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Hoyer CE, Liao C, Shumilov KD, Zhang T, Li X. State Interaction for Relativistic Four-Component Methods: Choose the Right Zeroth-Order Hamiltonian for Late-Row Elements. J Chem Theory Comput 2024. [PMID: 39257190 DOI: 10.1021/acs.jctc.4c00797] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/12/2024]
Abstract
We present several schemes based on the spin-separation of the Dirac-Coulomb-Breit Hamiltonian for the perturbative treatment of relativistic four-component Hamiltonians within the state interaction framework. While state interaction approaches traditionally use zeroth-order scalar-relativistic states, we develop augmented zeroth-order Hamiltonians with increasing accuracy and investigate convergence to the variational limit as a function of the choice of zeroth-order Hamiltonian. The state interaction schemes developed in this work are benchmarked using ground-state fine-structure splitting of late-row atoms and diatomic hyrides. Although the scalar-relativistic zeroth-order Hamiltonian exhibits significant errors in ground-state fine-structure splitting, the predictive accuracy can be improved by augmenting the zeroth-order Hamiltonian with one- and two-electron vector-relativistic operators (e.g., spin-orbit, spin-spin, orbit-orbit). This work lays the theoretical foundation for the development of low-scaling, high-accuracy perturbative relativistic methods suitable for late-row elements.
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Affiliation(s)
- Chad E Hoyer
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Can Liao
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Kirill D Shumilov
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Tianyuan Zhang
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
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2
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Liao C, Hoyer CE, Banerjee Ghosh R, Jenkins AJ, Knecht S, Frisch MJ, Li X. Comparison of Variational and Perturbative Spin-Orbit Coupling within Two-Component CASSCF. J Phys Chem A 2024. [PMID: 38489510 DOI: 10.1021/acs.jpca.3c08031] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/17/2024]
Abstract
The modeling of spin-orbit coupling (SOC) remains a challenge in computational chemistry due to the high computational cost. With the rising popularity of spin-driven processes and f-block metals in chemistry and materials science, it is incumbent on the community to develop accurate multiconfigurational SOC methods that scale to large systems and understand the limits of different treatments of SOC. Herein, we introduce an implementation of perturbative SOC in scalar-relativistic two-component CASSCF (srX2C-CASSCF-SO). Perspectives on the limitations and accuracy of srX2C-CASSCF-SO are presented via benchmark calculations.
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Affiliation(s)
- Can Liao
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Chad E Hoyer
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Rahoul Banerjee Ghosh
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Andrew J Jenkins
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Stefan Knecht
- Algorithmiq Ltd, Kanavakatu 3C, FI-00160 Helsinki, Finland
- ETH Zürich, Department of Chemistry and Applied Life Sciences, Vladimir-Prelog-Weg 1-5/10, CH-8093 Zürich, Switzerland
| | - Michael J Frisch
- Gaussian Inc., 340 Quinnipiac Street, Bldg 40, Wallingford, Connecticut 06492, United States
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
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3
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Amanollahi Z, Lampe L, Bensberg M, Neugebauer J, Feldt M. On the accuracy of orbital based multi-level approaches for closed-shell transition metal chemistry. Phys Chem Chem Phys 2023; 25:4635-4648. [PMID: 36662158 DOI: 10.1039/d2cp05056k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
Abstract
In this work, we investigate the accuracy of the local molecular orbital molecular orbital (LMOMO) scheme and projection-based wave function-in-density functional theory (WF-in-DFT) embedding for the prediction of reaction energies and barriers of typical reactions involving transition metals. To analyze the dependence of the accuracy on the system partitioning, we apply a manual orbital selection for LMOMO as well as the so-called direct orbital selection (DOS) for both approaches. We benchmark these methods on 30 closed shell reactions involving 16 different transition metals. This allows us to devise guidelines for the manual selection as well as settings for the DOS that provide accurate results within an error of 2 kcal mol-1 compared to local coupled cluster. To reach this accuracy, on average 55% of the occupied orbitals have to be correlated with coupled cluster for the current test set. Furthermore, we find that LMOMO gives more reliable relative energies for small embedded regions than WF-in-DFT embedding.
