1
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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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Zhang C, Peterson KA, Dyall KG, Cheng L. A new computational framework for spinor-based relativistic exact two-component calculations using contracted basis functions. J Chem Phys 2024; 161:054105. [PMID: 39087536 DOI: 10.1063/5.0217762] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2024] [Accepted: 07/14/2024] [Indexed: 08/02/2024] Open
Abstract
A new computational framework for spinor-based relativistic exact two-component (X2C) calculations is developed using contracted basis sets with a spin-orbit contraction scheme. Generally contracted, j-adapted basis sets of p-block elements using primitive functions in the correlation-consistent basis sets are constructed for the X2C Hamiltonian with atomic mean-field spin-orbit integrals (the X2CAMF scheme). The contraction coefficients are taken from atomic X2CAMF Hartree-Fock spinors, thereby following the simple concept of a linear combination of atomic orbitals. Benchmark calculations of spin-orbit splittings, equilibrium bond lengths, and harmonic vibrational frequencies demonstrate the accuracy and efficacy of the j-adapted spin-orbit contraction scheme.
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Affiliation(s)
- Chaoqun Zhang
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Kirk A Peterson
- Department of Chemistry, Washington State University, Pullman, Washington 99164, USA
| | | | - Lan Cheng
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
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3
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Majumder R, Sokolov AY. Consistent Second-Order Treatment of Spin-Orbit Coupling and Dynamic Correlation in Quasidegenerate N-Electron Valence Perturbation Theory. J Chem Theory Comput 2024; 20:4676-4688. [PMID: 38795071 DOI: 10.1021/acs.jctc.4c00458] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/27/2024]
Abstract
We present a formulation and implementation of second-order quasidegenerate N-electron valence perturbation theory (QDNEVPT2) that provides a balanced and accurate description of spin-orbit coupling and dynamic correlation effects in multiconfigurational electronic states. In our approach, the energies and wave functions of electronic states are computed by treating electron repulsion and spin-orbit coupling operators as equal perturbations to the nonrelativistic complete active-space wave functions, and their contributions are incorporated fully up to the second order. The spin-orbit effects are described using the Breit-Pauli (BP) or exact two-component Douglas-Kroll-Hess (DKH) Hamiltonians within spin-orbit mean-field approximation. The resulting second-order methods (BP2- and DKH2-QDNEVPT2) are capable of treating spin-orbit coupling effects in nearly degenerate electronic states by diagonalizing an effective Hamiltonian expanded in a compact non-relativistic basis. For a variety of atoms and small molecules across the entire periodic table, we demonstrate that DKH2-QDNEVPT2 is competitive in accuracy with variational two-component relativistic theories. BP2-QDNEVPT2 shows high accuracy for the second- and third-period elements, but its performance deteriorates for heavier atoms and molecules. We also consider the first-order spin-orbit QDNEVPT2 approximations (BP1- and DKH1-QDNEVPT2), among which DKH1-QDNEVPT2 is reliable but less accurate than DKH2-QDNEVPT2. Both DKH1- and DKH2-QDNEVPT2 hold promise as efficient and accurate electronic structure methods for treating electron correlation and spin-orbit coupling in a variety of applications.
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Affiliation(s)
- Rajat Majumder
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
| | - Alexander Yu Sokolov
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
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4
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Zhang T, Banerjee S, Koulias LN, Valeev EF, DePrince AE, Li X. Dirac-Coulomb-Breit Molecular Mean-Field Exact-Two-Component Relativistic Equation-of-Motion Coupled-Cluster Theory. J Phys Chem A 2024; 128:3408-3418. [PMID: 38651293 DOI: 10.1021/acs.jpca.3c08167] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/25/2024]
Abstract
We present a relativistic equation-of-motion coupled-cluster with single and double excitation formalism within the exact two-component framework (X2C-EOM-CCSD), where both scalar relativistic effects and spin-orbit coupling are variationally included at the reference level. Three different molecular mean-field treatments of relativistic corrections, including the one-electron, Dirac-Coulomb, and Dirac-Coulomb-Breit Hamiltonian, are considered in this work. Benchmark calculations include atomic excitations and fine-structure splittings arising from spin-orbit coupling. Comparison with experimental values and relativistic time-dependent density functional theory is also carried out. The computation of the oscillator strength using the relativistic X2C-EOM-CCSD approach allows for studies of spin-orbit-driven processes, such as the spontaneous phosphorescence lifetime.
