1
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Jørgensen FK, Delcey MG, Hedegård ED. Perspective: multi-configurational methods in bio-inorganic chemistry. Phys Chem Chem Phys 2024; 26:17443-17455. [PMID: 38868993 DOI: 10.1039/d4cp01297f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/14/2024]
Abstract
Transition metal ions play crucial roles in the structure and function of numerous proteins, contributing to essential biological processes such as catalysis, electron transfer, and oxygen binding. However, accurately modeling the electronic structure and properties of metalloproteins poses significant challenges due to the complex nature of their electronic configurations and strong correlation effects. Multiconfigurational quantum chemistry methods are, in principle, the most appropriate tools for addressing these challenges, offering the capability to capture the inherent multi-reference character and strong electron correlation present in bio-inorganic systems. Yet their computational cost has long hindered wider adoption, making methods such as density functional theory (DFT) the method of choice. However, advancements over the past decade have substantially alleviated this limitation, rendering multiconfigurational quantum chemistry methods more accessible and applicable to a wider range of bio-inorganic systems. In this perspective, we discuss some of these developments and how they have already been used to answer some of the most important questions in bio-inorganic chemistry. We also comment on ongoing developments in the field and how the future of the field may evolve.
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Affiliation(s)
- Frederik K Jørgensen
- Department of Physics, Chemistry, and Pharmacy, University of Southern Denmark, Campusvej 55, 5230 Odense, Denmark.
| | - Mickaël G Delcey
- Department of Chemistry, Lund University, Naturvetarvägen 14, 221 00 Lund, Sweden
| | - Erik D Hedegård
- Department of Physics, Chemistry, and Pharmacy, University of Southern Denmark, Campusvej 55, 5230 Odense, Denmark.
- Department of Chemistry, Lund University, Naturvetarvägen 14, 221 00 Lund, Sweden
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2
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Cheng Y, Ma H. Renormalized-Residue-Based Multireference Configuration Interaction Method for Strongly Correlated Systems. J Chem Theory Comput 2024; 20:1988-2009. [PMID: 38380619 DOI: 10.1021/acs.jctc.3c01247] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/22/2024]
Abstract
The implementation of multireference configuration interaction (MRCI) methods in quantum systems with large active spaces is hindered by the expansion of configuration bases or the intricate handling of reduced density matrices (RDMs). In this work, we present a spin-adapted renormalized-residue-based MRCI (RR-MRCI) approach that leverages renormalized residues to effectively capture the entanglement between active and inactive orbitals. This approach is reinforced by a novel efficient algorithm, which also facilitates an efficient deployment of spin-adapted matrix product state MRCI (MPS-MRCI). The RR-MRCI framework possesses several advantages: (1) It considers the orbital entanglement and utilizes highly compressed MPS structure, improving computational accuracy and efficiency compared with internally contracted (ic) MRCI. (2) Utilizing small-sized buffer environments of a few external orbitals as probes based on quantum information theory, it enhances computational efficiency over MPS-MRCI and offers potential application to large molecular systems. (3) The RR framework can be implemented in conjunction with ic-MRCI, eliminating the need for high-rank RDMs, by using distinct renormalized residues. We evaluated this method across nine diverse molecular systems, including Cu2O22+ with an active space of (24e,24o) and two complexes of lanthanide and actinide with active space (38e,36o), demonstrating the method's versatility and efficacy.
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Affiliation(s)
- Yifan Cheng
- School of Chemistry and Chemical Engineering, Nanjing University, Nanjing, Jiangsu 210023, China
| | - Haibo Ma
- Qingdao Institute for Theoretical and Computational Sciences, School of Chemistry and Chemical Engineering, Shandong University, Qingdao, Shandong 266237, China
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3
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Song Y, Huang W, Liu C, Lei Y, Suo B, Ma H. Spin-Adapted Externally Contracted Multireference Configuration Interaction Method Based on Selected Reference Configurations. J Phys Chem A 2024; 128:958-971. [PMID: 38272019 DOI: 10.1021/acs.jpca.3c07526] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2024]
Abstract
As one kind of approximation of the full configuration interaction solution, the selected configuration interaction (sCI) methods have been shown to be valuable for large active spaces. However, the inclusion of dynamic correlation beyond large active spaces is necessary for more quantitative results. Since the sCI wave function can provide a compact reference for multireference methods, previously, we proposed an externally contracted multireference configuration interaction method using the sCI reference reconstructed from the density matrix renormalization group wave function [J. Chem. Theory Comput. 2018, 14, 4747-4755]. The DMRG2sCI-EC-MRCI method is promising for dealing with more than 30 active orbitals and large basis sets. However, it suffers from two drawbacks: spin contamination and low efficiency when using Slater determinant bases. To solve these problems, in this work, we adopt configuration state function bases and introduce a new algorithm based on the hybrid of tree structure for convenient configuration space management and the graphical unitary group approach for efficient matrix element calculation. The test calculation of naphthalene shows that the spin-adapted version could achieve a speed-up of 6.0 compared with the previous version based on the Slater determinant. Examples of dinuclear copper(II) compound as well as Ln(III) and An(III) complexes show that the sCI-EC-MRCI can give quantitatively accurate results by including dynamic correlation over sCI for systems with large active spaces and basis sets.
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Affiliation(s)
- Yinxuan Song
- School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, People's Republic of China
| | - Wei Huang
- School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, People's Republic of China
| | - Chungen Liu
- School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, People's Republic of China
| | - Yibo Lei
- Key Laboratory of Synthetic and Natural Functional Molecule of the Ministry of Education, College of Chemistry & Materials Science, Shaanxi Key Laboratory of Physico-Inorganic Chemistry, Northwest University, Xi'an 710127, People's Republic of China
| | - Bingbing Suo
- Shaanxi Key Laboratory for Theoretical Physics Frontiers, Institute of Modern Physics, Northwest University, Xi'an 710127, People's Republic of China
| | - Haibo Ma
- Qingdao Institute for Theoretical and Computational Sciences, Qingdao Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao 266237, China
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4
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Xiang C, Jia W, Fang WH, Li Z. Distributed Multi-GPU Ab Initio Density Matrix Renormalization Group Algorithm with Applications to the P-Cluster of Nitrogenase. J Chem Theory Comput 2024; 20:775-786. [PMID: 38198503 DOI: 10.1021/acs.jctc.3c01228] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2024]
Abstract
The presence of many degenerate d/f orbitals makes polynuclear transition-metal compounds, such as iron-sulfur clusters in nitrogenase, challenging for state-of-the-art quantum chemistry methods. To address this challenge, we present the first distributed multi-graphics processing unit (GPU) ab initio density matrix renormalization group (DMRG) algorithm suitable for modern high-performance computing (HPC) infrastructures. The central idea is to parallelize the most computationally intensive part─the multiplication of O(K2) operators with a trial wave function, where K is the number of spatial orbitals, by combining operator parallelism for distributing the workload with a batched algorithm for performing contractions on GPU. With this new implementation, we are able to reach an unprecedentedly large bond dimension D = 14,000 on 48 GPUs (NVIDIA A100 80 GB SXM) for an active space model (114 electrons in 73 active orbitals) of the P-cluster, which is nearly 3 times larger than the bond dimensions reported in previous DMRG calculations for the same system using only central processing units (CPUs).
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Affiliation(s)
- Chunyang Xiang
- State Key Lab of Processors, Institute of Computing Technology, Chinese Academy of Sciences, Beijing 100190, China
- University of Chinese Academy of Sciences, Beijing 100190, China
| | - Weile Jia
- State Key Lab of Processors, Institute of Computing Technology, Chinese Academy of Sciences, Beijing 100190, China
- University of Chinese Academy of Sciences, Beijing 100190, China
| | - Wei-Hai Fang
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Zhendong Li
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
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5
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Zhai H, Larsson HR, Lee S, Cui ZH, Zhu T, Sun C, Peng L, Peng R, Liao K, Tölle J, Yang J, Li S, Chan GKL. Block2: A comprehensive open source framework to develop and apply state-of-the-art DMRG algorithms in electronic structure and beyond. J Chem Phys 2023; 159:234801. [PMID: 38108484 DOI: 10.1063/5.0180424] [Citation(s) in RCA: 9] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2023] [Accepted: 11/16/2023] [Indexed: 12/19/2023] Open
Abstract
block2 is an open source framework to implement and perform density matrix renormalization group and matrix product state algorithms. Out-of-the-box it supports the eigenstate, time-dependent, response, and finite-temperature algorithms. In addition, it carries special optimizations for ab initio electronic structure Hamiltonians and implements many quantum chemistry extensions to the density matrix renormalization group, such as dynamical correlation theories. The code is designed with an emphasis on flexibility, extensibility, and efficiency and to support integration with external numerical packages. Here, we explain the design principles and currently supported features and present numerical examples in a range of applications.
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Affiliation(s)
- Huanchen Zhai
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Henrik R Larsson
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Seunghoon Lee
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Zhi-Hao Cui
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Tianyu Zhu
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Chong Sun
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Linqing Peng
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Ruojing Peng
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Ke Liao
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Johannes Tölle
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Junjie Yang
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Shuoxue Li
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Garnet Kin-Lic Chan
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
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6
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Zhai H, Lee S, Cui ZH, Cao L, Ryde U, Chan GKL. Multireference Protonation Energetics of a Dimeric Model of Nitrogenase Iron-Sulfur Clusters. J Phys Chem A 2023; 127:9974-9984. [PMID: 37967028 PMCID: PMC10694817 DOI: 10.1021/acs.jpca.3c06142] [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: 09/12/2023] [Revised: 10/31/2023] [Accepted: 11/01/2023] [Indexed: 11/17/2023]
Abstract
Characterizing the electronic structure of the iron-sulfur clusters in nitrogenase is necessary to understand their role in the nitrogen fixation process. One challenging task is to determine the protonation state of the intermediates in the nitrogen fixing cycle. Here, we use a dimeric iron-sulfur model to study relative energies of protonation at C, S, or Fe. Using a composite method based on coupled cluster and density matrix renormalization group energetics, we converge the relative energies of four protonated configurations with respect to basis set and correlation level. We find that accurate relative energies require large basis sets as well as a proper treatment of multireference and relativistic effects. We have also tested ten density functional approximations for these systems. Most of them give large errors in their relative energies. The best performing functional in this system is B3LYP, which gives mean absolute and maximum deviations of only 10 and 13 kJ/mol with respect to our correlated wave function estimates, respectively, comparable to the uncertainty in our correlated estimates. Our work provides benchmark results for the calibration of new approximate electronic structure methods and density functionals for these problems.