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Affiliation(s)
- Zohreh Amanollahi
- Leibniz Institute for Catalysis (LIKAT), Albert-Einstein-Str. 29A, 18059 Rostock, Germany.
| | - Lukas Lampe
- Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, Westfälische Wilhelms-Universität Münster, Corrensstraße 36, 48149 Münster, Germany
| | - Moritz Bensberg
- ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Johannes Neugebauer
- Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, Westfälische Wilhelms-Universität Münster, Corrensstraße 36, 48149 Münster, Germany
| | - Milica Feldt
- Leibniz Institute for Catalysis (LIKAT), Albert-Einstein-Str. 29A, 18059 Rostock, Germany.
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Hoyer CE, Hu H, Lu L, Knecht S, Li X. Relativistic Kramers-Unrestricted Exact-Two-Component Density Matrix Renormalization Group. J Phys Chem A 2022; 126:5011-5020. [PMID: 35881436 DOI: 10.1021/acs.jpca.2c02150] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
In this work we develop a variational relativistic density matrix renormalization group (DMRG) approach within the exact-two-component (X2C) framework (X2C-DMRG), using spinor orbitals optimized with the two-component relativistic complete active space self-consistent field. We investigate fine-structure splittings of p- (Ga, In, Tl) and d-block (Sc, Y, La) atoms and excitation energies of monohydride molecules (GeH, SnH, and TlH) with X2C-DMRG calculations using an all-electron relativistic Hamiltonian in a Kramers-unrestricted basis. We find that X2C-DMRG yields accurate 2P and 2D splittings compared to multireference configuration interaction with singles and doubles (MRCISD). We also investigated the degree of symmetry breaking in the atomic multiplets and convergence of electron correlation in the total energies. Symmetry breaking can be large in some cases (∼30 meV); however, increasing the number of renormalized block states m for the DMRG optimization recovers the symmetry breaking by several orders of magnitude. Encouragingly, we find the convergence of electron correlation to be close to MRCISDTQ5 quality. Relativistic X2C-DMRG approaches are important for cases where spin-orbit coupling is significant and the underlying reference wave function requires a large determinantal space. We are able to obtain quantitatively correct fine-structure splittings for systems up to 1019 number of determinants with traditional CI approaches, which are currently unfeasible to converge for the field.
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Affiliation(s)
- Chad E Hoyer
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Hang Hu
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Lixin Lu
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Stefan Knecht
- Algorithmiq Ltd., Kanavakatu 3C, FI-00160 Helsinki, Finland.,Abteilung SHE Chemie, GSI Helmholtzzentrum für Schwerionenforschung, DE-64291 Darmstadt, Germany.,Department Chemie, Johannes-Gutenberg Universität Mainz, DE-55128 Mainz, Germany
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
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Grofe A, Li X. Relativistic nonorthogonal configuration interaction: application to L 2,3-edge X-ray spectroscopy. Phys Chem Chem Phys 2022; 24:10745-10756. [PMID: 35451435 DOI: 10.1039/d2cp01127a] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
In this article, we develop a relativistic exact-two-component nonorthogonal configuration interaction (X2C-NOCI) for computing L-edge X-ray spectra. This article to our knowledge is the first time NOCI has been used for relativistic wave functions. A set of molecular complexes, including SF6, SiCl4 and [FeCl6]3-, are used to demonstrate the accuracy and computational scaling of the X2C-NOCI method. Our results suggest that X2C-NOCI is able to satisfactorily capture the main features of the L2,3-edge X-ray absorption spectra. Excitations from the core require a large amount of orbital relaxation to yield reasonable energies and X2C-NOCI allows us to treat orbital optimization explicitly. However, the cost of computing the nonorthogonal coupling is higher than in conventional CI. Here, we propose an improved integral screening using overlap-scaled density combined with a continuous measure of the generalized Slater-Condon rules that allows us to estimate if an element is zero before attempting a two-electron integral contraction.
