Search

This repository contains all path integral Monte Carlo (PIMC) results for the article "Effective electronic forces and potentials from ab initio path integral Monte Carlo simulations" in the same units as they are plotted in Figs. 4, 5 and 8.

This repository contains the PIMC results from the article "Spin-resolved density response of the warm dense electron gas"; parameters are given in the file names; all results are unpolarized (Xi=0) unless otherwise stated; same units as in the original publication.

We present extensive new \textit{ab intio} path integral Monte Carlo results for the momentum distribution function $n(\mathbf{k})$ of the uniform electron gas (UEG) in the warm dense matter (WDM) regime over a broad range of densities and temperatures. This allows us to study the nontrivial exchange--correlation induced increase of low-momentum states around the Fermi temperature, and to investigate its connection to the related lowering of the kinetic energy compared to the ideal Fermi gas. In addition, we investigate the impact of quantum statistics on both $n(\mathbf{k})$ and the off-diagonal density matrix in coordinate space, and find that it cannot be neglected even in the strongly coupled electron liquid regime. Our results were derived without any nodal constraints, and thus constitute a benchmark for other methods and approximations.

We carry out extensive direct path integral Monte Carlo (PIMC) simulations of the uniform electron gas (UEG) at finite temperature for different values of the spin-polarization $\xi$. This allows us to unambiguously quantify the impact of spin-effects on the momentum distribution function $n(\mathbf{k})$ and related properties. We find that interesting physical effects like the interaction-induced increase in the occupation of the zero-momentum state $n(\mathbf{0})$ substantially depend on $\xi$. Our results further advance the current understanding of the UEG as a fundamental model system, and are of practical relevance for the description of transport properties of warm dense matter in an external magnetic field. All PIMC results are freely available online and can be used as a benchmark for the development of new methods and applications.

The exact exchange-correlation kernel is a functional derivative of the exact time-dependent exchange-correlation (XC) potential with respect to the time-dependent density, evaluated at the ground-state density. As the XC potential is not known, the exact kernel is also unavailable. Therefore, it must be modeled either using many-body perturbation theory or by satisfying the exact constraints for various prototype systems such as the paradigm uniform electron gas (UEG). The random phase approximation (RPA) neglects the kernel, therefore, fails to provide the accurate ground- and excited-state properties for various systems from a simple uniform electron gas to more complex periodic ones. There are numerous corrections to RPA available, including kernel-corrected RPA, often called the beyond-RPA (bRPA) methods. In this work, we employed various bRPA methods for a diverse set of systems together with RPA. At first, we applied RPA based methods to study the phase stability of the cesium halides. Cesium halides phase stability is one of the stringent tests for a density functional approximation to assess its accuracy for dispersion interaction. Experimentally, CsF prefers the rocksalt (B1) phase, while the other halides CsCl, CsBr, and CsI prefer the cesium chloride (B2) phase. Without dispersion interaction, PBE and PBE0 predict all halides to prefer the B1 phase. However, all RPA based methods predict the experimental observations. The bRPA methods usually improve the quantitative prediction over RPA for the ground-state equilibrium properties of cesium halides. Next, we explored binary intermetallic alloys, where we showed that RPA successfully predicts the accurate formation energies of weakly bonded alloys. However, a kernel corrected RPA is needed when dealing with strongly bonded alloys with partially filled d-band metals. We utilized the renormalized ALDA (rALDA) and rAPBE kernel as bRPA methods. Exact constraints and appropriate norms such as the uniform electron gas are very useful to construct various approximations for the exchange-correlation potentials in the ground-state, and the exchange-correlation kernel in the linear-response theory within the TDDFT. These mathematical formulations not only guide us to formulate more robust nonempirical methods, but they also have more predictive power. We showed the importance of these constraints by calculating plasmon dispersion of the uniform electron gas using the non-local, energy-optimized (NEO) kernel using only a few constraints. More predictive power comes with more constraint satisfaction. As a result, we developed a new wavevector- and frequency-dependent exchange-correlation kernel that satisfies all the constraints that it should satisfy with a real frequency. It gives accurate ground-state correlation energy and describes the charge density wave in low-density UEG. It also predicts an accurate plasmon dispersion with a finite lifetime at wavevectors less than the critical one, where the plasmon dispersion meets the electron-hole continuum.

The response of the uniform electron gas (UEG) to an external perturbation is of paramount importance for many applications. Recently, highly accurate results for the static density response function and the corresponding local field correction have been provided both for warm dense matter [\textit{J.~Chem.~Phys.}~\textbf{151}, 194104 (2019)] and strongly coupled electron liquid [\textit{Phys.~Rev.~B}~\textbf{101}, 045129 (2020)] conditions based on exact \textit{ab initio} path integral Monte Carlo (PIMC) simulations. In the present work, we further complete our current description of the UEG by exploring the high energy density regime, which is relevant for, e.g., astrophysical applications and inertial confinement fusion experiments. To this end, we present extensive new PIMC results for the static density response in the range of $0.05 \leq r_s \leq 0.5$ and $0.85\leq\theta\leq8$. These data are subsequently used to benchmark the accuracy of the widely used random phase approximation and the dielectric theory by Singwi, Tosi, Land, and Sj\"olander (STLS). Moreover, we compare our results to configuration PIMC data where they are available and find perfect agreement with a relative accuracy of $0.001-0.01\%$. All PIMC data are available online.