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Affiliation(s)
- Huanchen Zhai
- Division
of Chemistry and Chemical Engineering, California
Institute of Technology, Pasadena, California 91125, United States
| | - Seunghoon Lee
- Division
of Chemistry and Chemical Engineering, California
Institute of Technology, Pasadena, California 91125, United States
| | - Zhi-Hao Cui
- Division
of Chemistry and Chemical Engineering, California
Institute of Technology, Pasadena, California 91125, United States
| | - Lili Cao
- Department
of Theoretical Chemistry, Lund University, P.O. Box 124, SE-221 00 Lund, Sweden
| | - Ulf Ryde
- Department
of Theoretical Chemistry, Lund University, P.O. Box 124, SE-221 00 Lund, Sweden
| | - Garnet Kin-Lic Chan
- Division
of Chemistry and Chemical Engineering, California
Institute of Technology, Pasadena, California 91125, United States
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7
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Lee S, Zhai H, Chan GKL. An Ab Initio Correction Vector Restricted Active Space Approach to the L-Edge XAS and 2p3d RIXS Spectra of Transition Metal Complexes. J Chem Theory Comput 2023; 19:7753-7763. [PMID: 37853682 PMCID: PMC10653107 DOI: 10.1021/acs.jctc.3c00663] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/17/2023] [Indexed: 10/20/2023]
Abstract
We describe an ab initio approach to simulate L-edge X-ray absorption (XAS) and 2p3d resonant inelastic X-ray scattering (RIXS) spectroscopies. We model the strongly correlated electronic structure within a restricted active space and employ a correction vector formulation instead of sum-over-state expressions for the spectra, thus eliminating the need to calculate a large number of intermediate and final electronic states. We present benchmark simulations of the XAS and RIXS spectra of the iron complexes [FeCl4]1-/2- and [Fe(SCH3)4]1-/2- and interpret the spectra by deconvolving the correction vectors. Our approach represents a step toward simulating the X-ray spectroscopies of larger metal cluster systems that play a pivotal role in biology.
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Affiliation(s)
- Seunghoon Lee
- Department
of Chemistry, Seoul National University, Seoul 151-747, South Korea
- Division
of Chemistry and Chemical Engineering, California
Institute of Technology, Pasadena, California 91125, United States
| | - Huanchen Zhai
- Division
of Chemistry and Chemical Engineering, California
Institute of Technology, Pasadena, California 91125, United States
| | - Garnet Kin-Lic Chan
- Division
of Chemistry and Chemical Engineering, California
Institute of Technology, Pasadena, California 91125, United States
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8
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Izsák R, Ivanov AV, Blunt NS, Holzmann N, Neese F. Measuring Electron Correlation: The Impact of Symmetry and Orbital Transformations. J Chem Theory Comput 2023; 19:2703-2720. [PMID: 37022051 PMCID: PMC10210250 DOI: 10.1021/acs.jctc.3c00122] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2023] [Indexed: 04/07/2023]
Abstract
In this perspective, the various measures of electron correlation used in wave function theory, density functional theory and quantum information theory are briefly reviewed. We then focus on a more traditional metric based on dominant weights in the full configuration solution and discuss its behavior with respect to the choice of the N-electron and the one-electron basis. The impact of symmetry is discussed, and we emphasize that the distinction among determinants, configuration state functions and configurations as reference functions is useful because the latter incorporate spin-coupling into the reference and should thus reduce the complexity of the wave function expansion. The corresponding notions of single determinant, single spin-coupling and single configuration wave functions are discussed and the effect of orbital rotations on the multireference character is reviewed by analyzing a simple model system. In molecular systems, the extent of correlation effects should be limited by finite system size and in most cases the appropriate choices of one-electron and N-electron bases should be able to incorporate these into a low-complexity reference function, often a single configurational one.
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Affiliation(s)
- Róbert Izsák
- Riverlane, St Andrews House, 59 St Andrews
Street, Cambridge CB2 3BZ, United Kingdom
| | - Aleksei V. Ivanov
- Riverlane, St Andrews House, 59 St Andrews
Street, Cambridge CB2 3BZ, United Kingdom
| | - Nick S. Blunt
- Riverlane, St Andrews House, 59 St Andrews
Street, Cambridge CB2 3BZ, United Kingdom
| | - Nicole Holzmann
- Riverlane, St Andrews House, 59 St Andrews
Street, Cambridge CB2 3BZ, United Kingdom
| | - Frank Neese
- Max-Planck
Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, D-45470 Mülheim an der Ruhr, Germany
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9
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Han R, Luber S, Li Manni G. Magnetic Interactions in a [Co(II) 3Er(III)(OR) 4] Model Cubane through Forefront Multiconfigurational Methods. J Chem Theory Comput 2023; 19:2811-2826. [PMID: 37126736 DOI: 10.1021/acs.jctc.2c01318] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
Strong electron correlation effects are one of the major challenges in modern quantum chemistry. Polynuclear transition metal clusters are peculiar examples of systems featuring such forms of electron correlation. Multireference strategies, often based on but not limited to the concept of complete active space, are adopted to accurately account for strong electron correlation and to resolve their complex electronic structures. However, transition metal clusters already containing four magnetic centers with multiple unpaired electrons make conventional active space based strategies prohibitively expensive, due to their unfavorable scaling with the size of the active space. In this work, forefront techniques, such as density matrix renormalization group (DMRG), full configuration interaction quantum Monte Carlo (FCIQMC), and multiconfiguration pair-density functional theory (MCPDFT), are employed to overcome the computational limitation of conventional multireference approaches and to accurately investigate the magnetic interactions taking place in a [Co(II)3Er(III)(OR)4] (chemical formula [Co(II)3Er(III)(hmp)4(μ2-OAc)2(OH)3(H2O)], hmp = 2-(hydroxymethyl)-pyridine) model cubane water oxidation catalyst. Complete active spaces with up to 56 electrons in 56 orbitals have been constructed for the seven energetically lowest different spin states. Relative energies, local spin, and spin-spin correlation values are reported and provide crucial insights on the spin interactions for this model system, pivotal in the rationalization of the catalytic activity of this system in the water-splitting reaction. A ferromagnetic ground state is found with a very small, ∼50 cm-1, highest-to-lowest spin gap. Moreover, for the energetically lowest states, S = 3-6, the three Co(II) sites exhibit parallel aligned spins, and for the lower states, S = 0-2, two Co(II) sites retain strong parallel spin alignment.
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Affiliation(s)
- Ruocheng Han
- Department of Chemistry A, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
| | - Sandra Luber
- Department of Chemistry A, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
| | - Giovanni Li Manni
- Max Planck Institute for Solid State Research, Heisenbergstrasse 1, 70569 Stuttgart, Germany
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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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Lee S, Lee J, Zhai H, Tong Y, Dalzell AM, Kumar A, Helms P, Gray J, Cui ZH, Liu W, Kastoryano M, Babbush R, Preskill J, Reichman DR, Campbell ET, Valeev EF, Lin L, Chan GKL. Evaluating the evidence for exponential quantum advantage in ground-state quantum chemistry. Nat Commun 2023; 14:1952. [PMID: 37029105 PMCID: PMC10082187 DOI: 10.1038/s41467-023-37587-6] [Citation(s) in RCA: 25] [Impact Index Per Article: 25.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2023] [Accepted: 03/22/2023] [Indexed: 04/09/2023] Open
Abstract
Due to intense interest in the potential applications of quantum computing, it is critical to understand the basis for potential exponential quantum advantage in quantum chemistry. Here we gather the evidence for this case in the most common task in quantum chemistry, namely, ground-state energy estimation, for generic chemical problems where heuristic quantum state preparation might be assumed to be efficient. The availability of exponential quantum advantage then centers on whether features of the physical problem that enable efficient heuristic quantum state preparation also enable efficient solution by classical heuristics. Through numerical studies of quantum state preparation and empirical complexity analysis (including the error scaling) of classical heuristics, in both ab initio and model Hamiltonian settings, we conclude that evidence for such an exponential advantage across chemical space has yet to be found. While quantum computers may still prove useful for ground-state quantum chemistry through polynomial speedups, it may be prudent to assume exponential speedups are not generically available for this problem.
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Affiliation(s)
- Seunghoon Lee
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA, 91125, USA
| | - Joonho Lee
- Department of Chemistry, Columbia University, New York, NY, 10027, USA
| | - Huanchen Zhai
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA, 91125, USA
| | - Yu Tong
- Department of Mathematics, University of California, Berkeley, CA, 94720, USA
| | | | - Ashutosh Kumar
- Department of Chemistry, Virginia Tech, Blacksburg, VA, 24061, USA
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA
| | - Phillip Helms
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA, 91125, USA
| | - Johnnie Gray
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA, 91125, USA
| | - Zhi-Hao Cui
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA, 91125, USA
| | - Wenyuan Liu
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA, 91125, USA
| | - Michael Kastoryano
- AWS Center for Quantum Computing, Pasadena, CA, 91125, USA
- Amazon Quantum Solutions Lab, Seattle, WA, 98170, USA
| | - Ryan Babbush
- Google Quantum AI, 340 Main Street, Venice, CA, 90291, USA
| | - John Preskill
- AWS Center for Quantum Computing, Pasadena, CA, 91125, USA
- Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA, 91125, USA
| | - David R Reichman
- Department of Chemistry, Columbia University, New York, NY, 10027, USA
| | | | - Edward F Valeev
- Department of Chemistry, Virginia Tech, Blacksburg, VA, 24061, USA
| | - Lin Lin
- Department of Mathematics, University of California, Berkeley, CA, 94720, USA
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, USA
| | - Garnet Kin-Lic Chan
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA, 91125, USA.
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12
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Threatt SD, Rees DC. Biological nitrogen fixation in theory, practice, and reality: a perspective on the molybdenum nitrogenase system. FEBS Lett 2023; 597:45-58. [PMID: 36344435 PMCID: PMC10100503 DOI: 10.1002/1873-3468.14534] [Citation(s) in RCA: 9] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2022] [Revised: 10/30/2022] [Accepted: 10/31/2022] [Indexed: 11/09/2022]
Abstract
Nitrogenase is the sole enzyme responsible for the ATP-dependent conversion of atmospheric dinitrogen into the bioavailable form of ammonia (NH3 ), making this protein essential for the maintenance of the nitrogen cycle and thus life itself. Despite the widespread use of the Haber-Bosch process to industrially produce NH3 , biological nitrogen fixation still accounts for half of the bioavailable nitrogen on Earth. An important feature of nitrogenase is that it operates under physiological conditions, where the equilibrium strongly favours ammonia production. This biological, multielectron reduction is a complex catalytic reaction that has perplexed scientists for decades. In this review, we explore the current understanding of the molybdenum nitrogenase system based on experimental and computational research, as well as the limitations of the crystallographic, spectroscopic, and computational techniques employed. Finally, essential outstanding questions regarding the nitrogenase system will be highlighted alongside suggestions for future experimental and computational work to elucidate this essential yet elusive process.
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Affiliation(s)
- Stephanie D Threatt
- Division of Chemistry and Chemical Engineering, Howard Hughes Medical Institute, California Institute of Technology, Pasadena, CA, USA
| | - Douglas C Rees
- Division of Chemistry and Chemical Engineering, Howard Hughes Medical Institute, California Institute of Technology, Pasadena, CA, USA
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13
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Xie QX, Song Y, Zhao Y. Power of the Sine Hamiltonian Operator for Estimating the Eigenstate Energies on Quantum Computers. J Chem Theory Comput 2022; 18:7586-7602. [PMID: 36449783 DOI: 10.1021/acs.jctc.2c00759] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/02/2022]
Abstract
Quantum computers have been shown to have tremendous potential in solving difficult problems in quantum chemistry. In this paper, we propose a new classical-quantum hybrid method, named as power of sine Hamiltonian operator (PSHO), to evaluate the eigenvalues of a given Hamiltonian (Ĥ). In PSHO, for any reference state |φ0⟩, the normalized energy of the sinn(H^τ)|φ0⟩ state can be determined. With the increase of the power, the initial reference state can converge to the eigenstate with the largest |sin(Eiτ)| value in the coefficients of the expansion of |φ0⟩, and the normalized energy of the sinn(H^τ)|φ0⟩ state converges to Ei. The ground- and excited-state energies of a Hamiltonian can be determined by taking different τ values. The performance of the PSHO method is demonstrated by numerical calculations of the H4 and LiH molecules. Compared with the current popular variational quantum eigensolver method, PSHO does not need to design the ansatz circuits and avoids the complex nonlinear optimization problems. PSHO has great application potential in near-term quantum devices.