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Affiliation(s)
- Tianyuan Zhang
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Samragni Banerjee
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Lauren N Koulias
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Edward F Valeev
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - A Eugene DePrince
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, United States
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
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5
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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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6
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Liu W. Unified construction of relativistic Hamiltonians. J Chem Phys 2024; 160:084111. [PMID: 38415836 DOI: 10.1063/5.0188794] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2023] [Accepted: 02/09/2024] [Indexed: 02/29/2024] Open
Abstract
It is shown that the four-component (4C), quasi-four-component (Q4C), and exact two-component (X2C) relativistic Hartree-Fock equations can be implemented in a unified manner by making use of the atomic nature of the small components of molecular 4-spinors. A model density matrix approximation can first be invoked for the small-component charge/current density functions, which gives rise to a static, pre-molecular mean field to be combined with the one-electron term. As a result, only the nonrelativistic-like two-electron term of the 4C/Q4C/X2C Fock matrix needs to be updated during the iterations. A "one-center small-component" approximation can then be invoked in the evaluation of relativistic integrals, that is, all atom-centered small-component basis functions are regarded as extremely localized near the position of the atom to which they belong such that they have vanishing overlaps with all small- or large-component functions centered at other nuclei. Under these approximations, the 4C, Q4C, and X2C mean-field and many-electron Hamiltonians share precisely the same structure and accuracy. Beyond these is the effective quantum electrodynamics Hamiltonian that can be constructed in the same way. Such approximations lead to errors that are orders of magnitude smaller than other sources of errors (e.g., truncation errors in the one- and many-particle bases as well as uncertainties of experimental measurements) and are, hence, safe to use for whatever purposes. The quaternion forms of the 4C, Q4C, and X2C equations are also presented in the most general way, based on which the corresponding Kramers-restricted open-shell variants are formulated for "high-spin" open-shell systems.
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Affiliation(s)
- Wenjian Liu
- Qingdao Institute for Theoretical and Computational Sciences, School of Chemistry and Chemical Engineering, Shandong University, Qingdao, Shandong 266237, People's Republic of China
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7
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Liao C, Lambros E, Sun Q, Dyall KG, Li X. Exploring Locality in Molecular Dirac-Coulomb-Breit Calculations: A Perspective. J Chem Theory Comput 2023; 19:9009-9017. [PMID: 38090757 DOI: 10.1021/acs.jctc.3c01012] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2023]
Abstract
The Dirac-Coulomb-Breit (DCB) operator is widely recognized for its ability to accurately capture relativistic effects and spin-physics in molecular calculations. However, due to its high computational cost, there is a need to develop low-scaling approximations without compromising accuracy. To tackle this challenge, it becomes essential to gain a deeper understanding of the DCB operator's behavior. This work aims to explore local integral approximations, shedding light on the locality of the parts of the charge-current distribution due to the small component. In particular, we propose an atomic Breit approximation that leverages an analysis of the behavior observed in a series of gold chains. Through benchmark studies of metal complexes, we evaluated the accuracy and performance of the proposed atomic Breit approximation. This work provides a comprehensive understanding of the behavior of the charge-current distribution in terms of its contributions from its AO basis constituents, facilitating the development of low-scaling methods that strike a balance between computational efficiency and accuracy.
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Affiliation(s)
- Can Liao
- Department of Chemistry, University of Washington, Seattle, Washington, 98195 United States
| | - Eleftherios Lambros
- Department of Chemistry, University of Washington, Seattle, Washington, 98195 United States
| | - Qiming Sun
- AxiomQuant Investment Management LLC, Shanghai, 200120 China
| | | | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington, 98195 United States
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8
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Di Felice R, Mayes ML, Richard RM, Williams-Young DB, Chan GKL, de Jong WA, Govind N, Head-Gordon M, Hermes MR, Kowalski K, Li X, Lischka H, Mueller KT, Mutlu E, Niklasson AMN, Pederson MR, Peng B, Shepard R, Valeev EF, van Schilfgaarde M, Vlaisavljevich B, Windus TL, Xantheas SS, Zhang X, Zimmerman PM. A Perspective on Sustainable Computational Chemistry Software Development and Integration. J Chem Theory Comput 2023; 19:7056-7076. [PMID: 37769271 PMCID: PMC10601486 DOI: 10.1021/acs.jctc.3c00419] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/14/2023] [Indexed: 09/30/2023]
Abstract
The power of quantum chemistry to predict the ground and excited state properties of complex chemical systems has driven the development of computational quantum chemistry software, integrating advances in theory, applied mathematics, and computer science. The emergence of new computational paradigms associated with exascale technologies also poses significant challenges that require a flexible forward strategy to take full advantage of existing and forthcoming computational resources. In this context, the sustainability and interoperability of computational chemistry software development are among the most pressing issues. In this perspective, we discuss software infrastructure needs and investments with an eye to fully utilize exascale resources and provide unique computational tools for next-generation science problems and scientific discoveries.
