1
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Wei Y, Debnath S, Weber JL, Mahajan A, Reichman DR, Friesner RA. Scalable Ab Initio Electronic Structure Methods with Near Chemical Accuracy for Main Group Chemistry. J Phys Chem A 2024; 128:5796-5807. [PMID: 38970826 DOI: 10.1021/acs.jpca.4c02853] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/08/2024]
Abstract
This study evaluates the precision of widely recognized quantum chemical methodologies, CCSD(T), DLPNO-CCSD(T), and localized ph-AFQMC, for determining the thermochemistry of main group elements. DLPNO-CCSD(T) and localized ph-AFQMC, which offer greater scalability compared to canonical CCSD(T), have emerged over the past decade as pivotal in producing precise benchmark chemical data. Our investigation includes closed-shell, neutral molecules, focusing on their heat of formation and atomization energy sourced from four specific small molecule data sets. First, we selected molecules from the G2 and G3 data sets, noted for their reliable experimental heat of formation data. Additionally, we incorporate molecules from the W4-11 and W4-17 sets, which provide high-level theoretical reference values for atomization energy at 0 K. Our findings reveal that both DLPNO-CCSD(T) and ph-AFQMC methods are capable of achieving a root-mean-square deviation of less than 1 kcal/mol across the combined data set, aligning with the threshold for chemical accuracy. Moreover, we make efforts to confine the maximum deviations within 2 kcal/mol, a degree of precision that significantly broadens the applicability of these methods in fields such as biology and materials science.
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Affiliation(s)
- Yujing Wei
- Department of Chemistry, Columbia University, New York, New York 10027, United States
| | - Sibali Debnath
- Department of Chemistry, Columbia University, New York, New York 10027, United States
| | - John L Weber
- Department of Chemistry, Columbia University, New York, New York 10027, United States
| | - Ankit Mahajan
- Department of Chemistry, Columbia University, New York, New York 10027, United States
| | - David R Reichman
- Department of Chemistry, Columbia University, New York, New York 10027, United States
| | - Richard A Friesner
- Department of Chemistry, Columbia University, New York, New York 10027, United States
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2
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Kurian JS, Ye HZ, Mahajan A, Berkelbach TC, Sharma S. Toward Linear Scaling Auxiliary-Field Quantum Monte Carlo with Local Natural Orbitals. J Chem Theory Comput 2024; 20:134-142. [PMID: 38113195 DOI: 10.1021/acs.jctc.3c01122] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2023]
Abstract
We develop a local correlation variant of auxiliary-field quantum Monte Carlo (AFQMC) based on local natural orbitals (LNO-AFQMC). In LNO-AFQMC, independent AFQMC calculations are performed for each localized occupied orbital using a truncated set of tailored orbitals. Because the size of this space does not grow with the system size for a target accuracy, the method has linear scaling. Applying LNO-AFQMC to molecular problems containing a few hundred to a thousand orbitals, we demonstrate convergence of total energies with significantly reduced costs. The savings are more significant for larger systems and larger basis sets. However, even for our smallest system studied, we find that LNO-AFQMC is cheaper than canonical AFQMC, in contrast with many other reduced-scaling methods. Perhaps most significantly, we show that energy differences converge much more quickly than total energies, making the method ideal for applications in chemistry and material science. Our work paves the way for linear scaling AFQMC calculations of strongly correlated systems, which would have a transformative effect on ab initio quantum chemistry.
