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DOE OSTI2024

Monte Carlo Explicitly Correlated Second-Order Many-Body Green’s Function Calculations of Semiconductor Band Gaps

A systematically converging series of ab initio, post-density-functional, size-consistent, electron-correlated approximations is desired for predictive computing of felectronic band structures of insulating, semiconducting, and metallic solids. A series that meets all of these desiderata (except the applicability to metals) is ab initio many-body Green's function theory based on Gaussian-type-orbital (GTO) basis sets. Here, its leading-order approximation, the second-order Green's function (GF2) method in the diagonal and frequency-independent approximations with the aug-cc-pVDZ basis set, is applied to the fundamental band gaps of three semiconductors (diamond, silicon, and silicon carbide in the zincblende structure) using cluster models. Corrections are made to the basis-set-incompleteness errors by the explicit-correlation (F12) ansatz (GF2-F12) for the valence band edges. The crystals are modeled as surface-passivated clusters of increasing sizes, whose wave functions are expanded by up to 2709 GTO basis functions. Immense computational costs of these calculations are overcome by the highly scalable stochastic algorithm of the Monte Carlo GF2-F12 method, whose operation cost per state increases only as a cubic power of system size, which has a tiny memory footprint and easily achieves near-perfect parallel efficiency on thousands of CPUs or on hundreds of GPUs. The correlated, F12-corrected highest-occupied and lowest-unoccupied molecular-orbital energy (HOMO-LUMO) gap is 5.78 ± 0.07 eV for C 87 H 76 as compared with the experimental value of the fundamental (indirect) band gap of bulk diamond at 5.48 eV. The correlated, F12-corrected HOMO-LUMO gaps for Si 75 H 76 and Si 32 C 43 H 76 are 2.56 ± 0.15 eV and 3.50 ± 0.12 eV, respectively, which are expected to decrease further with increasing cluster sizes. As a result, the experimental fundamental (indirect) band gaps of bulk silicon and silicon carbide are 1.17 eV and 2.42 eV, respectively.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2016

Study of electromagnetic wave scattering from an inhomogeneous plasma layer using Green's function volume integral equation method

Gigahertz electromagnetic wave scattering from an inhomogeneous collisional plasma layer with bell-like and Epstein electron density distributions is studied by the Green's function volume integral equation method to find the reflectance, transmittance, and absorbance coefficients of this inhomogeneous plasma. Also, the effects of the frequency of the electromagnetic wave, plasma parameters, such as collision frequency, electron density, and plasma thickness, and the effects of the profile of the electron density on the electromagnetic wave scattering from this plasma slab are investigated. According to the results, when the electron density, collision frequency, and plasma thickness are increased, collisional absorbance is enhanced, and as a result, the absorbance bandwidth of plasma is broadened. Moreover, this broadening is more evident for plasma with bell-like electron density profile. Also, the bandwidth of the frequency and the range of pressure in which plasma behaves as a good reflector are determined in this article. According to the results, the bandwidth of the frequency is decreased for thicker plasma with bell-like profile, while it does not vary for a different plasma thickness with Epstein profile. Moreover, the range of the pressure is decreased for bell-like profile in comparison with Epstein profile. Furthermore, due to the sharp inhomogeneity of the Epstein profile, the coefficients of plasma that are uniform for plasma with bell-like profile are changed for plasma with Epstein profile, and some perturbations are seen.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Real-space Green's function approach for intrinsic losses in x-ray spectra

Intrinsic inelastic losses in x-ray spectra originate from excitations in an interacting electron system due to a suddenly created core-hole. These losses characterize the features observed in x-ray photoemission spectra (XPS), as well as many-body effects such as satellites and edge-singularities in x-ray absorption spectra (XAS). However, they are usually neglected in practical calculations. As shown by Langreth these losses can be treated within linear response in terms of a cumulant Green's function in momentum space. Here we present a complementary ab initio real-space Green's function generalization of the Langreth cumulant in terms of the dynamically screened core-hole interaction W c (ω) and the independent particle response function. Here we find that the cumulant kernel β⁡(ω) is analogous to XAS, but with the transition operator replaced by the core-hole potential with monopole selection rules. The behavior reflects the analytic structure of the loss function, with peaks near the zeros of the dielectric function, consistent with delocalized quasiboson excitations. The approach simplifies when W c (ω) is localized and spherically symmetric. In conclusion, illustrative results and comparisons are presented for the electron gas, sodium, and some early transition metal compounds.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Green’s function methods for excited states and x-ray spectra of functional materials

