Periodic Electronic Structure Calculations with the Density Matrix Embedding Theory

Pham, Hung Q.; Hermes, Matthew R.; Gagliardi, Laura

doi:10.1021/acs.jctc.9b00939

Title: Periodic Electronic Structure Calculations with the Density Matrix Embedding Theory

Journal Article · Mon Dec 09 00:00:00 EST 2019 · Journal of Chemical Theory and Computation

DOI:https://doi.org/10.1021/acs.jctc.9b00939· OSTI ID:1771014

^[1]; Hermes, Matthew R. ^[1];

^[1]

Univ. of Minnesota, Minneapolis, MN (United States)

We developed a periodic version of density matrix embedding theory, DMET, with which it is possible to perform electronic structure calculations on periodic systems and compute the band structure of solid-state materials. Electron correlation can be captured by means of a local impurity model using various wave function methods, such as full configuration interaction, coupled cluster, and multiconfigurational methods. The method is able to describe not only the ground-state energy but also the quasiparticle band picture via the real space-momentum space implementation. We investigate the performance of periodic DMET in describing the ground-state energy as well as the electronic band structure for one-dimensional solids. Here, our results show that DMET is in good agreement with other many-body techniques at a cheaper computational cost. We anticipate that periodic DMET can be a promising first principle method for strongly correlated materials.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Univ. of Minnesota, Minneapolis, MN (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0008688

OSTI ID:: 1771014

Journal Information:: Journal of Chemical Theory and Computation, Vol. 16, Issue 1; ISSN 1549-9618

Publisher:: American Chemical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

References (73)