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Affiliation(s)
- Jo S Kurian
- Department of Chemistry, University of Colorado, Boulder, Colorado 80302, United States
| | - Hong-Zhou Ye
- Department of Chemistry, Columbia University, New York, New York 10027, United States
| | - Ankit Mahajan
- Department of Chemistry, University of Colorado, Boulder, Colorado 80302, United States
- 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
| | - Sandeep Sharma
- Department of Chemistry, University of Colorado, Boulder, Colorado 80302, United States
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3
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Radoń M. Benchmarks for transition metal spin-state energetics: why and how to employ experimental reference data? Phys Chem Chem Phys 2023; 25:30800-30820. [PMID: 37938035 DOI: 10.1039/d3cp03537a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2023]
Abstract
Accurate prediction of energy differences between alternative spin states of transition metal complexes is essential in computational (bio)inorganic chemistry-for example, in characterization of spin crossover materials and in the theoretical modeling of open-shell reaction mechanisms-but it remains one of the most compelling problems for quantum chemistry methods. A part of this challenge is to obtain reliable reference data for benchmark studies, as even the highest-level applicable methods are known to give divergent results. This Perspective discusses two possible approaches to method benchmarking for spin-state energetics: using either theoretically computed or experiment-derived reference data. With the focus on the latter approach, an extensive general review is provided for the available experimental data of spin-state energetics and their interpretations in the context of benchmark studies, targeting the possibility of back-correcting the vibrational effects and the influence of solvents or crystalline environments. With a growing amount of experience, these effects can be now not only qualitatively understood, but also quantitatively modeled, providing the way to derive nearly chemically accurate estimates of the electronic spin-state gaps to be used as benchmarks and advancing our understanding of the phenomena related to spin states in condensed phases.
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Affiliation(s)
- Mariusz Radoń
- Faculty of Chemistry, Jagiellonian University, Gronostajowa 2, 30-387 Krakow, Krakow, Poland.
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4
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Weber JL, Vuong H, Friesner RA, Reichman DR. Expanding the Design Space of Constraints in Auxiliary-Field Quantum Monte Carlo. J Chem Theory Comput 2023; 19:7567-7576. [PMID: 37889331 DOI: 10.1021/acs.jctc.3c00654] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2023]
Abstract
We formulate and characterize a new constraint for auxiliary-field quantum Monte Carlo (AFQMC) applicable for general fermionic systems, which allows for the accumulation of phase in the random walk but disallows walkers with a magnitude of phase greater than π with respect to the trial wave function. For short imaginary times, before walkers accumulate sizable phase values, this approach is equivalent to exact free projection, allowing one to observe the accumulation of bias associated with the constraint and thus estimate its magnitude a priori. We demonstrate the stability of this constraint over arbitrary imaginary times and system sizes, highlighting the removal of noise due to the fermionic sign problem. Benchmark total energies for a variety of weakly and strongly correlated molecular systems reveal a distinct bias with respect to standard phaseless AFQMC, with a comparative increase in accuracy given sufficient quality of the trial wave function for the set of studied cases. We then take this constraint, termed linecut AFQMC (lc-AFQMC), and systematically release it (lcR-AFQMC), providing a route to obtain a smooth bridge between constrained AFQMC and the exact free projection results.
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Affiliation(s)
- John L Weber
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
| | - Hung Vuong
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
| | - Richard A Friesner
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
| | - David R Reichman
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
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5
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Neugebauer H, Pinski P, Grimme S, Neese F, Bursch M. Assessment of DLPNO-MP2 Approximations in Double-Hybrid DFT. J Chem Theory Comput 2023; 19:7695-7703. [PMID: 37862406 PMCID: PMC10653103 DOI: 10.1021/acs.jctc.3c00896] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/15/2023] [Indexed: 10/22/2023]
Abstract
The unfavorable scaling (N5) of the conventional second-order Møller-Plesset theory (MP2) typically prevents the application of double-hybrid (DH) density functionals to large systems with more than 100 atoms. A prominent approach to reduce the computational demand of electron correlation methods is the domain-based local pair natural orbital (DLPNO) approximation that is successfully used in the framework of DLPNO-CCSD(T). Its extension to MP2 [Pinski P.; Riplinger, C.; Valeev, E. F.; Neese, F. J. Chem. Phys. 2015, 143, 034108.] paved the way for DLPNO-based DH (DLPNO-DH) methods. In this work, we assess the accuracy of the DLPNO-DH approximation compared to conventional DHs on a large number of 7925 data points for thermochemistry and 239 data points for structural features, including main-group and transition-metal systems. It is shown that DLPNO-DH-DFT can be applied successfully to perform energy calculations and geometry optimizations for large molecules at a drastically reduced computational cost. Furthermore, PNO space extrapolation is shown to be applicable, similar to its DLPNO-CCSD(T) counterpart, to reduce the remaining error.
