Session M22: First-Principles Modeling of Excited-State Phenomena in Materials V: Method Development

Live

I will present recent developments in predicting electronic excitations using the combination of stochastic computational techniques and many-body theory. The methodology relies on operators' decomposition via random vectors and recasting expectation values as statistical estimators.
In practice, the implementation of diagrammatic methods employs real-time and real-space sampling.[1] This formalism leads to substantial computational savings and reduced scaling with the number of electrons; it enables first-principles predictions of quasiparticle energies in systems with thousands of atoms. In detail, I will describe our recent work on simulating nanoscale condensed systems within the linear scaling stochastic GW approximation.[2,3,4] Further, I will show that statistical sampling of interactions is an efficient route to go beyond GW: I will detail our work on the stochastic GWΓ approach, which combines non-local vertex corrections in the screened Coulomb interaction and self-energy.[5] I will demonstrate that the vertex corrections affect unoccupied states, improve the quasiparticle energies, and capture multi-quasiparticle excitations otherwise missing in GW.[5,6] Despite the increased complexity of the self-energy, the stochastic GWΓ scales linearly with the system size.

[1] V Vlcek, W Li, R Baer, E Rabani, D Neuhauser, Physical Review B 98 (7), 075107 (2018)
[2] J Brooks, G Weng, S Taylor, V Vlcek, Journal of Physics: Condensed Matter 32 (23), 234001 (2020)
[3] G Weng, V Vlcek The Journal of Physical Chemistry Letters 11 (17), 7177-7183 (2020)
[4] M Romanova, V Vlcek The Journal of Chemical Physics 153 (13), 134103 (2020)
[5] V Vlcek, Journal of Chemical Theory and Computation 15 (11), 6254-6266 (2019)
[6] C Mejuto-Zaera, et al., arXiv preprint arXiv:2009.0240122020   

Live

Time-dependent density-functional theory (TDDFT) is a computationally efficient first-principles approach for calculating optical spectra in insulators and semiconductors, including excitonic effects. We show how exciton wave functions can be obtained from TDDFT via the Kohn-Sham transition density matrix, both in the frequency-dependent linear-response regime and in real-time propagation. The method is illustrated using one-dimensional model solids.   

Live

In traditional GW implementations, the computational cost is growing as O(N⁴) in the system size N, which prohibits their application to many systems of interest. I present a GW algorithm in a Gaussian-type basis, whose computational cost scales with N² to N³. It will be shown that large minimax grids and resolution of the identity with the truncated Coulomb metric improve the accuracy of the low-scaling GW algorithm to < 0.01 eV for the GW100 test set. Large-scale applications of low-scaling GW will be discussed.   

Live

Koopmans-compliant functionals provide a novel orbital-density-dependent framework for an accurate evaluation of spectral properties, obtained imposing a generalized piecewise-linearity condition on the total energy of the system with respect to the occupation of each orbital. In
crystalline materials, due to the orbital-density-dependent nature of the functionals, minimization of the total energy leads to a ground-state set of variational orbitals that are localized and break the periodicity of the underlying lattice. Despite that, thanks to the Wannier-like character of the variational orbitals, we show that the Bloch states can be recovered and it is possible to describe the electronic energies through a band structure picture. In this talk I will present results for some benchmark semiconductors and insulators, obtained by unfolding the electronic bands obtained with direct minimization Gamma-point-only calculations.

[1] I. Dabo, A. Ferretti, N. Poilvert, Y. Li, N. Marzari, M. Cococcioni, Phys. Rev. B 82, 115121 (2010)
[2] N. L. Nguyen, N. Colonna, A. Ferretti, N. Marzari, Phys. Rev. X 8, 021051 (2018)
[3] N. Colonna, N. L. Nguyen, A. Ferretti, N. Marzari, J. of Chem. Theory Comput. 15, 1905 (2019)   

Live

The cumulant expansion of quasiparticle Green’s function has been quite popular and successful in going beyond the one-electron picture and describing electronic correlation that manifest as satellite sidebands¹. However, this method is not systematically improvable and only takes into account only some fraction of interband interaction because of the truncation of Dyson series. In this work, we provide a method to systematically improve the quasiparticle Green’s function by using power series corrections and self consistently including the corrections within the self energy. This method does not truncate the Dyson series and the final correction equations are recursive in nature. We also show the derivation of time-ordered and retarded cumulant expansion results from this method and elucidate the underlying approximations on self energy in both cases. Finally, we show an application of this method on a simple two band model and compare them to cumulant results.
¹Kas et al, Phys. Rev. B 90, 085112 (2014)   