Density-Matrix Embedding Theory Study of the One-Dimensional Hubbard–Holstein Model Reinhard, Teresa E.; Mordovina, Uliana; Hubig, Claudius Journal of Chemical Theory and Computation, Vol. 15, Issue 4 https://doi.org/10.1021/acs.jctc.8b01116	journal	February 2019
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
Ground-state phase diagram of the square lattice Hubbard model from density matrix embedding theory Zheng, Bo-Xiao; Chan, Garnet Kin-Lic Physical Review B, Vol. 93, Issue 3 https://doi.org/10.1103/PhysRevB.93.035126	journal	January 2016
Projected density matrix embedding theory with applications to the two-dimensional Hubbard model Wu, Xiaojie; Cui, Zhi-Hao; Tong, Yu The Journal of Chemical Physics, Vol. 151, Issue 6 https://doi.org/10.1063/1.5108818	journal	August 2019
Recovering hidden Bloch character: Unfolding electrons, phonons, and slabs Allen, P. B.; Berlijn, T.; Casavant, D. A. Physical Review B, Vol. 87, Issue 8 https://doi.org/10.1103/PhysRevB.87.085322	journal	February 2013
wannier90: A tool for obtaining maximally-localised Wannier functions Mostofi, Arash A.; Yates, Jonathan R.; Lee, Young-Su Computer Physics Communications, Vol. 178, Issue 9 https://doi.org/10.1016/j.cpc.2007.11.016	journal	May 2008
Strongly Correlated Materials: Insights From Dynamical Mean-Field Theory Kotliar, Gabriel; Vollhardt, Dieter Physics Today, Vol. 57, Issue 3 https://doi.org/10.1063/1.1712502	journal	March 2004
Density Matrix Embedding: A Simple Alternative to Dynamical Mean-Field Theory Knizia, Gerald; Chan, Garnet Kin-Lic Physical Review Letters, Vol. 109, Issue 18 https://doi.org/10.1103/PhysRevLett.109.186404	journal	November 2012
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
Multiconfiguration Self-Consistent Field and Multireference Configuration Interaction Methods and Applications Szalay, Péter G.; Müller, Thomas; Gidofalvi, Gergely Chemical Reviews, Vol. 112, Issue 1 https://doi.org/10.1021/cr200137a	journal	December 2011
Maximally localized generalized Wannier functions for composite energy bands Marzari, Nicola; Vanderbilt, David Physical Review B, Vol. 56, Issue 20 https://doi.org/10.1103/PhysRevB.56.12847	journal	November 1997
Applications of DFT + DMFT in Materials Science Paul, Arpita; Birol, Turan Annual Review of Materials Research, Vol. 49, Issue 1 https://doi.org/10.1146/annurev-matsci-070218-121825	journal	July 2019
Density functional theory and the band gap problem Perdew, John P. International Journal of Quantum Chemistry, Vol. 28, Issue S19 https://doi.org/10.1002/qua.560280846	journal	March 1985
Resolution of the Band Gap Prediction Problem for Materials Design Crowley, Jason M.; Tahir-Kheli, Jamil; Goddard, William A. The Journal of Physical Chemistry Letters, Vol. 7, Issue 7 https://doi.org/10.1021/acs.jpclett.5b02870	journal	March 2016
One-body Green's function for atoms and molecules: theory and application Cederbaum, L. S. Journal of Physics B: Atomic and Molecular Physics, Vol. 8, Issue 2 https://doi.org/10.1088/0022-3700/8/2/018	journal	February 1975
Electronic excitations: density-functional versus many-body Green’s-function approaches Onida, Giovanni; Reining, Lucia; Rubio, Angel Reviews of Modern Physics, Vol. 74, Issue 2 https://doi.org/10.1103/RevModPhys.74.601	journal	June 2002
Electron correlation in solids via density embedding theory Bulik, Ireneusz W.; Chen, Weibing; Scuseria, Gustavo E. The Journal of Chemical Physics, Vol. 141, Issue 5 https://doi.org/10.1063/1.4891861	journal	August 2014
Density-functional calculations of defect formation energies using the supercell method: Brillouin-zone sampling Shim, Jihye; Lee, Eok-Kyun; Lee, Young Joo Physical Review B, Vol. 71, Issue 24 https://doi.org/10.1103/PhysRevB.71.245204	journal	June 2005
Periodic density functional embedding theory for complete active space self-consistent field and configuration interaction calculations: Ground and excited states Klüner, Thorsten; Govind, Niranjan; Wang, Yan Alexander The Journal of Chemical Physics, Vol. 116, Issue 1 https://doi.org/10.1063/1.1420748	journal	January 2002
Multiconfigurational Self-Consistent Field Theory with Density Matrix Embedding: The Localized Active Space Self-Consistent Field Method Hermes, Matthew R.; Gagliardi, Laura Journal of Chemical Theory and Computation, Vol. 15, Issue 2 https://doi.org/10.1021/acs.jctc.8b01009	journal	November 2018