Many interesting properties of functional materials, such as dynamic response and thermodynamic behavior, depend on their excited state properties. These functional properties are often related to excitations in the system, such as phonons and plasmons, which lead to inelastic losses, lifetime, and other dynamic effects. The excitations are pure many-body correlation effects that are missing from independent particle theories. They are revealed in x-ray spectra such as photoemission and absorption, where they show up as satellites beyond the quasi-particle approximation. Our main focus in this work is the use of Green's function methods to describe these effects. In particular, we discuss how the cumulant Green's function provides a unified treatment of such dynamic correlation effects in many contexts. Besides a robust theoretical framework, these methods also yield widely applicable tools for practical calculations of many functional properties of materials. Furthermore, this methodology is illustrated with a number of applications ranging from optical and x-ray spectra to thermodynamic properties, and dynamic response. Some recent extensions for more correlated systems are also briefly discussed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2018

Polycrystal Plasticity Models Based on Green’s Functions: Mean-Field Self-Consistent and Full-Field Fast Fourier Transform Formulations

We review two crystal plasticity methodologies based on Green’s functions for the prediction of microstructure-property relations in polycrystalline aggregates. The first, known as the viscoplastic self-consistent (VPSC) formulation, is a mean-field theory. The second, known as the viscoplastic fast Fourier transform-based (VPFFT) formulation, is a full-field method. Finally, the assumptions and main equations of these Green’s function-based crystal plasticity formulations are presented using a unified notation, pointing out their similarities and differences and cross-validating their predictions.

36 MATERIALS SCIENCE↗

DOE OSTI2018

Process-Independent Effective Coupling from QCD Green's Functions to Phenomenology

This article reports on a very recent proposal for a new type of process-independent QCD effective charge (Binosi et al. in Phys Rev D 96(5):054026, 2017. https://doi.org/10.1103/PhysRevD.96.054026) defined, as an anologue of the Gell-Mann-Low effective charge in QCD, on the ground of nothing but the knowledge of the gauge-field two-point Green's function, albeit modified within a particular computational framework; namely, the combination of pinch technique and background field method which makes possible a systematic rearranging of classes of diagrams in order to redefine the Green's function and have them obey linear QED-like Slavnov-Taylor identities. We have here calculated that effective charge, shown how strikingly well it compares to a process-dependent effective charge based on the Bjorken sum rule; and, finally, employed it in an exploratory calculation of the proton electromagnetic form factor in the hard scattering regime.

confinement↗

DOE OSTI2015

Quasielastic scattering with the relativistic Green’s function approach

A relativistic model for quasielastic (QE) lepton-nucleus scattering is presented. The effects of final-state interactions (FSI) between the ejected nucleon and the residual nucleus are described in the relativistic Green’s function (RGF) model where FSI are consistently described with exclusive scattering using a complex optical potential. The results of the model are compared with experimental results of electron and neutrino scattering.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Perturbation theory and thermal transport in mass-disordered alloys: Insights from Green's function methods

Lowest-order quantum perturbation theory (Fermi's golden rule) for phonon-disorder scattering has been used to predict thermal conductivities in several semiconducting alloys with surprising success given its underlying hypothesis of weak and dilute disorder. In this paper, we explain how this is possible by focusing on the case of maximally mass-disordered Mg 2 Si 1-x Sn x . In this work, we use a Chebyshev polynomials Green's function method, which allows a full treatment of disorder on very large systems (tens of millions of atoms) to probe individual phonon linewidths and frequency-resolved thermal transport. We demonstrate that the success of perturbation theory originates from the specific form of mass disorder terms in the phonon Green's function and from the interplay between anharmonic and disorder scattering.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Coupled Cluster Green's function formulations based on the effective Hamiltonians

