1
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Ye HZ, Berkelbach TC. Periodic Local Coupled-Cluster Theory for Insulators and Metals. J Chem Theory Comput 2024. [PMID: 39376105 DOI: 10.1021/acs.jctc.4c00936] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/09/2024]
Abstract
We describe the implementation details of periodic local coupled-cluster theory with single and double excitations (CCSD) and perturbative triple excitations [CCSD(T)] using local natural orbitals (LNOs) and k-point symmetry. We discuss and compare several choices for orbital localization, fragmentation, and LNO construction. By studying diamond and lithium, we demonstrate that periodic LNO-CC theory can be applied with equal success to both insulators and metals, achieving speedups of 2 to 3 orders of magnitude even for moderately sized k-point meshes. Our final predictions of the equilibrium cohesive energy, lattice constant, and bulk modulus for diamond and lithium are in good agreement with previous theoretical predictions and experimental results.
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Affiliation(s)
- Hong-Zhou Ye
- Department of Chemistry, Columbia University, New York, New York 10027, United States
| | - Timothy C Berkelbach
- Department of Chemistry, Columbia University, New York, New York 10027, United States
- Initiative for Computational Catalysis, Flatiron Institute, New York, New York 10010, United States
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2
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Carbone JP, Irmler A, Gallo A, Schäfer T, Van Benschoten WZ, Shepherd JJ, Grüneis A. CO adsorption on Pt(111) studied by periodic coupled cluster theory. Faraday Discuss 2024. [PMID: 39169819 PMCID: PMC11339635 DOI: 10.1039/d4fd00085d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2024] [Accepted: 05/01/2024] [Indexed: 08/23/2024]
Abstract
We present an application of periodic coupled-cluster theory to the calculation of CO adsorption energies on the Pt(111) surface for different adsorption sites. The calculations employ a range of recently developed theoretical and computational methods. In particular, we use a recently introduced coupled-cluster ansatz, denoted as CCSD(cT), to compute correlation energies of the metallic Pt surface with and without adsorbed CO molecules. The convergence of Hartree-Fock adsorption energy contributions with respect to randomly shifted k-meshes is discussed. Recently introduced basis set incompleteness error corrections make it possible to achieve well-converged correlation energy contributions to the adsorption energies. We show that CCSD(cT) theory predicts the correct order of adsorption energies for the considered adsorption sites. Furthermore, we find that binding of the CO molecule to the top and fcc site is dominated by Hartree-Fock and correlation energy contributions, respectively.
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Affiliation(s)
- Johanna P Carbone
- Institute for Theoretical Physics, TU Wien, Wiedner Hauptstraße 8-10/136, 1040 Vienna, Austria.
| | - Andreas Irmler
- Institute for Theoretical Physics, TU Wien, Wiedner Hauptstraße 8-10/136, 1040 Vienna, Austria.
| | - Alejandro Gallo
- Institute for Theoretical Physics, TU Wien, Wiedner Hauptstraße 8-10/136, 1040 Vienna, Austria.
| | - Tobias Schäfer
- Institute for Theoretical Physics, TU Wien, Wiedner Hauptstraße 8-10/136, 1040 Vienna, Austria.
| | | | - James J Shepherd
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA
| | - Andreas Grüneis
- Institute for Theoretical Physics, TU Wien, Wiedner Hauptstraße 8-10/136, 1040 Vienna, Austria.
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3
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Annaberdiyev A, Ganesh P, Krogel JT. Enhanced Twist-Averaging Technique for Magnetic Metals: Applications Using Quantum Monte Carlo. J Chem Theory Comput 2024; 20:2786-2797. [PMID: 38498904 DOI: 10.1021/acs.jctc.4c00058] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/20/2024]
Abstract
We propose an improved twist-averaging (TA) scheme for quantum Monte Carlo methods that use converged Kohn-Sham or Hartree-Fock orbitals as the reference. This TA technique is tailored to sample the Brillouin zone of magnetic metals, although it naturally extends to nonmagnetic (NM) conducting systems. The proposed scheme aims to reproduce the reference magnetization and achieves charge neutrality by construction, thus avoiding the large energy fluctuations and the postprocessing needed to correct the energies. It shows the most robust convergence of total energy and magnetism to the thermodynamic limit (TDL) when compared to four other TA schemes. Diffusion Monte Carlo applications are shown on NM Al and ferromagnetic α-Fe. The cohesive energy of Al in the TDL shows an excellent agreement with the experimental result. Furthermore, the magnetic moments in α-Fe exhibit rapid convergence with an increasing number of twists.
