arXiv subjects

Jakub Kocák

Publications and source records attributed to Jakub Kocák.

4 recordsLinked to original sources

arXiv2022

The Geometric Potential of the Exact Electron Factorization: Meaning, significance and application

The theoretical and computational description of materials properties is a task of utmost scientific and technological importance. A first-principles description of electron-electron interactions poses an immense challenge that is usually approached by converting the many-electron problem to an effective one-electron problem. There are different ways to obtain an exact one-electron theory for a many-electron system. An emergent method is the exact electron factorization (EEF) -- one of the branches of the Exact Factorization approach to many-body systems. In the EEF, the Schrödinger equation for one electron, in the environment of all other electrons, is formulated. The influence of the environment is reflected in the potential $v^{\rm H}$, which represents the energy of the environment, and in a potential $v^{\rm G}$, which has a geometrical meaning. In this paper, we focus on $v^{\rm G}$ and study its properties in detail. We investigate the geometric origin of $v^{\rm G}$ as a metric measuring the change of the environment, exemplify how translation and scaling of the state of the environment are reflected in $v^{\rm G}$, and explain its shape for homo- and heteronuclear diatomic model systems. Based on the close connection between the EEF and density functional theory, we also use $v^{\rm G}$ to provide an alternative interpretation to the Pauli potential in orbital-free density functional theory.

physics.chem-ph↗

arXiv2021

On the Geometric Potential and the Relationship between the Exact Electron Factorization and Density Functional Theory

There are different ways to obtain an exact one-electron theory for a many-electron system, and the exact electron factorization (EEF) is one of them. In the EEF, the Schrödinger equation for one electron in the environment of other electrons is constructed. The environment provides the potentials that appear in this equation: A scalar potential $v^{\rm H}$ representing the energy of the environment and another scalar potential $v^{\rm G}$ as well as a vector potential that have geometric meaning. By replacing the interacting many-electron system with the non-interacting Kohn-Sham (KS) system, we show how the EEF is related to density functional theory (DFT) and we interpret the Hartree-exchange-correlation potential as well as the Pauli potential in terms of the EEF. In particular, we show that from the EEF viewpoint, the Pauli potential does not represent the difference between a fermionic and a bosonic non-interacting system, but that it corresponds to $v^{\rm G}$ and partly to $v^{\rm H}$ for the (fermionic) KS system. We then study the meaning of $v^{\rm G}$ in detail: Its geometric origin as a metric measuring the change of the environment is presented. Additionally, its behavior for a simple model of a homo- and heteronucler diatomic is investigated and interpreted with the help of a two-state model. In this way, we provide a physical interpretation for the one-electron potentials that appear in the EEF and in DFT.

physics.chem-ph↗

arXiv2021

Charge-transfer steps in Density Functional Theory from the perspective of the Exact Electron Factorization

When a molecule dissociates, the exact Kohn-Sham (KS) and Pauli potentials may form step structures. Reproducing these steps correctly is central for the description of dissociation and charge-transfer processes in density functional theory (DFT): The steps align the KS eigenvalues of the dissociating subsystems relative to each other and determine where electrons localize. While the step height can be calculated from the asymptotic behavior of the KS orbitals, this provides limited insight into what causes the steps. We give an explanation of the steps with an exact mapping of the many-electron problem to a one-electron problem, the exact electron factorizaton (EEF). The potentials appearing in the EEF have a clear physical meaning that translates to the DFT potentials by replacing the interacting many-electron system with the KS system. With a simple model of a diatomic, we illustrate that the steps are a consequence of spatial electron entanglement and are the result of a charge transfer. From this mechanism, the step height can immediately be deduced. Moreover, two methods to approximately reproduce the potentials during dissociation suggest themselves. One is based on the states of the dissociated system, while the other one is based on an analogy to the Born-Oppenheimer treatment of a molecule. The latter method also shows that the steps connect adiabatic potential energy surfaces. The view of DFT from the EEF thus provides a better understanding of how many-electron effects are encoded in a one-electron theory and how they can be modeled.

physics.chem-ph↗

arXiv2020

Many-electron effects of strong-field ionization described in an exact one-electron theory

If one-electron observables of a many-electron system are of interest, a many-electron dynamics can be represented exactly by a one-electron dynamics with effective potentials. The formalism for this reduction is provided by the Exact Electron Factorization (EEF). We study the time-dependent features of the EEF effective potentials for a model of an atom ionized by an ultrastrong and ultrashort laser pulse, with the aim of understanding what is needed to develop computationally feasible approximations. It is found that the simplest approximation, the so-called time-independent conditional amplitude (TICA) approximation, is complementary to single-active electron (SAE) approaches as it reproduced the exact dynamics well for high photon frequencies of the laser field or large Keldysh parameter. For relatively low frequencies of the laser field or for smaller Keldysh parameters, we find that excited state dynamics in the core region of the atom leads to a time-dependent ionization barrier in the EEF potential. The time-dependence of the barrier needs to be described accurately to correctly model many-electron effects, and we conclude that a multi-state extension of the TICA approximation is a possible route how this can be achieved. In general, our study sheds a different light on one-electron pictures of strong-field ionization and shows that many-electron effects for such processes may be included by solving a one-electron Schrödinger equation, provided the core dynamics can be modeled successfully.

physics.chem-ph↗