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Affiliation(s)
- Rosa Di Felice
- Departments
of Physics and Astronomy and Quantitative and Computational Biology, University of Southern California, Los Angeles, California 90089, United States
- CNR-NANO
Modena, Modena 41125, Italy
| | - Maricris L. Mayes
- Department
of Chemistry and Biochemistry, University
of Massachusetts Dartmouth, North Dartmouth, Massachusetts 02747, United States
| | | | | | - Garnet Kin-Lic Chan
- Division
of Chemistry and Chemical Engineering, California
Institute of Technology, Pasadena, California 91125, United States
| | - Wibe A. de Jong
- Lawrence
Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Niranjan Govind
- Physical
Sciences Division, Pacific Northwest National
Laboratory, Richland, Washington 99354, United States
| | - Martin Head-Gordon
- Pitzer Center
for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, United States
| | - Matthew R. Hermes
- Department
of Chemistry, Chicago Center for Theoretical Chemistry, University of Chicago, Chicago, Illinois 60637, United States
| | - Karol Kowalski
- Physical
Sciences Division, Pacific Northwest National
Laboratory, Richland, Washington 99354, United States
| | - Xiaosong Li
- Department
of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Hans Lischka
- Department
of Chemistry and Biochemistry, Texas Tech
University, Lubbock, Texas 79409, United States
| | - Karl T. Mueller
- Physical
and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Erdal Mutlu
- Advanced
Computing, Mathematics, and Data Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Anders M. N. Niklasson
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Mark R. Pederson
- Department
of Physics, The University of Texas at El
Paso, El Paso, Texas 79968, United States
| | - Bo Peng
- Physical
Sciences Division, Pacific Northwest National
Laboratory, Richland, Washington 99354, United States
| | - Ron Shepard
- Chemical
Sciences and Engineering Division, Argonne
National Laboratory, Lemont, Illinois 60439, United States
| | - Edward F. Valeev
- Department
of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | | | - Bess Vlaisavljevich
- Department
of Chemistry, University of South Dakota, Vermillion, South Dakota 57069, United States
| | - Theresa L. Windus
- Department
of Chemistry, Iowa State University and
Ames Laboratory, Ames, Iowa 50011, United States
| | - Sotiris S. Xantheas
- Department
of Chemistry, University of Washington, Seattle, Washington 98195, United States
- Advanced
Computing, Mathematics and Data Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Xing Zhang
- Division
of Chemistry and Chemical Engineering, California
Institute of Technology, Pasadena, California 91125, United States
| | - Paul M. Zimmerman
- Department
of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
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9
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Banerjee S, Zhang T, Dyall KG, Li X. Relativistic resolution-of-the-identity with Cholesky integral decomposition. J Chem Phys 2023; 159:114119. [PMID: 37728204 DOI: 10.1063/5.0161871] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2023] [Accepted: 08/28/2023] [Indexed: 09/21/2023] Open
Abstract
In this study, we present an efficient integral decomposition approach called the restricted-kinetic-balance resolution-of-the-identity (RKB-RI) algorithm, which utilizes a tunable RI method based on the Cholesky integral decomposition for in-core relativistic quantum chemistry calculations. The RKB-RI algorithm incorporates the restricted-kinetic-balance condition and offers a versatile framework for accurate computations. Notably, the Cholesky integral decomposition is employed not only to approximate symmetric large-component electron repulsion integrals but also those involving small-component basis functions. In addition to comprehensive error analysis, we investigate crucial conditions, such as the kinetic balance condition and variational stability, which underlie the applicability of Dirac relativistic electronic structure theory. We compare the computational cost of the RKB-RI approach with the full in-core method to assess its efficiency. To evaluate the accuracy and reliability of the RKB-RI method proposed in this work, we employ actinyl oxides as benchmark systems, leveraging their properties for validation purposes. This investigation provides valuable insights into the capabilities and performance of the RKB-RI algorithm and establishes its potential as a powerful tool in the field of relativistic quantum chemistry.
