Using the charge-stabilization technique in the double ionization potential equation-of-motion calculations with dianion references

Abstract

The charge-stabilization method is applied to double ionization potential equation-of-motion (EOM-DIP) calculations to stabilize unstable dianion reference functions. The auto-ionizing character of the dianionic reference states spoils the numeric performance of EOM-DIP limiting applications of this method. We demonstrate that reliable excitation energies can be computed by EOM-DIP using a stabilized resonance wave function instead of the lowest energy solution corresponding to the neutral + free electron(s) state of the system. The details of charge-stabilization procedure are discussed and illustrated by examples. The choice of optimal stabilizing Coulomb potential, which is strong enough to stabilize the dianion reference, yet, minimally perturbs the target states of the neutral, is the crux of the approach. Two algorithms of choosing optimal parameters of the stabilization potential are presented. One is based on the orbital energies, and another--on the basis set dependence of the total Hartree-Fock energy of the reference. Our benchmark calculations of the singlet-triplet energy gaps in several diradicals show a remarkable improvement of the EOM-DIP accuracy in problematic cases. Overall, the excitation energies in diradicals computed using the stabilized EOM-DIP are within 0.2 eV from the reference EOM spin-flip values.

Q‐Chem: an engine for innovation

“…Different EOM models are defined by choosing the reference and the form of \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$\hat{R}$\end{document} (Figure 4). Q‐Chem features the following EOM models:40 EOM‐EE (excitation energies), EOM‐IP (ionization potentials), EOM‐EA (electron affinities), EOM‐SF (spin‐flip, for triplet and quartet references44), EOM‐2SF (double SF, for quintet references45), and EOM‐DIP (double IP46). Analytic gradients and properties are available for most of the EOM models, including such important functionality as the ability to compute transition properties between different EOM states and the calculation of Dyson orbitals 47.…”

Advances in molecular quantum chemistry contained in the Q-Chem 4 program package

“…The equationof-motion (EOM) approach extends single-reference CC methods to various multi-configurational wave functions. Q-CHEM 4 includes EOM-CC methods for electronically excited states (EOM-EE), ionised/electron-attached ones (EOM-IP/EA), as well as doubly ionised (EOM-DIP) [178] and spin-flip (EOM-SF and EOM-2SF) [179,180] extensions that enable robust and reliable treatment of bondbreaking, diradicals/triradicals, and other selected multiconfigurational wave functions. Gradient and properties calculations (including interstate properties) are available for most CC/EOM-CC methods.…”

EOM-CC guide to Fock-space travel: the C2 edition

“…This is similar to metastable radical monoanions where the extra electron is trapped behind an angularmomentum barrier also affording resonance character. In a computational treatment using a sufficiently large basis, the wave function of a resonance becomes more and more diffuse, approximating a continuum state corresponding to an electron-detached system and a free electron [70][71][72] .…”

“…The easiest and most commonly used one is to use a relatively small basis set, such that the reference state is artificially stabilized 50,60,61,64-66,76 . Kuś and Krylov have investigated an alternative strategy, stabilization of the resonance using an artificial Coulomb potential with a subsequent de-perturbative correction 71,72 . Here we show that in the case of C 2 using the aug-cc-pVTZ basis provides a robust description of the dianionic reference, delivering accurate results for the target states.…”