arXiv subjects

Pavel Pokhilko

Publications and source records attributed to Pavel Pokhilko.

13 recordsLinked to original sources

arXiv2026

Self-consistent vertex corrected $GW$ with static and dynamic screening using tensor hypercontraction: assessment of molecular charged excitations

We investigate self-consistent vertex corrections to the $GW$ self-energy for ionization potentials (IPs) and electron affinities (EAs). We benchmark IPs against $Δ$CCSD(T) references in the $G_0W_0Γ$29 and GW100 sets and compare GW100 EAs with EOM-CCSD references. Because many anions are metastable, these addition energies are model quantities and should not be interpreted as experimental EAs. Tensor hypercontraction (THC) of the Coulomb integrals enables efficient self-consistent $GWΓ_Σ$ implementations, where vertex corrections are included only in the self-energy. We establish a hierarchy of vertex-corrected self-energies relative to sc$GW$, ordered from least to most negative as SOX $>$ SOSEX $>$ G3W2 $>$ 2SOSEX $>$ sc$GW$. Equivalently, the absolute magnitude increases along this sequence. This trend follows an effective-screening picture, in which increasing screening progressively reduces exchange contributions. Static and dynamic variants show consistent differences due to the frequency dependence of the screened interaction. Across all methods, vertex corrections act as an approximately frequency-uniform self-energy renormalization rather than altering its spectral structure. In terms of accuracy, sc$GWΓ_Σ$ does not uniformly improve IPs or the EA model quantities over sc$GW$. For IPs, SOX and SOSEX usually degrade performance, whereas 2SOSEX and G3W2 remain close to sc$GW$, with only marginal improvements for selected systems at higher cost. Although the tested variants reduce EA MAEs, this should not be interpreted as a general improvement for physical anions because many nominal EA states are metastable. These results indicate that generic vertex insertions are insufficient to outperform sc$GW$; systematic improvements require designed diagrammatic approximations combined with efficient tensor factorization.

cond-mat.str-el↗

arXiv2026

The Python Simulations of Chemistry Framework: 10 years of an open-source quantum chemistry project

Over the past decade, the Python-based Simulations of Chemistry Framework (PySCF) has developed into a widely used open-source platform for electronic structure theory and quantum chemical method development. This article reviews the major advances since the previous overview in 2020, covering new modules and methodology, infrastructure changes, and performance benchmarks.

physics.chem-ph↗

arXiv2025

Homotopy continuation method for solving Dyson equation fully self-consistently: theory and application to NdNiO2

Solution of the Dyson equation for the small-gap systems can be plagued by large non-converging iterations. In addition to the convergence issues, due to a high non-linearity, the Dyson equation may have multiple solutions. We apply the homotopy continuation approach to control the behavior of iterations. We used the homotopy continuation to locate multiple fully self-consistent GW solutions for NdNiO2 solid and to establish the corresponding Hartree-Fock limits. Some of the solutions found are qualitatively new and help to understand the nature of electron correlation in this material. We show that there are multiple low-energy charge-transfer solutions leading to a formation of charge-density waves. Our results qualitatively agree with the experimental conductivity measurements. To rationalize the structure of solutions, we compare the k-point occupations and generalize the concept of natural difference orbitals for correlated periodic solids.

cond-mat.str-el↗

arXiv2024

Tensor hypercontraction for self-consistent vertex corrected GW with static and dynamic screening; applications to molecules and solids with superexchange

