Ab initio calculations in atoms, molecules, and solids, treating spin–orbit coupling and electron interaction on an equal footing

Eskridge, Brandon; Krakauer, Henry; Shi, Hao; Zhang, Shiwei

doi:10.1063/5.0075900

Title: Ab initio calculations in atoms, molecules, and solids, treating spin–orbit coupling and electron interaction on an equal footing

Journal Article · 02 January 2022 · Journal of Chemical Physics

DOI: https://doi.org/10.1063/5.0075900 · OSTI ID:1979002

^[1];

^[2];

^[3];

^[4]

College of William and Mary, Williamsburg, VA (United States); College of William and Mary, Williamsburg, VA (United States)
College of William and Mary, Williamsburg, VA (United States)
University of Delaware, Newark, DE (United States)
Flatiron Institute, New York, NY (United States)

We incorporate explicit, non-perturbative treatment of spin–orbit coupling into ab initio auxiliary-field quantum Monte Carlo (AFQMC) calculations. The approach allows a general computational framework for molecular and bulk systems in which material specificity, electron correlation, and spin–orbit coupling effects can be captured accurately and on an equal footing, with favorable computational scaling vs system size. We adopt relativistic effective-core potentials that have been obtained by fitting to fully relativistic data and that have demonstrated a high degree of reliability and transferability in molecular systems. This results in a two-component spin-coupled Hamiltonian, which is then treated by generalizing the ab initio AFQMC approach. We demonstrate the method by computing the electron affinity in Pb, the bond dissociation energy in Br₂ and I₂, and solid Bi.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: College of William and Mary, Williamsburg, VA (United States)

Sponsoring Organization:: Simons Foundation; USDOE; USDOE Office of Science (SC)

Grant/Contract Number:: SC0001303

OSTI ID:: 1979002

Journal Information:: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 1 Vol. 156; ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

References (70)