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Affiliation(s)
- Adam Grofe
- Department of Chemistry, University of Washington, Seattle, Washington 98195, USA.
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, USA.
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Sharma P, Jenkins AJ, Scalmani G, Frisch MJ, Truhlar DG, Gagliardi L, Li X. Exact-Two-Component Multiconfiguration Pair-Density Functional Theory. J Chem Theory Comput 2022; 18:2947-2954. [PMID: 35384665 DOI: 10.1021/acs.jctc.2c00062] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Molecules containing late-row elements exhibit large relativistic effects. To account for both relativistic effects and electron correlation in a computationally inexpensive way, we derived a formulation of multiconfiguration pair-density functional theory with the relativistic exact-two-component Hamiltonian (X2C-MC-PDFT). In this new method, relativistic effects are included during variational optimization of a reference wave function by exact-two-component complete active-space self-consistent-field (X2C-CASSCF) theory, followed by an energy evaluation using pair-density functional theory. Benchmark studies of excited-state and ground-state fine-structure splitting of atomic species show that X2C-MC-PDFT can significantly improve the X2C-CASSCF results by introducing additional state-specific electron correlation.
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Affiliation(s)
- Prachi Sharma
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Andrew J Jenkins
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Giovanni Scalmani
- Gaussian Inc., 340 Quinnipiac Street, Building 40, Wallingford, Connecticut 06492, United States
| | - Michael J Frisch
- Gaussian Inc., 340 Quinnipiac Street, Building 40, Wallingford, Connecticut 06492, United States
| | - Donald G Truhlar
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota 55455, United States
| | - Laura Gagliardi
- Department of Chemistry, University of Chicago, 5735 S Ellis Avenue, Chicago, Illinois 60637, United States
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
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7
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Kasper JM, Li X, Kozimor SA, Batista ER, Yang P. Relativistic Effects in Modeling the Ligand K-Edge X-ray Absorption Near-Edge Structure of Uranium Complexes. J Chem Theory Comput 2022; 18:2171-2179. [PMID: 35274960 DOI: 10.1021/acs.jctc.1c00851] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Abstract
Accurate modeling of the complex electronic structure of actinide complexes requires full inclusion of relativistic effects. In this study, we examine the effect of explicit inclusion of spin-orbit coupling (SOC) versus scalar relativistic effects on the predicted spectra for heavy-element complexes. In this study, we employ a relativistic two-component Hamiltonian in the X2C form with all of the electrons in the system being considered explicitly to compare and contrast with previous studies that included the relativistic effects by means of relativistic effective core potentials (RECPs). A few uranium complexes are chosen as model systems. Comparison of the computed Cl K-edge X-ray absorption spectra with experimental data shows significantly improved agreement when a variational relativistic treatment of SOC is performed. In particular, we note the importance of SOC terms to obtain not only correct transition energies but also correct intensities for these heavy-element complexes because of the redistribution of ligand bonding character among the valence MOs. While RECPs generally agree well with all-electron scalar relativistic calculations, there are some differences in the predicted spectra of open-shell systems. These methods are still suitable for broad application to analyze the qualitative nature of transitions in X-ray absorption spectra, but caution is recommended for quantitative analysis, as SOC can be non-negligible for both open- and closed-shell heavy-element systems.