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Affiliation(s)
- Hagen Neugebauer
- Mulliken
Center for Theoretical Chemistry, Clausius Institute for Physical
and Theoretical Chemistry, University of
Bonn, Beringstraße 4, D-53115 Bonn, Germany
| | - Peter Pinski
- HQS
Quantum Simulations GmbH, Rintheimer Straße 23, D-76131 Karlsruhe, Germany
| | - Stefan Grimme
- Mulliken
Center for Theoretical Chemistry, Clausius Institute for Physical
and Theoretical Chemistry, University of
Bonn, Beringstraße 4, D-53115 Bonn, Germany
| | - Frank Neese
- Max-Planck-Institut
für Kohlenforschung, Kaiser-Wilhelm-Platz 1, D-45470 Mülheim an der Ruhr, Germany
| | - Markus Bursch
- Max-Planck-Institut
für Kohlenforschung, Kaiser-Wilhelm-Platz 1, D-45470 Mülheim an der Ruhr, Germany
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6
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Neugebauer H, Vuong HT, Weber JL, Friesner RA, Shee J, Hansen A. Toward Benchmark-Quality Ab Initio Predictions for 3d Transition Metal Electrocatalysts: A Comparison of CCSD(T) and ph-AFQMC. J Chem Theory Comput 2023; 19:6208-6225. [PMID: 37655473 DOI: 10.1021/acs.jctc.3c00617] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/02/2023]
Abstract
Generating accurate ab initio ionization energies for transition metal complexes is an important step toward the accurate computational description of their electrocatalytic reactions. Benchmark-quality data is required for testing existing theoretical methods and developing new ones but is complicated to obtain for many transition metal compounds due to the potential presence of both strong dynamical and static electron correlation. In this regime, it is questionable whether the so-called gold standard, coupled cluster with singles, doubles, and perturbative triples (CCSD(T)), provides the desired level of accuracy─roughly 1-3 kcal/mol. In this work, we compiled a test set of 28 3d metal-containing molecules relevant to homogeneous electrocatalysis (termed 3dTMV) and computed their vertical ionization energies (ionization potentials) with CCSD(T) and phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) in the def2-SVP basis set. A substantial effort has been made to converge away the phaseless bias in the ph-AFQMC reference values. We assess a wide variety of multireference diagnostics and find that spin-symmetry breaking of the CCSD wave function and the PBE0 density functional correlate well with our analysis of multiconfigurational wave functions. We propose quantitative criteria based on symmetry breaking to delineate correlation regimes inside of which appropriately performed CCSD(T) can produce mean absolute deviations from the ph-AFQMC reference values of roughly 2 kcal/mol or less and outside of which CCSD(T) is expected to fail. We also present a preliminary assessment of density functional theory (DFT) functionals on the 3dTMV set.
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Affiliation(s)
- Hagen Neugebauer
- Mulliken Center for Theoretical Chemistry, Clausius Institute for Physical and Theoretical Chemistry, University of Bonn, Beringstr. 4, D-53115 Bonn, Germany
| | - Hung T Vuong
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
| | - John L Weber
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
| | - Richard A Friesner
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
| | - James Shee
- Department of Chemistry, Rice University, Houston, Texas 77005, United States
| | - Andreas Hansen
- Mulliken Center for Theoretical Chemistry, Clausius Institute for Physical and Theoretical Chemistry, University of Bonn, Beringstr. 4, D-53115 Bonn, Germany
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7
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Sukurma Z, Schlipf M, Humer M, Taheridehkordi A, Kresse G. Benchmark Phaseless Auxiliary-Field Quantum Monte Carlo Method for Small Molecules. J Chem Theory Comput 2023; 19:4921-4934. [PMID: 37470356 PMCID: PMC10413869 DOI: 10.1021/acs.jctc.3c00322] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2023] [Indexed: 07/21/2023]
Abstract
We report a scalable Fortran implementation of the phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) and demonstrate its excellent performance and beneficial scaling with respect to system size. Furthermore, we investigate modifications of the phaseless approximation that can help to reduce the overcorrelation problems common to the ph-AFQMC. We apply the method to the 26 molecules in the HEAT set, the benzene molecule, and water clusters. We observe a mean absolute deviation of the total energy of 1.15 kcal/mol for the molecules in the HEAT set, close to chemical accuracy. For the benzene molecule, the modified algorithm despite using a single-Slater-determinant trial wavefunction yields the same accuracy as the original phaseless scheme with 400 Slater determinants. Despite these improvements, we find systematic errors for the CN, CO2, and O2 molecules that need to be addressed with more accurate trial wavefunctions. For water clusters, we find that the ph-AFQMC yields excellent binding energies that differ from CCSD(T) by typically less than 0.5 kcal/mol.
