arXiv subjects

Jerryman A. Gyamfi

Publications and source records attributed to Jerryman A. Gyamfi.

5 recordsLinked to original sources

arXiv2023

A new strategy to optimize complex absorbing potentials for the computation of resonance energies and widths

Complex absorbing potentials (CAPs) are artificial potentials added to electronic Hamiltonians to make the wave function of metastable electronic states square-integrable. This makes electronic-structure theory of resonances comparable to that of bound states, thus reducing the complexity of the problem. However, the most often used box and Voronoi CAPs depend on several parameters that have a substantial impact on the numerical results. Among these parameters are the CAP strength and a set of spatial parameters that define the onset of the CAP. It has been a common practice to minimize the perturbation of the resonance states due to the CAP by optimizing the strength parameter while fixing the onset parameters although the performance of this approach strongly depends on the chosen onset. Here we introduce a more general approach that allows one to optimize not only the CAP strength but also the spatial parameters. We show that fixing the CAP strength and optimizing the spatial parameters is a reliable way for minimizing CAP perturbations. We illustrate the performance of this new approach by computing resonance energies and widths of the temporary anions of dinitrogen, ethylene, and formic acid. This is done at the Hartree-Fock and equation-of-motion coupled-cluster singles and doubles levels of theory, using full and projected box and Voronoi CAPs.

physics.chem-ph↗

arXiv2022

Analysis and Optimization of Resonance Energies and Widths Using Complex Absorbing Potentials

Complex absorbing potentials (CAPs) are artificial potentials added to electronic Hamiltonians to make the wavefunction of metastable electronic states square-integrable. This makes the electronic structure problem of electronic resonances comparable to that of electronic bound states, thus reducing the complexity of the problem. CAPs depend on two types of parameters: the coupling parameter $η$ and a set of spatial parameters which define the onset of the CAP. It has been a common practice over the years to minimize the CAP perturbation on the physical electronic Hamiltonian by running an $η-$trajectory, whereby one fixes the spatial parameters and varies $η$. The optimal $η$ is chosen according to the minimum log-velocity criterion. But the effectiveness of an $η-$trajectory strongly depends on the values of the fixed spatial parameters. In this work, we propose a more general criterion, called the $ξ-$criterion, which allows one to minimize any CAP parameter, including the CAP spatial parameters. Indeed, we show that fixing $η$ and varying the spatial parameters according to a scheme (i.e., running a spatial trajectory) is a more efficient and reliable way of minimizing the CAP perturbations (which is assessed using the $ξ-$criterion). We illustrate the method by determining the resonance energy and width of the temporary anion of dinitrogen, at the Hartree-Fock and EOM-EA-CCSD levels, using two different types of CAPs: the box- and the smooth Voronoi-CAPs.

physics.chem-ph↗

arXiv2022

$Ab\ initio$ molecular dynamics of temporary anions using complex absorbing potentials

Dissociative electron attachment, that is, the cleavage of chemical bonds induced by low-energy electrons, is difficult to model with standard quantum-chemical methods because the involved anions are not bound but subject to autodetachment. We present here a new computational development for simulating the dynamics of temporary anions on complex-valued potential energy surfaces. The imaginary part of these surfaces describes electron loss, whereas the gradient of the real part represents the force on the nuclei. In our method, the forces are computed analytically based on Hartree-Fock theory with a complex absorbing potential. $Ab\ initio$ molecular dynamics simulations for the temporary anions of dinitrogen, ethylene, chloroethane, and the five mono- to tetrachlorinated ethylenes show qualitative agreement with experiments and offer mechanistic insights into dissociative electron attachments. The results also demonstrate how our method evenhandedly deals with molecules that may undergo dissociation upon electron attachment and those which only undergo autodetachment.

physics.chem-ph↗

arXiv2020

Fundamentals of Quantum Mechanics in Liouville Space

The purpose of this paper is to articulate a coherent and easy-to-understand way of doing quantum mechanics in any finite-dimensional Liouville space, based on the use of Kronecker product and what we have termed the `bra-flipper' operator. One of the greater strengths of the formalism expatiated on here is the striking similarities it bears with Dirac's bra-ket notation. For the purpose of illustrating how the formalism can be effectively employed, we use it to solve a quantum optical master equation for a two-level quantum system and find its Kraus operator sum representation. The paper is addressed to students and researchers with some basic knowledge of linear algebra who want to acquire a deeper understanding of the Liouville space formalism. The concepts are conveyed so as to make the application of the formalism to more complex problems in quantum physics straightforward and unencumbered.

quant-ph↗

arXiv2020

Semiclassical Quantum Markovian Master Equations. Case Study: Continuous Wave Magnetic Resonance of Multispin Systems

We propose a method for deriving Lindblad-like master equations when the environment/reservoir is consigned to a classical description. As a proof of concept, we apply the method to continuous wave (CW) magnetic resonance. We make use of a perturbation scheme we have termed "affine commutation perturbation" (ACP). Unlike traditional perturbation methods, ACP has the advantage of incorporating some effects of the perturbation even at the zeroth-order approximation. Indeed, we concentrate here on the zeroth-order, and show how -- even at this lowest order -- the ACP scheme can still yield non-trivial and equally important results. In contradistinction to the purely quantum Markovian master equations in the literature, we explicitly keep the term linear in the system-environment interaction -- at all orders of the perturbation. At the zeroth-order, we show that this results in a dynamics whose map is non-CP (Completely Positive) but approaches asymptotically a CP map as $t \to +\infty$. We also argue that this linear term accounts for the linear response of the system to the presence of the environment -- thus the harbinger for a linear response theory (LRT) within the confines of such (semiclassical) Lindblad-like master equations. The adiabatic process limit of the dynamics is also defined, and considerably explored in the context of CW magnetic resonance. Here, the same linear term emerges as the preeminent link between standard (adiabatic process) LRT (as formulated by Kubo and co.) and Lindblad-like master equations. And with it, we show how simple stick-plot CW magnetic resonance spectra of multispin systems can be easily generated under certain conditions.

quant-ph↗