For molecules and solids, we developed efficient MPI-parallel algorithms for evaluating the second-order exchange term with bare, statically screened, and dynamically screened interactions. We employ the resulting term in a fully self-consistent manner together with scGW, resulting in the following vertex-corrected scGW schemes: scGWSOX, scGWSOSEX, scGW2SOSEX, and scG3W2theories. We show that for the vertex evaluation, the reduction of scaling by tensor hypercontraction (THC) has two limiting execution regimes. We used the resulting code to perform the largest (by the number of orbitals) fully self-consistent calculations with the SOX term. We demonstrate that our procedure allows for a reliable evaluation of even small energy differences. Utilizing a broken-symmetry approach, we explore the influence of the SOX term on the effective magnetic exchange couplings. We show that the treatment of SOX has a significant impact on the obtained values of the effective exchange constants, which we explain through a self-energy dependence on an effective dielectric constant. We confirm this explanation by analyzing natural orbitals and local changes in charge transfer quantifying superexchange. Our analysis explains the structure of weak electron correlation responsible for the modulation of superexchange in both molecules and solids. Finally, for solids, we evaluate Neel temperatures utilizing the high-temperature expansion and compare the results obtained with experimental measurements.

cond-mat.str-el↗

arXiv2024

Green/WeakCoupling: Implementation of fully self-consistent finite-temperature many-body perturbation theory for molecules and solids

The accurate ab initio simulation of molecules and periodic solids with diagrammatic perturbation theory is an important task in quantum chemistry, condensed matter physics, and materials science. In this article, we present the WeakCoupling module of the open-source software package Green, which implements fully self-consistent diagrammatic weak coupling simulations, capable of dealing with real materials in the finite-temperature formalism. The code is licensed under the permissive MIT license. We provide self-consistent GW (scGW) and self-consistent second-order Green's function perturbation theory (GF2) solvers, analysis tools, and post-processing methods. This paper summarizes the theoretical methods implemented and provides background, tutorials and practical instructions for running simulations.

cond-mat.mtrl-sci↗

arXiv2024

Tensor hypercontraction for fully self-consistent imaginary-time GF2 and GWSOX methods: theory, implementation, and role of the Green's function second-order exchange for intermolecular interactions

We apply tensor hypercontraction (THC) to reduce the computational scaling of expensive fully self-consistent Green's function methods. We present an efficient MPI-parallel algorithm and its implementation for evaluating the correlated second-order exchange term (SOX). This approach enabled us to conduct the largest fully self-consistent calculations with over 1100 atomic orbitals (AOs), with negligible errors attributed to THC fitting. Utilizing our THC implementation for scGW, scGF2, and scGWSOX (GW plus the SOX term iterated to achieve full Green's function self-consistency), we evaluated energies of intermolecular interactions. This approach allowed us to circumvent issues related to reference dependence and ambiguity in energy evaluation, which are common challenges in non-self-consistent calculations. We demonstrate that scGW exhibits a slight overbinding tendency for large systems, contrary to the underbinding observed with non-self-consistent RPA. Conversely, scGWSOX exhibits a slight underbinding tendency for such systems. This behavior is both physical and systematic and is caused by exclusion-principle violating diagrams or corresponding corrections. Our analysis elucidates the role played by these different diagrams, which is crucial for the construction of rigorous, accurate, and systematic methods. Finally, we explicitly show that all perturbative fully self-consistent Green's function methods are size-extensive.

physics.chem-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

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↗

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

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↗

arXiv2020

Is solid copper oxalate a spin chain or a mixture of entangled spin pairs?

Macroscopic assemblies of interacting spins give rise to a broad spectrum of behaviors determined by the spatial arrangement of the magnetic sites and the electronic interactions between them. Compounds of copper (II), in which each copper carries spin $\frac{1}{2}$, exhibit a vast variety of physical properties. For antiferromagnetically coupled spin sites, there are two limiting scenarios: spin chains in which the spins can exhibit a long-range order or a mixture of dimers in which the spins within each pair are entangled but do not communicate with the spins from other dimers. In principle, the two types can be distinguished on the basis of experimental observations and modeling using empirically parameterized effective Hamiltonians, but in practice, ambiguity may persist for decades, as is the case for copper oxalate. Here we use high-level ab initio calculations to establish the validity of the nearest-site Heisenberg model and to predict the interaction strength between the magnetic sites. The computed magnetic susceptibility provides an unambiguous interpretation of magnetic experiments performed throughout half a century, clearly supporting the infinite spin-chain behavior of solid copper oxalate.

cond-mat.str-el↗