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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. [PMID: 38976839 DOI: 10.1021/acs.jctc.4c00224] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [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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2
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Tchakoua T, Jansen T, van Nies Y, van den Elshout RFA, van Boxmeer BAB, Poort SP, Ackermans MG, Beltrão GS, Hildebrand SA, Beekman SEJ, van der Drift T, Kaart S, Šantić A, Spuijbroek EE, Gerrits N, Somers MF, Kroes GJ. Constructing Mixed Density Functionals for Describing Dissociative Chemisorption on Metal Surfaces: Basic Principles. J Phys Chem A 2023; 127:10481-10498. [PMID: 38051300 PMCID: PMC10726370 DOI: 10.1021/acs.jpca.3c01932] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/07/2023]
Abstract
The production of a majority of chemicals involves heterogeneous catalysis at some stage, and the rates of many heterogeneously catalyzed processes are governed by transition states for dissociative chemisorption on metals. Accurate values of barrier heights for dissociative chemisorption on metals are therefore important to benchmarking electronic structure theory in general and density functionals in particular. Such accurate barriers can be obtained using the semiempirical specific reaction parameter (SRP) approach to density functional theory. However, this approach has thus far been rather ad hoc in its choice of the generic expression of the SRP functional to be used, and there is a need for better heuristic approaches to determining the mixing parameters contained in such expressions. Here we address these two issues. We investigate the ability of several mixed, parametrized density functional expressions combining exchange at the generalized gradient approximation (GGA) level with either GGA or nonlocal correlation to reproduce barrier heights for dissociative chemisorption on metal surfaces. For this, seven expressions of such mixed density functionals are tested on a database consisting of results for 16 systems taken from a recently published slightly larger database called SBH17. Three expressions are derived that exhibit high tunability and use correlation functionals that are either of the PBE GGA form or of one of two limiting nonlocal forms also describing the attractive van der Waals interaction in an approximate way. We also find that, for mixed density functionals incorporating GGA correlation, the optimum fraction of repulsive RPBE GGA exchange obtained with a specific GGA density functional is correlated with the charge-transfer parameter, which is equal to the difference in the work function of the metal surface and the electron affinity of the molecule. However, the correlation is generally not large and not large enough to obtain accurate guesses of the mixing parameter for the systems considered, suggesting that it does not give rise to a very effective search strategy.
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Affiliation(s)
- Théophile Tchakoua
- Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, P.O. Box 9502, 2300 RA Leiden, The Netherlands
| | - Tim Jansen
- Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, P.O. Box 9502, 2300 RA Leiden, The Netherlands
| | - Youri van Nies
- Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, P.O. Box 9502, 2300 RA Leiden, The Netherlands
| | | | - Bart A B van Boxmeer
- Faculty of Applied Engineering, University of Antwerp, Groenenborgerlaan 171, 2020 Antwerpen, Belgium
| | - Saskia P Poort
- Department of Chemical Engineering, Delft University of Technology, 2629 HZ Delft, The Netherlands
| | - Michelle G Ackermans
- Department of Chemical Engineering, Delft University of Technology, 2629 HZ Delft, The Netherlands
| | - Gabriel Spiller Beltrão
- Department of Chemical Engineering, Delft University of Technology, 2629 HZ Delft, The Netherlands
| | - Stefan A Hildebrand
- Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, P.O. Box 9502, 2300 RA Leiden, The Netherlands
| | - Steijn E J Beekman
- Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, P.O. Box 9502, 2300 RA Leiden, The Netherlands
| | - Thijs van der Drift
- Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, P.O. Box 9502, 2300 RA Leiden, The Netherlands
| | - Sam Kaart
- Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, P.O. Box 9502, 2300 RA Leiden, The Netherlands
| | - Anthonie Šantić
- Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, P.O. Box 9502, 2300 RA Leiden, The Netherlands
| | - Esmee E Spuijbroek
- Department of Chemical Engineering, Delft University of Technology, 2629 HZ Delft, The Netherlands
| | - Nick Gerrits
- Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, P.O. Box 9502, 2300 RA Leiden, The Netherlands
| | - Mark F Somers
- Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, P.O. Box 9502, 2300 RA Leiden, The Netherlands
| | - Geert-Jan Kroes
- Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, P.O. Box 9502, 2300 RA Leiden, The Netherlands
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3
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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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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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Abstract
Structures and processes at water/metal interfaces play an important technological role in electrochemical energy conversion and storage, photoconversion, sensors, and corrosion, just to name a few. However, they are also of fundamental significance as a model system for the study of solid-liquid interfaces, which requires combining concepts from the chemistry and physics of crystalline materials and liquids. Particularly interesting is the fact that the water-water and water-metal interactions are of similar strength so that the structures at water/metal interfaces result from a competition between these comparable interactions. Because water is a polar molecule and water and metal surfaces are both polarizable, explicit consideration of the electronic degrees of freedom at water/metal interfaces is mandatory. In principle, ab initio molecular dynamics simulations are thus the method of choice to model water/metal interfaces, but they are computationally still rather demanding. Here, ab initio simulations of water/metal interfaces will be reviewed, starting from static systems such as the adsorption of single water molecules, water clusters, and icelike layers, followed by the properties of liquid water layers at metal surfaces. Technical issues such as the appropriate first-principles description of the water-water and water-metal interactions will be discussed, and electrochemical aspects will be addressed. Finally, more approximate but numerically less demanding approaches to treat water at metal surfaces from first-principles will be briefly discussed.