Ab initiomolecular dynamics for liquid metals Kresse, G.; Hafner, J. Physical Review B, Vol. 47, Issue 1, p. 558-561 https://doi.org/10.1103/PhysRevB.47.558	journal	January 1993
Visualizing electronic structures of quantum materials by angle-resolved photoemission spectroscopy Yang, Haifeng; Liang, Aiji; Chen, Cheng Nature Reviews Materials, Vol. 3, Issue 9 https://doi.org/10.1038/s41578-018-0047-2	journal	August 2018
Angle-Resolved Photoemission Studies of Quantum Materials Lu, Donghui; Vishik, Inna M.; Yi, Ming Annual Review of Condensed Matter Physics, Vol. 3, Issue 1 https://doi.org/10.1146/annurev-conmatphys-020911-125027	journal	March 2012
Density-Functional Theory of the Energy Gap Sham, L. J.; Schlüter, M. Physical Review Letters, Vol. 51, Issue 20 https://doi.org/10.1103/PhysRevLett.51.1888	journal	November 1983
Partial third‐order quasiparticle theory: Comparisons for closed‐shell ionization energies and an application to the Borazine photoelectron spectrum Ortiz, J. V. The Journal of Chemical Physics, Vol. 104, Issue 19 https://doi.org/10.1063/1.471468	journal	May 1996
Thermodynamics of Small Systems Hill, Terrell L. The Journal of Chemical Physics, Vol. 36, Issue 12 https://doi.org/10.1063/1.1732447	journal	June 1962
Unfolding First-Principles Band Structures Ku, Wei; Berlijn, Tom; Lee, Chi-Cheng Physical Review Letters, Vol. 104, Issue 21 https://doi.org/10.1103/PhysRevLett.104.216401	journal	May 2010
Gaussian-Based Coupled-Cluster Theory for the Ground-State and Band Structure of Solids McClain, James; Sun, Qiming; Chan, Garnet Kin-Lic Journal of Chemical Theory and Computation, Vol. 13, Issue 3 https://doi.org/10.1021/acs.jctc.7b00049	journal	February 2017
Orbital Optimization in the Active Space Decomposition Model Kim, Inkoo; Parker, Shane M.; Shiozaki, Toru Journal of Chemical Theory and Computation, Vol. 11, Issue 8 https://doi.org/10.1021/acs.jctc.5b00429	journal	July 2015
Physical Content of the Exact Kohn-Sham Orbital Energies: Band Gaps and Derivative Discontinuities Perdew, John P.; Levy, Mel Physical Review Letters, Vol. 51, Issue 20 https://doi.org/10.1103/PhysRevLett.51.1884	journal	November 1983
Self-Consistent Equations Including Exchange and Correlation Effects Kohn, W.; Sham, L. J. Physical Review, Vol. 140, Issue 4A, p. A1133-A1138 https://doi.org/10.1103/PhysRev.140.A1133	journal	November 1965
Angle-resolved photoemission studies of the cuprate superconductors Damascelli, Andrea; Hussain, Zahid; Shen, Zhi-Xun Reviews of Modern Physics, Vol. 75, Issue 2 https://doi.org/10.1103/RevModPhys.75.473	journal	April 2003
Density‐functional thermochemistry. III. The role of exact exchange Becke, Axel D. The Journal of Chemical Physics, Vol. 98, Issue 7, p. 5648-5652 https://doi.org/10.1063/1.464913	journal	April 1993
Toward a predictive theory of correlated materials Kent, Paul R. C.; Kotliar, Gabriel Science, Vol. 361, Issue 6400 https://doi.org/10.1126/science.aat5975	journal	July 2018
Density Matrix Embedding: A Strong-Coupling Quantum Embedding Theory Knizia, Gerald; Chan, Garnet Kin-Lic Journal of Chemical Theory and Computation, Vol. 9, Issue 3 https://doi.org/10.1021/ct301044e	journal	February 2013
Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set Kresse, G.; Furthmüller, J. Computational Materials Science, Vol. 6, Issue 1, p. 15-50 https://doi.org/10.1016/0927-0256(96)00008-0	journal	July 1996
Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density Lee, Chengteh; Yang, Weitao; Parr, Robert G. Physical Review B, Vol. 37, Issue 2 https://doi.org/10.1103/PhysRevB.37.785	journal	January 1988
Combining GW calculations with exact-exchange density-functional theory: an analysis of valence-band photoemission for compound semiconductors Rinke, Patrick; Qteish, Abdallah; Neugebauer, Jörg New Journal of Physics, Vol. 7 https://doi.org/10.1088/1367-2630/7/1/126	journal	January 2005
Intrinsic Atomic Orbitals: An Unbiased Bridge between Quantum Theory and Chemical Concepts Knizia, Gerald Journal of Chemical Theory and Computation, Vol. 9, Issue 11 https://doi.org/10.1021/ct400687b	journal	October 2013
Predicting Band Gaps with Hybrid Density Functionals Garza, Alejandro J.; Scuseria, Gustavo E. The Journal of Physical Chemistry Letters, Vol. 7, Issue 20 https://doi.org/10.1021/acs.jpclett.6b01807	journal	October 2016