Relativistic energy-consistent pseudopotentials?Recent developments Stoll, Hermann; Metz, Bernhard; Dolg, Michael Journal of Computational Chemistry, Vol. 23, Issue 8 https://doi.org/10.1002/jcc.10037	journal	April 2002
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
Ab initio computations of molecular systems by the auxiliary-field quantum Monte Carlo method Motta, Mario; Zhang, Shiwei Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 8, Issue 5 https://doi.org/10.1002/wcms.1364	journal	May 2018
Characterization of the Ground State of Br2 by Laser-Induced Fluorescence Fourier Transform Spectroscopy of the B3Π0+u–X1Σ+g System Focsa, C.; Li, H.; Bernath, P. F. Journal of Molecular Spectroscopy, Vol. 200, Issue 1 https://doi.org/10.1006/jmsp.1999.8039	journal	March 2000
Molecular Spectra and Molecular Structure Huber, K. P.; Herzberg, G. https://doi.org/10.1007/978-1-4757-0961-2	book	January 1979
Zur Quantenmechanik des magnetischen Elektrons Pauli, W. Zeitschrift für Physik, Vol. 43, Issue 9-10 https://doi.org/10.1007/bf01397326	journal	September 1927
Generalized Trotter's formula and systematic approximants of exponential operators and inner derivations with applications to many-body problems Suzuki, Masuo Communications in Mathematical Physics, Vol. 51, Issue 2 https://doi.org/10.1007/bf01609348	journal	June 1976
Stability conditions and nuclear rotations in the Hartree-Fock theory Thouless, D. J. Nuclear Physics, Vol. 21 https://doi.org/10.1016/0029-5582(60)90048-1	journal	November 1960
Accurate computations of Rashba spin-orbit coupling in interacting systems: From the Fermi gas to real materials Rosenberg, Peter; Shi, Hao; Zhang, Shiwei Journal of Physics and Chemistry of Solids, Vol. 128 https://doi.org/10.1016/j.jpcs.2017.12.026	journal	May 2019
The restricted active space (RAS) state interaction approach with spin–orbit coupling Malmqvist, Per Åke; Roos, Björn O.; Schimmelpfennig, Bernd Chemical Physics Letters, Vol. 357, Issue 3-4 https://doi.org/10.1016/s0009-2614(02)00498-0	journal	May 2002
Taming the Sign Problem in Auxiliary-Field Quantum Monte Carlo Using Accurate Wave Functions Mahajan, Ankit; Sharma, Sandeep Journal of Chemical Theory and Computation, Vol. 17, Issue 8 https://doi.org/10.1021/acs.jctc.1c00371	journal	July 2021
Spin–Orbit Coupling via Four-Component Multireference Methods: Benchmarking on p-Block Elements and Tentative Recommendations Zhang, Boyi; Vandezande, Jonathon E.; Reynolds, Ryan D. Journal of Chemical Theory and Computation, Vol. 14, Issue 3 https://doi.org/10.1021/acs.jctc.7b00989	journal	February 2018
One-Step Treatment of Spin–Orbit Coupling and Electron Correlation in Large Active Spaces Mussard, Bastien; Sharma, Sandeep Journal of Chemical Theory and Computation, Vol. 14, Issue 1 https://doi.org/10.1021/acs.jctc.7b01019	journal	December 2017
Local Embedding and Effective Downfolding in the Auxiliary-Field Quantum Monte Carlo Method Eskridge, Brandon; Krakauer, Henry; Zhang, Shiwei Journal of Chemical Theory and Computation, Vol. 15, Issue 7 https://doi.org/10.1021/acs.jctc.8b01244	journal	June 2019
On Achieving High Accuracy in Quantum Chemical Calculations of 3 d Transition Metal-Containing Systems: A Comparison of Auxiliary-Field Quantum Monte Carlo with Coupled Cluster, Density Functional Theory, and Experiment for Diatomic Molecules Shee, James; Rudshteyn, Benjamin; Arthur, Evan J. Journal of Chemical Theory and Computation, Vol. 15, Issue 4 https://doi.org/10.1021/acs.jctc.9b00083	journal	March 2019
Relativistic Pseudopotentials: Their Development and Scope of Applications Dolg, Michael; Cao, Xiaoyan Chemical Reviews, Vol. 112, Issue 1 https://doi.org/10.1021/cr2001383	journal	September 2011
Frozen-Orbital and Downfolding Calculations with Auxiliary-Field Quantum Monte Carlo Purwanto, Wirawan; Zhang, Shiwei; Krakauer, Henry Journal of Chemical Theory and Computation, Vol. 9, Issue 11 https://doi.org/10.1021/ct4006486	journal	October 2013
On the Spectroscopic and Thermochemical Properties of ClO, BrO, IO, and Their Anions Peterson, Kirk A.; Shepler, Benjamin C.; Figgen, Detlev The Journal of Physical Chemistry A, Vol. 110, Issue 51 https://doi.org/10.1021/jp065887l	journal	December 2006