Live

First, we present a new embedding approach [1] in the stochastic GW technique that enables efficient treatment of the impurity states with high accuracy and minimal effort. The method is based on a partitioning of the Green’s function and screened Coulomb potential into the deterministic subspace (of localized states) and the stochastic subspace. The enhanced stochastic-deterministic sampling minimizes statistical errors in energies of localized quasiparticles.
Further, we present a new technique for the stochastic decomposition of the many-body interactions into additive subspace contributions. We partition the Hilbert space and compute the polarization self-energy via sampling selected charge density fluctuations in real space and time. The method allows to identify couplings among different areas, e.g., screening contributions in quantum interfaces.
We exemplify our approaches on N-vacancy defects in monolayer and hBN - graphene bilayer (> 2,000 electrons). We demonstrate the new hybrid approach reduces statistical errors and leads to significant savings in computational time.
1. M. Romanova, V. Vlcek, J. Chem. Phys. 153, 134103, 2020   

Live

Accurate prediction of fundamental band gaps of crystalline solid state systems entirely within density functional theory is a long standing challenge. Here, we present a simple and inexpensive method that achieves this by means of non-empirical optimal tuning of the parameters of a screened range-separated hybrid functional. The tuning involves the enforcement of a generalization of the ionization potential theorem to the removal of an electron in an occupied state described by a localized Wannier function in a modestly sized supercell calculation. The method is benchmarked on a set of systems ranging from narrow band gap semiconductors to large band gap insulators, spanning a range of band gaps from 0.2 to 14.2 eV and is found to yield quantitative accuracy across the board, with a mean absolute error of ∼0.1 eV and a maximal error of ∼0.2 eV.   

Live

The single-site Korringa-Kohn-Rostoker coherent potential approximation (KKR-CPA) ignores short-range ordering present in disordered metallic systems. We establish a technique to fix this shortcoming by embedding an averaged cluster that displays chemical short-range order (SRO). The degree of SRO can be tuned by externally defined order parameters. This averaged cluster can be embedded in the single-site CPA medium or a self-consistently obtained effective medium that contains SRO information. The validity of this method is demonstrated by applying it to two alloy systems—the CuZn body-centered cubic (BCC) solid solution, and AlCrTiV, a four-element BCC high entropy alloy. A comparison between the non-self-consistent and self-consistent modes is also provided for the two above-mentioned systems.   

Live

We propose a computationally efficient Kerker mixing scheme for robust, rapidly and system-size independent converging selfconsistent-field calculations using all-electron first-principles electronic structure methods based on the muffin-tin partitioning of space. We construct the Kerker preconditioner by determining the screened Coulomb potential in real space, solving a modified Helmholtz equation by adopting Weinert’s pseudocharge method for calculating the Poisson equation for periodic charge densities. We have related the preconditioning parameter to the density of states of the delocalized electrons at the Fermi energy and developed a model to choose the preconditioning parameter either prior to the calculation or on the fly. The method has been extend to the slab-model for 2D films with semi-infinte surfaces. Results are presented using the FLAPW method FLEUR (www.flapw.de) and the KKR-Greenfunction code KKRnano (jukkr.fz-juelich.de).   

Live

We present the open-source VOTCA-XTP software [1] for the calculation of the excited-state electronic structure of molecules using many-body Green’s functions theory in the GW approximation with the Bethe–Salpeter Equation (BSE). Its implementation is based on Gaussian orbitals, including, i .a., resolution-of-identity techniques, different methods for the frequency integration of the self-energy, acceleration with a hybrid OpenMP/Cuda scheme, or inclusion of a classical polarizable environment in a coupled quantum- and molecular-mechanics (QM/MM) scheme. Two showcase examples are discussed: First, a multiscale simulation framework for quantitative predictions of the high-energy part of ultraviolet photoelectron spectroscopy (UPS) spectra of amorphous molecular solids [2]. Second, we investigate the intermolecular charge-transfer excited states in morphologies of low-donor content rubrene-C60 mixtures using different variants of GW-BSE/MM setup.
[1] Excited-State Electronic Structure of Molecules Using Many-Body Green's Functions: Quasiparticles and Electron-Hole Excitations with VOTCA-XTP, J. Chem. Phys. 152, 114103 (2020)
[2] Quantitative Predictions of Photoelectron Spectra in Amorphous Molecular Solids from Multiscale Quasiparticle Embedding, Phys. Rev. B 101, 035402 (2020)   

Live

For first-principles excited-state calculations, there exist in the literature various schemes to do “self-consistent” GW calculations at different levels going beyond the one-shot G₀W₀ approach. For single-particle excitations (e.g., the quasiparticle bandgap in semiconductors), a straightforward self-consistent update of both the single-particle Green’s function G and the screened Coulomb interaction W within the random-phase approximation (RPA) for the self-energy generally gives less satisfactory results than those from the G₀W₀ approach as compared to experiments. This is because the dielectric screening is underestimated within RPA using quasiparticle energies and the error will be accumulated, since electron-hole interactions (excitonic effects) are neglected in the RPA polarizability. In this work, we investigate the importance of electron-hole interactions in modifying W in the GW self-energy. The theoretical formalism is presented, along with first-principles results for various semiconductors.