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Affiliation(s)
- Abdulgani Annaberdiyev
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States
| | - Panchapakesan Ganesh
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States
| | - Jaron T Krogel
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States
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4
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Liang YH, Ye HZ, Berkelbach TC. Can Spin-Component Scaled MP2 Achieve kJ/mol Accuracy for Cohesive Energies of Molecular Crystals? J Phys Chem Lett 2023; 14:10435-10441. [PMID: 37956873 DOI: 10.1021/acs.jpclett.3c02411] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2023]
Abstract
Attaining kJ/mol accuracy in cohesive energy for molecular crystals is a persistent challenge in computational materials science. In this study, we evaluate second-order Møller-Plesset perturbation theory (MP2) and its spin-component scaled models for calculating cohesive energies for 23 molecular crystals (X23 data set). Using periodic boundary conditions and Brillouin zone sampling, we converge results to the thermodynamic and complete basis set limits, achieving an accuracy of about 2 kJ/mol (0.5 kcal/mol), which is rarely achieved in previous MP2 calculations for molecular crystals. When compared to experimental data, our results have a mean absolute error of 12.9 kJ/mol, comparable to Density Functional Theory with the PBE functional and TS dispersion correction. By separately scaling the opposite-spin and same-spin correlation energy components, using predetermined parameters, we reduce the mean absolute error to 9.5 kJ/mol. Further fine-tuning of these scaling parameters specifically for the X23 data set brings the mean absolute error down to 7.5 kJ/mol.
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Affiliation(s)
- Yu Hsuan Liang
- Department of Chemistry, Columbia University, New York, New York 10027, United States
| | - Hong-Zhou Ye
- Department of Chemistry, Columbia University, New York, New York 10027, United States
| | - Timothy C Berkelbach
- Department of Chemistry, Columbia University, New York, New York 10027, United States
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5
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Shi B, Zen A, Kapil V, Nagy PR, Grüneis A, Michaelides A. Many-Body Methods for Surface Chemistry Come of Age: Achieving Consensus with Experiments. J Am Chem Soc 2023; 145:25372-25381. [PMID: 37948071 PMCID: PMC10683001 DOI: 10.1021/jacs.3c09616] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/02/2023] [Revised: 10/15/2023] [Accepted: 10/17/2023] [Indexed: 11/12/2023]
Abstract
The adsorption energy of a molecule onto the surface of a material underpins a wide array of applications, spanning heterogeneous catalysis, gas storage, and many more. It is the key quantity where experimental measurements and theoretical calculations meet, with agreement being necessary for reliable predictions of chemical reaction rates and mechanisms. The prototypical molecule-surface system is CO adsorbed on MgO, but despite intense scrutiny from theory and experiment, there is still no consensus on its adsorption energy. In particular, the large cost of accurate many-body methods makes reaching converged theoretical estimates difficult, generating a wide range of values. In this work, we address this challenge, leveraging the latest advances in diffusion Monte Carlo (DMC) and coupled cluster with single, double, and perturbative triple excitations [CCSD(T)] to obtain accurate predictions for CO on MgO. These reliable theoretical estimates allow us to evaluate the inconsistencies in published temperature-programed desorption experiments, revealing that they arise from variations in employed pre-exponential factors. Utilizing this insight, we derive new experimental estimates of the (electronic) adsorption energy with a (more) precise pre-exponential factor. As a culmination of all of this effort, we are able to reach a consensus between multiple theoretical calculations and multiple experiments for the first time. In addition, we show that our recently developed cluster-based CCSD(T) approach provides a low-cost route toward achieving accurate adsorption energies. This sets the stage for affordable and reliable theoretical predictions of chemical reactions on surfaces to guide the realization of new catalysts and gas storage materials.