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Affiliation(s)
- Zoran Sukurma
- Faculty
of Physics and Center for Computational Materials Science, University of Vienna, Kolingasse 14-16, A-1090 Vienna, Austria
- Faculty
of Physics & Vienna Doctoral School in Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria
| | | | - Moritz Humer
- Faculty
of Physics and Center for Computational Materials Science, University of Vienna, Kolingasse 14-16, A-1090 Vienna, Austria
- Faculty
of Physics & Vienna Doctoral School in Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria
| | - Amir Taheridehkordi
- Faculty
of Physics and Center for Computational Materials Science, University of Vienna, Kolingasse 14-16, A-1090 Vienna, Austria
| | - Georg Kresse
- Faculty
of Physics and Center for Computational Materials Science, University of Vienna, Kolingasse 14-16, A-1090 Vienna, Austria
- VASP
Software GmbH, Sensengasse 8, 1090 Vienna, Austria
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8
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Zhao H, Pan Y, Lau KC. Ferrocene/ferrocenium, cobaltocene/cobaltocenium and nickelocene/nickelocenium: from gas phase ionization energy to one-electron reduction potential in solvated medium. Phys Chem Chem Phys 2023. [PMID: 37325896 DOI: 10.1039/d3cp01904g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
We propose a theoretical procedure for accurate determination of reduction potentials for three metallocene couples, Cp2M+/Cp2M, where M = Fe, Co and Ni. This procedure first computes the gas phase ionization energy (IE) using the explicitly correlated CCSD(T)-F12 method and includes the zero-point energy correction, core-valence electronic correlation, and relativistic and spin-orbit coupling effects. By means of Born-Haber thermochemical cycle, the one-electron reduction potential is obtained as the sum of the gas phase IE and the corresponding Gibbs free energies of solvation (ΔGsolv) for both the neutral and cationic species. Among the three solvent models (PCM, SMD and uESE) investigated here, it turns out that only the SMD model (computed at the DFT level) gives the best estimation of the value for "ΔGsolv(cation) - ΔGsolv(neutral)" and thus, combining with the accurate IE values, the theoretical protocol is capable of yielding reliable values (in V) for , and . These predictions compare favorably with the available experimental data (in V): , , and . We show that our theoretical procedure is reliable for accurate reduction potential predictions of Cp2Fe+/Cp2Fe, Cp2Co+/Cp2Co and Cp2Ni+/Cp2Ni redox couples in aqueous and non-aqueous media; the maximum absolute deviation is as small as ≈120 mV, which outperforms those of the existing theoretical methods.
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Affiliation(s)
- Hongyan Zhao
- Department of Chemistry, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong.
| | - Yi Pan
- Department of Chemistry, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong.
| | - Kai-Chung Lau
- Department of Chemistry, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong.
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9
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Yang KR, Kyro GW, Batista VS. The landscape of computational approaches for artificial photosynthesis. NATURE COMPUTATIONAL SCIENCE 2023; 3:504-513. [PMID: 38177419 DOI: 10.1038/s43588-023-00450-1] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/14/2022] [Accepted: 04/11/2023] [Indexed: 01/06/2024]
Abstract
Artificial photosynthesis is an attractive strategy for converting solar energy into fuels, largely because the Earth receives enough solar energy in one hour to meet humanity's energy needs for an entire year. However, developing devices for artificial photosynthesis remains difficult and requires computational approaches to guide and assist the interpretation of experiments. In this Perspective, we discuss current and future computational approaches, as well as the challenges of designing and characterizing molecular assemblies that absorb solar light, transfer electrons between interfaces, and catalyze water-splitting and fuel-forming reactions.
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Affiliation(s)
- Ke R Yang
- Department of Chemistry, Yale University, New Haven, CT, USA
- Energy Sciences Institute, Yale University, West Haven, CT, USA
| | - Gregory W Kyro
- Department of Chemistry, Yale University, New Haven, CT, USA
| | - Victor S Batista
- Department of Chemistry, Yale University, New Haven, CT, USA.