Implementation of the projector augmented-wave LDA+U method: Application to the electronic structure of NiO Bengone, O.; Alouani, M.; Blöchl, P. Physical Review B, Vol. 62, Issue 24 https://doi.org/10.1103/PhysRevB.62.16392	journal	December 2000
Challenges for Density Functional Theory Cohen, Aron J.; Mori-Sánchez, Paula; Yang, Weitao Chemical Reviews, Vol. 112, Issue 1 https://doi.org/10.1021/cr200107z	journal	December 2011
A real-time extension of density matrix embedding theory for non-equilibrium electron dynamics Kretchmer, Joshua S.; Chan, Garnet Kin-Lic The Journal of Chemical Physics, Vol. 148, Issue 5 https://doi.org/10.1063/1.5012766	journal	February 2018
Special points for Brillouin-zone integrations Monkhorst, Hendrik J.; Pack, James D. Physical Review B, Vol. 13, Issue 12, p. 5188-5192 https://doi.org/10.1103/PhysRevB.13.5188	journal	June 1976
Natural Spin‐Orbitals and Generalized Overlap Amplitudes Goscinski, O.; Lindner, P. Journal of Mathematical Physics, Vol. 11, Issue 4 https://doi.org/10.1063/1.1665261	journal	April 1970
Localized Magnetic States in Metals Anderson, P. W. Physical Review, Vol. 124, Issue 1 https://doi.org/10.1103/PhysRev.124.41	journal	October 1961
Electronic Structure: Basic Theory and Practical Methods, by Richard M. Martin: Scope: graduate level textbook. Level: theoretical materials scientists/condensed matter physicists/computational chemists Probert, Matt Contemporary Physics, Vol. 52, Issue 1 https://doi.org/10.1080/00107514.2010.509989	journal	January 2011
Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set Kresse, G.; Furthmüller, J. Physical Review B, Vol. 54, Issue 16, p. 11169-11186 https://doi.org/10.1103/PhysRevB.54.11169	journal	October 1996
Density functional theory in materials science: Density functional theory in materials science Neugebauer, Jörg; Hickel, Tilmann Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 3, Issue 5 https://doi.org/10.1002/wcms.1125	journal	January 2013
Toward Computational Materials Design: The Impact of Density Functional Theory on Materials Research Hafner, Jürgen; Wolverton, Christopher; Ceder, Gerbrand MRS Bulletin, Vol. 31, Issue 9 https://doi.org/10.1557/mrs2006.174	journal	September 2006
Can Density Matrix Embedding Theory with the Complete Activate Space Self-Consistent Field Solver Describe Single and Double Bond Breaking in Molecular Systems? Pham, Hung Q.; Bernales, Varinia; Gagliardi, Laura Journal of Chemical Theory and Computation, Vol. 14, Issue 4 https://doi.org/10.1021/acs.jctc.7b01248	journal	February 2018
Correlated electrons in high-temperature superconductors Dagotto, Elbio Reviews of Modern Physics, Vol. 66, Issue 3 https://doi.org/10.1103/RevModPhys.66.763	journal	July 1994
Direct calculation of ionization energies: I. Closed shells† Supported by the Swedish Natural Sciences Research Council. Pickup, B. T.; Goscinski, O. Molecular Physics, Vol. 26, Issue 4 https://doi.org/10.1080/00268977300102261	journal	October 1973
Separable dual-space Gaussian pseudopotentials Goedecker, S.; Teter, M.; Hutter, J. Physical Review B, Vol. 54, Issue 3 https://doi.org/10.1103/PhysRevB.54.1703	journal	July 1996
Inhomogeneous Electron Gas Hohenberg, P.; Kohn, W. Physical Review, Vol. 136, Issue 3B, p. B864-B871 https://doi.org/10.1103/PhysRev.136.B864	journal	November 1964
Topological quantum chemistry Bradlyn, Barry; Elcoro, L.; Cano, Jennifer Nature, Vol. 547, Issue 7663 https://doi.org/10.1038/nature23268	journal	July 2017
Electronic properties of linear carbon chains: Resolving the controversy Al-Backri, Amaal; Zólyomi, Viktor; Lambert, Colin J. The Journal of Chemical Physics, Vol. 140, Issue 10 https://doi.org/10.1063/1.4867635	journal	March 2014
Using SCF metadynamics to extend density matrix embedding theory to excited states Tran, Henry K.; Van Voorhis, Troy; Thom, Alex J. W. The Journal of Chemical Physics, Vol. 151, Issue 3 https://doi.org/10.1063/1.5096177	journal	July 2019
Bootstrap Embedding for Molecules Ye, Hong-Zhou; Ricke, Nathan D.; Tran, Henry K. Journal of Chemical Theory and Computation, Vol. 15, Issue 8 https://doi.org/10.1021/acs.jctc.9b00529	journal	June 2019