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Affiliation(s)
- Axel Groß
- Institute of Theoretical Chemistry, Ulm University, 89069 Ulm, Germany.,Electrochemical Energy Storage, Helmholtz Institute Ulm (HIU), 89069 Ulm, Germany
| | - Sung Sakong
- Institute of Theoretical Chemistry, Ulm University, 89069 Ulm, Germany
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Kroes GJ. Computational approaches to dissociative chemisorption on metals: towards chemical accuracy. Phys Chem Chem Phys 2021; 23:8962-9048. [PMID: 33885053 DOI: 10.1039/d1cp00044f] [Citation(s) in RCA: 33] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We review the state-of-the-art in the theory of dissociative chemisorption (DC) of small gas phase molecules on metal surfaces, which is important to modeling heterogeneous catalysis for practical reasons, and for achieving an understanding of the wealth of experimental information that exists for this topic, for fundamental reasons. We first give a quick overview of the experimental state of the field. Turning to the theory, we address the challenge that barrier heights (Eb, which are not observables) for DC on metals cannot yet be calculated with chemical accuracy, although embedded correlated wave function theory and diffusion Monte-Carlo are moving in this direction. For benchmarking, at present chemically accurate Eb can only be derived from dynamics calculations based on a semi-empirically derived density functional (DF), by computing a sticking curve and demonstrating that it is shifted from the curve measured in a supersonic beam experiment by no more than 1 kcal mol-1. The approach capable of delivering this accuracy is called the specific reaction parameter (SRP) approach to density functional theory (DFT). SRP-DFT relies on DFT and on dynamics calculations, which are most efficiently performed if a potential energy surface (PES) is available. We therefore present a brief review of the DFs that now exist, also considering their performance on databases for Eb for gas phase reactions and DC on metals, and for adsorption to metals. We also consider expressions for SRP-DFs and briefly discuss other electronic structure methods that have addressed the interaction of molecules with metal surfaces. An overview is presented of dynamical models, which make a distinction as to whether or not, and which dissipative channels are modeled, the dissipative channels being surface phonons and electronically non-adiabatic channels such as electron-hole pair excitation. We also discuss the dynamical methods that have been used, such as the quasi-classical trajectory method and quantum dynamical methods like the time-dependent wave packet method and the reaction path Hamiltonian method. Limits on the accuracy of these methods are discussed for DC of diatomic and polyatomic molecules on metal surfaces, paying particular attention to reduced dimensionality approximations that still have to be invoked in wave packet calculations on polyatomic molecules like CH4. We also address the accuracy of fitting methods, such as recent machine learning methods (like neural network methods) and the corrugation reducing procedure. In discussing the calculation of observables we emphasize the importance of modeling the properties of the supersonic beams in simulating the sticking probability curves measured in the associated experiments. We show that chemically accurate barrier heights have now been extracted for DC in 11 molecule-metal surface systems, some of which form the most accurate core of the only existing database of Eb for DC reactions on metal surfaces (SBH10). The SRP-DFs (or candidate SRP-DFs) that have been derived show transferability in many cases, i.e., they have been shown also to yield chemically accurate Eb for chemically related systems. This can in principle be exploited in simulating rates of catalyzed reactions on nano-particles containing facets and edges, as SRP-DFs may be transferable among systems in which a molecule dissociates on low index and stepped surfaces of the same metal. In many instances SRP-DFs have allowed important conclusions regarding the mechanisms underlying observed experimental trends. An important recent observation is that SRP-DFT based on semi-local exchange DFs has so far only been successful for systems for which the difference of the metal work function and the molecule's electron affinity exceeds 7 eV. A main challenge to SRP-DFT is to extend its applicability to the other systems, which involve a range of important DC reactions of e.g. O2, H2O, NH3, CO2, and CH3OH. Recent calculations employing a PES based on a screened hybrid exchange functional suggest that the road to success may be based on using exchange functionals of this category.
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Affiliation(s)
- Geert-Jan Kroes
- Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, P.O. Box 9502, 2300 RA Leiden, The Netherlands.
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Needs RJ, Towler MD, Drummond ND, López Ríos P, Trail JR. Variational and diffusion quantum Monte Carlo calculations with the CASINO code. J Chem Phys 2020; 152:154106. [DOI: 10.1063/1.5144288] [Citation(s) in RCA: 35] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- R. J. Needs
- TCM Group, Cavendish Laboratory, University of Cambridge, 19 J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - M. D. Towler
- University College London, London WC1E 6BT, United Kingdom
| | - N. D. Drummond
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
| | - P. López Ríos
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
| | - J. R. Trail
- TCM Group, Cavendish Laboratory, University of Cambridge, 19 J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
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Irmler A, Gallo A, Hummel F, Grüneis A. Duality of Ring and Ladder Diagrams and Its Importance for Many-Electron Perturbation Theories. PHYSICAL REVIEW LETTERS 2019; 123:156401. [PMID: 31702324 DOI: 10.1103/physrevlett.123.156401] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/14/2019] [Indexed: 06/10/2023]
Abstract
We present a diagrammatic decomposition of the transition pair correlation function for the uniform electron gas. We demonstrate explicitly that ring and ladder diagrams are dual counterparts that capture significant long- and short-ranged interelectronic correlation effects, respectively. Our findings help to guide the further development of approximate many-electron theories and reveal that the contribution of the ladder diagrams to the electronic correlation energy can be approximated in an effective manner using second-order perturbation theory. We employ the latter approximation to reduce the computational cost of coupled cluster theory calculations for insulators and semiconductors by 2 orders of magnitude without compromising accuracy.
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Affiliation(s)
- 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
| | - 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
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