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Affiliation(s)
- Qing-Xing Xie
- The Institute of Technological Sciences, Wuhan University, Wuhan430072, People's Republic of China
| | - Yi Song
- The Institute of Technological Sciences, Wuhan University, Wuhan430072, People's Republic of China
| | - Yan Zhao
- The Institute of Technological Sciences, Wuhan University, Wuhan430072, People's Republic of China
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14
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Rutledge HL, Field MJ, Rittle J, Green MT, Akif Tezcan F. Role of Serine Coordination in the Structural and Functional Protection of the Nitrogenase P-Cluster. J Am Chem Soc 2022; 144:22101-22112. [PMID: 36445204 PMCID: PMC9957664 DOI: 10.1021/jacs.2c09480] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/03/2022]
Abstract
Nitrogenase catalyzes the multielectron reduction of dinitrogen to ammonia. Electron transfer in the catalytic protein (MoFeP) proceeds through a unique [8Fe-7S] cluster (P-cluster) to the active site (FeMoco). In the reduced, all-ferrous (PN) state, the P-cluster is coordinated by six cysteine residues. Upon two-electron oxidation to the P2+ state, the P-cluster undergoes conformational changes in which a highly conserved oxygen-based residue (a Ser or a Tyr) and a backbone amide additionally ligate the cluster. Previous studies of Azotobacter vinelandii (Av) MoFeP revealed that when the oxygen-based residue, βSer188, was mutated to a noncoordinating residue, Ala, the P-cluster became redox-labile and reversibly lost two of its eight Fe centers. Surprisingly, the Av strain with a MoFeP variant that lacked the serine ligand (Av βSer188Ala MoFeP) displayed the same diazotrophic growth and in vitro enzyme turnover rates as wild-type Av MoFeP, calling into question the necessity of this conserved ligand for nitrogenase function. Based on these observations, we hypothesized that βSer188 plays a role in protecting the P-cluster under nonideal conditions. Here, we investigated the protective role of βSer188 both in vivo and in vitro by characterizing the ability of Av βSer188Ala cells to grow under suboptimal conditions (high oxidative stress or Fe limitation) and by determining the tendency of βSer188Ala MoFeP to be mismetallated in vitro. Our results demonstrate that βSer188 (1) increases Av cell survival upon exposure to oxidative stress in the form of hydrogen peroxide, (2) is necessary for efficient Av diazotrophic growth under Fe-limiting conditions, and (3) may protect the P-cluster from metal exchange in vitro. Taken together, our findings suggest a structural adaptation of nitrogenase to protect the P-cluster via Ser ligation, which is a previously unidentified functional role of the Ser residue in redox proteins and adds to the expanding functional roles of non-Cys ligands to FeS clusters.
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Affiliation(s)
- Hannah L. Rutledge
- Department of Chemistry and Biochemistry, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093-0340, United States
| | - Mackenzie J. Field
- Department of Chemistry, University of California, Irvine, Irvine, California 92697, United States
| | - Jonathan Rittle
- Department of Chemistry and Biochemistry, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093-0340, United States
| | - Michael T. Green
- Department of Chemistry, University of California, Irvine, Irvine, California 92697, United States.,Department of Molecular Biology and Biochemistry, University of California, Irvine, Irvine, California 92697, United States
| | - F. Akif Tezcan
- Department of Chemistry and Biochemistry, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093-0340, United States.,Corresponding Author:
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15
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Larsson HR, Zhai H, Umrigar CJ, Chan GKL. The Chromium Dimer: Closing a Chapter of Quantum Chemistry. J Am Chem Soc 2022; 144:15932-15937. [PMID: 36001866 PMCID: PMC9460780 DOI: 10.1021/jacs.2c06357] [Citation(s) in RCA: 14] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The complex electronic structure and unusual potential energy curve of the chromium dimer have fascinated scientists for decades, with agreement between theory and experiment so far elusive. Here, we present a new ab initio simulation of the potential energy curve and vibrational spectrum that significantly improves on all earlier estimates. Our data support a shift in earlier experimental assignments of a cluster of vibrational frequencies by one quantum number. The new vibrational assignment yields an experimentally derived potential energy curve in quantitative agreement with theory across all bond lengths and across all measured frequencies. By solving this long-standing problem, our results raise the possibility of quantitative quantum chemical modeling of transition metal clusters with spectroscopic accuracy.
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Affiliation(s)
- Henrik R Larsson
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States.,Department of Chemistry and Biochemistry, University of California Merced, Merced, California 95343, United States
| | - Huanchen Zhai
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - C J Umrigar
- Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, United States
| | - Garnet Kin-Lic Chan
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
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16
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Chen Z, Yang J. Bonding properties of molecular cerium oxides tuned by the 4 f-block from ab initio perspective. J Chem Phys 2022; 156:211101. [DOI: 10.1063/5.0090214] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Probing chemical bonding in molecules containing lanthanide elements is of theoretical interest, yet it is computationally challenging because of the large valence space, relativistic effects, and considerable electron correlation. We report a high-level ab initio study that quantifies the many-body nature of Ce–O bonding with the coordination environment of the Ce center and particularly the roles of the 4 f orbitals. The growing significance of the overlap between Ce 4 f and O 2 p orbitals with the increasing coordination of Ce atoms enhances Ce–O bond covalency and in return directs the molecular geometry. Upon partial reduction from neutral to anionic ceria, the excessive electrons populate the Ce-centered localized 4 f orbital. The interplay between the admixture and localization of the 4 f-block dually modulates bonding patterns of cerium oxide molecules, underlying the importance of many-body interactions between ligands and various lanthanide elements.
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Affiliation(s)
- Ziyong Chen
- Department of Chemistry, The University of Hong Kong, Hong Kong, China
| | - Jun Yang
- Department of Chemistry, The University of Hong Kong, Hong Kong, China
- Hong Kong Quantum AI Lab Ltd., Hong Kong Science Park, Hong Kong, China
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17
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Motta M, Rice JE. Emerging quantum computing algorithms for quantum chemistry. WIRES COMPUTATIONAL MOLECULAR SCIENCE 2022. [DOI: 10.1002/wcms.1580] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Affiliation(s)
- Mario Motta
- IBM Quantum, IBM Research‐Almaden San Jose California USA
| | - Julia E. Rice
- IBM Quantum, IBM Research‐Almaden San Jose California USA
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18
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Li W, Ren J, Yang H, Shuai Z. On the fly swapping algorithm for ordering of degrees of freedom in density matrix renormalization group. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:254003. [PMID: 35378514 DOI: 10.1088/1361-648x/ac640e] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/23/2022] [Accepted: 04/04/2022] [Indexed: 06/14/2023]
Abstract
Density matrix renormalization group (DMRG) and its time-dependent variants have found widespread applications in quantum chemistry, includingab initioelectronic structure of complex bio-molecules, spectroscopy for molecular aggregates, and charge transport in bulk organic semiconductors. The underlying wavefunction ansatz for DMRG, matrix product state (MPS), requires mapping degrees of freedom (DOF) into a one-dimensional topology. DOF ordering becomes a crucial factor for DMRG accuracy. In this work, we propose swapping neighboring DOFs during the DMRG sweeps for DOF ordering, which we term 'on the fly swapping' (OFS) algorithm. We show that OFS is universal for both static and time-dependent DMRG with minimum computational overhead. Examples are given for one dimensional antiferromagnetic Heisenberg model,ab initioelectronic structure of N2molecule, and the S1/S2internal conversion dynamics of pyrazine molecule. It is found that OFS can indeed improve accuracy by finding better DOF ordering in all cases.
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Affiliation(s)
- Weitang Li
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, Beijing, People's Republic of China
| | - Jiajun Ren
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, Beijing, People's Republic of China
| | - Hengrui Yang
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, Beijing, People's Republic of China
| | - Zhigang Shuai
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, Beijing, People's Republic of China
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19
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Wang B, Wu P, Shaik S. Critical Roles of Exchange and Superexchange Interactions in Dictating Electron Transfer and Reactivity in Metalloenzymes. J Phys Chem Lett 2022; 13:2871-2877. [PMID: 35325545 DOI: 10.1021/acs.jpclett.2c00513] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Electron transfer (ET) is a fundamental process in transition-metal-dependent metalloenzymes. In these enzymes, the spin-spin interactions within the same metal center and/or between different metal sites can play a pivotal role in the catalytic cycle and reactivity. This Perspective highlights that the exchange and/or superexchange interactions can intrinsically modulate the inner-sphere and long-range electron transfer, thus controlling the mechanism and activity of metalloenzymes. For mixed-valence diiron oxygenases, the spin-regulated inner-sphere ET can be dictated by exchange interactions, leading to efficient O-O bond activations. Likewise, the spin-regulated inner-sphere ET can be enhanced by both exchange and superexchange interactions in [Fe4S4]-dependent SAM enzymes, which enable the efficient cleavage of the S─C(γ) or S─C5' bond of SAM. In addition to inner-sphere ET, superexchange interactions may modulate the long-range ET between metalloenzymes. We anticipate that the exchange and superexchange enhanced reactivity could be applicable in other important metalloenzymes, such as Photosystem II and nitrogenases.
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Affiliation(s)
- Binju Wang
- State Key Laboratory of Physical Chemistry of Solid Surfaces and Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, P.R. China
| | - Peng Wu
- State Key Laboratory of Physical Chemistry of Solid Surfaces and Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, P.R. China
| | - Sason Shaik
- Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
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20
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Liu J, Fan Y, Li Z, Yang J. Quantum algorithms for electronic structures: basis sets and boundary conditions. Chem Soc Rev 2022; 51:3263-3279. [PMID: 35352716 DOI: 10.1039/d1cs01184g] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The advantages of quantum computers are believed to significantly change the research paradigm of chemical and materials sciences, where computational characterization and theoretical design play an increasingly important role. It is especially desirable to solve the electronic structure problem, a central problem in chemistry and materials science, efficiently and accurately with well-designed quantum algorithms. Various quantum electronic-structure algorithms have been proposed in the literature. In this article, we briefly review recent progress in this direction with a special emphasis on the basis sets and boundary conditions. Compared to classical electronic structure calculations, there are new considerations in choosing a basis set in quantum algorithms. For example, the effect of the basis set on the circuit complexity is very important in quantum algorithm design. Electronic structure calculations should be performed with an appropriate boundary condition. Simply using a wave function ansatz designed for molecular systems in a material system with a periodic boundary condition may lead to significant errors. Artificial boundary conditions can be used to partition a large system into smaller fragments to save quantum resources. The basis sets and boundary conditions are expected to play a crucial role in electronic structure calculations on future quantum computers, especially for realistic systems.
