DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Accelerating the convergence of auxiliary-field quantum Monte Carlo in solids with optimized Gaussian basis sets

Journal Article · · Journal of Chemical Physics
DOI: https://doi.org/10.1063/5.0025390 · OSTI ID:1720183

We investigate the use of optimized correlation-consistent Gaussian basis sets for the study of insulating solids with auxiliary-field quantum Monte Carlo (AFQMC). The exponents of the basis set are optimized through the minimization of the second-order Møller–Plesset perturbation theory (MP2) energy in a small unit cell of the solid. We compare against other alternative basis sets proposed in the literature, namely, calculations in the Kohn–Sham basis and in the natural orbitals of an MP2 calculation. We find that our optimized basis sets accelerate the convergence of the AFQMC correlation energy compared to a Kohn–Sham basis and offer similar convergence to MP2 natural orbitals at a fraction of the cost needed to generate them. We also suggest the use of an improved, method independent, MP2-based basis set correction that significantly reduces the required basis set sizes needed to converge the correlation energy. With these developments, we study the relative performance of these basis sets in LiH, Si, and MgO and determine that our optimized basis sets yield the most consistent results as a function of volume. Using these optimized basis sets, we systematically converge the AFQMC calculations to the complete basis set and thermodynamic limit and find excellent agreement with experiment for the systems studied. Although we focus on AFQMC, our basis set generation procedure is independent of the subsequent correlated wavefunction method used.

Sponsoring Organization:
USDOE
OSTI ID:
1720183
Journal Information:
Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Vol. 153 Journal Issue: 19; ISSN 0021-9606
Publisher:
American Institute of PhysicsCopyright Statement
Country of Publication:
United States
Language:
English

References (68)

