arXiv subjects

Dominika Zgid

Publications and source records attributed to Dominika Zgid.

At least 37 records · Page 2Linked to original sources

arXiv2024

Challenges with relativistic GW calculations in solids and molecules

For molecules and solids containing heavy elements, accurate electronic structure calculations require accounting not only for electronic correlations but also for relativistic effects. In molecules, relativity can lead to severe changes in the ground-state description. In solids, the interplay between both correlation and relativity can change the stability of phases or it can lead to an emergence of completely new phases. Traditionally, the simplest illustration of relativistic effects can be done either by including pseudopotentials in non-relativistic calculations or alternatively by employing large all electron basis sets in relativistic methods. By analyzing different electronic properties (band structure, equilibrium lattice constant and bulk modulus) in semiconductors and insulators, we show that capturing the interplay of relativity and electron correlation can be rather challenging in Green's function methods. For molecular problems with heavy elements, we also observe that similar problems persist. We trace these challenges to three major problems: deficiencies in pseudopotential treatment as applied to Green's function methods, the scarcity of accurate and compact all-electron basis-sets that can be converged with respect to the basis-set size, and linear dependencies arising in all-electron basis-sets particularly when employing Gaussian orbitals. Our analysis provides detailed insight into these problems and opens a discussion about potential approaches to mitigate them.

physics.chem-ph↗

arXiv2024

Relativistic fully self-consistent $GW$ for molecules: Total energies and ionization potentials

The fully self-consistent $GW$ (sc$GW$) method with the iterative solution of Dyson equation provides a consistent approach for describing the ground and excited states without any dependence on the mean-field reference. In this work, we present a relativistic version of sc$GW$ for molecules containing heavy element using the exact two-component (X2C) Coulomb approximation. We benchmark $\texttt{SOC-81}$ dataset containing closed shell heavy elements for the first ionization potential using the fully self-consistent $GW$ as well as one-shot $GW$. The self-consistent $GW$ provides superior result compared to $G_0W_0$ with PBE reference and comparable to $G_0W_0$ with PBE0 while also removing the starting point dependence. The photoelectron spectra obtained at the X2C level demonstrate very good agreement with experimental spectra. We also observe that sc$GW$ provides very good estimation of ionization potential for the inner $d$ shell orbitals. Additionally, using the well conserved total energy, we investigate the equilibrium bond length and harmonic frequencies of few halogen dimers using sc$GW$. Overall, our findings demonstrate the applicability of the fully self-consistent $GW$ method for accurate ionization potential, photoelectron spectra and total energies in finite systems with heavy elements with a reasonable computational scaling.

physics.chem-ph↗

arXiv2023

Quantum algorithm for imaginary-time Green's functions

Green's function methods lead to ab initio, systematically improvable simulations of molecules and materials while providing access to multiple experimentally observable properties such as the density of states and the spectral function. The calculation of the exact one-particle Green's function remains a significant challenge for classical computers and was attempted only on very small systems. Here, we present a hybrid quantum-classical algorithm to calculate the imaginary-time one-particle Green's function. The proposed algorithm combines variational quantum eigensolver and quantum subspace expansion to calculate Green's function in Lehmann's representation. We demonstrate the validity of this algorithm by simulating H$_2$ and H$_4$ on quantum simulators and on IBM's quantum devices.

quant-ph↗

arXiv2023

Natural orbitals and two-particle correlators as tools for analysis of effective exchange couplings in solids

Using generalizations of natural orbitals, spin-averaged natural orbitals, and two-particle charge correlators for solids, we investigate electronic structure of antiferromagnetic transition-metal oxides with a fully self-consistent, finite-temperature GW method. Our findings disagree with Goodenough-Kanamori (GK) rules, commonly used for qualitative interpretation of such solids. First, we found a strong dependence of natural orbital occupancies on momenta contradicting GK assumptions. Second, along the momentum path, the character of natural orbitals changes. In particular, contributions of oxygen 2s orbitals are important, which has not been considered in the GK rules. To analyze the influence of electronic correlation on the values of effective exchange coupling constants, we use both natural orbitals and two-particle correlators and show that electronic screening modulates the degree of superexchange by stabilizing the charge-transfer contributions, greatly affecting these coupling constants. Finally, we give a set of predictions and recommendations regarding the use of density functional, Green's function, and wave-function methods for evaluating effective magnetic couplings in molecules and solids.

cond-mat.str-el↗

arXiv2023

Evaluation of Neel temperatures from fully self-consistent broken-symmetry GW and high-temperature expansion: application to cubic transition-metal oxides

