Reflection-free complex absorbing potential for electronic structure calculations: Feshbach-type autoionization resonances of molecules

Abstract

The reflection-free complex absorbing potential (RF-CAP) method has been already applied to the study of the autoionization resonance of helium [Sajeev et al., Chem. Phys. 329, 307 (2006)]. The present work introduces a systematic way for implementing RF-CAP for the electronic structure calculations using Gaussian basis sets for molecules. As a test case study we applied the RF-CAP method to the lowest (1)Sigma(g) (+) and (1)Sigma(u) (+) Feshbach-type autoionization resonances of hydrogen molecule. Since thin RF-CAP absorbs fast electrons much better than the slow ones, a weak dc field has been added to the RF-CAP in the peripheral region of the molecule.

Complex-scaled equation-of-motion coupled-cluster method with single and double substitutions for autoionizing excited states: Theory, implementation, and examples

“…The CAP methods, in which complex potential −iηŴ devised to absorb the diverging tail of the resonance wave function is added to the Hamiltonian, were originally developed for shape resonances, and a special care should be taken when the approach is used for Feshbach resonances. 39 Moreover, CAPs give rise to reflections, and, consequently, the eigenvalues of the modified Hamiltonian coincide with the resonance poles only in the limit of the zero CAP strength (even in the complete one-electron basis set). 40 Several approaches for construction of reflection-free CAPs have been suggested.…”

“…40 Several approaches for construction of reflection-free CAPs have been suggested. [39][40][41] Complex scaling formalism 17,18,[31][32][33] is an elegant and mathematically rigorous way to deal with the excited states embedded in the continuum (it can also be used for nuclear scattering problem). By scaling all electronic (and, in principle, nuclear) coordinates by a complex number e iθ (dilation transformation), one arrives to a non-Hermitian Hamiltonian operator that has the same discrete spectrum as the unscaled operator and whose continuum states are rotated into the complex plane by 2θ exposing the resonances, as illustrated in Fig.…”

Atomic and Molecular Complex Resonances from Real Eigenvalues Using Standard (Hermitian) Electronic Structure Calculations

“…CPESs can be obtained by using complex basis functions [1], analytical continuation of the Hamiltonian's matrix elements [2] or one of the complex scaling transformations, such as the uniform [3], exterior [4] or smooth exterior scaling [5]. Alternatively, CPESs can be obtained by introducing a complex absorbing potential (CAP) [6,7] or a reflection-free CAP (RF-CAP) to the Hamiltonian [8].…”

Complex absorbing potentials for stark resonances

“…Notice that the use of SES‐CAP is also equivalent to the use of complex basis functions for calculating resonances . The SES‐CAP has been used for calculating field‐free molecular autoionization resonances . Unlike other types of CAPs, introducing the SES‐CAP in the region where the physical potential is not negligible, without tuning the CAP strength to zero, does not cause any artificial effects, because the physical potential is also scaled by the SES contour which is associated with the SES‐CAP.…”