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Affiliation(s)
- Samragni Banerjee
- Department of Chemistry, University of Washington, Seattle, Washington 98195, USA
| | - Tianyuan Zhang
- 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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10
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Ehrman J, Martinez-Baez E, Jenkins AJ, Li X. Improving One-Electron Exact-Two-Component Relativistic Methods with the Dirac-Coulomb-Breit-Parameterized Effective Spin-Orbit Coupling. J Chem Theory Comput 2023; 19:5785-5790. [PMID: 37589436 DOI: 10.1021/acs.jctc.3c00479] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/18/2023]
Abstract
In photochemical processes, spin-orbit coupling plays a crucial role in determining the outcome of the reaction. However, the exact treatment of the Dirac-Coulomb-Breit two-electron operator required for rigorous inclusion of spin-orbit coupling is computationally prohibitive. To address this challenge, we present a Dirac-Coulomb-Breit-parameterized screened-nuclear spin-orbit factor to approximate two-electron spin-orbit couplings in the effective one-electron spin-orbit Hamiltonian. We propose two schemes, the universal and row-dependent parameterizations, to further improve the accuracy of the method. Benchmark calculations on both atomic and molecular systems are performed and compared to results from the computationally expensive four-component Dirac-Coulomb-Breit method. The Dirac-Coulomb-Breit-parameterized approach offers a more computationally feasible method for accurate spin-orbit coupling calculations.
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Affiliation(s)
- Jordan Ehrman
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Ernesto Martinez-Baez
- 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
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
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11
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Sun S, Ehrman J, Zhang T, Sun Q, Dyall KG, Li X. Scalar Breit interaction for molecular calculations. J Chem Phys 2023; 158:2888154. [PMID: 37139994 DOI: 10.1063/5.0144359] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2023] [Accepted: 04/24/2023] [Indexed: 05/05/2023] Open
Abstract
Variational treatment of the Dirac-Coulomb-Gaunt or Dirac-Coulomb-Breit two-electron interaction at the Dirac-Hartree-Fock level is the starting point of high-accuracy four-component calculations of atomic and molecular systems. In this work, we introduce, for the first time, the scalar Hamiltonians derived from the Dirac-Coulomb-Gaunt and Dirac-Coulomb-Breit operators based on spin separation in the Pauli quaternion basis. While the widely used spin-free Dirac-Coulomb Hamiltonian includes only the direct Coulomb and exchange terms that resemble nonrelativistic two-electron interactions, the scalar Gaunt operator adds a scalar spin-spin term. The spin separation of the gauge operator gives rise to an additional scalar orbit-orbit interaction in the scalar Breit Hamiltonian. Benchmark calculations of Aun (n = 2-8) show that the scalar Dirac-Coulomb-Breit Hamiltonian can capture 99.99% of the total energy with only 10% of the computational cost when real-valued arithmetic is used, compared to the full Dirac-Coulomb-Breit Hamiltonian. The scalar relativistic formulation developed in this work lays the theoretical foundation for the development of high-accuracy, low-cost correlated variational relativistic many-body theory.