- Energy Sciences Institute, Yale University, West Haven, CT, USA.
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10
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Shee J, Weber JL, Reichman DR, Friesner RA, Zhang S. On the potentially transformative role of auxiliary-field quantum Monte Carlo in quantum chemistry: A highly accurate method for transition metals and beyond. J Chem Phys 2023; 158:140901. [PMID: 37061483 PMCID: PMC10089686 DOI: 10.1063/5.0134009] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/17/2023] Open
Abstract
Approximate solutions to the ab initio electronic structure problem have been a focus of theoretical and computational chemistry research for much of the past century, with the goal of predicting relevant energy differences to within "chemical accuracy" (1 kcal/mol). For small organic molecules, or in general, for weakly correlated main group chemistry, a hierarchy of single-reference wave function methods has been rigorously established, spanning perturbation theory and the coupled cluster (CC) formalism. For these systems, CC with singles, doubles, and perturbative triples is known to achieve chemical accuracy, albeit at O(N7) computational cost. In addition, a hierarchy of density functional approximations of increasing formal sophistication, known as Jacob's ladder, has been shown to systematically reduce average errors over large datasets representing weakly correlated chemistry. However, the accuracy of such computational models is less clear in the increasingly important frontiers of chemical space including transition metals and f-block compounds, in which strong correlation can play an important role in reactivity. A stochastic method, phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC), has been shown to be capable of producing chemically accurate predictions even for challenging molecular systems beyond the main group, with relatively low O(N3 - N4) cost and near-perfect parallel efficiency. Herein, we present our perspectives on the past, present, and future of the ph-AFQMC method. We focus on its potential in transition metal quantum chemistry to be a highly accurate, systematically improvable method that can reliably probe strongly correlated systems in biology and chemical catalysis and provide reference thermochemical values (for future development of density functionals or interatomic potentials) when experiments are either noisy or absent. Finally, we discuss the present limitations of the method and where we expect near-term development to be most fruitful.
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Affiliation(s)
- James Shee
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - John L Weber
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, USA
| | - David R Reichman
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, USA
| | - Richard A Friesner
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, USA
| | - Shiwei Zhang
- Center for Computational Quantum Physics, Flatiron Institute, 162 5th Avenue, New York, New York 10010, USA
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11
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Aðalsteinsson HM, Bjornsson R. Ionization energies of metallocenes: a coupled cluster study of cobaltocene. Phys Chem Chem Phys 2023; 25:4570-4587. [PMID: 36723003 DOI: 10.1039/d2cp04715b] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
Abstract
Open-shell transition metal chemistry presents challenges to contemporary electronic structure methods, based on either density functional or wavefunction theory. While CCSD(T) is the well-trusted gold standard for maingroup thermochemistry, the accuracy and robustness of the method is less clear for open-shell transition metal chemistry, requiring benchmarking of CCSD(T)-based protocols against either higher-level theory or experiment. Ionization energies (IEs) of metallocenes provide an interesting test case with metallocenes being common redox reagents as well as playing roles as redox mediators and cocatalysts in redox catalysis. Using highly accurate ZEKE-MATI experimental measurements of gas phase adiabatic (5.3275 ± 0.0006 eV) and vertical (5.4424 ± 0.0006 eV) ionization energies of cobaltocene, we systematically assessed the accuracy of the local coupled-cluster method DLPNO-CCSD(T) with respect to geometry, reference determinant, basis set size and extrapolation schemes, PNO cut-off and extrapolation, local triples approximation, relativistic effects and core-valence correlation. We show that PNO errors are controllable via the recently introduced PNO extrapolation schemes and that the expensive iterative triples (T1) contribution can be made more manageable by calculating it as a smaller-basis/smaller PNO-cutoff correction. The reference determinant turns out to be a critical aspect in these calculations with the HF determinant resulting in large DLPNO-CCSD(T) errors, likely due to the qualitatively flawed molecular orbital spectrum. The BP86 functional on the other hand was found to provide reference orbitals giving small DLPNO-CCSD(T) errors, likely due to more realistic orbitals as suggested by the more consistent MO spectrum compared to HF. A protocol including complete basis set extrapolations with correlation-consistent basis sets, complete PNO space extrapolations, iterative triples- and core-valence correlation corrections was found to give errors of -0.07 eV and -0.03 eV for adiabatic- and vertical-IE of cobaltocene, respectively, giving close to chemical accuracy for both properties. A computationally efficient DLPNO-CCSD(T) protocol was devised and tested against adiabatic ionization energies of 6 different metallocenes (V, Cr, Mn, Fe, Co, Ni). For the other metallocenes, the iterative triples (T1) and PNO extrapolation contributions turn out to be even more important. The results give errors close to the experimental uncertainty, similar to recent auxiliary-field quantum Monte Carlo results. The quality of the reference determinant orbitals is identified as the main source of uncertainty in CCSD(T) calculations of metallocenes.
