1
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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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2
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Masios N, Hummel F, Grüneis A, Irmler A. Investigating the Basis Set Convergence of Diagrammatically Decomposed Coupled-Cluster Correlation Energy Contributions for the Uniform Electron Gas. J Chem Theory Comput 2024; 20:5937-5950. [PMID: 38976839 PMCID: PMC11270826 DOI: 10.1021/acs.jctc.4c00224] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2024] [Revised: 05/28/2024] [Accepted: 05/29/2024] [Indexed: 07/10/2024]
Abstract
We investigate the convergence of coupled-cluster (CC) correlation energies and related quantities with respect to the employed basis set size for the uniform electron gas (UEG) to gain a better understanding of the basis set incompleteness error (BSIE). To this end, coupled-cluster doubles (CCD) theory is applied to the three-dimensional UEG for a range of densities, basis set sizes, and electron numbers. We present a detailed analysis of individual diagrammatically decomposed contributions to the amplitudes at the level of CCD theory. In particular, we show that only two terms from the amplitude equations contribute to the asymptotic large-momentum behavior of the transition structure factor, corresponding to the cusp region at short interelectronic distances. However, due to the coupling present in the amplitude equations, all decomposed correlation energy contributions show the same asymptotic convergence behavior to the complete basis set limit. These findings provide an additional rationale for the success of a recently proposed correction to the BSIE of CC theory. Lastly, we examine the BSIE in the CCD plus perturbative triples [CCD(T)] method, as well as in the newly proposed CCD plus complete perturbative triples [CCD(cT)] method.
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Affiliation(s)
- Nikolaos Masios
- Institute for Theoretical Physics, TU Wien, Wiedner Hauptstraße 8-10/136, 1040 Vienna, Austria
| | - Felix Hummel
- 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
| | - Andreas Irmler
- Institute for Theoretical Physics, TU Wien, Wiedner Hauptstraße 8-10/136, 1040 Vienna, Austria
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3
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Sukurma Z, Schlipf M, Humer M, Taheridehkordi A, Kresse G. Toward Large-Scale AFQMC Calculations: Large Time Step Auxiliary-Field Quantum Monte Carlo. J Chem Theory Comput 2024; 20:4205-4217. [PMID: 38750634 PMCID: PMC11137827 DOI: 10.1021/acs.jctc.4c00304] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2024] [Revised: 04/29/2024] [Accepted: 05/06/2024] [Indexed: 05/29/2024]
Abstract
We report modifications of the ph-AFQMC algorithm that allow the use of large time steps and reliable time step extrapolation. Our modified algorithm eliminates size-consistency errors present in the standard algorithm when large time steps are employed. We investigate various methods to approximate the exponential of the one-body operator within the AFQMC framework, distinctly demonstrating the superiority of Krylov methods over the conventional Taylor expansion. We assess various propagators within AFQMC and demonstrate that the Split-2 propagator is the optimal method, exhibiting the smallest time-step errors. For the HEAT set molecules, the time-step extrapolated energies deviate on average by only 0.19 kcal/mol from the accurate small time-step energies. For small water clusters, we obtain accurate complete basis-set binding energies using time-step extrapolation with a mean absolute error of 0.07 kcal/mol compared to CCSD(T). Using large time-step ph-AFQMC for the N2 dimer, we show that accurate bond lengths can be obtained while reducing CPU time by an order of magnitude.
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Affiliation(s)
- Zoran Sukurma
- University
of Vienna, Faculty of Physics and Center for Computational Materials
Science, Kolingasse 14-16, A-1090 Vienna, Austria
- University
of Vienna, Faculty of Physics
& Vienna Doctoral School in Physics, Boltzmanngasse 5, A-1090 Vienna, Austria
| | - Martin Schlipf
- VASP
Software GmbH, Berggasse
21/14, 1090 Vienna, Austria
| | - Moritz Humer
- University
of Vienna, Faculty of Physics and Center for Computational Materials
Science, Kolingasse 14-16, A-1090 Vienna, Austria
- University
of Vienna, Faculty of Physics
& Vienna Doctoral School in Physics, Boltzmanngasse 5, A-1090 Vienna, Austria
| | - Amir Taheridehkordi
- University
of Vienna, Faculty of Physics and Center for Computational Materials
Science, Kolingasse 14-16, A-1090 Vienna, Austria
| | - Georg Kresse
- University
of Vienna, Faculty of Physics and Center for Computational Materials
Science, Kolingasse 14-16, A-1090 Vienna, Austria
- VASP
Software GmbH, Sensengasse
8, 1090 Vienna, Austria
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4
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Schäfer T, Van Benschoten WZ, Shepherd JJ, Grüneis A. Sampling the reciprocal Coulomb potential in finite anisotropic cells. J Chem Phys 2024; 160:051101. [PMID: 38310470 DOI: 10.1063/5.0182729] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2023] [Accepted: 01/07/2024] [Indexed: 02/05/2024] Open
Abstract
We present a robust strategy to numerically sample the Coulomb potential in reciprocal space for periodic Born-von Karman cells of general shape. Our approach tackles two common issues of plane-wave based implementations of Coulomb integrals under periodic boundary conditions: the treatment of the singularity at the Brillouin-zone center and discretization errors, which can cause severe convergence problems in anisotropic cells, necessary for the calculation of low-dimensional systems. We apply our strategy to the Hartree-Fock and coupled cluster (CC) theories and discuss the consequences of different sampling strategies on different theories. We show that sampling the Coulomb potential via the widely used probe-charge Ewald method is unsuitable for CC calculations in anisotropic cells. To demonstrate the applicability of our developed approach, we study two representative, low-dimensional use cases: the infinite carbon chain, for which we report the first periodic CCSD(T) potential energy surface, and a surface slab of lithium hydride, for which we demonstrate the impact of different sampling strategies for calculating surface energies. We find that our Coulomb sampling strategy serves as a vital solution, addressing the critical need for improved accuracy in plane-wave based CC calculations for low-dimensional systems.
