Resonance Energies and Lifetimes from the Analytic Continuation of the Coupling Constant Method: Robust Algorithms and a Critical Analysis

Abstract

The energy of a metastable state can be computed by adding an artificial stabilizing potential to the Hamiltonian, increasing the stabilization until the metastable state is turned into a bound one, and then further increasing the stabilization until enough bound-state data have been collected so that these can be extrapolated back to vanishing stabilization. The lifetime of the metastable state can be obtained from the same data, but only if the extrapolation is performed by analytic continuation. This extrapolation method is called analytic continuation of the coupling constant (ACCC). Here we introduce preconditioning schemes for two of the three established extrapolation algorithms and critically compare results from all three extrapolation schemes in a variety of situations: As examples for resonance states serve the π* temporary anions of ethylene and formaldehyde as well as a model potential, which provides a case where input data with full numeric precision are available. In the data collection step, three different stabilizing potentials are employed, a Coulomb potential, a short-range Coulomb potential, and a soft-box Voronoi potential. Effects of different orders of the extrapolating Padé approximant are investigated, and last, the energy range of input data for the extrapolation is studied. Moreover, all ACCC results are compared to resonance parameters that have been independently obtained with the same theoretical method, but with a different continuum approach-complex scaling for the model and complex absorbing potentials for the temporary anions.

Temporary Anion States of Ethene Interacting with Single Molecules of Methane, Ethane, and Water

“…The computed fixed-nuclei resonance position for isolated ethene is about 0.2 eV too high in comparison with that in experiment; however, that is expected for the most part owing to vibrational effects . Both position and width agree favorably with earlier theoretical work. − Small differences are due to different geometries, different basis sets, different electronic structure methods, and different methods to address the continuum nature of the wave function.…”

“…If an excess electron is added into an unoccupied π* orbital of a typical organic molecule, the resulting anion states are, as a rule, not bound, but rather so-called temporary anions with finite lifetimes. For examples, the temporary anion created by adding an electron into the π* orbital of ethene shows a lifetime of 1–2 fs. − Exceptions are the lowest π* orbitals of molecules with strongly electron-withdrawing groups. For example, for 1,4-benzoquinone, the lowest π* anion is bound, while the higher π* anion states are temporary in nature.…”

Computing resonance energies directly: method comparison for a model potential

“…Nonetheless, in practical electronic structure calculations, scaling the nuclear charges has turned out to work well [18,40,41,44,45] presumably because representation of the Coulomb potential in the compact Gaussian basis sets suppresses the long-range part of the interaction. In fact, in a Gaussian basis set, attractive Coulomb potentials and explicitly attenuated Coulomb potentials behave effectively identically [46,47].…”

Combination of a Voronoi-Type Complex Absorbing Potential with the XMS-CASPT2 Method and Pilot Applications

“…In this paper, the focus is on the complex absorbing potential (CAP) method, , which is a standard L 2 -method. Other examples for L 2 -methods include the complex scaling method, stabilization method, and analytical continuation of the coupling constant (ACCC) method. − In all L 2 -methods, the resonance parameters, E r and Γ, are found by analyzing the eigenvalues of a parametrized Hamiltonian. Thus, a “single-point calculation” of a single E r and Γ pair involves the computation of several eigenvalues for several values of the parameter, and in general, multistate electronic structure methods are needed, such as configuration interaction-type methods, Green’s function approaches, or equation-of-motion type approaches.…”