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Affiliation(s)
- Jie Liu
- Hefei National Laboratory for Physical Sciences at Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China.
| | - Yi Fan
- Hefei National Laboratory for Physical Sciences at Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China.
| | - Zhenyu Li
- Hefei National Laboratory for Physical Sciences at Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China.
| | - Jinlong Yang
- Hefei National Laboratory for Physical Sciences at Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China.
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21
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Chica B, Ruzicka J, Pellows LM, Kallas H, Kisgeropoulos E, Vansuch GE, Mulder DW, Brown KA, Svedruzic D, Peters JW, Dukovic G, Seefeldt LC, King PW. Dissecting Electronic-Structural Transitions in the Nitrogenase MoFe Protein P-Cluster during Reduction. J Am Chem Soc 2022; 144:5708-5712. [PMID: 35315658 PMCID: PMC8991001 DOI: 10.1021/jacs.1c13311] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The [8Fe-7S] P-cluster of nitrogenase MoFe protein mediates electron transfer from nitrogenase Fe protein during the catalytic production of ammonia. The P-cluster transitions between three oxidation states, PN, P+, P2+ of which PN↔P+ is critical to electron exchange in the nitrogenase complex during turnover. To dissect the steps in formation of P+ during electron transfer, photochemical reduction of MoFe protein at 231-263 K was used to trap formation of P+ intermediates for analysis by EPR. In complexes with CdS nanocrystals, illumination of MoFe protein led to reduction of the P-cluster P2+ that was coincident with formation of three distinct EPR signals: S = 1/2 axial and rhombic signals, and a high-spin S = 7/2 signal. Under dark annealing the axial and high-spin signal intensities declined, which coincided with an increase in the rhombic signal intensity. A fit of the time-dependent changes of the axial and high-spin signals to a reaction model demonstrates they are intermediates in the formation of the P-cluster P+ resting state and defines how spin-state transitions are coupled to changes in P-cluster oxidation state in MoFe protein during electron transfer.
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Affiliation(s)
- Bryant Chica
- Biosciences Center, National Renewable Energy Laboratory, Golden, Colorado 80401, United States
| | - Jesse Ruzicka
- Department of Chemistry, University of Colorado Boulder, Boulder, Colorado 80309, United States
| | - Lauren M Pellows
- Department of Chemistry, University of Colorado Boulder, Boulder, Colorado 80309, United States
| | - Hayden Kallas
- Department of Chemistry and Biochemistry, Utah State University, Logan, Utah 84322, United States
| | - Effie Kisgeropoulos
- Biosciences Center, National Renewable Energy Laboratory, Golden, Colorado 80401, United States
| | - Gregory E Vansuch
- Biosciences Center, National Renewable Energy Laboratory, Golden, Colorado 80401, United States
| | - David W Mulder
- Biosciences Center, National Renewable Energy Laboratory, Golden, Colorado 80401, United States
| | - Katherine A Brown
- Biosciences Center, National Renewable Energy Laboratory, Golden, Colorado 80401, United States
| | - Drazenka Svedruzic
- Biosciences Center, National Renewable Energy Laboratory, Golden, Colorado 80401, United States
| | - John W Peters
- Institute of Biological Chemistry, Washington State University, Pullman, Washington 99163, United States
| | - Gordana Dukovic
- Department of Chemistry, University of Colorado Boulder, Boulder, Colorado 80309, United States.,Renewable and Sustainable Energy Institute (RASEI), University of Colorado Boulder, Boulder, Colorado 80309, United States.,Materials Science and Engineering, University of Colorado Boulder, Boulder, Colorado 80303, United States
| | - Lance C Seefeldt
- Department of Chemistry and Biochemistry, Utah State University, Logan, Utah 84322, United States
| | - Paul W King
- Biosciences Center, National Renewable Energy Laboratory, Golden, Colorado 80401, United States.,Renewable and Sustainable Energy Institute (RASEI), University of Colorado Boulder, Boulder, Colorado 80309, United States
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22
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Benediktsson B, Bjornsson R. Analysis of the Geometric and Electronic Structure of Spin-Coupled Iron-Sulfur Dimers with Broken-Symmetry DFT: Implications for FeMoco. J Chem Theory Comput 2022; 18:1437-1457. [PMID: 35167749 PMCID: PMC8908755 DOI: 10.1021/acs.jctc.1c00753] [Citation(s) in RCA: 16] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023]
Abstract
![]()
The open-shell electronic
structure of iron–sulfur clusters
presents considerable challenges to quantum chemistry, with the complex
iron–molybdenum cofactor (FeMoco) of nitrogenase representing
perhaps the ultimate challenge for either wavefunction or density
functional theory. While broken-symmetry density functional theory
has seen some success in describing the electronic structure of such
cofactors, there is a large exchange–correlation functional
dependence in calculations that is not fully understood. In this work,
we present a geometric benchmarking test set, FeMoD11, of synthetic
spin-coupled Fe–Fe and Mo–Fe dimers, with relevance
to the molecular and electronic structure of the Mo-nitrogenase FeMo
cofactor. The reference data consists of high-resolution crystal structures
of metal dimer compounds in different oxidation states. Multiple density
functionals are tested on their ability to reproduce the local geometry,
specifically the Fe–Fe/Mo–Fe distance, for both antiferromagnetically
coupled and ferromagnetically coupled dimers via the broken-symmetry
approach. The metal–metal distance is revealed not only to
be highly sensitive to the amount of exact exchange in the functional
but also to the specific exchange and correlation functionals. For
the antiferromagnetically coupled dimers, the calculated metal–metal
distance correlates well with the covalency of the bridging metal–ligand
bonds, as revealed via the corresponding orbital analysis, Hirshfeld
S/Fe charges, and Fe–S Mayer bond order. Superexchange via
bridging ligands is expected to be the dominant interaction in these
dimers, and our results suggest that functionals that predict accurate
Fe–Fe and Mo–Fe distances describe the overall metal–ligand
covalency more accurately and in turn the superexchange of these systems.
The best performing density functionals of the 16 tested for the FeMoD11
test set are revealed to be either the nonhybrid functionals r2SCAN and B97-D3 or hybrid functionals with 10–15% exact
exchange: TPSSh and B3LYP*. These same four functionals are furthermore
found to reproduce the high-resolution X-ray structure of FeMoco well
according to quantum mechanics/molecular mechanics (QM/MM) calculations.
Almost all nonhybrid functionals systematically underestimate Fe–Fe
and Mo–Fe distances (with r2SCAN and B97-D3 being
the sole exceptions), while hybrid functionals with >15% exact
exchange
(including range-separated hybrid functionals) overestimate them.
The results overall suggest r2SCAN, B97-D3, TPSSh, and
B3LYP* as accurate density functionals for describing the electronic
structure of iron–sulfur clusters in general, including the
complex FeMoco cluster of nitrogenase.
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Affiliation(s)
- Bardi Benediktsson
- Science Institute, University of Iceland, Dunhagi 3, 107 Reykjavik, Iceland
| | - Ragnar Bjornsson
- Science Institute, University of Iceland, Dunhagi 3, 107 Reykjavik, Iceland.,Max-Planck Institute for Chemical Energy Conversion, Stiftstrasse 34-36, 45470 Mülheim an der Ruhr, Germany
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23
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Ye HZ, Berkelbach TC. Correlation-Consistent Gaussian Basis Sets for Solids Made Simple. J Chem Theory Comput 2022; 18:1595-1606. [PMID: 35192359 DOI: 10.1021/acs.jctc.1c01245] [Citation(s) in RCA: 15] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The rapidly growing interest in simulating condensed-phase materials using quantum chemistry methods calls for a library of high-quality Gaussian basis sets suitable for periodic calculations. Unfortunately, most standard Gaussian basis sets commonly used in molecular simulation show significant linear dependencies when used in close-packed solids, leading to severe numerical issues that hamper the convergence to the complete basis set (CBS) limit, especially in correlated calculations. In this work, we revisit Dunning's strategy for construction of correlation-consistent basis sets and examine the relationship between accuracy and numerical stability in periodic settings. We find that limiting the number of primitive functions avoids the appearance of problematic small exponents while still providing smooth convergence to the CBS limit. As an example, we generate double-, triple-, and quadruple-ζ correlation-consistent Gaussian basis sets for periodic calculations with Goedecker-Teter-Hutter (GTH) pseudopotentials. Our basis sets cover the main-group elements from the first three rows of the periodic table. Especially for atoms on the left side of the periodic table, our basis sets are less diffuse than those used in molecular calculations. We verify the fast and reliable convergence to the CBS limit in both Hartree-Fock and post-Hartree-Fock (MP2) calculations, using a diverse test set of 19 semiconductors and insulators.
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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.,Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, United States
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24
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Cheng Y, Xie Z, Ma H. Post-Density Matrix Renormalization Group Methods for Describing Dynamic Electron Correlation with Large Active Spaces. J Phys Chem Lett 2022; 13:904-915. [PMID: 35049302 DOI: 10.1021/acs.jpclett.1c04078] [Citation(s) in RCA: 15] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
The ab initio density matrix renormalization group (DMRG) method has been well-established and has become one of the most accurate numerical methods for the precise electronic structure solution of large active spaces. In the past few years, to capture the missing dynamic correlation, various post-DMRG approaches have been proposed through the combination of DMRG and multireference quantum chemical methods or density functional theory. With this in mind, this work provides a brief overview of ab initio DMRG principles and the new developments within post-DMRG methods. For clarity, post-DMRG methods are classified into two main categories depending on whether high-order n-electron reduced density matrices are used, and their merits and disadvantages are properly discussed. Finally, we conclude by discussing unsolved bottlenecks and giving development perspectives of post-DMRG approaches, which are expected to yield quantitative descriptions of complex electronic structures in large strongly correlated molecules and materials.