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Affiliation(s)
- Joseph M Kasper
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States.,Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States.,Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Stosh A Kozimor
- Chemistry Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Enrique R Batista
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Ping Yang
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
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Bensberg M, Neugebauer J. Direct orbital selection within the domain-based local pair natural orbital coupled-cluster method. J Chem Phys 2021; 155:224102. [PMID: 34911318 DOI: 10.1063/5.0071347] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Domain-based local pair natural orbital coupled cluster (DLPNO-CC) has become increasingly popular to calculate relative energies (e.g., reaction energies and reaction barriers). It can be applied within a multi-level DLPNO-CC-in-DLPNO-CC ansatz to reduce the computational cost and focus the available computational resources on a specific subset of the occupied orbitals. We demonstrate how this multi-level DLPNO-CC ansatz can be combined with our direct orbital selection (DOS) approach [M. Bensberg and J. Neugebauer, J. Chem. Phys. 150, 214106 (2019)] to automatically select orbital sets for any multi-level calculation. We find that the parameters for the DOS procedure can be chosen conservatively such that they are transferable between reactions. The resulting automatic multi-level DLPNO-CC method requires no user input and is extremely robust and accurate. The computational cost is easily reduced by a factor of 3 without sacrificing accuracy. We demonstrate the accuracy of the method for a total of 61 reactions containing up to 174 atoms and use it to predict the relative stability of conformers of a Ru-based catalyst.
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Affiliation(s)
- Moritz Bensberg
- Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, Westfälische Wilhelms-Universität Münster, Corrensstraße 36, 48149 Münster, Germany
| | - Johannes Neugebauer
- Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, Westfälische Wilhelms-Universität Münster, Corrensstraße 36, 48149 Münster, Germany
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Grofe A, Gao J, Li X. Exact-two-component block-localized wave function: A simple scheme for the automatic computation of relativistic ΔSCF. J Chem Phys 2021; 155:014103. [PMID: 34241404 DOI: 10.1063/5.0054227] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Block-localized wave function is a useful method for optimizing constrained determinants. In this article, we extend the generalized block-localized wave function technique to a relativistic two-component framework. Optimization of excited state determinants for two-component wave functions presents a unique challenge because the excited state manifold is often quite dense with degenerate states. Furthermore, we test the degree to which certain symmetries result naturally from the ΔSCF optimization such as time-reversal symmetry and symmetry with respect to the total angular momentum operator on a series of atomic systems. Variational optimizations may often break the symmetry in order to lower the overall energy, just as unrestricted Hartree-Fock breaks spin symmetry. Overall, we demonstrate that time-reversal symmetry is roughly maintained when using Hartree-Fock, but less so when using Kohn-Sham density functional theory. Additionally, maintaining total angular momentum symmetry appears to be system dependent and not guaranteed. Finally, we were able to trace the breaking of total angular momentum symmetry to the relaxation of core electrons.
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Affiliation(s)
- Adam Grofe
- Department of Chemistry, University of Washington, Seattle, Washington 98195, USA
| | - Jiali Gao
- Institute of Systems and Physical Biology, Shenzhen Bay Laboratory, Shenzhen 518055, China; Department of Chemistry and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455, USA; and Beijing University Shenzhen Graduate School, Shenzhen 518055, China
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, USA
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10
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Bensberg M, Neugebauer J. Density functional theory based embedding approaches for transition-metal complexes. Phys Chem Chem Phys 2020; 22:26093-26103. [PMID: 33201953 DOI: 10.1039/d0cp05188h] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Abstract
Transition metal species are commonly discussed by considering the metal atom embedded in a ligand environment. This apparently makes them interesting targets for modern embedding strategies based on Kohn-Sham density functional theory (DFT), which aim at modelling accurate predictions for large systems by combining different quantum chemical methods. In this perspective, we will focus on subsystem density functional theory and projection-based embedding. We review the developments in the field for transition metal species, demonstrate benefits, drawbacks and analyse error sources of the different strategies using the example of chromium hexacarbonyle, before giving a perspective where the field is currently heading.
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Affiliation(s)
- Moritz Bensberg
- Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, Westfälische Wilhelms-Universität Münster Corrensstraße 36, 48149 Münster, Germany.
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