Analytical continuation in coupling constant method; application to the calculation of resonance energies and widths for organic molecules: Glycine, alanine and valine and dimer of formic acid

The energy of a temporary anion can be computed by adding a stabilizing potential to the molecular Hamiltonian, increasing the stabilization until the temporary state is turned into a bound state, and then further increasing the stabilization until enough bound state energies have been collected so that these can be extrapolated back to vanishing stabilization. The lifetime can be obtained from the same data, but only if the extrapolation is done through analytic continuation of the momentum as a function of the square root of a shifted stabilizing parameter. This method is known as analytic continuation of the coupling constant, and it requires--at least in principle--that the bound-state input data are computed with a short-range stabilizing potential. In the context of molecules and ab initio packages, long-range Coulomb stabilizing potentials are, however, far more convenient and have been used in the past with some success, although the error introduced by the long-rang nature of the stabilizing potential remains unknown. Here, we introduce a soft-Voronoi box potential that can serve as a short-range stabilizing potential. The difference between a Coulomb and the new stabilization is analyzed in detail for a one-dimensional model system as well as for the (2)Πu resonance of CO2(-), and in both cases, the extrapolation results are compared to independently computed resonance parameters, from complex scaling for the model, and from complex absorbing potential calculations for CO2(-). It is important to emphasize that for both the model and for CO2(-), all three sets of results have, respectively, been obtained with the same electronic structure method and basis set so that the theoretical description of the continuum can be directly compared. The new soft-Voronoi-box-based extrapolation is then used to study the influence of the size of diffuse and the valence basis sets on the computed resonance parameters.

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Short-range stabilizing potential for computing energies and lifetimes of temporary anions with extrapolation methods

Sommerfeld

Ehara

2015

“…Recently, these two methods have been combined and applied to molecular shape resonances. 25,[27][28][29][30] In most of these studies, a Coulomb potential is used to bind the resonance as in the method of scaled nuclear charges. The exception is the manifestly short-range Voronoi potential suggested by Sommerfeld et al 28 Sommerfeld and coworkers noted that the long-range Coulomb potential is not formally applicable and obtained much more consistent results with their Voronoi potential.…”

Section: Introductionmentioning

confidence: 99%

Stabilizing potentials in bound state analytic continuation methods for electronic resonances in polyatomic molecules

White

Head‐Gordon

McCurdy

2017

The computation of Siegert energies by analytic continuation of bound state energies has recently been applied to shape resonances in polyatomic molecules by several authors. We critically evaluate a recently proposed analytic continuation method based on low order (type III) Padé approximants as well as an analytic continuation method based on high order (type II) Padé approximants. We compare three classes of stabilizing potentials: Coulomb potentials, Gaussian potentials, and attenuated Coulomb potentials. These methods are applied to a model potential where the correct answer is known exactly and to the 2 Π g shape resonance of N − 2 which has been studied extensively by other methods. Both the choice of stabilizing potential and method of analytic continuation prove to be important to the accuracy of the results. We conclude that an attenuated Coulomb potential is the most effective of the three for bound state analytic continuation methods. With the proper potential, such methods show promise for algorithmic determination of the positions and widths of molecular shape resonances.

“…Recently, a method originally proposed in the field of nuclear physics-the method of analytical continuation in coupling constant (ACCC) 2,4,5 -has been applied with considerable success to molecular anions: nitrogen 6 N 2 , valine, glycine, adenine, formic acid, dimer of formic acid, 7 ethylene, 8 and carbon dioxide 9 CO 2 . The ACCC method is based on the introduction of a perturbation potential which transforms resonance states into bound states.…”

Section: Introductionmentioning

confidence: 99%

On a simple way to calculate electronic resonances for polyatomic molecules

Horáček

Paidarová

Čurík

2015

Self Cite

We propose a simple method for calculation of low-lying shape electronic resonances of polyatomic molecules. The method introduces a perturbation potential and requires only routine bound-state type calculations in the real domain of energies. Such a calculation is accessible by most of the free or commercial quantum chemistry software. The presented method is based on the analytical continuation in a coupling constant model, but unlike its previous variants, we experience a very stable and robust behavior for higher-order extrapolation functions. Moreover, the present approach is independent of the correlation treatment used in quantum many-electron computations and therefore we are able to apply Coupled Clusters (CCSD-T) level of the correlation model. We demonstrate these properties on determination of the resonance position and width of the (2)Πu temporary negative ion state of diacetylene using CCSD-T level of theory.