In this work, we demonstrate that the effective Hamiltonians obtained with the downfolding procedure based on double unitary coupled cluster (DUCC) ansatz can be used in the context of Green’s function coupled cluster (GFCC) formalism to calculate spectral functions of molecular systems. This combined approach (DUCC-GFCC) provides a significant reduction of numerical effort and good agreement with the corresponding all-orbital GFCC methods in energy windows that are consistent with the choice of active space. These features are demonstrated on the example of two benchmark systems: H 2 O and N 2 , where DUCC-GFCC calculations were performed for active spaces of various sizes.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2019

Quasinormal modes, echoes and the causal structure of the Green's function

Quasinormal modes describe the return to equilibrium of a perturbed system, in particular the ringdown phase of a black hole merger. But as globally-defined quantities, the quasinormal spectrum can be highly sensitive to global structure, including distant small perturbations to the potential. In what sense are quasinormal modes a property of the resulting black hole? We explore this question for the linearized perturbation equation with two potentials having disjoint bounded support. We give a composition law for the Wronskian that determines the quasinormal frequencies of the combined system. We show that over short time scales the evolution is governed by the quasinormal frequencies of the individual potentials, while the sensitivity to global structure can be understood in terms of echoes. We introduce an echo expansion of the Green’s function and show that, as expected on general grounds, at any finite time causality limits the number of echoes that can contribute. We illustrate our results with the soluble example of a pair of -function potentials. We explicate the causal structure of the Green’s function, demonstrating under what conditions two very different quasinormal spectra give rise to very similar ringdown waveforms.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

Estimates for the Green's function and parameters of exponential dichotomy of a hyperbolic operator semigroup and linear relations

By applying Lyapunov's equation, the method of similar operators, and the methods of harmonic analysis, we obtain estimates for the parameters of exponential dichotomy and for the Green's function constructed for a hyperbolic operator semigroup and a hyperbolic linear relation. Estimates are obtained using quantities which are determined by the resolvent of the infinitesimal operator of the operator semigroup and of the linear relation. Bibliography: 51 titles.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

Combining molecular dynamics with mesoscopic Green’s function reaction dynamics simulations

In many reaction-diffusion processes, ranging from biochemical networks, catalysis, to complex self-assembly, the spatial distribution of the reactants and the stochastic character of their interactions are crucial for the macroscopic behavior. The recently developed mesoscopic Green’s Function Reaction Dynamics (GFRD) method enables efficient simulation at the particle level provided the microscopic dynamics can be integrated out. Yet, many processes exhibit non-trivial microscopic dynamics that can qualitatively change the macroscopic behavior, calling for an atomistic, microscopic description. We propose a novel approach that combines GFRD for simulating the system at the mesoscopic scale where particles are far apart, with a microscopic technique such as Langevin dynamics or Molecular Dynamics (MD), for simulating the system at the microscopic scale where reactants are in close proximity. This scheme defines the regions where the particles are close together and simulated with high microscopic resolution and those where they are far apart and simulated with lower mesoscopic resolution, adaptively on the fly. The new multi-scale scheme, called MD-GFRD, is generic and can be used to efficiently simulate reaction-diffusion systems at the particle level.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2019

Stochastic resolution of identity second-order Matsubara Green’s function theory

We create a stochastic resolution of identity representation to the second-order Matsubara Green’s function (sRI-GF2) theory. Using a stochastic resolution of the Coulomb integrals, the second order Born self-energy in GF2 is decoupled and reduced to matrix products/ contractions, which reduces the computational cost from O(N 5 ) to O(N 3 ) (with N being the number of atomic orbitals). Currently, the method can be viewed as an extension to our previous work on stochastic resolution of identity second order Møller-Plesset perturbation theory [T. Y. Takeshita et al., J. Chem. Theory Comput. 13, 4605 (2017)] and offers an alternative to previous stochastic GF2 formulations [D. Neuhauser et al., J. Chem. Theory Comput. 13, 5396 (2017)]. We show that sRI-GF2 recovers the deterministic GF2 results for small systems, is computationally faster than deterministic GF2 for N > 80, and is a practical approach to describe weak correlations in systems with 10 3 electrons and more.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1996

