Title: Efficient Temperature-Dependent Green’s Functions Methods for Realistic Systems: Compact Grids for Orthogonal Polynomial Transforms

Journal Article · · Journal of Chemical Theory and Computation
 [1];  [2];  [2]
  1. Univ. of Michigan, Ann Arbor, MI (United States); University of Michigan
  2. Univ. of Michigan, Ann Arbor, MI (United States)
+ Show Author Affiliations

The Matsubara Green’s function that is used to describe temperature-dependent behavior is expressed on a numerical grid. While such a grid usually has a couple of hundred points for low-energy model systems, for realistic systems with large basis sets the size of an accurate grid can be tens of thousands of points, constituting a severe computational and memory bottleneck. In this paper, we determine efficient imaginary time grids for the temperature-dependent Matsubara Green’s function formalism that can be used for calculations on realistic systems. Here we show that, because of the use of an orthogonal polynomial transform, we can restrict the imaginary time grid to a few hundred points and reach micro-Hartree accuracy in the electronic energy evaluation. Moreover, we show that only a limited number of orthogonal polynomial expansion coefficients are necessary to preserve accuracy when working with a dual representation of the Green’s function or self-energy and transforming between the imaginary time and frequency domain.

Research Organization:
Univ. of Michigan, Ann Arbor, MI (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
SC0010381
OSTI ID:
1843754
Journal Information:
Journal of Chemical Theory and Computation, Journal Name: Journal of Chemical Theory and Computation Journal Issue: 2 Vol. 12; ISSN 1549-9618
Publisher:
American Chemical SocietyCopyright Statement
Country of Publication:
United States
Language:
English

References (57)

Real-space grids and the Octopus code as tools for the development of new simulation approaches for electronic systems journal January 2015
The role of databases in support of computational chemistry calculations journal October 1996
Radial quadrature for multiexponential integrands journal April 2003
Elimination of energy denominators in Møller—Plesset perturbation theory by a Laplace transform approach journal June 1991
A standard grid for density functional calculations journal July 1993
Global minima of water clusters (H2O)n, n≤21, described by an empirical potential journal April 1998
Basis Set Exchange:  A Community Database for Computational Sciences journal March 2007
Low Scaling Algorithms for the Random Phase Approximation: Imaginary Time and Laplace Transformations journal May 2014
Ab Initio Potential Energy Surface and Vibrational−Rotational Energy Levels of X 2 Σ + CaOH journal October 2002
Multiresolution quantum chemistry in multiwavelet bases: excited states from time-dependent Hartree–Fock and density functional theory via linear response journal January 2015
Confined helium on Lagrange meshes journal January 2015
An adaptive finite-element method for large-scale ab initio molecular dynamics simulations journal January 2015
Edge reconstruction in armchair phosphorene nanoribbons revealed by discontinuous Galerkin density functional theory journal January 2015
Numerically accurate linear response-properties in the configuration-interaction singles (CIS) approximation journal January 2015
Real-space grids and the Octopus code as tools for the development of new simulation approaches for electronic systems journal January 2015
Configuration interaction singles based on the real-space numerical grid method: Kohn–Sham versus Hartree–Fock orbitals journal January 2015
Accurate and efficient linear scaling DFT calculations with universal applicability journal January 2015
Optimized multi-site local orbitals in the large-scale DFT program CONQUEST journal January 2015
Orbital free DFT versus single density equation: a perspective through quantum domain behavior of a classically chaotic system journal January 2015
An auxilliary grid method for the calculation of electrostatic terms in density functional theory on a real-space grid journal January 2015
Fock-exchange for periodic structures in the real-space formalism and the KLI approximation journal January 2015
The grid-based fast multipole method – a massively parallel numerical scheme for calculating two-electron interaction energies journal January 2015
Singular analysis and coupled cluster theory journal January 2015
Optimizing a parametrized Thomas–Fermi–Dirac–Weizsäcker density functional for atoms journal January 2015
An economic prediction of the finer resolution level wavelet coefficients in electronic structure calculations journal January 2015
Tensor numerical methods in quantum chemistry: from Hartree–Fock to excitation energies journal January 2015
A real-space stochastic density matrix approach for density functional electronic structure journal January 2015
High order forces and nonlocal operators in a Kohn–Sham Hamiltonian journal January 2015
Wavelet formulation of the polarizable continuum model. II. Use of piecewise bilinear boundary elements journal January 2015
On the use of the Laplace transform in local correlation methods journal January 2008
Resolution of the identity atomic orbital Laplace transformed second order Møller–Plesset theory for nonconducting periodic systems journal January 2008
Tighter multipole-based integral estimates and parallel implementation of linear-scaling AO–MP2 theory journal January 2008
Gaussian Basis Functions for Use in Molecular Calculations. I. Contraction of (9s5p) Atomic Basis Sets for the First‐Row Atoms journal October 1970
Gaussian Basis Functions for Use in Molecular Calculations. III. Contraction of (10s6p) Atomic Basis Sets for the First‐Row Atoms journal July 1971
An O ( N 3 ) implementation of Hedin's GW approximation for molecules journal August 2011
Cu and Ag as one‐valence‐electron atoms: Pseudopotential results for Cu 2 , Ag 2 , CuH, AgH, and the corresponding cations journal December 1983
Energy‐adjusted a b i n i t i o pseudopotentials for the first row transition elements journal January 1987
A multicenter numerical integration scheme for polyatomic molecules journal February 1988
Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen journal January 1989
Laplace transform techniques in Mo/ller–Plesset perturbation theory journal January 1992
Gaussian basis sets for use in correlated molecular calculations. III. The atoms aluminum through argon journal January 1993
Gaussian basis sets for use in correlated molecular calculations. IV. Calculation of static electrical response properties journal February 1994
Improved radial grids for quadrature in molecular density‐functional calculations journal June 1996
Linear scaling second-order Moller–Plesset theory in the atomic orbital basis for large molecular systems journal February 1999
Communication: The description of strong correlation within self-consistent Green's function second-order perturbation theory journal June 2014
Fractional charge and spin errors in self-consistent Green’s function theory journal May 2015
Quadrature schemes for integrals of density functional theory journal March 1993
Acceleration of the Stochastic Analytic Continuation Method via an Orthogonal Polynomial Representation of the Spectral Function journal September 2013
Hybridization expansion impurity solver: General formulation and application to Kondo lattice and two-orbital models journal October 2006
Orthogonal polynomial representation of imaginary-time Green’s functions journal August 2011
Machine learning for many-body physics: The case of the Anderson impurity model journal October 2014
Systematically improvable multiscale solver for correlated electron systems journal March 2015
Space-Time Method for Ab Initio Calculations of Self-Energies and Dielectric Response Functions of Solids journal March 1995
Band-Gap Problem in Semiconductors Revisited: Effects of Core States and Many-Body Self-Consistency journal August 2002
Continuous-Time Solver for Quantum Impurity Models journal August 2006
The kernel polynomial method journal March 2006
Continuous-time Monte Carlo methods for quantum impurity models journal May 2011