Using fully self-consistent thermal broken-symmetry GW we construct effective magnetic Heisenberg Hamiltonians for a series of transition metal oxides (NiO, CoO, FeO, MnO), capturing a rigorous but condensed description of the magnetic states. Then applying high-temperature expansion, we find the decomposition coefficients for spin susceptibility and specific heat. The radius of convergence of the found series determine the Neel temperature. The NiO, CoO, and FeO contain a small ferromagnetic interaction between the nearest neighbors (NN) and the dominant antiferromagnetic interaction between the next-nearest neighbors (NNN). For them the derived Neel temperatures are in a good agreement with experiment. The case of MnO is different because both NN and NNN couplings are antiferromagnetic and comparable in magnitude, for which the error in the estimated Neel temperature is larger, which is a signature of additional effects not captured by electronic structure calculations.

cond-mat.mtrl-sci↗

arXiv2022

Triple excitations in Green's function coupled cluster solver for studies of strongly correlated systems in the framework of self-energy embedding theory

Embedding theories became important approaches used for accurate calculations of both molecules and solids. In these theories, a small chosen subset of orbitals is treated with an accurate method, called an impurity solver, capable of describing higher correlation effects. Ideally, such a chosen fragment should contain multiple orbitals responsible for the chemical and physical behavior of the compound. Handing a large number of chosen orbitals presents a very significant challenge for the current generation of solvers used in the physics and chemistry community. Here, we develop a Green's function coupled cluster singles doubles and triples (GFCCSDT) solver that can be used for a quantitative description in both molecules and solids. This solver allows us to treat orbital spaces that are inaccessible to other accurate solvers. At the same time, GFCCSDT maintains high accuracy of the resulting self-energy. Moreover, in conjunction with the GFCCSD solver, it allows us to test the systematic convergence of computational studies. Developing the CC family of solvers paves the road to fully systematic Green's function embedding calculations in solids. In this paper, we focus on the investigation of GFCCSDT self-energies for a strongly correlated problem of SrMnO$_3$ solid. Subsequently, we apply this solver to solid MnO showing that an approximate variant of GFCCSDT is capable of yielding a high accuracy orbital resolved spectral function.

physics.chem-ph↗

arXiv2022

Fully Self-Consistent Finite-Temperature $GW$ in Gaussian Bloch Orbitals for Solids

We present algorithmic and implementation details for the fully self-consistent finite-temperature $GW$ method in Gaussian Bloch orbitals for solids. Our implementation is based on the finite-temperature Green's function formalism in which all equations are solved on the imaginary axis, without resorting to analytical continuation during the self-consistency. No quasiparticle approximation is employed and all matrix elements of the self-energy are explicitly evaluated. The method is tested by evaluating the band gaps of selected semiconductors and insulators. We show agreement with other, differently formulated finite-temperature sc$GW$ implementations when finite-size corrections and basis set errors are taken into account. By migrating computationally intensive calculations to GPUs, we obtain scalable results on large supercomputers with nearly optimal performance. Our work demonstrates the applicability of Gaussian orbital based sc$GW$ for $\emph{ab initio}$ correlated materials simulations and provides a sound starting point for embedding methods built on top of $GW$.

cond-mat.mtrl-sci↗

arXiv2022

Broken-symmetry self-consistent GW approach: degree of spin contamination and evaluation of effective exchange couplings in solid antiferromagnets

We adopt a broken-symmetry strategy for evaluating effective magnetic constants $J$ within the fully self-consistent GW method. To understand the degree of spin contamination present in broken-symmetry periodic solutions, we propose several size-extensive quantities that demonstrate that the unrestricted self-consistent GW preserves well the broken-symmetry character of the unrestricted Hartree--Fock solutions. The extracted $J$ are close to the ones obtained from multireference wave-function calculations. In this paper, we establish a robust computational procedure for finding magnetic coupling constants from self-consistent GW calculations and apply it to solid antiferromagnetic nickel and manganese oxides.

cond-mat.mtrl-sci↗

arXiv2022

Relativistic Self-Consistent $GW$: Exact Two-Component Formalism with One-Electron Approximation for Solids

We present a formulation of relativistic self-consistent $GW$ for solids based on the exact two-component formalism with one-electron approximation (X2C1e) and non-relativistic Coulomb interactions. Our theory allows us to study scalar relativistic effects, spin-orbit coupling, and the interplay of relativistic effects with electron correlation without adjustable parameters. Our all-electron implementation is fully $ab$ $initio$ and does not require a pseudopotential constructed from atomic calculations. We examine the effect of the X2C1e approximation by comparison to the established four-component formalism and reach excellent agreement. The simplicity of X2C1e enables the construction of higher order theories, such as embedding theories, on top of perturbative calculations.