In the last decade, stochastic versions of quantum chemistry methods such as coupled cluster Monte Carlo (CCMC) or full configuration interaction quantum Monte Carlo (FCIQMC) have made highly accurate energy calculations possible that are not accessible to the corresponding deterministic methods (full configuration interaction and coupled cluster) at the same accuracy. CCMC and FCIQMC parallelize well and exploit the sparsity in the wavefunction which decreases memory costs and makes calculations in larger systems tractable. With CCMC it is straightforward to set up high order coupled cluster calculations, such as CCSDTQ5, which includes quintuple excitations explicitly. In this thesis, the convergence of the energy accuracy with the coupled cluster levels up to CCSDTQ5 was tested on the uniform electron gas, a model solid system, for various degrees of electron correlation. This gave information on what coupled cluster level is needed to reach sufficient accuracy when modelling a solid system. Before large solid systems can be modelled, the CCMC and FCIQMC algorithms need to be optimised. The efficiency in one of the crucial steps in these algorithms, the $spawn$ step, was improved, keeping computational and memory costs as low as possible. Furthermore, the convergence of CCMC and FCIQMC was accelerated by employing a quasi-Newton propagation. Using the model system information of what coupled cluster level is needed and having made great progress towards accelerating these methods, the computation of highly accurate energies in solid or large molecular systems should be more feasible in the future.

An accurate expression for the exchange-correlation free energy f_{xc} of homogeneous electron fluids at finite temperatures is presented on the basis of Singwi-Tosi-Land-Sjolander (STLS) approximation. In addition to the derivation for the paramagnetic state, that for the ferromagnetic state is newly carried out in which a correction in the strong Coulomb coupling regime is incorporated into the construction of analytic expression as a function of the coupling constant and the Fermi degeneracy. The fitting formula for f_{xc} is then extended over any degree of spin polarization with the aid of available interpolation scheme. The proposed equation of state, called iSTLS formula, shows reasonable agreements with the existing quantum Monte Carlo evaluations at finite temperatures in the paramagnetic state, thus giving a consensus for the thermodynamic functions between many-body theories and computer simulations. On the other hand, the current status for the agreement among various evaluations of f_{xc} is relatively unsatisfactory in the ferromagnetic state, suggesting the necessity of further investigations., Comment: 19 page manuscript, 13 figures, and Supplemental Material; Submitted to Contrib. Plasma Phys

We give the first mathematically rigorous justification of the Local Density Approximation in Density Functional Theory. We provide a quantitative estimate on the difference between the grand-canonical Levy-Lieb energy of a given density (the lowest possible energy of all quantum states having this density) and the integral over the Uniform Electron Gas energy of this density. The error involves gradient terms and justifies the use of the Local Density Approximation in the situation where the density is very flat on sufficiently large regions in space., Comment: Final version to appear in Pure and Applied Analysis

The response of the uniform electron gas (UEG) to an external perturbation is of paramount importance for many applications. Recently, highly accurate results for the static density response function and the corresponding local field correction have been provided both for warm dense matter [J. Chem. Phys. 151, 194 104 (2019)] and strongly coupled electron liquid [Phys. Rev. B 101, 045 129 (2020)] conditions based on exact ab initio path integral Monte Carlo (PIMC) simulations. In the present work, we further complete our current description of the UEG by exploring the high energy density regime, which is relevant for, e.g. astrophysical applications and inertial confinement fusion experiments. To this end, we present extensive new PIMC results for the static density response in the range of 0.05 ≤ r s ≤ 0.5 and 0.85 ≤ θ ≤ 8. These data are subsequently used to benchmark the accuracy of the widely used random phase approximation and the dielectric theory by Singwi, Tosi, Land, and Sjölander (STLS). Moreover, we compare our results to configuration PIMC data where they are available and find perfect agreement with a relative accuracy of 0.001 − 0.01%. All PIMC data are available online.

The properties of the macroscopic world around us, and of which we are a part, are largely determined by the low energy, collective behaviour of many interacting particles, including the nuclei and, especially, the electrons present. Although the fundamental laws governing the behaviour of these many-body systems are believed to be known in principle, the practical solution of the equations of quantum mechanics remains a challenging area of research. This thesis is concerned with the application of quantum Monte Carlo methods to two model systems: the spin-polarised homogeneous electron gas, and a hole-doped electron gas. Electronic structure theory is briefly reviewed before discussing in more detail the quantum Monte Carlo methods used in this thesis. A study of the three-dimensional spin-polarised homogeneous electron gas (HEG) is then reported, where the relatively new technique of twist averaging is investigated in detail and accurate energies and pair correlation functions are obtained over densities $r_s = 0.5 – 20$ a.u. and the full range of spin-polarisation, allowing comparison with the Perdew-Zunger interpolation scheme used in local spin density approximation exchange-correlation functionals. Following this, an impurity is added to the electron gas in the form of a positively charged hole, and the interaction is studied. Relaxation energies, pair correlation functions and momentum densities are reported. Trion formation is observed over a range of carrier densities and electron-hole mass ratios in agreement with experiment. Isolated trions are also studied, where the diffusion Monte Carlo method is exact. Methodological innovations developed while carrying out this work are discussed, including a variance reduction technique for twist-averaged calculations and a new trial wave function for impurity-in-HEG calculations., Financial support provided by the Engineering and Physical Sciences Research Council (EPSRC)