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Finite Temperature Auxiliary Field Quantum Monte Carlo in the Canonical Ensemble text January 2020
Self-consistent second-order Green’s function perturbation theory for periodic systems journal February 2016
Exploring connections between statistical mechanics and Green’s functions for realistic systems: Temperature dependent electronic entropy and internal energy from a self-consistent second-order Green’s function journal November 2016
Comparison of Green’s functions for transition metal atoms using self-energy functional theory and coupled-cluster singles and doubles (CCSD) journal June 2018
Stochastic resolution of identity second-order Matsubara Green’s function theory journal July 2019
Finite temperature quantum embedding theories for correlated systems journal February 2017
Effect of propagator renormalization on the band gap of insulating solids journal August 2019
Sparse sampling approach to efficient ab initio calculations at finite temperature journal January 2020
Compressing Green's function using intermediate representation between imaginary-time and real-frequency domains journal July 2017
Testing self-energy embedding theory in combination with GW journal October 2017
Spectral properties from Matsubara Green's function approach: Application to molecules journal March 2018
Stochastic density functional theory at finite temperatures journal March 2018
Performance analysis of a physically constructed orthogonal representation of imaginary-time Green's function journal July 2018
Chebyshev polynomial representation of imaginary-time response functions journal August 2018
Towards the Solution of the Many-Electron Problem in Real Materials: Equation of State of the Hydrogen Chain with State-of-the-Art Many-Body Methods journal September 2017
Exploring connections between statistical mechanics and Green's functions for realistic systems. Temperature dependent electronic entropy and internal energy from a self-consistent second-order Green's function text January 2016
Finite temperature quantum embedding theories for correlated systems text January 2016
Towards the solution of the many-electron problem in real materials: equation of state of the hydrogen chain with state-of-the-art many-body methods text January 2017
Spectral properties from Matsubara Green's function approach - application to molecules text January 2017
Comparison of Green's functions for transition metal atoms using self-energy functional theory and coupled-cluster singles and doubles (CCSD) text January 2018
Performance analysis of a physically constructed orthogonal representation of imaginary-time Green's function text January 2018
Effect of propagator renormalization on the band gap of insulating solids text January 2018

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37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
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