Relativistic Four-Component Potential Energy Curves for the Lowest 23 Covalent States of Molecular Bromine (Br ₂ ) Gomes, José da Silva; Gargano, Ricardo; Martins, João B. L. The Journal of Physical Chemistry A, Vol. 118, Issue 31 https://doi.org/10.1021/jp4114283	journal	May 2014
One-dimensional topological edge states of bismuth bilayers Drozdov, Ilya K.; Alexandradinata, A.; Jeon, Sangjun Nature Physics, Vol. 10, Issue 9 https://doi.org/10.1038/nphys3048	journal	August 2014
Higher-order topology in bismuth Schindler, Frank; Wang, Zhijun; Vergniory, Maia G. Nature Physics, Vol. 14, Issue 9 https://doi.org/10.1038/s41567-018-0224-7	journal	July 2018
Small-core multiconfiguration-Dirac–Hartree–Fock-adjusted pseudopotentials for post- d main group elements: Application to PbH and PbO Metz, Bernhard; Stoll, Hermann; Dolg, Michael The Journal of Chemical Physics, Vol. 113, Issue 7 https://doi.org/10.1063/1.1305880	journal	August 2000
Systematically convergent basis sets with relativistic pseudopotentials. I. Correlation consistent basis sets for the post- d group 13–15 elements Peterson, Kirk A. The Journal of Chemical Physics, Vol. 119, Issue 21 https://doi.org/10.1063/1.1622923	journal	December 2003
Systematically convergent basis sets with relativistic pseudopotentials. II. Small-core pseudopotentials and correlation consistent basis sets for the post- d group 16–18 elements Peterson, Kirk A.; Figgen, Detlev; Goll, Erich The Journal of Chemical Physics, Vol. 119, Issue 21 https://doi.org/10.1063/1.1622924	journal	December 2003
Quasirelativistic theory equivalent to fully relativistic theory Kutzelnigg, Werner; Liu, Wenjian The Journal of Chemical Physics, Vol. 123, Issue 24 https://doi.org/10.1063/1.2137315	journal	December 2005
Auxiliary-field quantum Monte Carlo calculations of molecular systems with a Gaussian basis Al-Saidi, W. A.; Zhang, Shiwei; Krakauer, Henry The Journal of Chemical Physics, Vol. 124, Issue 22 https://doi.org/10.1063/1.2200885	journal	June 2006
An infinite-order two-component relativistic Hamiltonian by a simple one-step transformation Iliaš, Miroslav; Saue, Trond The Journal of Chemical Physics, Vol. 126, Issue 6 https://doi.org/10.1063/1.2436882	journal	February 2007
Quasirelativistic theory. II. Theory at matrix level Liu, Wenjian; Kutzelnigg, Werner The Journal of Chemical Physics, Vol. 126, Issue 11 https://doi.org/10.1063/1.2710258	journal	March 2007
Eliminating spin contamination in auxiliary-field quantum Monte Carlo: Realistic potential energy curve of F2 Purwanto, Wirawan; Al-Saidi, W. A.; Krakauer, Henry The Journal of Chemical Physics, Vol. 128, Issue 11 https://doi.org/10.1063/1.2838983	journal	March 2008
Excited state calculations using phaseless auxiliary-field quantum Monte Carlo: Potential energy curves of low-lying C2 singlet states Purwanto, Wirawan; Zhang, Shiwei; Krakauer, Henry The Journal of Chemical Physics, Vol. 130, Issue 9 https://doi.org/10.1063/1.3077920	journal	March 2009
Molecular core-valence correlation effects involving the post-d elements Ga–Rn: Benchmarks and new pseudopotential-based correlation consistent basis sets Peterson, Kirk A.; Yousaf, Kazim E. The Journal of Chemical Physics, Vol. 133, Issue 17 https://doi.org/10.1063/1.3503659	journal	November 2010
Assessing weak hydrogen binding on Ca ⁺ centers: An accurate many-body study with large basis sets Purwanto, Wirawan; Krakauer, Henry; Virgus, Yudistira The Journal of Chemical Physics, Vol. 135, Issue 16 https://doi.org/10.1063/1.3654002	journal	October 2011
Perspective: Relativistic effects Autschbach, Jochen The Journal of Chemical Physics, Vol. 136, Issue 15 https://doi.org/10.1063/1.3702628	journal	April 2012
Electron affinities of B, Al, Bi, and Pb Feigerle, C. S.; Corderman, R. R.; Lineberger, W. C. The Journal of Chemical Physics, Vol. 74, Issue 2 https://doi.org/10.1063/1.441174	journal	January 1981
Relativistic and correlation effects on molecular properties. I. The dihalogens F ₂ , Cl ₂ , Br ₂ , I ₂ , and At ₂ Visscher, L.; Dyall, K. G. The Journal of Chemical Physics, Vol. 104, Issue 22 https://doi.org/10.1063/1.471636	journal	June 1996
Interfacing relativistic and nonrelativistic methods. I. Normalized elimination of the small component in the modified Dirac equation Dyall, Kenneth G. The Journal of Chemical Physics, Vol. 106, Issue 23 https://doi.org/10.1063/1.473860	journal	June 1997
