, other Time-Dependent methods (TD-CIS, TD-SE, TD-CI), − or in non-Hermitian exceptional point (EPs) degeneracies .…”

Distant Symmetry Control in Electron-Induced Bond Cleavage

“…Some standard approaches from quantum chemistry upon their modification can be used to describe electronic resonances; − however, each has inherent limitations. Resonant and virtual states naturally appear in scattering methods which are able to describe wave functions extending over all space.…”