A Green's function method for high charge and energy ion transport

A heavy-ion transport code using Green's function methods is developed. The low-order perturbation terms exhibiting the greatest energy variation are used as dominant energy-dependent terms, and the higher order collision terms are evaluated using nonperturbative methods. The recently revised NUCFRG database is used to evaluate the solution for comparison with experimental data for 625A MeV 20Ne and 517A MeV 40Ar ion beams. Improved agreements with the attenuation characteristics for neon ions are found, and reasonable agreement is obtained for the transport of argon ions in water.

Energy Transfer↗

NASA NTRS1996

Two-Flux Green's Function Analysis for Transient Spectral Radiation in a Composite

An analysis is developed for obtaining transient temperatures in a two-layer semitransparent composite with spectrally dependent properties. Each external boundary of the composite is subjected to radiation and convection. The two-flux radiative transfer equations are solved by deriving a Green's function. This yields the local radiative heat source needed to numerically solve the transient energy equation. An advantage of the two-flux method is that isotropic scattering is included without added complexity. The layer refractive indices are larger than one. This produces internal reflections at the boundaries and the internal interface; the reflections are assumed diffuse. Spectral results using the Green's function method are verified by comparing with numerical solutions using the exact radiative transfer equations. Transient temperature distributions are given to illustrate the effect of radiative heating on one side of a composite with external convective cooling. The protection of a material from incident radiation is illustrated by adding scattering to the layer adjacent to the radiative source.

Siegel, Robert↗

DOE OSTI2023

The Generalized Green’s function Cluster Expansion: A Python package for simulating polarons

We present an efficient implementation of the Generalized Green’s function Cluster Expansion (GGCE), which is a new method for computing the ground-state properties and dynamics of polarons (single electrons coupled to lattice vibrations) in model electron-phonon systems. The GGCE works at arbitrary temperature and is well suited for a variety of electron-phonon couplings, including, but not limited to, site and bond Holstein and Peierls (Su-SchriefferHeeger) couplings, and couplings to multiple phonon modes with different energy scales and coupling strengths. Quick calculations can be performed efficiently on a laptop using solvers from NumPy and SciPy, or in parallel at scale using the PETSc sparse linear solver engine.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Range-separated stochastic resolution of identity: Formulation and application to second-order Green’s function theory

We develop a range-separated stochastic resolution of identity (RS-SRI) approach for the four-index electron repulsion integrals, where the larger terms (above a predefined threshold) are treated using a deterministic RI and the remaining terms are treated using a SRI. The approach is implemented within a second-order Green’s function formalism with an improved O(N 3 ) scaling with the size of the basis set, N. Moreover, the RS approach greatly reduces the statistical error compared to the full stochastic version [T. Y. Takeshita et al., J. Chem. Phys. 151, 044114 (2019)], resulting in computational speedups of ground and excited state energies of nearly two orders of magnitude, as demonstrated for hydrogen dimer chains and water clusters.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Tidal Love numbers and Green’s functions in black hole spacetimes

Tidal interactions play a crucial role in deciphering gravitational wave signals emitted by the coalescence of binary systems. They are usually quantified by a set of complex coefficients which include tidal Love numbers, describing the conservative response to an external perturbation. In the static case, these are found to vanish exactly for asymptotically flat black holes in general relativity in four space-time dimensions, and recently they have been generalized to dynamical interactions. In the context of response theory, the retarded Green’s function provides the complete description of the behavior of dynamical systems. Here, in this work we investigate the relation between Love numbers and Green’s functions, and highlight the relevance of radiation reaction effects to their connection. As a special case, we discuss Banados-Teitelboim-Zanelli black holes, where the absence of radiative modes allows us to make a direct link between them.

classical black holes↗