The relativistic Fock-space coupled-cluster method for molecules: CdH and its ions Eliav, Ephraim; Kaldor, Uzi; Hess, Bernd A. The Journal of Chemical Physics, Vol. 108, Issue 9 https://doi.org/10.1063/1.475740	journal	March 1998
An auxiliary-field quantum Monte Carlo study of the chromium dimer Purwanto, Wirawan; Zhang, Shiwei; Krakauer, Henry The Journal of Chemical Physics, Vol. 142, Issue 6 https://doi.org/10.1063/1.4906829	journal	February 2015
A state interaction spin-orbit coupling density matrix renormalization group method Sayfutyarova, Elvira R.; Chan, Garnet Kin-Lic The Journal of Chemical Physics, Vol. 144, Issue 23 https://doi.org/10.1063/1.4953445	journal	June 2016
Quantum Monte Carlo with variable spins Melton, Cody A.; Bennett, M. Chandler; Mitas, Lubos The Journal of Chemical Physics, Vol. 144, Issue 24 https://doi.org/10.1063/1.4954726	journal	June 2016
Electron correlation within the relativistic no-pair approximation Almoukhalalati, Adel; Knecht, Stefan; Jensen, Hans Jørgen Aa. The Journal of Chemical Physics, Vol. 145, Issue 7 https://doi.org/10.1063/1.4959452	journal	August 2016
Two-component relativistic coupled-cluster methods using mean-field spin-orbit integrals Liu, Junzi; Shen, Yue; Asthana, Ayush The Journal of Chemical Physics, Vol. 148, Issue 3 https://doi.org/10.1063/1.5009177	journal	January 2018
An atomic mean-field spin-orbit approach within exact two-component theory for a non-perturbative treatment of spin-orbit coupling Liu, Junzi; Cheng, Lan The Journal of Chemical Physics, Vol. 148, Issue 14 https://doi.org/10.1063/1.5023750	journal	April 2018
QMCPACK: Advances in the development, efficiency, and application of auxiliary field and real-space variational and diffusion quantum Monte Carlo Kent, P. R. C.; Annaberdiyev, Abdulgani; Benali, Anouar The Journal of Chemical Physics, Vol. 152, Issue 17 https://doi.org/10.1063/5.0004860	journal	May 2020
Q uantum ESPRESSO toward the exascale Giannozzi, Paolo; Baseggio, Oscar; Bonfà, Pietro The Journal of Chemical Physics, Vol. 152, Issue 15 https://doi.org/10.1063/5.0005082	journal	April 2020
Recent developments in the P y SCF program package Sun, Qiming; Zhang, Xing; Banerjee, Samragni The Journal of Chemical Physics, Vol. 153, Issue 2 https://doi.org/10.1063/5.0006074	journal	July 2020
Essentials of relativistic quantum chemistry Liu, Wenjian The Journal of Chemical Physics, Vol. 152, Issue 18 https://doi.org/10.1063/5.0008432	journal	May 2020
Some recent developments in auxiliary-field quantum Monte Carlo for real materials Shi, Hao; Zhang, Shiwei The Journal of Chemical Physics, Vol. 154, Issue 2 https://doi.org/10.1063/5.0031024	journal	January 2021
Ab initio calculations of bismuth properties, including spin–orbit coupling Gonze, X.; Michenaud, J-P; Vigneron, J-P Physica Scripta, Vol. 37, Issue 5 https://doi.org/10.1088/0031-8949/37/5/022	journal	May 1988
QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials Giannozzi, Paolo; Baroni, Stefano; Bonini, Nicola Journal of Physics: Condensed Matter, Vol. 21, Issue 39, Article No. 395502 https://doi.org/10.1088/0953-8984/21/39/395502	journal	September 2009
Advanced capabilities for materials modelling with Quantum ESPRESSO Giannozzi, P.; Andreussi, O.; Brumme, T. Journal of Physics: Condensed Matter, Vol. 29, Issue 46 https://doi.org/10.1088/1361-648X/aa8f79	journal	October 2017
On the product of semi-groups of operators Trotter, H. F. Proceedings of the American Mathematical Society, Vol. 10, Issue 4 https://doi.org/10.1090/s0002-9939-1959-0108732-6	journal	April 1959
Dirac's Equation and the Spin-Spin Interactions of Two Electrons Breit, G. Physical Review, Vol. 39, Issue 4 https://doi.org/10.1103/physrev.39.616	journal	February 1932
Applicability of the no-pair equation with free-particle projection operators to atomic and molecular structure calculations Hess, Bernd A. Physical Review A, Vol. 32, Issue 2 https://doi.org/10.1103/physreva.32.756	journal	August 1985
Relativistic electronic-structure calculations employing a two-component no-pair formalism with external-field projection operators Hess, Bernd A. Physical Review A, Vol. 33, Issue 6 https://doi.org/10.1103/physreva.33.3742	journal	June 1986
Total-energy calculations of the structural properties of the group-V element arsenic Needs, Richard J.; Martin, Richard M.; Nielsen, O. H. Physical Review B, Vol. 33, Issue 6 https://doi.org/10.1103/physrevb.33.3778	journal	March 1986