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Affiliation(s)
- Tobias Schäfer
- Institute for Theoretical Physics, TU Wien, Wiedner Hauptstraße 8-10/136, A-1040 Vienna, Austria
| | | | - James J Shepherd
- Department of Chemistry, University of Iowa, Iowa City, Iowa 52242, USA
| | - Andreas Grüneis
- Institute for Theoretical Physics, TU Wien, Wiedner Hauptstraße 8-10/136, A-1040 Vienna, Austria
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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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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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7
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Banerjee S, Sokolov AY. Non-Dyson Algebraic Diagrammatic Construction Theory for Charged Excitations in Solids. J Chem Theory Comput 2022; 18:5337-5348. [PMID: 35976918 DOI: 10.1021/acs.jctc.2c00565] [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 the first implementation and applications of non-Dyson algebraic diagrammatic construction theory for charged excitations in three-dimensional periodic solids (EA/IP-ADC). The EA/IP-ADC approach has a computational cost similar to the ground-state Møller-Plesset perturbation theory, enabling efficient calculations of a variety of crystalline excited-state properties (e.g., band structure, band gap, density of states) sampled in the Brillouin zone. We use EA/IP-ADC to compute the quasiparticle band structures and band gaps of several materials (from large-gap atomic and ionic solids to small-gap semiconductors) and analyze the errors of EA/IP-ADC approximations up to the third order in perturbation theory. Our work also reports the first-ever calculations of ground-state properties (equation-of-state and lattice constants) of three-dimensional crystalline systems using a periodic implementation of third-order Møller-Plesset perturbation theory (MP3).
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Affiliation(s)
- Samragni Banerjee
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
| | - Alexander Yu Sokolov
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
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8
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Keller E, Tsatsoulis T, Reuter K, Margraf JT. Regularized second-order correlation methods for extended systems. J Chem Phys 2022; 156:024106. [PMID: 35032995 DOI: 10.1063/5.0078119] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023] Open
Abstract
Second-order Møller-Plesset perturbation theory (MP2) constitutes the simplest form of many-body wavefunction theory and often provides a good compromise between efficiency and accuracy. There are, however, well-known limitations to this approach. In particular, MP2 is known to fail or diverge for some prototypical condensed matter systems like the homogeneous electron gas (HEG) and to overestimate dispersion-driven interactions in strongly polarizable systems. In this paper, we explore how the issues of MP2 for metallic, polarizable, and strongly correlated periodic systems can be ameliorated through regularization. To this end, two regularized second-order methods (including a new, size-extensive Brillouin-Wigner approach) are applied to the HEG, the one-dimensional Hubbard model, and the graphene-water interaction. We find that regularization consistently leads to improvements over the MP2 baseline and that different regularizers are appropriate for the various systems.
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Affiliation(s)
- Elisabeth Keller
- Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany
| | - Theodoros Tsatsoulis
- Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany
| | - Karsten Reuter
- Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany
| | - Johannes T Margraf
- Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany
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9
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Schäfer T, Gallo A, Irmler A, Hummel F, Grüneis A. Surface science using coupled cluster theory via local Wannier functions and in-RPA-embedding: The case of water on graphitic carbon nitride. J Chem Phys 2021; 155:244103. [PMID: 34972356 DOI: 10.1063/5.0074936] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A first-principles study of the adsorption of a single water molecule on a layer of graphitic carbon nitride is reported employing an embedding approach for many-electron correlation methods. To this end, a plane-wave based implementation to obtain intrinsic atomic orbitals and Wannier functions for arbitrary localization potentials is presented. In our embedding scheme, the localized occupied orbitals allow for a separate treatment of short-range and long-range correlation contributions to the adsorption energy by a fragmentation of the simulation cell. In combination with unoccupied natural orbitals, the coupled cluster ansatz with single, double, and perturbative triple particle-hole excitation operators is used to capture the correlation in local fragments centered around the adsorption process. For the long-range correlation, a seamless embedding into the random phase approximation yields rapidly convergent adsorption energies with respect to the local fragment size. Convergence of computed binding energies with respect to the virtual orbital basis set is achieved employing a number of recently developed techniques. Moreover, we discuss fragment size convergence for a range of approximate many-electron perturbation theories. The obtained benchmark results are compared to a number of density functional calculations.
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Affiliation(s)
- Tobias Schäfer
- Institute for Theoretical Physics, TU Wien, Wiedner Hauptstraße 8-10/136, A-1040 Vienna, Austria
| | - Alejandro Gallo
- Institute for Theoretical Physics, TU Wien, Wiedner Hauptstraße 8-10/136, A-1040 Vienna, Austria
| | - Andreas Irmler
- Institute for Theoretical Physics, TU Wien, Wiedner Hauptstraße 8-10/136, A-1040 Vienna, Austria
| | - Felix Hummel
- Institute for Theoretical Physics, TU Wien, Wiedner Hauptstraße 8-10/136, A-1040 Vienna, Austria
| | - Andreas Grüneis
- Institute for Theoretical Physics, TU Wien, Wiedner Hauptstraße 8-10/136, A-1040 Vienna, Austria
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