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Affiliation(s)
| | - Ragnar Bjornsson
- Science Institute, University of Iceland, 107 Reykjavik, Iceland.,Univ Grenoble Alpes, CNRS, CEA, IRIG, Laboratoire de Chimie et Biologie des Métaux, 17 Rue des Martyrs, F-38054 Grenoble Cedex, France.
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12
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Mandal S, Kar R, Meyer B, Nair NN. Hybrid Functional and Plane Waves based Ab Initio Molecular Dynamics Study of the Aqueous Fe 2+ /Fe 3+ Redox Reaction. Chemphyschem 2023; 24:e202200617. [PMID: 36169153 DOI: 10.1002/cphc.202200617] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2022] [Revised: 09/27/2022] [Indexed: 02/03/2023]
Abstract
Kohn-Sham density functional theory and plane wave basis set based ab initio molecular dynamics (AIMD) simulation is a powerful tool for studying complex reactions in solutions, such as electron transfer (ET) reactions involving Fe2+ /Fe3+ ions in water. In most cases, such simulations are performed using density functionals at the level of Generalized Gradient Approximation (GGA). The challenge in modelling ET reactions is the poor quality of GGA functionals in predicting properties of such open-shell systems due to the inevitable self-interaction error (SIE). While hybrid functionals can minimize SIE, standard plane-wave based AIMD at that level of theory is typically 150 times slower than GGA for systems containing ∼100 atoms. Among several approaches reported to speed-up AIMD simulations with hybrid functionals, the noise-stabilized MD (NSMD) procedure, together with the use of localized orbitals to compute the required exchange integrals, is an attractive option. In this work, we demonstrate the application of the NSMD approach for studying the Fe2+ /Fe3+ redox reaction in water. It is shown here that long AIMD trajectories at the level of hybrid density functionals can be obtained using this approach. Redox properties of the aqueous Fe2+ /Fe3+ system computed from these simulations are compared with the available experimental data for validation.
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Affiliation(s)
- Sagarmoy Mandal
- Department of Chemistry, Indian Institute of Technology Kanpur (IITK), 208016, Kanpur, India.,Interdisciplinary Center for Molecular Materials and Computer Chemistry Center, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Nägelsbachstr. 25, 91052, Erlangen, Germany.,Erlangen National High Performance Computing Center (NHR@FAU), Friedrich-Alexander-Universität Erlangen-Nürnberg, Martensstr. 1, 91058, Erlangen, Germany
| | - Ritama Kar
- Department of Chemistry, Indian Institute of Technology Kanpur (IITK), 208016, Kanpur, India
| | - Bernd Meyer
- Interdisciplinary Center for Molecular Materials and Computer Chemistry Center, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Nägelsbachstr. 25, 91052, Erlangen, Germany.,Erlangen National High Performance Computing Center (NHR@FAU), Friedrich-Alexander-Universität Erlangen-Nürnberg, Martensstr. 1, 91058, Erlangen, Germany
| | - Nisanth N Nair
- Department of Chemistry, Indian Institute of Technology Kanpur (IITK), 208016, Kanpur, India
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13
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Lee J, Pham HQ, Reichman DR. Twenty Years of Auxiliary-Field Quantum Monte Carlo in Quantum Chemistry: An Overview and Assessment on Main Group Chemistry and Bond-Breaking. J Chem Theory Comput 2022; 18:7024-7042. [PMID: 36255074 DOI: 10.1021/acs.jctc.2c00802] [Citation(s) in RCA: 15] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Abstract
In this work, we present an overview of the phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) approach from a computational quantum chemistry perspective and present a numerical assessment of its performance on main group chemistry and bond-breaking problems with a total of 1004 relative energies. While our benchmark study is somewhat limited, we make recommendations for the use of ph-AFQMC for general main-group chemistry applications. For systems where single determinant wave functions are qualitatively accurate, we expect the accuracy of ph-AFQMC in conjunction with a single-determinant trial wave function to be between that of coupled-cluster with singles and doubles (CCSD) and CCSD with perturbative triples (CCSD(T)). For these applications, ph-AFQMC should be a method of choice when canonical CCSD(T) is too expensive to run. For systems where multireference (MR) wave functions are needed for qualitative accuracy, ph-AFQMC is far more accurate than MR perturbation theory methods and competitive with MR configuration interaction (MRCI) methods. Due to the computational efficiency of ph-AFQMC compared to MRCI, we recommended ph-AFQMC as a method of choice for handling dynamic correlation in MR problems. We conclude with a discussion of important directions for future development of the ph-AFQMC approach.