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Affiliation(s)
- Yifan Cheng
- School of Chemistry and Chemical Engineering, Jiangsu Key Laboratory of Vehicle Emissions Control, Nanjing University, Nanjing 210023, China
| | - Zhaoxuan Xie
- School of Chemistry and Chemical Engineering, Jiangsu Key Laboratory of Vehicle Emissions Control, Nanjing University, Nanjing 210023, China
| | - Haibo Ma
- School of Chemistry and Chemical Engineering, Jiangsu Key Laboratory of Vehicle Emissions Control, Nanjing University, Nanjing 210023, China
- Chemistry and Biomedicine Innovation Center (ChemBIC), Nanjing University, Nanjing 210023, China
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25
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Larsson HR, Zhai H, Gunst K, Chan GKL. Matrix Product States with Large Sites. J Chem Theory Comput 2022; 18:749-762. [DOI: 10.1021/acs.jctc.1c00957] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Henrik R. Larsson
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Huanchen Zhai
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Klaas Gunst
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
- Center for Molecular Modeling, Ghent University, Technologiepark 46, B-9052 Zwijnaarde, Belgium
- Department of Physics and Astronomy, Ghent University, Krijgslaan 281, S9, B-9000 Ghent, Belgium
| | - Garnet Kin-Lic Chan
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
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26
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Mejuto-Zaera C, Tzeli D, Williams-Young D, Tubman NM, Matoušek M, Brabec J, Veis L, Xantheas SS, de Jong WA. The Effect of Geometry, Spin, and Orbital Optimization in Achieving Accurate, Correlated Results for Iron-Sulfur Cubanes. J Chem Theory Comput 2022; 18:687-702. [PMID: 35034448 DOI: 10.1021/acs.jctc.1c00830] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Abstract
Iron-sulfur clusters comprise an important functional motif in the catalytic centers of biological systems, capable of enabling important chemical transformations at ambient conditions. This remarkable capability derives from a notoriously complex electronic structure that is characterized by a high density of states that is sensitive to geometric changes. The spectral sensitivity to subtle geometric changes has received little attention from correlated, large active space calculations, owing partly to the exceptional computational complexity for treating these large and correlated systems accurately. To provide insight into this aspect, we report the first Complete Active Space Self Consistent Field (CASSCF) calculations for different geometries of the [Fe(II/III)4S4(SMe)4]-2 clusters using two complementary, correlated solvers: spin-pure Adaptive Sampling Configuration Interaction (ASCI) and Density Matrix Renormalization Group (DMRG). We find that the previously established picture of a double-exchange driven magnetic structure, with minute energy gaps (<1 mHa) between consecutive spin states, has a weak dependence on the underlying geometry. However, the spin gap between the singlet and the spin state 2S + 1 = 19, corresponding to a maximal number of Fe-d electrons being unpaired and of parallel spin, is strongly geometry dependent, changing by a factor of 3 upon slight deformations that are still within biologically relevant parameters. The CASSCF orbital optimization procedure, using active spaces as large as 86 electrons in 52 orbitals, was found to reduce this gap compared to typical mean-field orbital approaches. Our results show the need for performing large active space calculations to unveil the challenging electronic structure of these complex catalytic centers and should serve as accurate starting points for fully correlated treatments upon inclusion of dynamical correlation outside the active space.
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Affiliation(s)
- Carlos Mejuto-Zaera
- University of California, Berkeley, California 94720, United States.,Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Demeter Tzeli
- Laboratory of Physical Chemistry, Department of Chemistry, National and Kapodistrian University of Athens, Panepistimiopolis Zografou, Athens 15784, Greece.,Theoretical and Physical Chemistry Institute, National Hellenic Research Foundation, Vas. Constantinou 48, Athens 11635, Greece
| | - David Williams-Young
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Norm M Tubman
- Quantum Artificial Intelligence Lab. (QuAIL), Exploration Technology Directorate, NASA Ames Research Center, Moffett Field, California 94035, United States
| | - Mikuláš Matoušek
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
| | - Jiri Brabec
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
| | - Libor Veis
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
| | - Sotiris S Xantheas
- Advanced Computing, Mathematics and Data Division, Pacific Northwest National Laboratory, 902 Battelle Boulevard, P.O. Box 999, MS K1-83, Richland, Washington 99352, United States.,Department of Chemistry, University of Washington, Seattle, Washington 98185, United States
| | - Wibe A de Jong
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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27
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Li W, Huang Z, Cao C, Huang Y, Shuai Z, Sun X, Sun J, Yuan X, Lv D. Toward practical quantum embedding simulation of realistic chemical systems on near-term quantum computers. Chem Sci 2022; 13:8953-8962. [PMID: 36091203 PMCID: PMC9365244 DOI: 10.1039/d2sc01492k] [Citation(s) in RCA: 14] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2022] [Accepted: 07/11/2022] [Indexed: 01/04/2023] Open
Abstract
Quantum computing has recently exhibited great potential in predicting chemical properties for various applications in drug discovery, material design, and catalyst optimization. Progress has been made in simulating small molecules, such as LiH and hydrogen chains of up to 12 qubits, by using quantum algorithms such as variational quantum eigensolver (VQE). Yet, originating from the limitations of the size and the fidelity of near-term quantum hardware, the accurate simulation of large realistic molecules remains a challenge. Here, integrating an adaptive energy sorting strategy and a classical computational method—the density matrix embedding theory, which respectively reduces the circuit depth and the problem size, we present a means to circumvent the limitations and demonstrate the potential of near-term quantum computers toward solving real chemical problems. We numerically test the method for the hydrogenation reaction of C6H8 and the equilibrium geometry of the C18 molecule, using basis sets up to cc-pVDZ (at most 144 qubits). The simulation results show accuracies comparable to those of advanced quantum chemistry methods such as coupled-cluster or even full configuration interaction, while the number of qubits required is reduced by an order of magnitude (from 144 qubits to 16 qubits for the C18 molecule) compared to conventional VQE. Our work implies the possibility of solving industrial chemical problems on near-term quantum devices. Quantum embedding simulation greatly enhanced the capability of near-term quantum computers on realistic chemical systems and reach accuracy comparable to advanced quantum chemistry methods.![]()
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Affiliation(s)
- Weitang Li
- ByteDance Inc, Zhonghang Plaza, No. 43, North 3rd Ring West Road, Haidian District, Beijing, China
- Department of Chemistry, Tsinghua University, Beijing 100084, China
| | - Zigeng Huang
- ByteDance Inc, Zhonghang Plaza, No. 43, North 3rd Ring West Road, Haidian District, Beijing, China
| | - Changsu Cao
- ByteDance Inc, Zhonghang Plaza, No. 43, North 3rd Ring West Road, Haidian District, Beijing, China
| | - Yifei Huang
- ByteDance Inc, Zhonghang Plaza, No. 43, North 3rd Ring West Road, Haidian District, Beijing, China
| | - Zhigang Shuai
- Department of Chemistry, Tsinghua University, Beijing 100084, China
| | - Xiaoming Sun
- Institute of Computing Technology, Chinese Academy of Sciences, China
- University of Chinese Academy of Sciences, China
| | - Jinzhao Sun
- Center on Frontiers of Computing Studies, Peking University, Beijing 100871, China
| | - Xiao Yuan
- Clarendon Laboratory, University of Oxford, Oxford OX1 3PU, UK
| | - Dingshun Lv
- ByteDance Inc, Zhonghang Plaza, No. 43, North 3rd Ring West Road, Haidian District, Beijing, China
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28
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Yuan C, Jin WT, Zhou ZH. Statistical analysis of PN clusters in Mo/VFe protein crystals using a bond valence method toward their electronic structures. RSC Adv 2022; 12:5214-5224. [PMID: 35425536 PMCID: PMC8981338 DOI: 10.1039/d1ra08507g] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/21/2021] [Accepted: 01/26/2022] [Indexed: 11/21/2022] Open
Abstract
Iron valences of 129 P-clusters from FeMo/V proteins were analyzed using a bond valence method, supposing the existence of Fe3+ in a generally considered all-ferrous PN cluster in solution with excess reducing agent.
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Affiliation(s)
- Chang Yuan
- State Key Laboratory for Physical Chemistry of Solid Surfaces, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, P. R. China
| | - Wan-Ting Jin
- State Key Laboratory for Physical Chemistry of Solid Surfaces, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, P. R. China
| | - Zhao-Hui Zhou
- State Key Laboratory for Physical Chemistry of Solid Surfaces, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, P. R. China
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29
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Spiller N, Bjornsson R, DeBeer S, Neese F. Carbon Monoxide Binding to the Iron-Molybdenum Cofactor of Nitrogenase: a Detailed Quantum Mechanics/Molecular Mechanics Investigation. Inorg Chem 2021; 60:18031-18047. [PMID: 34767349 PMCID: PMC8653219 DOI: 10.1021/acs.inorgchem.1c02649] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Carbon monoxide (CO) is a well-known inhibitor of nitrogenase activity. Under turnover conditions, CO binds to FeMoco, the active site of Mo nitrogenase. Time-resolved IR measurements suggest an initial terminal CO at 1904 cm-1 that converts to a bridging CO at 1715 cm-1, and an X-ray structure shows that CO can displace one of the bridging belt sulfides of FeMoco. However, the CO-binding redox state(s) of FeMoco (En) and the role of the protein environment in stabilizing specific CO-bound intermediates remain elusive. In this work, we carry out an in-depth analysis of the CO-FeMoco interaction based on quantum chemical calculations addressing different aspects of the electronic structure. (1) The local electronic structure of the Fe-CO bond is studied through diamagnetically substituted FeMoco. (2) A cluster model of FeMoco within a polarizable continuum illustrates how CO binding may affect the spin-coupling between the metal centers. (3) A QM/MM model incorporates the explicit influence of the amino acid residues surrounding FeMoco in the MoFe protein. The QM/MM model predicts both a terminal and a bridging CO in the E1 redox state. The scaled calculated CO frequencies (1922 and 1716 cm-1, respectively) are in good agreement with the experimentally observed IR bands supporting CO binding to the E1 state. Alternatively, an E2 state QM/MM model, which has the same atomic structure as the CO-bound X-ray structure, features a semi-bridging CO with a scaled calculated frequency (1718 cm-1) similar to the bridging CO in the E1 model.
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Affiliation(s)
- Nico Spiller
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany
| | - Ragnar Bjornsson
- Max Planck Institute for Chemical Energy Conversion, Stiftstr 34-36, 45470 Mülheim an der Ruhr, Germany
| | - Serena DeBeer
- Max Planck Institute for Chemical Energy Conversion, Stiftstr 34-36, 45470 Mülheim an der Ruhr, Germany
| | - Frank Neese
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany
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30
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Beran P, Matoušek M, Hapka M, Pernal K, Veis L. Density Matrix Renormalization Group with Dynamical Correlation via Adiabatic Connection. J Chem Theory Comput 2021; 17:7575-7585. [PMID: 34762423 DOI: 10.1021/acs.jctc.1c00896] [Citation(s) in RCA: 21] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The quantum chemical version of the density matrix renormalization group (DMRG) method has established itself as one of the methods of choice for calculations of strongly correlated molecular systems. Despite its great ability to capture strong electronic correlation in large active spaces, it is not suitable for computations of dynamical electron correlation. In this work, we present a new approach to the electronic structure problem of strongly correlated molecules, in which DMRG is responsible for a proper description of the strong correlation, whereas dynamical correlation is computed via the recently developed adiabatic connection (AC) technique which requires only up to two-body active space reduced density matrices. We report the encouraging results of this approach on typical candidates for DMRG computations, namely, n-acenes (n = 2 → 7), Fe(II)-porphyrin, and the Fe3S4 cluster.