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Affiliation(s)
- Benjamin
X. Shi
- Yusuf
Hamied Department of Chemistry, University
of Cambridge, Lensfield Road, CB2 1EW Cambridge, U.K.
| | - Andrea Zen
- Dipartimento
di Fisica Ettore Pancini, Università
di Napoli Federico II, Monte S. Angelo, I-80126 Napoli, Italy
- Department
of Earth Sciences, University College London, Gower Street, WC1E 6BT London, U.K.
| | - Venkat Kapil
- Yusuf
Hamied Department of Chemistry, University
of Cambridge, Lensfield Road, CB2 1EW Cambridge, U.K.
| | - Péter R. Nagy
- Department
of Physical Chemistry and Materials Science, Faculty of Chemical Technology
and Biotechnology, Budapest University of
Technology and Economics, Müegyetem rkp. 3, H-1111 Budapest, Hungary
- HUN-REN-BME
Quantum Chemistry Research Group, Müegyetem rkp. 3, H-1111 Budapest, Hungary
- MTA-BME
Lendület Quantum Chemistry Research Group, Müegyetem rkp. 3, H-1111 Budapest, Hungary
| | - Andreas Grüneis
- Institute
for Theoretical Physics, TU Wien, Wiedner Hauptstraße 8-10/136, 1040 Vienna, Austria
| | - Angelos Michaelides
- Yusuf
Hamied Department of Chemistry, University
of Cambridge, Lensfield Road, CB2 1EW Cambridge, U.K.
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6
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Neufeld VA, Berkelbach TC. Highly Accurate Electronic Structure of Metallic Solids from Coupled-Cluster Theory with Nonperturbative Triple Excitations. PHYSICAL REVIEW LETTERS 2023; 131:186402. [PMID: 37977636 DOI: 10.1103/physrevlett.131.186402] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/11/2023] [Accepted: 09/28/2023] [Indexed: 11/19/2023]
Abstract
Coupled-cluster theory with single, double, and perturbative triple excitations (CCSD(T))-often considered the "gold standard" of main-group quantum chemistry-is inapplicable to three-dimensional metals due to an infrared divergence, preventing its application to many important problems in materials science. We study the full, nonperturbative inclusion of triple excitations (CCSDT) and propose a new, iterative method, which we call ring-CCSDT, that resums the essential triple excitations with the same N^{7} run-time scaling as CCSD(T). CCSDT and ring-CCSDT are used to calculate the correlation energy of the uniform electron gas at metallic densities and the structural properties of solid lithium. Inclusion of connected triple excitations is shown to be essential to achieving high accuracy. We also investigate semiempirical CC methods based on spin-component scaling and the distinguishable cluster approximation and find that they enhance the accuracy of their parent ab initio methods.
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Affiliation(s)
- Verena A Neufeld
- 1Department of Chemistry, Columbia University, New York, New York 10027, USA
- 2Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
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7
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Masios N, Irmler A, Schäfer T, Grüneis A. Averting the Infrared Catastrophe in the Gold Standard of Quantum Chemistry. PHYSICAL REVIEW LETTERS 2023; 131:186401. [PMID: 37977639 DOI: 10.1103/physrevlett.131.186401] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/28/2023] [Accepted: 09/27/2023] [Indexed: 11/19/2023]
Abstract
Coupled-cluster theories can be used to compute ab initio electronic correlation energies of real materials with systematically improvable accuracy. However, the widely used coupled cluster singles and doubles plus perturbative triples [CCSD(T)] method is only applicable to insulating materials. For zero-gap materials the truncation of the underlying many-body perturbation expansion leads to an infrared catastrophe. Here, we present a novel perturbative triples formalism denoted as (cT) that yields convergent correlation energies in metallic systems. Furthermore, the computed correlation energies for the three-dimensional uniform electron gas at metallic densities are in good agreement with quantum Monte Carlo results. At the same time the newly proposed method retains all desirable properties of CCSD(T) such as its accuracy for insulating systems as well as its low computational cost compared to a full inclusion of the triples. This paves the way for ab initio calculations of real metals with chemical accuracy.