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Affiliation(s)
- Joonho Lee
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
| | - Hung Q Pham
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
| | - David R Reichman
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
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14
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Rettig A, Shee J, Lee J, Head-Gordon M. Revisiting the Orbital Energy-Dependent Regularization of Orbital-Optimized Second-Order Møller-Plesset Theory. J Chem Theory Comput 2022; 18:5382-5392. [PMID: 36050889 DOI: 10.1021/acs.jctc.2c00641] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Optimizing orbitals in the presence of electron correlation, as in orbital-optimized second-order Møller-Plesset perturbation theory (OOMP2), can remove artifacts associated with mean-field orbitals such as spin contamination and artificial symmetry-breaking. However, OOMP2 is known to suffer from divergent correlation energies in regimes of small orbital energy gaps. To address this issue, several approaches to amplitude regularization have been explored, with those featuring energy-gap-dependent regularizers appearing to be most transferable and physically justifiable. For instance, κ-OOMP2 was shown to address the energy divergence issue in, for example, bond-breaking processes while offering a significant improvement in accuracy for the W4-11 thermochemistry data set, and a parameter of κ = 1.45 was recommended. A more recent investigation of regularized MP2 with Hartree-Fock orbitals revealed that stronger regularization (i.e., smaller values of κ) than what had previously been recommended for κ-OOMP2 may offer huge improvements in certain cases such as noncovalent interactions while retaining a high level of accuracy for main-group thermochemistry data sets. In this study, we investigate the transferability of those findings to κ-OOMP2 and assess the implications of stronger regularization on the ability of κ-OOMP2 to diagnose strong static correlation. We found similar results using κ-OOMP2 for several main-group thermochemistry, barrier height, and noncovalent interaction data sets including both closed shell and open shell species. However, stronger regularization yielded substantially higher accuracy for open-shell transition-metal (TM) thermochemistry and is necessary to provide qualitatively correct spin symmetry breaking behavior for several large and electrochemically relevant TM systems. We therefore find a single κ value insufficient to treat all systems using κ-OOMP2.
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Affiliation(s)
- Adam Rettig
- Department of Chemistry, University of California, Berkeley, California 94720, United States.,Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - James Shee
- Department of Chemistry, University of California, Berkeley, California 94720, United States
| | - Joonho Lee
- Department of Chemistry, Columbia University, New York, New York 10027, United States
| | - Martin Head-Gordon
- Department of Chemistry, University of California, Berkeley, California 94720, United States.,Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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15
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Meng Q, Chen J, Ma J, Zhang X, Chen J. Adiabatic models for the quantum dynamics of surface scattering with lattice effects. Phys Chem Chem Phys 2022; 24:16415-16436. [PMID: 35766107 DOI: 10.1039/d2cp01560a] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
In this contribution, we review models for the lattice effects in quantum dynamics calculations on surface scattering, which is important to modeling heterogeneous catalysis for achieving an interpretation of experimental measurements. Unlike dynamics models for reactions in the gas phase, those for heterogeneous reactions have to include the effects of the surface. For manageable computational costs in calculations, the effects of static surface (SS) are firstly modeled as this is simply and easily implemented. Then, the SS model has to be improved to include the effects of the flexible surface, that is the lattice effects. To do this, various surface models have been designed where the coordinates of the surface atoms are introduced in the Hamiltonian operator, especially those of the top surface atom. Based on this model Hamiltonian operator, extensive multi-dimension quantum dynamics calculations can be performed to recover the lattice effects. Here, we first review an overview of the techniques in constructing the Hamiltonian operator, which is a sum of the kinetic energy operator (KEO) and potential energy surface (PES). Since the PES containing the coordinates of the surface atoms in a cell is still expensive, the SS model is often accepted. We consider a mathematical model, called the coupled harmonic oscillator (CHO) model, to introduce the concepts of adiabatic and diabatic representations for separating the molecule and surface. Under the adiabatic model, we further introduce the expansion model where the potential function is Taylor expanded around the optimized geometry of the surface. By an expansion model truncated at the first and second order, various coupling surface models between the molecule and surface are derived. Moreover, by further and deeply understanding the adiabatic representation, an effective Hamiltonian operator is obtained by optimizing the total wave function in factorized form. By this factorized form of wave function and effective Hamiltonian operator, the geometry phase of the surface wave function is theoretically found. This theoretical prediction may be measured by carefully designing experiments. Finally, discussions on the adiabatic representation, the PES construction, and possibility of the classical-dynamics solutions are given. Based on these discussions, a simple outlook on the dynamics of photocatalytics is finally given.