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Affiliation(s)
- Shichao Sun
- Department of Chemistry, University of Washington, Seattle, Washington 98195, USA
| | - Jordan Ehrman
- Department of Chemistry, University of Washington, Seattle, Washington 98195, USA
| | - Tianyuan Zhang
- Department of Chemistry, University of Washington, Seattle, Washington 98195, USA
| | - Qiming Sun
- AxiomQuant Investment Management LLC, Shanghai 200120, China
| | | | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, USA
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12
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Liao C, Kasper JM, Jenkins AJ, Yang P, Batista ER, Frisch MJ, Li X. State Interaction Linear Response Time-Dependent Density Functional Theory with Perturbative Spin-Orbit Coupling: Benchmark and Perspectives. JACS AU 2023; 3:358-367. [PMID: 36873704 PMCID: PMC9975852 DOI: 10.1021/jacsau.2c00659] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/04/2022] [Revised: 01/17/2023] [Accepted: 01/18/2023] [Indexed: 06/18/2023]
Abstract
Spin-orbit coupling (SOC) is an important driving force in photochemistry. In this work, we develop a perturbative spin-orbit coupling method within the linear response time-dependent density function theory framework (TDDFT-SO). A full state interaction scheme, including singlet-triplet and triplet-triplet coupling, is introduced to describe not only the coupling between the ground and excited states, but also between excited states with all couplings between spin microstates. In addition, expressions to compute spectral oscillator strengths are presented. Scalar relativity is included variationally using the second-order Douglas-Kroll-Hess Hamiltonian, and the TDDFT-SO method is validated against variational SOC relativistic methods for atomic, diatomic, and transition metal complexes to determine the range of applicability and potential limitations. To demonstrate the robustness of TDDFT-SO for large-scale chemical systems, the UV-Vis spectrum of Au25(SR)18 - is computed and compared to experiment. Perspectives on the limitation, accuracy, and capability of perturbative TDDFT-SO are presented via analyses of benchmark calculations. Additionally, an open-source Python software package (PyTDDFT-SO) is developed and released to interface with the Gaussian 16 quantum chemistry software package to perform this calculation.
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Affiliation(s)
- Can Liao
- Department
of Chemistry, University of Washington, Seattle, Washington98195, United States
| | - Joseph M. Kasper
- Theoretical
Division, Los Alamos National Laboratory, Los Alamos, New Mexico87545, United States
| | - Andrew J. Jenkins
- Department
of Chemistry, University of Washington, Seattle, Washington98195, United States
| | - Ping Yang
- Theoretical
Division, Los Alamos National Laboratory, Los Alamos, New Mexico87545, United States
| | - Enrique R. Batista
- Theoretical
Division, Los Alamos National Laboratory, Los Alamos, New Mexico87545, United States
| | - Michael J. Frisch
- Gaussian
Inc., 340 Quinnipiac Street, Bldg 40, Wallingford, Connecticut06492, United States
| | - Xiaosong Li
- Department
of Chemistry, University of Washington, Seattle, Washington98195, United States
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13
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Hoyer CE, Lu L, Hu H, Shumilov KD, Sun S, Knecht S, Li X. Correlated Dirac-Coulomb-Breit multiconfigurational self-consistent-field methods. J Chem Phys 2023; 158:044101. [PMID: 36725503 DOI: 10.1063/5.0133741] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
Abstract
The fully correlated frequency-independent Dirac-Coulomb-Breit Hamiltonian provides the most accurate description of electron-electron interaction before going to a genuine relativistic quantum electrodynamics theory of many-electron systems. In this work, we introduce a correlated Dirac-Coulomb-Breit multiconfigurational self-consistent-field method within the frameworks of complete active space and density matrix renormalization group. In this approach, the Dirac-Coulomb-Breit Hamiltonian is included variationally in both the mean-field and correlated electron treatment. We also analyze the importance of the Breit operator in electron correlation and the rotation between the positive- and negative-orbital space in the no-virtual-pair approximation. Atomic fine-structure splittings and lanthanide contraction in diatomic fluorides are used as benchmark studies to understand the contribution from the Breit correlation.