Efficient Explicitly Correlated Many-Electron Perturbation Theory for Solids: Application to the Schottky Defect in MgO journal August 2015
P y SCF: the Python-based simulations of chemistry framework : The PySCF program
  • Sun, Qiming; Berkelbach, Timothy C.; Blunt, Nick S.
  • Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 8, Issue 1 https://doi.org/10.1002/wcms.1340
journal September 2017
Communications: Accurate and efficient approximations to explicitly correlated coupled-cluster singles and doubles, CCSD-F12 journal June 2010
Overcoming the Memory Bottleneck in Auxiliary Field Quantum Monte Carlo Simulations with Interpolative Separable Density Fitting journal November 2018
Møller-plesset calculations taking care of the correlation CUSP journal February 1987
Daubechies wavelets as a basis set for density functional pseudopotential calculations journal July 2008
Energy band gaps and lattice parameters evaluated with the Heyd-Scuseria-Ernzerhof screened hybrid functional journal November 2005
Gaussian Basis Sets for Crystalline Solids: All-Purpose Basis Set Libraries vs System-Specific Optimizations journal March 2020
Ab-initio simulations of materials using VASP: Density-functional theory and beyond journal October 2008
Auxiliary-field quantum Monte Carlo calculations of the structural properties of nickel oxide journal October 2018
QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials journal September 2009
Second-Order Møller–Plesset Perturbation Theory in the Condensed Phase: An Efficient and Massively Parallel Gaussian and Plane Waves Approach journal September 2012
In pursuit of the ab initio limit for conformational energy prototypes journal June 1998
Fast local-MP2 method with density-fitting for crystals. II. Test calculations and application to the carbon dioxide crystal journal August 2007
Fast local-MP2 method with density-fitting for crystals. I. Theory and algorithms journal August 2007
An error analysis for Hartree-Fock crystal orbital calculations journal July 1982
Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen journal January 1989
Momentum-space formalism for the total energy of solids journal November 1979
General orbital invariant MP2-F12 theory journal April 2007
Explicitly Correlated Electrons in Molecules journal December 2011
Electron affinities of the first‐row atoms revisited. Systematic basis sets and wave functions journal May 1992
Improved hybrid functional for solids: The HSEsol functional journal January 2011
Coulombic potential energy integrals and approximations journal May 1973
QMCPACK: Advances in the development, efficiency, and application of auxiliary field and real-space variational and diffusion quantum Monte Carlo journal May 2020
Approaching the theoretical limit in periodic local MP2 calculations with atomic-orbital basis sets: The case of LiH journal June 2011
Gaussian basis sets for use in correlated molecular calculations. III. The atoms aluminum through argon journal January 1993
QWalk: A quantum Monte Carlo program for electronic structure journal May 2009
RPA natural orbitals and their application to post-Hartree-Fock electronic structure methods journal December 2019
Density functional theory is straying from the path toward the exact functional journal January 2017
Second-order Møller–Plesset perturbation theory applied to extended systems. II. Structural and energetic properties journal August 2010
Perspective: Explicitly correlated electronic structure theory for complex systems journal February 2017
Accelerating Auxiliary-Field Quantum Monte Carlo Simulations of Solids with Graphical Processing Units journal May 2020
CRYSTAL: a computational tool for the ab initio study of the electronic properties of crystals journal January 2005
Self-consistent molecular Hartree—Fock—Slater calculations I. The computational procedure journal September 1973
Systematically convergent basis sets for transition metals. I. All-electron correlation consistent basis sets for the 3d elements Sc–Zn journal August 2005
Gaussian-Based Coupled-Cluster Theory for the Ground-State and Band Structure of Solids journal February 2017
Frozen-Orbital and Downfolding Calculations with Auxiliary-Field Quantum Monte Carlo journal October 2013
Gaussian basis sets for use in correlated molecular calculations. IV. Calculation of static electrical response properties journal February 1994
Wave functions with terms linear in the interelectronic coordinates to take care of the correlation cusp. I. General theory journal February 1991
Gaussian basis sets for accurate calculations on molecular systems in gas and condensed phases journal September 2007
Fermion Monte Carlo without fixed nodes: A game of life, death, and annihilation in Slater determinant space journal January 2009
Excited state calculations in solids by auxiliary-field quantum Monte Carlo journal September 2013
Duality of Ring and Ladder Diagrams and Its Importance for Many-Electron Perturbation Theories journal October 2019
The heat of formation of NCO journal September 1993
Gaussian basis sets for use in correlated molecular calculations. V. Core‐valence basis sets for boron through neon journal September 1995
Random-phase approximation and its applications in computational chemistry and materials science journal June 2012
The correlation-consistent composite approach: Application to the G3/99 test set journal September 2006
Atomic orbital Laplace-transformed second-order Møller–Plesset theory for periodic systems journal December 2001
Data for "Accelerating the Convergence of Auxiliary-Field Quantum Monte Carlo inSolids with Optimized Gaussian Basis Sets" dataset January 2020
From plane waves to local Gaussians for the simulation of correlated periodic systems journal August 2016
Communications: Survival of the fittest: Accelerating convergence in full configuration-interaction quantum Monte Carlo journal January 2010
Assessment of correlation energies based on the random-phase approximation journal April 2012
Electron repulsion integral approximations and error bounds: Molecular applications journal September 1974
Exact-exchange Hartree-Fock calculations for periodic systems. I. Illustration of the method journal March 1980
Exascale applications: skin in the game
  • Alexander, Francis; Almgren, Ann; Bell, John
  • Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 378, Issue 2166 https://doi.org/10.1098/rsta.2019.0056
journal January 2020
An Assessment of Theoretical Methods for Nonbonded Interactions: Comparison to Complete Basis Set Limit Coupled-Cluster Potential Energy Curves for the Benzene Dimer, the Methane Dimer, Benzene−Methane, and Benzene−H 2 S journal September 2009
Periodic local Møller–Plesset second order perturbation theory method applied to molecular crystals: Study of solid NH3 and CO2 using extended basis sets journal April 2010
Towards an exact description of electronic wavefunctions in real solids journal December 2012
On the convergence of the (ΔECCSD(T)−ΔEMP2) term for complexes with multiple H-bonds journal October 2002
First principles methods using CASTEP journal January 2005
Optimization algorithm for the generation of ONCV pseudopotentials journal November 2015
Second-order Mo̸ller–Plesset perturbation theory applied to extended systems. I. Within the projector-augmented-wave formalism using a plane wave basis set journal January 2009
Natural Orbitals for Wave Function Based Correlated Calculations Using a Plane Wave Basis Set journal August 2011
An optimized twist angle to find the twist-averaged correlation energy applied to the uniform electron gas journal May 2019
Explicitly correlated plane waves: Accelerating convergence in periodic wavefunction expansions journal August 2013
Particle-particle ladder based basis-set corrections applied to atoms and molecules using coupled-cluster theory journal September 2019
cp2k: atomistic simulations of condensed matter systems
  • Hutter, Jürg; Iannuzzi, Marcella; Schiffmann, Florian
  • Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 4, Issue 1 https://doi.org/10.1002/wcms.1159
journal June 2013
Recent developments in the P y SCF program package journal July 2020