cond-mat.str-el↗

arXiv2021

Iterative subspace algorithms for finite-temperature solution of Dyson equation

One-particle Green's functions obtained from the self-consistent solution of the Dyson equation can be employed in evaluation of spectroscopic and thermodynamic properties for both molecules and solids. However, typical acceleration techniques used in the traditional quantum chemistry self-consistent algorithms cannot be easily deployed for the Green's function methods, because of non-convex grand potential functional and non-idempotent density matrix. Moreover, the inclusion of correlation effects in the form of the self-energy matrix and changing chemical potential or fluctuations in the number of particles can make the optimization problem more difficult. In this paper, we study acceleration techniques to target the self-consistent solution of the Dyson equation directly. We use the direct inversion in the iterative subspace (DIIS), the least-squared commutator in the iterative subspace (LCIIS), and the Krylov space accelerated inexact Newton method (KAIN). We observe that the definition of the residual has a significant impact on the convergence of the iterative procedure. Based on the Dyson equation, we generalize the concept of the commutator residual used in DIIS (CDIIS) and LCIIS, and compare it with the difference residual used in DIIS and KAIN. The commutator residuals outperform the difference residuals for all considered molecular and solid systems within both GW and GF2. The generalized CDIIS and LCIIS methods successfully converged restricted GF2 calculations for a number of strongly correlated systems, which could not be converged before. We also provide practical recommendations to guide convergence in such pathological cases.

physics.chem-ph↗

arXiv2021

Exploring Coupled Cluster Green's function as a method for treating system and environment in Green's function embedding methods

Within the self-energy embedding theory (SEET) framework, we study coupled cluster Green's function (GFCC) method in two different contexts: as a method to treat either the system or environment present in the embedding construction. Our study reveals that when GFCC is used to treat the environment we do not see improvement in total energies in comparison to the coupled cluster method itself. To rationalize this puzzling result, we analyze the performance of GFCC as an impurity solver with a series of transition metal oxides. These studies shed light on strength and weaknesses of such a solver and demonstrate that such a solver gives very accurate results when the size of the impurity is small. We investigate if it is possible to achieve a systematic accuracy of the embedding solution when we increase the size of the impurity problem. We found that in such a case, the performance of the solver worsens, both in terms of finding the ground state solution of the impurity problem as well as the self-energies produced. We concluded that increasing the rank of GFCC solver is necessary to be able to enlarge impurity problems and achieve a reliable accuracy. We also have shown that natural orbitals from weakly correlated perturbative methods are better suited than symmetrized atomic orbitals (SAO) when the total energy of the system is the target quantity.

physics.chem-ph↗

arXiv2021

Analytical Continuation of Matrix-Valued Functions: Carathéodory Formalism

Finite-temperature quantum field theories are formulated in terms of Green's functions and self-energies on the Matsubara axis. In multi-orbital systems, these quantities are related to positive semidefinite matrix-valued functions of the Carathéodory and Schur class. Analysis, interpretation and evaluation of derived quantities such as real-frequency response functions requires analytic continuation of the off-diagonal elements to the real axis. We derive the criteria under which such functions exist for given Matsubara data and present an interpolation algorithm that intrinsically respects their mathematical properties. For small systems with precise Matsubara data, we find that the continuation exactly recovers all off-diagonal and diagonal elements. In real-materials systems, we show that the precision of the continuation is sufficient for the analytic continuation to commute with the Dyson equation, and we show that the commonly used truncation of off-diagonal self-energy elements leads to considerable approximation artifacts. Our method paves the way for the systematic evaluation of Matsubara data with equations of many-body theory on the real-frequency axis.

cond-mat.str-el↗

arXiv2021

Electron correlations in cubic paramagnetic perovskite Sr(V,Mn)O$_{3}$ -- Results from fully self-consistent self-energy embedding calculations

In this work, we use the thermodynamically consistent and conserving self-energy embedding theory (SEET) to study the spectra of the prototypical undistorted cubic perovskites SrVO$_3$ and SrMnO$_3$. In the strongly correlated metallic SrVO$_3$ we find that the usual attribution of the satellite peaks at -1.8eV to Hund or Hubbard physics in the $t_{2g}$ orbitals is inconsistent with our calculations. In the strongly correlated insulator SrMnO$_3$ we recover insulating behavior due to a feedback effect between the strongly correlated orbitals and the weakly correlated environment. Our calculation shows a systematic convergence of spectral features as the space of strongly correlated orbitals is enlarged, paving the way to a systematic parameter free study of correlated perovskites.

cond-mat.str-el↗

arXiv2021

Material specific optimization of Gaussian basis sets against plane wave data

Since in periodic systems, a given element may be present in different spatial arrangements displaying vastly different physical and chemical properties, an elemental basis set that is independent of physical properties of materials may lead to significant simulation inaccuracies. To avoid such a lack of material specificity within a given basis set, we present a material-specific Gaussian basis optimization scheme for solids, which simultaneously minimizes the total energy of the system and optimizes the band energies when compared to the reference plane wave calculation while taking care of the overlap matrix condition number. To assess this basis set optimization scheme, we compare the quality of the Gaussian basis sets generated for diamond, graphite, and silicon via our method against the existing basis sets. The optimization scheme of this work has also been tested on the existing Gaussian basis sets for periodic systems such as MoS$_2$ and NiO yielding improved results.