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Affiliation(s)
- Nikolaos Masios
- Institute for Theoretical Physics, TU Wien, Wiedner Hauptstraße 8-10/136, 1040 Vienna, Austria
| | - Andreas Irmler
- Institute for Theoretical Physics, TU Wien, Wiedner Hauptstraße 8-10/136, 1040 Vienna, Austria
| | - Tobias Schäfer
- Institute for Theoretical Physics, TU Wien, Wiedner Hauptstraße 8-10/136, 1040 Vienna, Austria
| | - Andreas Grüneis
- Institute for Theoretical Physics, TU Wien, Wiedner Hauptstraße 8-10/136, 1040 Vienna, Austria
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8
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Mihm TN, Weiler L, Shepherd JJ. How the Exchange Energy Can Affect the Power Laws Used to Extrapolate the Coupled Cluster Correlation Energy to the Thermodynamic Limit. J Chem Theory Comput 2023; 19:1686-1697. [PMID: 36918372 PMCID: PMC10061680 DOI: 10.1021/acs.jctc.2c00737] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2022] [Indexed: 03/16/2023]
Abstract
Finite size error is commonly removed from coupled cluster theory calculations by N-1 extrapolations over correlation energy calculations of different system sizes (N), where the N-1 scaling comes from the total energy rather than the correlation energy. However, previous studies in the quantum Monte Carlo community suggest an exchange-energy-like power law of N-2/3 should also be present in the correlation energy when using the conventional Coulomb interaction. The rationale for this is that the total energy goes as N-1 and the exchange energy goes as N-2/3; thus, the correlation energy should be a combination of these two power laws. Further, in coupled cluster theory, these power laws are related to the low G scaling of the transition structure factor, S(G), which is a property of the coupled cluster wave function calculated from the amplitudes. We show here that data from coupled cluster doubles calculations on the uniform electron gas fit a function with a low G behavior of S(G) ∼ G. The prefactor for this linear term is derived from the exchange energy to be consistent with an N-2/3 power law at large N. Incorporating the exchange structure factor into the transition structure factor results in a combined structure factor of S(G) ∼ G2, consistent with an N-1 scaling of the exchange-correlation energy. We then look for the presence of an N-2/3 power law in the energy. To do so, we first develop a plane-wave cutoff scheme with less noise than the traditional basis set used for the uniform electron gas. Then, we collect data from a wide range of electron numbers and densities to systematically test five methods using N-1 scaling, N-2/3 scaling, or combinations of both scaling behaviors. We find that power laws that incorporate both N-1 and N-2/3 scaling perform better than either alone, especially when the prefactor for N-2/3 scaling can be found from exchange energy calculations.
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Affiliation(s)
- Tina N. Mihm
- Department of Chemistry, University of Iowa, Iowa City, Iowa 52242-1294, United States
| | - Laura Weiler
- Department of Chemistry, University of Iowa, Iowa City, Iowa 52242-1294, United States
| | - James J. Shepherd
- Department of Chemistry, University of Iowa, Iowa City, Iowa 52242-1294, United States
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9
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Bintrim SJ, Berkelbach TC, Ye HZ. Integral-Direct Hartree-Fock and Møller-Plesset Perturbation Theory for Periodic Systems with Density Fitting: Application to the Benzene Crystal. J Chem Theory Comput 2022; 18:5374-5381. [PMID: 35969856 DOI: 10.1021/acs.jctc.2c00640] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We present an algorithm and implementation of integral-direct, density-fitted Hartree-Fock (HF) and second-order Møller-Plesset perturbation theory (MP2) for periodic systems. The new code eliminates the formerly prohibitive storage requirements and allows us to study systems 1 order of magnitude larger than before at the periodic MP2 level. We demonstrate the significance of the development by studying the benzene crystal in both the thermodynamic limit and the complete basis set limit, for which we predict an MP2 cohesive energy of -72.8 kJ/mol, which is about 10-15 kJ/mol larger in magnitude than all previously reported MP2 calculations. Compared to the best theoretical estimate from literature, several modified MP2 models approach chemical accuracy in the predicted cohesive energy of the benzene crystal and hence may be promising cost-effective choices for future applications on molecular crystals.
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Affiliation(s)
- Sylvia J Bintrim
- Department of Chemistry, Columbia University, New York, New York 10027, United States
| | - Timothy C Berkelbach
- Department of Chemistry, Columbia University, New York, New York 10027, United States.,Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, United States
| | - Hong-Zhou Ye
- Department of Chemistry, Columbia University, New York, New York 10027, United States
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