Constrained path Monte Carlo method for fermion ground states Zhang, Shiwei; Carlson, J.; Gubernatis, J. E. Physical Review B, Vol. 55, Issue 12 https://doi.org/10.1103/physrevb.55.7464	journal	March 1997
Relativistic separable dual-space Gaussian pseudopotentials from H to Rn Hartwigsen, C.; Goedecker, S.; Hutter, J. Physical Review B, Vol. 58, Issue 7 https://doi.org/10.1103/physrevb.58.3641	journal	August 1998
From ultrasoft pseudopotentials to the projector augmented-wave method Kresse, G.; Joubert, D. Physical Review B, Vol. 59, Issue 3, p. 1758-1775 https://doi.org/10.1103/physrevb.59.1758	journal	January 1999
Phaseless auxiliary-field quantum Monte Carlo calculations with plane waves and pseudopotentials: Applications to atoms and molecules Suewattana, Malliga; Purwanto, Wirawan; Zhang, Shiwei Physical Review B, Vol. 75, Issue 24 https://doi.org/10.1103/physrevb.75.245123	journal	June 2007
Phonon band structure and interatomic force constants for bismuth: Crucial role of spin-orbit interaction Díaz-Sánchez, L. E.; Romero, A. H.; Gonze, X. Physical Review B, Vol. 76, Issue 10 https://doi.org/10.1103/physrevb.76.104302	journal	September 2007
Optimized norm-conserving Vanderbilt pseudopotentials Hamann, D. R. Physical Review B, Vol. 88, Issue 8 https://doi.org/10.1103/physrevb.88.085117	journal	August 2013
Finite-Size Correction in Many-Body Electronic Structure Calculations Kwee, Hendra; Zhang, Shiwei; Krakauer, Henry Physical Review Letters, Vol. 100, Issue 12 https://doi.org/10.1103/physrevlett.100.126404	journal	March 2008
Rashba Spin-Orbit Coupling, Strong Interactions, and the BCS-BEC Crossover in the Ground State of the Two-Dimensional Fermi Gas Shi, Hao; Rosenberg, Peter; Chiesa, Simone Physical Review Letters, Vol. 117, Issue 4 https://doi.org/10.1103/physrevlett.117.040401	journal	July 2016
Ultracold Atoms in a Square Lattice with Spin-Orbit Coupling: Charge Order, Superfluidity, and Topological Signatures Rosenberg, Peter; Shi, Hao; Zhang, Shiwei Physical Review Letters, Vol. 119, Issue 26 https://doi.org/10.1103/physrevlett.119.265301	journal	December 2017
Calculation of Partition Functions Hubbard, J. Physical Review Letters, Vol. 3, Issue 2 https://doi.org/10.1103/physrevlett.3.77	journal	July 1959
Constrained Path Quantum Monte Carlo Method for Fermion Ground States Zhang, Shiwei; Carlson, J.; Gubernatis, J. E. Physical Review Letters, Vol. 74, Issue 18 https://doi.org/10.1103/physrevlett.74.3652	journal	May 1995
Quantum Monte Carlo Method using Phase-Free Random Walks with Slater Determinants Zhang, Shiwei; Krakauer, Henry Physical Review Letters, Vol. 90, Issue 13 https://doi.org/10.1103/physrevlett.90.136401	journal	April 2003
Quantum Spin Hall Effect and Enhanced Magnetic Response by Spin-Orbit Coupling Murakami, Shuichi Physical Review Letters, Vol. 97, Issue 23 https://doi.org/10.1103/physrevlett.97.236805	journal	December 2006
Effect of the Spin-Orbit Interaction on the Thermodynamic Properties of Crystals: Specific Heat of Bismuth Díaz-Sánchez, L. E.; Romero, A. H.; Cardona, M. Physical Review Letters, Vol. 99, Issue 16 https://doi.org/10.1103/physrevlett.99.165504	journal	October 2007

Similar Records

AB Initio spin-orbit coupling constants for potential exotic interstellar molecules

Journal Article · 1983 · Astrophys. J.; (United States) · OSTI ID:6051542

Cooper, D L

Non-perturbative many-body treatment of molecular magnets

Journal Article · 2023 · Journal of Chemical Physics · OSTI ID:1992081

Eskridge, Brandon; Krakauer, Henry; Zhang, Shiwei

Ab initio electronic density in solids by many-body plane-wave auxiliary-field quantum Monte Carlo calculations

Journal Article · 2021 · Physical Review. B · OSTI ID:1850737

Chen, Siyuan; Motta, Mario; Ma, Fengjie; +1 more

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Monte Carlo methods
Slater determinant
ab-initio methods
chemical bonding
density functional theory
electronic correlation
relativistic effective core potentials
spin-orbit interactions

Title: Ab initio calculations in atoms, molecules, and solids, treating spin–orbit coupling and electron interaction on an equal footing

Citation Formats

References (70)

Similar Records

Related Subjects