The Clusterization Technique: A Systematic Search for the Resonance Energies Obtained via Padé

Abstract

Atomic and molecular resonances play an important role in many physical processes, hence developing theoretical tools to properly calculate these states is required. Recently, we introduced a method for calculating the electronic resonance complex energies from stabilization graphs via analytical continuation, specifically, using the Padé approximant. This method was shown to be efficient, for example, in interpreting the results of cold molecular collisions. However, we observed that the complex energies obtained by Padé depend on the selected set of input points from the stabilization graph. In addition, unphysical solutions (noise) may appear and need to be eliminated. Therefore, applying the method to systems in which the resonance values are unavailable is difficult. The excited Li–He* Feshbach states, for which autoionization was recently observed, present such a challenge. Herein, we introduce a statistical approach to single out the resonance energy from the false solutions by identifying it as a cluster of Padé solutions. This clusterization technique was applied to study several electronic resonance states, for which we obtained excellent agreement with available data (exact or other theoretical solutions and an experimental result). Following this, the technique successfully identified the most likely Li–He* Feshbach resonance energy. Moreover, we concluded that large input sets generate much noise while restricting the number of points facilitates clusterization, which makes this approach more attractive, since input points are obtained from computationally demanding electronic-structure calculations. Overall, the use of analytical continuation via Padé, along with the statistical technique presented herein, offers an efficient approach to calculate resonances.

Resonance study: Effect of partial triples excitation using complex absorbing potential‐based Fock‐space multi‐reference coupled cluster

“…The active space in Fock space consists of 24 orbitals. The resonance energy and width as observed from the η-plot are shown in Table 3 along with other reported values using various experimental and theoretical methods [12,19,47,[62][63][64][65][66]. The aug-cc-PVTZ+ 10s5p basis gives the resonance energy 2.88 eV and width 0.37 eV at the CCSD level.…”

“…We use the CS technique for the FSMRCC method to treat such metastable resonance states. In such a method, a CAP is added to the Hamiltonian making it non-Hermitian such that one of the square-integrable eigen functions of this Hamiltonian corresponds to the resonance states [12][13][14][15][16][17][18][19][20][21]. The Hamiltonian can be written in the presence of the complex perturbation as:…”

“…We compare our results with other theoretical and experimental studies reported in the literature. All the results are presented in the Table 4 [12,47,[67][68][69][70][71][72]. Ghosh et al [47] reported the resonance energy and decay width for the 2 Π state of CO À with the same d-aug-cc-pVDZ basis using CAP-EOMCCSD method as 1.49 and 0.78 eV respectively [47].…”

“…In CAP approach, an imaginary one particle potential is added to the Hamiltonian in order to describe the resonance state as an L 2 -integrable discrete state. Quadratic CAP is the easiest to implement in the electronic structure theory for calculation of resonance energies within the non-Hermitian Hamiltonian methods [12][13][14][15][16][17][18][19][20][21]. In this method a resonance state is described by a single discretized eigen value.…”

“…The CAP-approach has been implemented within many bound state ab initio electronic structure methods with existing Gaussian basis sets without affecting the internal structure of the physical Hamiltonian. Different quantum chemical methods for addressing resonances in atoms and molecules are continuously advancing during the recent years [12][13][14][15][16][17][18][19][20][21].…”