physics.chem-ph↗

arXiv2021

Interpretation of multiple solutions in fully iterative GF2 and GW schemes using local analysis of two-particle density matrices

Due to non-linear structure, iterative Green's function methods can result in multiple different solutions even for simple molecular systems. In contrast to the wave-function methods, a detailed and careful analysis of such molecular solutions was not performed before. In this work, we use two-particle density matrices to investigate local spin and charge correlators that quantify the charge-resonance and covalent characters of these solutions. When applied within unrestricted orbital set, spin correlators elucidate the broken symmetry of the solutions, containing necessary information for building effective magnetic Hamiltonians. Based on GW and GF2 calculations of simple molecules and transition metal complexes, we construct Heisenberg Hamiltonians, four-spin-four-center corrections, as well as biquadratic spin-spin interactions. These Hamiltonian parametrizations are compared to prior wave-function calculations.

physics.chem-ph↗

arXiv2021

Evaluation of two-particle properties within finite-temperature self-consistent one-particle Green's function methods: theory and application to GW and GF2

One-particle Green's function methods can model molecular and solid spectra at zero or non-zero temperatures. One-particle Green's functions directly provide electronic energies and one-particle properties, such as dipole moment. However, the evaluation of two-particle properties, such as $\langle{S^2}\rangle$ and $\langle{N^2}\rangle$ can be challenging, because they require a solution of the computationally expensive Bethe--Salpeter equation to find two-particle Green's functions. We demonstrate that the solution of the Bethe--Salpeter equation can be complitely avoided. Applying the thermodynamic Hellmann--Feynman theorem to self-consistent one-particle Green's function methods, we derive expressions for two-particle density matrices in a general case and provide explicit expressions for GF2 and GW methods. Such density matrices can be decomposed into an antisymmetrized product of correlated one-electron density matrices and the two-particle electronic cumulant of the density matrix. Cumulant expressions reveal a deviation from ensemble representability for GW, explaining its known deficiencies. We analyze the temperature dependence of $\langle{S^2}\rangle$ and $\langle{N^2}\rangle$ for a set of small closed-shell systems. Interestingly, both GF2 and GW show a non-zero spin contamination and a non-zero fluctuation of the number of particles for closed-shell systems at the zero-temperature limit.

physics.chem-ph↗

arXiv2021

Dynamical Self-energy Mapping (DSEM) for quantum computing

For noisy intermediate-scale quantum (NISQ) devices only a moderate number of qubits with a limited coherence is available thus enabling only shallow circuits and a few time evolution steps in the currently performed quantum computations. Here, we present how to bypass this challenge in practical molecular chemistry simulations on NISQ devices by employing a classical-quantum hybrid algorithm allowing us to produce a sparse Hamiltonian which contains only $\mathcal{O}(n^2)$ terms in a Gaussian orbital basis when compared to the $\mathcal{O}(n^4)$ terms of a standard Hamiltonian, where $n$ is the number of orbitals in the system. Classical part of this hybrid entails parameterization of the sparse, fictitious Hamiltonian in such a way that it recovers the self-energy of the original molecular system. Quantum machine then uses this fictitious Hamiltonian to calculate the self-energy of the system. We show that the developed hybrid algorithm yields very good total energies for small molecular test cases while reducing the depth of the quantum circuit by at least an order of magnitude when compared with simulations involving a full Hamiltonian.

quant-ph↗

arXiv2020

Testing the GFCCSD impurity solver on real materials within the self-energy embedding theory framework

We apply the Green's function coupled cluster singles and doubles (GFCCSD) impurity solver to realistic impurity problems arising for strongly correlated solids within the self-energy embedding theory (SEET) framework. We describe the details of our GFCC solver implementation, investigate its performance, and highlight potential advantages and problems on examples of impurities created during the self-consistent SEET for antiferromagnetic MnO and paramagnetic SrMnO$_{3}$. GFCCSD provides satisfactory descriptions for weakly and moderately correlated impurities with sizes that are intractable by existing accurate impurity solvers such as exact diagonalization (ED). However, our data also shows that when correlations become strong, the singles and doubles approximation used in GFCC could lead to instabilities in searching for the particle number present in impurity problems. These instabilities appears especially severe when the impurity size gets larger and multiple degenerate orbitals with strong correlations are present. We conclude that to fully check the reliability of GFCCSD results and use them in fully {\em ab initio} calculations in the absence of experiments, a verification from a GFCC solver with higher order excitations is necessary.

cond-mat.str-el↗