Density matrix embedding theory for interacting electron-phonon systems Sandhoefer, Barbara; Chan, Garnet Kin-Lic Physical Review B, Vol. 94, Issue 8 https://doi.org/10.1103/PhysRevB.94.085115	journal	August 2016
Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions Georges, Antoine; Kotliar, Gabriel; Krauth, Werner Reviews of Modern Physics, Vol. 68, Issue 1 https://doi.org/10.1103/RevModPhys.68.13	journal	January 1996
Performance of Bootstrap Embedding for long-range interactions and 2D systems Ricke, Nathan; Welborn, Matthew; Ye, Hong-Zhou Molecular Physics, Vol. 115, Issue 17-18 https://doi.org/10.1080/00268976.2017.1290839	journal	February 2017
Strongly Correlated Materials Morosan, Emilia; Natelson, Douglas; Nevidomskyy, Andriy H. Advanced Materials, Vol. 24, Issue 36 https://doi.org/10.1002/adma.201202018	journal	August 2012
Metal-Insulator Transition Mott, N. F. Reviews of Modern Physics, Vol. 40, Issue 4 https://doi.org/10.1103/RevModPhys.40.677	journal	October 1968
Bootstrap embedding: An internally consistent fragment-based method Welborn, Matthew; Tsuchimochi, Takashi; Van Voorhis, Troy The Journal of Chemical Physics, Vol. 145, Issue 7 https://doi.org/10.1063/1.4960986	journal	August 2016
Rationale for mixing exact exchange with density functional approximations Perdew, John P.; Ernzerhof, Matthias; Burke, Kieron The Journal of Chemical Physics, Vol. 105, Issue 22, p. 9982-9985 https://doi.org/10.1063/1.472933	journal	December 1996
Spin-State Ordering in Metal-Based Compounds Using the Localized Active Space Self-Consistent Field Method Pandharkar, Riddhish; Hermes, Matthew R.; Cramer, Christopher J. The Journal of Physical Chemistry Letters, Vol. 10, Issue 18 https://doi.org/10.1021/acs.jpclett.9b02077	journal	August 2019
Communication: Active-space decomposition for molecular dimers Parker, Shane M.; Seideman, Tamar; Ratner, Mark A. The Journal of Chemical Physics, Vol. 139, Issue 2 https://doi.org/10.1063/1.4813827	journal	July 2013
Communication: Active space decomposition with multiple sites: Density matrix renormalization group algorithm Parker, Shane M.; Shiozaki, Toru The Journal of Chemical Physics, Vol. 141, Issue 21 https://doi.org/10.1063/1.4902991	journal	December 2014
A general method to obtain well localized Wannier functions for composite energy bands in linear combination of atomic orbital periodic calculations Zicovich-Wilson, Claudio M.; Dovesi, Roberto; Saunders, Victor R. The Journal of Chemical Physics, Vol. 115, Issue 21 https://doi.org/10.1063/1.1415745	journal	December 2001
Implementation and performance of the frequency-dependent $G W$ method within the PAW framework Shishkin, M.; Kresse, G. Physical Review B, Vol. 74, Issue 3 https://doi.org/10.1103/PhysRevB.74.035101	journal	July 2006
Projection-Based Correlated Wave Function in Density Functional Theory Embedding for Periodic Systems Chulhai, Dhabih V.; Goodpaster, Jason D. Journal of Chemical Theory and Computation, Vol. 14, Issue 4 https://doi.org/10.1021/acs.jctc.7b01154	journal	March 2018
A Practical Guide to Density Matrix Embedding Theory in Quantum Chemistry Wouters, Sebastian; Jiménez-Hoyos, Carlos A.; Sun, Qiming Journal of Chemical Theory and Computation, Vol. 12, Issue 6 https://doi.org/10.1021/acs.jctc.6b00316	journal	May 2016

Similar Records

Spin-State Ordering in Metal-Based Compounds Using the Localized Active Space Self-Consistent Field Method

Journal Article · Tue Aug 20 00:00:00 EDT 2019 · Journal of Physical Chemistry Letters · OSTI ID:1771014

Pandharkar, Riddhish; Hermes, Matthew R.; Cramer, Christopher J.; +1 more

Excited States of Crystalline Point Defects with Multireference Density Matrix Embedding Theory

Journal Article · Mon Nov 29 00:00:00 EST 2021 · Journal of Physical Chemistry Letters · OSTI ID:1771014

Mitra, Abhishek; Pham, Hung Q.; Pandharkar, Riddhish; +2 more

Periodic Density Matrix Embedding for CO Adsorption on the MgO(001) Surface

Journal Article · Mon Aug 08 00:00:00 EDT 2022 · Journal of Physical Chemistry Letters · OSTI ID:1771014

Mitra, Abhishek; Hermes, Matthew R.; Cho, Minsik; +2 more

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
Band structure
Embedding
Electrical energy
Chemical calculations
Electrical conductivity

Title: Periodic Electronic Structure Calculations with the Density Matrix Embedding Theory

Citation Formats

References (73)

Similar Records

Related Subjects