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Affiliation(s)
- Pavel Beran
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic.,Faculty of Mathematics and Physics, Charles University, 121 16 Prague, Czech Republic
| | - Mikuláš Matoušek
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic.,Faculty of Mathematics and Physics, Charles University, 121 16 Prague, Czech Republic
| | - Michał Hapka
- Institute of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland.,Faculty of Chemistry, University of Warsaw, ul. L. Pasteura 1, 02-093 Warsaw, Poland
| | - Katarzyna Pernal
- Institute of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland
| | - Libor Veis
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
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31
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Li Manni G. Modeling magnetic interactions in high-valent trinuclear [Mn 3(IV)O 4] 4+ complexes through highly compressed multi-configurational wave functions. Phys Chem Chem Phys 2021; 23:19766-19780. [PMID: 34525156 DOI: 10.1039/d1cp03259c] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
In this work we apply a quantum chemical framework, recently designed in our laboratories, to rationalize the low-energy electronic spectrum and the magnetic properties of an homo-valent trinuclear [Mn3(IV)O4]4+ model of the oxygen-evolving center in photosystem II. The method is based on chemically motivated molecular orbital unitary transformations, and the optimization of spin-adapted many-body wave functions, both for ground- and excited-states, in the transformed MO basis. In this basis, the configuration interaction Hamiltonian matrix of exchange-coupled multi-center clusters is extremely sparse and characterized by a unique block diagonal structure. This property leads to highly compressed wave functions (oligo- or single-reference) and crucially enables state-specific optimizations. This work is the first showing that compression and selective targeting of ground- and excited-states wave functions is possible for systems with three magnetic centers that are not exactly half-filled, and that potentially exhibit frustrated spin interactions. The reduced multi-reference character of the wave function greatly simplifies the interpretation of the ground- and excited-state electronic structures, and provides a route for the direct rationalization of magnetic interactions in these compounds, often considered a challenge in polynuclear transition-metal chemistry. In this study, strong electron correlation effects have explicitly been described by conventional and stochastic multiconfigurational methodologies, while dynamic correlation effects have been accounted for by multiconfigurational second order perturbation theory, CASPT2. Ab initio results for the [Mn3(IV)O4]4+ system have been mapped to a three-site Heisenberg model with two magnetic coupling constants. The magnetic coupling constants and the temperature dependence of the effective magnetic moment predicted by the ab initio calculations are in good agreement with the available experimental data, and confirm the antiferromagnetic interaction among the three magnetic centers, while providing a simple and rigorous description of the noncollinearity of the local spins, that characterize most of the low-energy states for this system.
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Affiliation(s)
- Giovanni Li Manni
- Department of Electronic Structure Theory, Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany.
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32
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Khedkar A, Roemelt M. Modern multireference methods and their application in transition metal chemistry. Phys Chem Chem Phys 2021; 23:17097-17112. [PMID: 34355719 DOI: 10.1039/d1cp02640b] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
Transition metal chemistry is a challenging playground for quantum chemical methods owing to the simultaneous presence of static and dynamic electron correlation effects in many systems. Wavefunction based multireference (MR) methods constitute a physically sound and systematically improvable Ansatz to deal with this complexity but suffer from some conceptual difficulties and high computational costs. The latter problem partially arises from the unfavorable scaling of the Full Configuration Interaction (Full-CI) problem which in the majority of MR methods is solved for a subset of the molecular orbital space, the so-called active space. In the last years multiple methods such as modern variants of selected CI, Full-CI Quantum Monte Carlo (FCIQMC) and the density matrix renormalization group (DMRG) have been developed that solve the Full-CI problem approximately for a fraction of the computational cost required by conventional techniques thereby significantly extending the range of applicability of modern MR methods. This perspective review outlines recent advancements in the field of MR electronic structure methods together with the resulting chances and challenges for theoretical studies in the field of transition metal chemistry. In light of its emerging importance a special focus is put on the selection of adequate active spaces and the concomitant development of numerous selection aides in recent years.
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Affiliation(s)
- Abhishek Khedkar
- Lehrstuhl für theoretische Chemie, Ruhr-Universität Bochum, D-44780 Bochum, Germany.
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33
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Abraham V, Mayhall NJ. Cluster many-body expansion: A many-body expansion of the electron correlation energy about a cluster mean field reference. J Chem Phys 2021; 155:054101. [PMID: 34364343 DOI: 10.1063/5.0057752] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Abstract
The many-body expansion (MBE) is an efficient tool that has a long history of use for calculating interaction energies, binding energies, lattice energies, and so on. In the past, applications of MBE to correlation energy have been unfeasible for large systems, but recent improvements to computing resources have sparked renewed interest in capturing the correlation energy using the generalized nth order Bethe-Goldstone equation. In this work, we extend this approach, originally proposed for a Slater determinant, to a tensor product state (TPS) based wavefunction. By partitioning the active space into smaller orbital clusters, our approach starts from a cluster mean field reference TPS configuration and includes the correlation contribution of the excited TPSs using the MBE. This method, named cluster MBE (cMBE), improves the convergence of MBE at lower orders compared to directly doing a block-based MBE from a RHF reference. We present numerical results for strongly correlated systems, such as the one- and two-dimensional Hubbard models and the chromium dimer. The performance of the cMBE method is also tested by partitioning the extended π space of several large π-conjugated systems, including a graphene nano-sheet with a very large active space of 114 electrons in 114 orbitals, which would require 1066 determinants for the exact FCI solution.
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Affiliation(s)
- Vibin Abraham
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24060, USA
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34
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Moula G, Nagasaki A, Matsumoto T, Miehlich ME, Meyer K, Cramer RE, Tatsumi K. Synthesis of a Nitrogenase P
N
‐Cluster Model with [Fe
8
S
7
(μ‐S
thiolate
)
2
] Core from the All‐Ferric [Fe
4
S
4
(S
thiolate
)
4
] Cubane Synthon. Angew Chem Int Ed Engl 2021. [DOI: 10.1002/ange.202102369] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Affiliation(s)
- Golam Moula
- Research Center for Materials Science Nagoya University Furo-cho, Chikusa-ku Nagoya 464-8602 Japan
| | - Ayaka Nagasaki
- Research Center for Materials Science Nagoya University Furo-cho, Chikusa-ku Nagoya 464-8602 Japan
| | - Tsuyoshi Matsumoto
- Institute of Transformative Bio-Molecules (WPI-ITbM) Nagoya University Furo-cho, Chikusa-ku Nagoya 464-8601 Japan
| | - Matthias E. Miehlich
- Department of Chemistry and Pharmacy Inorganic Chemistry Friedrich-Alexander-University Erlangen-Nürnberg (FAU) Egerlandstrasse 1 91058 Erlangen Germany
| | - Karsten Meyer
- Department of Chemistry and Pharmacy Inorganic Chemistry Friedrich-Alexander-University Erlangen-Nürnberg (FAU) Egerlandstrasse 1 91058 Erlangen Germany
| | - Roger E. Cramer
- Department of Chemistry University of Hawaii Honolulu HI 96822 USA
| | - Kazuyuki Tatsumi
- Research Center for Materials Science Nagoya University Furo-cho, Chikusa-ku Nagoya 464-8602 Japan
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35
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Moula G, Nagasaki A, Matsumoto T, Miehlich ME, Meyer K, Cramer RE, Tatsumi K. Synthesis of a Nitrogenase P N -Cluster Model with [Fe 8 S 7 (μ-S thiolate ) 2 ] Core from the All-Ferric [Fe 4 S 4 (S thiolate ) 4 ] Cubane Synthon. Angew Chem Int Ed Engl 2021; 60:15792-15797. [PMID: 33928749 DOI: 10.1002/anie.202102369] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2021] [Revised: 03/31/2021] [Indexed: 11/06/2022]
Abstract
Constructing synthetic models of the nitrogenase PN -cluster has been a long-standing synthetic challenge. Here, we report an optimal nitrogenase PN -cluster model [{(TbtS)(OEt2 )Fe4 S3 }2 (μ-STbt)2 (μ6 -S)] (2) [Tbt=2,4,6-tris{bis(trimethylsilyl)methyl}phenyl] that is the closest synthetic mimic constructed to date. Of note is that two thiolate ligands and one hexacoordinated sulfide are connecting the two Fe4 S3 incomplete cubanes similar to the native PN -cluster, which has never been achieved. Cluster 2 has been characterized by X-ray crystallography and relevant physico-chemical methods. The variable temperature magnetic moments of 2 indicate a singlet ground state (S=0). The Mössbauer spectrum of 2 exhibits two doublets with an intensity ratio of 3:1, which suggests the presence of two types of iron sites. The synthetic pathway of the cluster 2 could indicate the native PN -cluster maturation process as it has been achieved from the Fe4 S4 cubane Fe4 S4 (STbt)4 (1).
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Affiliation(s)
- Golam Moula
- Research Center for Materials Science, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8602, Japan
| | - Ayaka Nagasaki
- Research Center for Materials Science, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8602, Japan
| | - Tsuyoshi Matsumoto
- Institute of Transformative Bio-Molecules (WPI-ITbM), Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8601, Japan
| | - Matthias E Miehlich
- Department of Chemistry and Pharmacy, Inorganic Chemistry, Friedrich-Alexander-University Erlangen-Nürnberg (FAU), Egerlandstrasse 1, 91058, Erlangen, Germany
| | - Karsten Meyer
- Department of Chemistry and Pharmacy, Inorganic Chemistry, Friedrich-Alexander-University Erlangen-Nürnberg (FAU), Egerlandstrasse 1, 91058, Erlangen, Germany
| | - Roger E Cramer
- Department of Chemistry, University of Hawaii, Honolulu, HI, 96822, USA
| | - Kazuyuki Tatsumi
- Research Center for Materials Science, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8602, Japan
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36
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Zhai H, Chan GKL. Low communication high performance ab initio density matrix renormalization group algorithms. J Chem Phys 2021; 154:224116. [DOI: 10.1063/5.0050902] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Huanchen Zhai
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Garnet Kin-Lic Chan
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
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37
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Lee S, Zhai H, Sharma S, Umrigar CJ, Chan GKL. Externally Corrected CCSD with Renormalized Perturbative Triples (R-ecCCSD(T)) and the Density Matrix Renormalization Group and Selected Configuration Interaction External Sources. J Chem Theory Comput 2021; 17:3414-3425. [PMID: 34018739 DOI: 10.1021/acs.jctc.1c00205] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We investigate the renormalized perturbative triples correction together with the externally corrected coupled-cluster singles and doubles (ecCCSD) method. We use the density matrix renormalization group (DMRG) and heat-bath CI (HCI) as external sources for the ecCCSD equations. The accuracy is assessed for the potential energy surfaces of H2O, N2, and F2. We find that the triples correction significantly improves upon ecCCSD, and we do not see any instability of the renormalized triples with respect to dissociation. We explore how to balance the cost of computing the external source amplitudes against the accuracy of the subsequent CC calculation. In this context, we find that very approximate wave functions (and their large amplitudes) serve as an efficient and accurate external source. Finally, we characterize the domain of correlation treatable using the ecCCSD and renormalized triples combination studied in this work via a well-known wave function diagnostic.
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Affiliation(s)
- Seunghoon Lee
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Huanchen Zhai
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Sandeep Sharma
- Department of Chemistry, The University of Colorado at Boulder, Boulder, Colorado 80302, United States
| | - C J Umrigar
- Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, United States
| | - Garnet Kin-Lic Chan
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
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38
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Guo Y, Sivalingam K, Neese F. Approximations of density matrices in N-electron valence state second-order perturbation theory (NEVPT2). I. Revisiting the NEVPT2 construction. J Chem Phys 2021; 154:214111. [PMID: 34240991 DOI: 10.1063/5.0051211] [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
Over the last decade, the second-order N-electron valence state perturbation theory (NEVPT2) has developed into a widely used multireference perturbation method. To apply NEVPT2 to systems with large active spaces, the computational bottleneck is the construction of the fourth-order reduced density matrix. Both its generation and storage become quickly problematic beyond the usual maximum active space of about 15 active orbitals. To reduce the computational cost of handling fourth-order density matrices, the cumulant approximation (CU) has been proposed in several studies. A more conventional strategy to address the higher-order density matrices is the pre-screening approximation (PS), which is the default one in the ORCA program package since 2010. In the present work, the performance of the CU, PS, and extended PS (EPS) approximations for the fourth-order density matrices is compared. Following a pedagogical introduction to NEVPT2, contraction schemes, as well as the approximations to density matrices, and the intruder state problem are discussed. The CU approximation, while potentially leading to large computational savings, virtually always leads to intruder states. With the PS approximation, the computational savings are more modest. However, in conjunction with conservative cutoffs, it produces stable results. The EPS approximation to the fourth-order density matrices can reproduce very accurate NEVPT2 results without any intruder states. However, its computational cost is not much lower than that of the canonical algorithm. Moreover, we found that a good indicator of intrude states problems in any approximation to high order density matrices is the eigenspectra of the Koopmans matrices.