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Affiliation(s)
- Qingyong Meng
- Department of Chemistry, Northwestern Polytechnical University, West Youyi Road 127, 710072 Xi'an, China.
| | - Junbo Chen
- Department of Chemistry, Northwestern Polytechnical University, West Youyi Road 127, 710072 Xi'an, China. .,Xi'an Modern Chemistry Research Institute, China North Industries Group Corp., Ltd., East Zhangba Road 168, 710065 Xi'an, China
| | - Jianxing Ma
- Department of Chemistry, Northwestern Polytechnical University, West Youyi Road 127, 710072 Xi'an, China.
| | - Xingyu Zhang
- Department of Chemistry, Northwestern Polytechnical University, West Youyi Road 127, 710072 Xi'an, China.
| | - Jun Chen
- State Key Laboratory of Structural Chemistry, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Yangqiao Road West 155, 350002 Fuzhou, China.,Fujian Science & Technology Innovation Laboratory for Optoelectronic Information of China, Optoelectronic Industry Base at High-tech Zone, 350108 Fuzhou, China
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16
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Weber JL, Vuong H, Devlaminck PA, Shee J, Lee J, Reichman DR, Friesner RA. A Localized-Orbital Energy Evaluation for Auxiliary-Field Quantum Monte Carlo. J Chem Theory Comput 2022; 18:3447-3459. [PMID: 35507769 DOI: 10.1021/acs.jctc.2c00111] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) has recently emerged as a promising method for the production of benchmark-level simulations of medium- to large-sized molecules because of its accuracy and favorable polynomial scaling with system size. Unfortunately, the memory footprints of standard energy evaluation algorithms are nontrivial, which can significantly impact timings on graphical processing units (GPUs) where memory is limited. Previous attempts to reduce scaling by taking advantage of the low-rank structure of the Coulombic integrals have been successful but exhibit high prefactors, making their utility limited to very large systems. Here we present a complementary cubic-scaling route to reduce memory and computational scaling based on the low rank of the Coulombic interactions between localized orbitals, focusing on the application to ph-AFQMC. We show that the error due to this approximation, which we term localized-orbital AFQMC (LO-AFQMC), is systematic and controllable via a single variable and that the method is computationally favorable even for small systems. We present results demonstrating robust retention of accuracy versus both experiment and full ph-AFQMC for a variety of test cases chosen for their potential difficulty for localized-orbital-based methods, including the singlet-triplet gaps of the polyacenes benzene through pentacene, the heats of formation for a set of Platonic hydrocarbon cages, and the total energy of ferrocene, Fe(Cp)2. Finally, we reproduce our previous result for the gas-phase ionization energy of Ni(Cp)2, agreeing with full ph-AFQMC to within statistical error while using less than 1/15th of the computer time.
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Affiliation(s)
- John L Weber
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
| | - Hung Vuong
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
| | - Pierre A Devlaminck
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
| | - James Shee
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, United States
| | - Joonho Lee
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
| | - David R Reichman
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
| | - Richard A Friesner
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
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