We introduce an electron force field (eFF) that makes simulation of large scale excited electron dynamics possible and practical. The forces acting on thousands of electrons and nuclei can be computed in less than a second on a single modern processor. Just as conventional force fields parameterize the ground state potential between nuclei, with electrons implicitly included, electron force fields parameterize the potential between nuclei and simplified electrons, with more detailed degrees of freedom implicitly included. The electrons in an electron force field are Gaussian wave packets whose only parameters are its position and its size. Using a simple version of the electron force field, we compute the dissociation and ionization behavior of dense hydrogen, and obtain equations of state and shock Hugoniot curves that are in agreement with results obtained from vastly more expensive path integral Monte Carlo methods. We also compute the Auger dissociation of hydrocarbons, and observe core hole decays, valence electron ionizations, and nuclear fragmentation patterns consistent with experiment. We show we can describe p-like valence electrons using spherical Gaussian functions, enabling us to compute accurate ionization potentials and polarizabilities for first row atoms, and accurate dissociation energies and geometries of atom hydrides and hydrocarbons. We show also that we can describe delocalized electrons in a uniform electron gas using localized eFF orbitals. We reproduce the energy of a uniform electron gas, including correlation effects; and following the historical development of density functional theory, we develop a preliminary eFF that can compute accurate exchange and correlation energies of atoms and simple molecules.

This thesis constitutes a contribution to the multideterminantal extension of the Kohn-Sham scheme of density functional theory, that is based on a long-range/short-range decomposition of the electron-electron interaction and aims at improving the calculation of (near-)degeneracy correlation effects in atomic and molecular systems. This approach involves a wave function type calculation for the long-range contribution supplemented in a self-consistent manner by a density functional for the short-range contribution. We have reexamine the long-range/short-range decomposition of the energy. We have studied some theoretical properties of the short-range exchange-correlation functional and analyzed its local density approximation. Finally, we have explored several approximations for this functional which go beyond the local density approximation and applied the method to a few atomic and molecular systems displaying important (near-)degeneracy correlation effects.; Cette thèse constitue une contribution à l'extension multidéterminantale de la méthode de Kohn-Sham en théorie de la fonctionnelle de la densité, basée sur une décomposition longue portée/courte portée de l'interaction électronique et visant à améliorer le calcul des effets de corrélation de (quasi-)dégénérescence des systèmes atomiques et moléculaires. Cette approche met en jeu un calcul de type fonction d'onde pour la contribution de longue portée à l'énergie complété de façon autocohérente par une fonctionnelle de la densité pour la contribution de courte portée. Nous avons réexaminé la décomposition longue portée/courte portée de l'énergie. Nous avons étudié des propriétés théoriques de la fonctionnelle d'échange-corrélation de courte portée et analysé son approximation locale. Enfin, nous avons exploré diverses approximations pour cette fonctionnelle dépassant l'approximation locale et appliqué la méthode à quelques systèmes atomiques et moléculaires présentant des effets de corrélation de (quasi-)dégénérescence importants.

This thesis constitutes a contribution to the multideterminantal extension of the Kohn-Sham scheme of density functional theory, that is based on a long-range/short-range decomposition of the electron-electron interaction and aims at improving the calculation of (near-)degeneracy correlation effects in atomic and molecular systems. This approach involves a wave function type calculation for the long-range contribution supplemented in a self-consistent manner by a density functional for the short-range contribution. We have reexamine the long-range/short-range decomposition of the energy. We have studied some theoretical properties of the short-range exchange-correlation functional and analyzed its local density approximation. Finally, we have explored several approximations for this functional which go beyond the local density approximation and applied the method to a few atomic and molecular systems displaying important (near-)degeneracy correlation effects.; Cette thèse constitue une contribution à l'extension multidéterminantale de la méthode de Kohn-Sham en théorie de la fonctionnelle de la densité, basée sur une décomposition longue portée/courte portée de l'interaction électronique et visant à améliorer le calcul des effets de corrélation de (quasi-)dégénérescence des systèmes atomiques et moléculaires. Cette approche met en jeu un calcul de type fonction d'onde pour la contribution de longue portée à l'énergie complété de façon autocohérente par une fonctionnelle de la densité pour la contribution de courte portée. Nous avons réexaminé la décomposition longue portée/courte portée de l'énergie. Nous avons étudié des propriétés théoriques de la fonctionnelle d'échange-corrélation de courte portée et analysé son approximation locale. Enfin, nous avons exploré diverses approximations pour cette fonctionnelle dépassant l'approximation locale et appliqué la méthode à quelques systèmes atomiques et moléculaires présentant des effets de corrélation de (quasi-)dégénérescence importants.