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Affiliation(s)
- Yang Guo
- Qingdao Institute for Theoretical and Computational Sciences, Shandong University, Qingdao, Shandong 266237, China
| | - Kantharuban Sivalingam
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, D-45470 Mülheim an der Ruhr, Germany
| | - Frank Neese
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, D-45470 Mülheim an der Ruhr, Germany
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39
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Liao RZ, Zhang JX, Lin Z, Siegbahn PE. Antiferromagnetically coupled [Fe8S9] cluster catalyzed acetylene reduction in a nitrogenase-like enzyme DCCPCh: Insights from QM/MM calculations. J Catal 2021. [DOI: 10.1016/j.jcat.2021.04.009] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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40
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Li Manni G, Dobrautz W, Bogdanov NA, Guther K, Alavi A. Resolution of Low-Energy States in Spin-Exchange Transition-Metal Clusters: Case Study of Singlet States in [Fe(III) 4S 4] Cubanes. J Phys Chem A 2021; 125:4727-4740. [PMID: 34048648 PMCID: PMC8201447 DOI: 10.1021/acs.jpca.1c00397] [Citation(s) in RCA: 19] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
![]()
Polynuclear transition-metal
(PNTM) clusters owe their catalytic
activity to numerous energetically low-lying spin states and stable
oxidation states. The characterization of their electronic structure
represents one of the greatest challenges of modern chemistry. We
propose a theoretical framework that enables the resolution of targeted
electronic states with ease and apply it to two [Fe(III)4S4] cubanes. Through direct access to their many-body
wave functions, we identify important correlation mechanisms and their
interplay with the geometrical distortions observed in these clusters,
which are core properties in understanding their catalytic activity.
The simulated magnetic coupling constants predicted by our strategy
allow us to make qualitative connections between spin interactions
and geometrical distortions, demonstrating its predictive power. Moreover,
despite its simplicity, the strategy provides magnetic coupling constants
in good agreement with the available experimental ones. The complexes
are intrinsically frustrated anti-ferromagnets, and the obtained spin
structures together with the geometrical distortions represent two
possible ways to release spin frustration (spin-driven Jahn–Teller
distortion). Our paradigm provides a simple, yet rigorous, route to
uncover the electronic structure of PNTM clusters and may be applied
to a wide variety of such clusters.
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Affiliation(s)
- Giovanni Li Manni
- Department of Electronic Structure Theory, Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
| | - Werner Dobrautz
- Department of Electronic Structure Theory, Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
| | - Nikolay A Bogdanov
- Department of Electronic Structure Theory, Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
| | - Kai Guther
- Department of Electronic Structure Theory, Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
| | - Ali Alavi
- Department of Electronic Structure Theory, Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany.,Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, U.K
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41
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Jiang T, Chen Y, Bogdanov NA, Wang E, Alavi A, Chen J. A full configuration interaction quantum Monte Carlo study of ScO, TiO, and VO molecules. J Chem Phys 2021; 154:164302. [PMID: 33940817 DOI: 10.1063/5.0046464] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Accurate ab initio calculations of 3d transition metal monoxide molecules have attracted extensive attention because of their relevance in physical and chemical science as well as theoretical challenges in treating strong electron correlation. Meanwhile, recent years have witnessed the rapid development of the full configuration interaction quantum Monte Carlo (FCIQMC) method to tackle electron correlation. In this study, we carry out FCIQMC simulations to ScO, TiO, and VO molecules and obtain accurate descriptions of 13 low-lying electronic states (ScO 2Σ+, 2Δ, 2Π; TiO 3Δ, 1Δ, 1Σ+, 3Π, 3Φ; VO 4Σ-, 4Φ, 4Π, 2Γ, 2Δ), including states that have significant multi-configurational character. The FCIQMC results are used to assess the performance of several other wave function theory and density functional theory methods. Our study highlights the challenging nature of the electronic structure of transition metal oxides and demonstrates FCIQMC as a promising technique going forward to treat more complex transition metal oxide molecules and materials.
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Affiliation(s)
- Tonghuan Jiang
- School of Physics, Peking University, Beijing 100871, People's Republic of China
| | - Yilin Chen
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, People's Republic of China
| | - Nikolay A Bogdanov
- Max Planck Institute for Solid State Research, Heisenbergstrasse 1, 70569 Stuttgart, Germany
| | - Enge Wang
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, People's Republic of China
| | - Ali Alavi
- Max Planck Institute for Solid State Research, Heisenbergstrasse 1, 70569 Stuttgart, Germany
| | - Ji Chen
- School of Physics, Peking University, Beijing 100871, People's Republic of China
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42
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Abstract
The double-cubane cluster (DCC) refers to an [Fe8S9] iron-sulfur complex that is otherwise only known to exist in nitrogenases. Containing a bridging µ2-S ligand, the DCC in the DCC-containing protein (DCCP) is covalently linked to the protein scaffold via six coordinating cysteine residues. In this study, the nature of spin coupling and the effect of spin states on the cluster’s geometry are investigated computationally. Using density functional theory (DFT) and a broken symmetry (BS) approach to study the electronic ground state of the system, we computed the exchange interaction between the spin-coupled spins of the four FeFe dimers contained in the DCC. This treatment yields results that are in excellent agreement with both computed and experimentally determined exchange parameters for analogously coupled di-iron complexes. Hybrid quantum mechanical (QM)/molecular mechanical (MM) geometry optimizations show that cubane cluster A closest to charged amino acid side chains (Arg312, Glu140, Lys146) is less compact than cluster B, indicating that electrons of the same spin in a charged environment seek maximum separation. Overall, this study provides the community with a fundamental reference for subsequent studies of DCCP, as well as for investigations of other [Fe8S9]-containing enzymes.
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43
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Brabec J, Brandejs J, Kowalski K, Xantheas S, Legeza Ö, Veis L. Massively parallel quantum chemical density matrix renormalization group method. J Comput Chem 2020; 42:534-544. [DOI: 10.1002/jcc.26476] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/09/2020] [Revised: 11/22/2020] [Accepted: 11/26/2020] [Indexed: 01/19/2023]
Affiliation(s)
- Jiri Brabec
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic Prague Czech Republic
| | - Jan Brandejs
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic Prague Czech Republic
- Faculty of Mathematics and Physics Charles University Prague Czech Republic
| | - Karol Kowalski
- Pacific Northwest National Laboratory Richland Washington USA
| | | | - Örs Legeza
- Strongly Correlated Systems “Lendület” Research group, Wigner Research Centre for Physics Budapest Hungary
| | - Libor Veis
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic Prague Czech Republic
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44
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Lukoyanov DA, Yang ZY, Dean DR, Seefeldt LC, Raugei S, Hoffman BM. Electron Redistribution within the Nitrogenase Active Site FeMo-Cofactor During Reductive Elimination of H 2 to Achieve N≡N Triple-Bond Activation. J Am Chem Soc 2020; 142:21679-21690. [PMID: 33326225 DOI: 10.1021/jacs.0c07914] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Nitrogen fixation by nitrogenase begins with the accumulation of four reducing equivalents at the active-site FeMo-cofactor (FeMo-co), generating a state (denoted E4(4H)) with two [Fe-H-Fe] bridging hydrides. Recently, photolytic reductive elimination (re) of the E4(4H) hydrides showed that enzymatic re of E4(4H) hydride yields an H2-bound complex (E4(H2,2H)), in a process corresponding to a formal 2-electron reduction of the metal-ion core of FeMo-co. The resulting electron-density redistribution from Fe-H bonds to the metal ions themselves enables N2 to bind with concomitant H2 release, a process illuminated here by QM/MM molecular dynamics simulations. What is the nature of this redistribution? Although E4(H2,2H) has not been trapped, cryogenic photolysis of E4(4H) provides a means to address this question. Photolysis of E4(4H) causes hydride-re with release of H2, generating doubly reduced FeMo-co (denoted E4(2H)*), the extreme limit of the electron-density redistribution upon formation of E4(H2,2H). Here we examine the doubly reduced FeMo-co core of the E4(2H)* limiting-state by 1H, 57Fe, and 95Mo ENDOR to illuminate the partial electron-density redistribution upon E4(H2,2H) formation during catalysis, complementing these results with corresponding DFT computations. Inferences from the E4(2H)* ENDOR results as extended by DFT computations include (i) the Mo-site participates negligibly, and overall it is unlikely that Mo changes valency throughout the catalytic cycle; and (ii) two distinctive E4(4H) 57Fe signals are suggested as associated with structurally identified "anchors" of one bridging hydride, two others with identified anchors of the second, with NBO-analysis further identifying one anchor of each hydride as a major recipient of electrons released upon breaking Fe-H bonds.
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Affiliation(s)
- Dmitriy A Lukoyanov
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States
| | - Zhi-Yong Yang
- Department of Chemistry and Biocemistry, Utah State University, Logan, Utah 84322, United States
| | - Dennis R Dean
- Department of Biochemistry, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, United States
| | - Lance C Seefeldt
- Department of Chemistry and Biochemistry, Utah State University, Logan, Utah 84322, United States
| | - Simone Raugei
- Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Brian M Hoffman
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States
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45
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Stepanovic S, Lai R, Elstner M, Gruden M, Garcia-Fernandez P, Cui Q. Improvement of d-d interactions in density functional tight binding for transition metal ions with a ligand field model: assessment of a DFTB3+ U model on nickel coordination compounds. Phys Chem Chem Phys 2020; 22:27084-27095. [PMID: 33220674 PMCID: PMC7737908 DOI: 10.1039/d0cp04694a] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
Abstract
To improve the description of interactions among the localized d, f electrons in transition metals, we have introduced a ligand-field motivated contribution into the Density Functional Tight Binding (DFTB) model. Referred to as DFTB3+U, the approach treats the d, f electron repulsions with rotationally invariant orbital-orbital interactions and a Hartree-Fock model; this represents a major conceptual improvement over the original DFTB3 approach, which treats the d, f-shell interactions in a highly averaged fashion without orbital level of description. The DFTB3+U approach is tested using a series of nickel compounds that feature Ni(ii) and Ni(iii) oxidation states. By using parameters developed with the original DFTB3 Hamiltonian and empirical +U parameters (F0/2/4 Slater integrals), we observe that the DFTB3+U model indeed provides substantial improvements over the original DFTB3 model for a number of properties of the nickel compounds, including the population and spin polarization of the d-shell, nature of the frontier orbitals, ligand field splitting and the energy different between low and high spin states at OPBE optimized structures. This proof-of-concept study suggests that with self-consistent parameterization of the electronic and +U parameters, the DFTB3+U model can develop into a promising model that can be used to efficiently study reactive events involving transition metals ion condensed phase systems. The methodology can be integrated with other approximate QM methods as well, such as the extended tight binding (xTB) approach.
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Affiliation(s)
- Stepan Stepanovic
- Institute of Physical Chemistry and Institute of Biological Interfaces (IBG-2), Karlsruhe Institute of Technology, D-76131 Karlsruhe, Germany
- Institute of Chemistry, Technology and Metallurgy, University of Belgrade, Njegoševa 12, 11000, Belgrade, Serbia
| | - Rui Lai
- Departments of Chemistry, Physics, Biomedical Engineering, Boston University, 590 Commonwealth Avenue, Boston, MA 02215, United States
| | - Marcus Elstner
- Institute of Physical Chemistry and Institute of Biological Interfaces (IBG-2), Karlsruhe Institute of Technology, D-76131 Karlsruhe, Germany
| | - Maja Gruden
- University of Belgrade-Faculty of Chemistry, Studentski trg 12-16, 11001 Belgrade, Serbia
| | - Pablo Garcia-Fernandez
- Departamento de Ciencias de la Tierra y Fısica de la Materia Condensada, Universidad de Cantabria, Cantabria Campus Internacional, Avenida de los Castros s/n, 39005 Santander, Spain
| | - Qiang Cui
- Departments of Chemistry, Physics, Biomedical Engineering, Boston University, 590 Commonwealth Avenue, Boston, MA 02215, United States
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46
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Bauer B, Bravyi S, Motta M, Chan GKL. Quantum Algorithms for Quantum Chemistry and Quantum Materials Science. Chem Rev 2020; 120:12685-12717. [DOI: 10.1021/acs.chemrev.9b00829] [Citation(s) in RCA: 134] [Impact Index Per Article: 33.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023]
Affiliation(s)
- Bela Bauer
- Microsoft Quantum, Station Q, University of California
, Santa Barbara, California 93106, United States
| | - Sergey Bravyi
- IBM Quantum, IBM T. J. Watson Research Center
, Yorktown Heights, New York 10598, United States
| | - Mario Motta
- IBM Quantum, IBM Research Almaden
, San Jose, California 95120, United States
| | - Garnet Kin-Lic Chan
- Division of Chemistry and Chemical Engineering, California Institute of Technology
, Pasadena, California 91125, United States
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47
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Zou J, Niu K, Ma H, Li S, Fang W. Automatic Selection of Active Orbitals from Generalized Valence Bond Orbitals. J Phys Chem A 2020; 124:8321-8329. [PMID: 32894939 DOI: 10.1021/acs.jpca.0c05216] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The accurate multireference (MR) calculation of a strongly correlated chemical system usually relies on a correct preselection of a small number of active orbitals from numerous molecular orbitals. Currently, the active orbitals are generally determined by using a trial-and-error method. Such a preselection by chemical intuition and personal experience may be tedious or unreliable, especially for large complicated systems, and accordingly, the construction of active space becomes a bottleneck for large-scale MR calculations. In this work, we propose to automatically select the active orbitals according to the natural orbital occupation numbers by performing black box generalized valence bond calculations. We demonstrate the accuracy of this method through testing calculations of the ground states in various systems, ranging from bond dissociation of diatomic molecules (N2, C2, Cr2) to conjugated molecules (pentacene, hexacene, and heptacene) as well as a binuclear transition-metal complex [Mn2O2(H2O)2(terpy)2]3+ (terpy = 2,2':6,2″-terpyridine) with active spaces up to (30e, 30o) and comparing with the complete active space self-consistent field (CASSCF), density matrix renormalization group (DMRG)-CASSCF references, and other recently proposed inexpensive strategies for constructing active spaces. The results indicate that our method is among the most successful ones within our comparison, providing high-quality initial active orbitals very close to the finally optimized (DMRG-)CASSCF orbitals. The method proposed here is expected to greatly benefit the practical implementation of large active space ground-state MR calculations, for example, large-scale DMRG calculations.
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Affiliation(s)
- Jingxiang Zou
- Key Laboratory of Mesoscopic Chemistry of MOE, School of Chemistry and Chemical Engineering, Institute of Theoretical and Computational Chemistry, Nanjing University, Nanjing 210023, China
| | - Ke Niu
- Key Laboratory of Mesoscopic Chemistry of MOE, School of Chemistry and Chemical Engineering, Institute of Theoretical and Computational Chemistry, Nanjing University, Nanjing 210023, China
| | - Haibo Ma
- Key Laboratory of Mesoscopic Chemistry of MOE, School of Chemistry and Chemical Engineering, Institute of Theoretical and Computational Chemistry, Nanjing University, Nanjing 210023, China
| | - Shuhua Li
- Key Laboratory of Mesoscopic Chemistry of MOE, School of Chemistry and Chemical Engineering, Institute of Theoretical and Computational Chemistry, Nanjing University, Nanjing 210023, China
| | - Weihai Fang
- School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, China.,Key Laboratory of Theoretical and Computational Photochemistry of Ministry of Education, Department of Chemistry, Beijing Normal University, Beijing 100875, China
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48
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Larsson HR, Jiménez-Hoyos CA, Chan GKL. Minimal Matrix Product States and Generalizations of Mean-Field and Geminal Wave Functions. J Chem Theory Comput 2020; 16:5057-5066. [DOI: 10.1021/acs.jctc.0c00463] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Henrik R. Larsson
- Department of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | | | - Garnet Kin-Lic Chan
- Department of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
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49
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Sun Q, Zhang X, Banerjee S, Bao P, Barbry M, Blunt NS, Bogdanov NA, Booth GH, Chen J, Cui ZH, Eriksen JJ, Gao Y, Guo S, Hermann J, Hermes MR, Koh K, Koval P, Lehtola S, Li Z, Liu J, Mardirossian N, McClain JD, Motta M, Mussard B, Pham HQ, Pulkin A, Purwanto W, Robinson PJ, Ronca E, Sayfutyarova ER, Scheurer M, Schurkus HF, Smith JET, Sun C, Sun SN, Upadhyay S, Wagner LK, Wang X, White A, Whitfield JD, Williamson MJ, Wouters S, Yang J, Yu JM, Zhu T, Berkelbach TC, Sharma S, Sokolov AY, Chan GKL. Recent developments in the PySCF program package. J Chem Phys 2020; 153:024109. [DOI: 10.1063/5.0006074] [Citation(s) in RCA: 151] [Impact Index Per Article: 37.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023] Open
Affiliation(s)
- Qiming Sun
- AxiomQuant Investment Management LLC, Shanghai 200120, China
| | - Xing Zhang
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Samragni Banerjee
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
| | - Peng Bao
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China
| | - Marc Barbry
- Simbeyond B.V., P.O. Box 513, NL-5600 MB, Eindhoven, The Netherlands
| | - Nick S. Blunt
- Department of Chemistry, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Nikolay A. Bogdanov
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
| | - George H. Booth
- Department of Physics, King’s College London, Strand, London WC2R 2LS, United Kingdom
| | - Jia Chen
- Department of Physics, University of Florida, Gainesville, Florida 32611, USA
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, USA
| | - Zhi-Hao Cui
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Janus J. Eriksen
- School of Chemistry, University of Bristol, Cantock’s Close, Bristol BS8 1TS, United Kingdom
| | - Yang Gao
- Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California 91125, USA
| | - Sheng Guo
- Google Inc., Mountain View, California 94043, USA
| | - Jan Hermann
- FU Berlin, Department of Mathematics and Computer Science, Arnimallee 6, 14195 Berlin, Germany
- TU Berlin, Machine Learning Group, Marchstr. 23, 10587 Berlin, Germany
| | - Matthew R. Hermes
- Department of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota 55455, USA
| | - Kevin Koh
- Department of Chemistry and Biochemistry, The University of Notre Dame du Lac, 251 Nieuwland Science Hall, Notre Dame, Indiana 46556, USA
| | - Peter Koval
- Simune Atomistics S.L., Avenida Tolosa 76, Donostia-San Sebastian, Spain
| | - Susi Lehtola
- Department of Chemistry, University of Helsinki, P.O. Box 55 (A. I. Virtasen aukio 1), FI-00014 Helsinki, Finland
| | - Zhendong Li
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Junzi Liu
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Narbe Mardirossian
- AMGEN Research, One Amgen Center Drive, Thousand Oaks, California 91320, USA
| | | | - Mario Motta
- IBM Almaden Research Center, San Jose, California 95120, USA
| | - Bastien Mussard
- Department of Chemistry, University of Colorado, Boulder, Colorado 80302, USA
| | - Hung Q. Pham
- Department of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota 55455, USA
| | - Artem Pulkin
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, The Netherlands
| | - Wirawan Purwanto
- Information Technology Services, Old Dominion University, Norfolk, Virginia 23529, USA
| | - Paul J. Robinson
- Department of Chemistry, Columbia University, New York, New York 10027, USA
| | - Enrico Ronca
- Istituto per i Processi Chimico Fisici del CNR (IPCF-CNR), Via G. Moruzzi, 1, 56124 Pisa, Italy
| | - Elvira R. Sayfutyarova
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, USA
| | - Maximilian Scheurer
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University of Heidelberg, 205 Im Neuenheimer Feld, 69120 Heidelberg, Germany
| | - Henry F. Schurkus
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - James E. T. Smith
- Department of Chemistry, University of Colorado, Boulder, Colorado 80302, USA
| | - Chong Sun
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Shi-Ning Sun
- Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California 91125, USA
| | - Shiv Upadhyay
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
| | - Lucas K. Wagner
- Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Illinois 61801, USA
| | - Xiao Wang
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA
| | - Alec White
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - James Daniel Whitfield
- Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire 03755, USA
| | - Mark J. Williamson
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | | | - Jun Yang
- Department of Chemistry, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China
| | - Jason M. Yu
- Department of Chemistry, University of California, Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, USA
| | - Tianyu Zhu
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Timothy C. Berkelbach
- Department of Chemistry, Columbia University, New York, New York 10027, USA
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA
| | - Sandeep Sharma
- Department of Chemistry, University of Colorado, Boulder, Colorado 80302, USA
| | - Alexander Yu. Sokolov
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
| | - Garnet Kin-Lic Chan
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
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50
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Abstract
Nitrogenase is the only enzyme capable of reducing N2 to NH3. This challenging reaction requires the coordinated transfer of multiple electrons from the reductase, Fe-protein, to the catalytic component, MoFe-protein, in an ATP-dependent fashion. In the last two decades, there have been significant advances in our understanding of how nitrogenase orchestrates electron transfer (ET) from the Fe-protein to the catalytic site of MoFe-protein and how energy from ATP hydrolysis transduces the ET processes. In this review, we summarize these advances, with focus on the structural and thermodynamic redox properties of nitrogenase component proteins and their complexes, as well as on new insights regarding the mechanism of ET reactions during catalysis and how they are coupled to ATP hydrolysis. We also discuss recently developed chemical, photochemical, and electrochemical methods for uncoupling substrate reduction from ATP hydrolysis, which may provide new avenues for studying the catalytic mechanism of nitrogenase.
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Affiliation(s)
- Hannah L Rutledge
- Department of Chemistry and Biochemistry, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093-0340, United States
| | - F Akif Tezcan
- Department of Chemistry and Biochemistry, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093-0340, United States
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