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Affiliation(s)
- Chad E Hoyer
- Department of Chemistry, University of Washington, Seattle, Washington 98195, USA
| | - Lixin Lu
- Department of Chemistry, University of Washington, Seattle, Washington 98195, USA
| | - Hang Hu
- Department of Chemistry, University of Washington, Seattle, Washington 98195, USA
| | - Kirill D Shumilov
- Department of Chemistry, University of Washington, Seattle, Washington 98195, USA
| | - Shichao Sun
- Department of Chemistry, University of Washington, Seattle, Washington 98195, USA
| | - Stefan Knecht
- Algorithmiq Ltd., Kanavakatu 3C, FI-00160 Helsinki, Finland
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, USA
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14
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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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15
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Sun S, Ehrman JN, Sun Q, Li X. Efficient Evaluation of the Breit Operator in the Pauli Spinor Basis. J Chem Phys 2022; 157:064112. [DOI: 10.1063/5.0098828] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The frequency-independent Coulomb-Breit operator gives rise to the most accurate treatment of two-electron interaction in the non-quantum-electrodynamics regime. The Breit interaction in the Coulomb gauge consists of magnetic and gauge contributions. The high computational cost of the gauge term limits the application of the Breit interaction in relativistic molecular calculations. In this work, we apply the Pauli component integral-density matrix contraction scheme for gauge interaction with a maximum spin- and component separation scheme. We also present two different computational algorithms for evaluating gauge integrals. One is the generalized Obara-Saika algorithm, where the Laplace transformation is used to transform the gauge operator into Gaussian functions and the Obara-Saika recursion is used for reducing the angular momentum. The other algorithm is the second derivative of inverse Coulomb interaction evaluated with Rys-quadrature. This work improves the efficiency of performing Dirac-Hartree-Fock with variational treatment of Breit interaction for molecular systems. We use this formalism to examine relativistic trends in the periodic table, and analyze the relativistic two-electron interaction contributions in heavy-element complexes.
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Affiliation(s)
- Shichao Sun
- Chemistry, University of Washington, United States of America
| | | | - Qiming Sun
- Anxian Investment Management Co. Ltd, China
| | - Xiaosong Li
- Department of Chemistry, University of Washington, United States of America
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16
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Zhang C, Cheng L. Atomic Mean-Field Approach within Exact Two-Component Theory Based on the Dirac-Coulomb-Breit Hamiltonian. J Phys Chem A 2022; 126:4537-4553. [PMID: 35763592 DOI: 10.1021/acs.jpca.2c02181] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
An extension of the exact two-component theory with atomic mean-field integrals (the X2CAMF scheme) to the treatment of the Breit term together with efficient implementation using an atomic Dirac-Coulomb-Breit Hartree-Fock program is reported. The accuracy of the X2CAMF scheme for treating the contributions from the Breit term to the molecular properties is demonstrated using benchmark calculations of equilibrium bond lengths, harmonic frequencies, and dipole moments for molecules containing elements across the periodic table. Calculations of the properties for molecules containing period four elements aiming at high accuracy as well as for Th- and U-containing molecules are also presented and compared with experimental results to demonstrate the usefulness of the X2CAMF scheme in combination with accurate treatments of electron correlation by the coupled-cluster (CC) methods. The combination of CC methods and the X2CAMF scheme shows potential to extend the accuracy of CC calculations to heavy elements, e.g., to computational heavy-element thermochemistry.
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Affiliation(s)
- Chaoqun Zhang
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, United States
| | - Lan Cheng
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, United States
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17
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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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18
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Abstract
Intersystem crossing (ISC), a vital component of the electronic and nuclear transitions that compose photophysics, has been successfully simulated in light elements and transition metal complexes. Derived from the Z-dependent spin-orbit coupling (SOC), ISC is expected to be of greater importance in heavier elements, but few attempts have been made at the simulation of ISC in lanthanides or actinides. In this work, we explore several of the challenges that will need to be overcome in order to treat ISC in late-row elements, including the loss of spin as a good quantum number, the need to include SOC variationally via two- or four-component electronic structure, and the high density of states present in late-row complexes. Density functional theory (DFT) calculations are used to illustrate several of these effects, while a model Hamiltonian is used to illustrate the importance of momentum rescaling in surface hopping simulations of strongly coupled states.
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Affiliation(s)
- Andrew J S Valentine
- 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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19
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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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20
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Konecny L, Vicha J, Komorovsky S, Ruud K, Repisky M. Accurate X-ray Absorption Spectra near L- and M-Edges from Relativistic Four-Component Damped Response Time-Dependent Density Functional Theory. Inorg Chem 2022; 61:830-846. [PMID: 34958215 PMCID: PMC8767545 DOI: 10.1021/acs.inorgchem.1c02412] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/07/2021] [Indexed: 11/27/2022]
Abstract
The simulation of X-ray absorption spectra requires both scalar and spin-orbit (SO) relativistic effects to be taken into account, particularly near L- and M-edges where the SO splitting of core p and d orbitals dominates. Four-component Dirac-Coulomb Hamiltonian-based linear damped response time-dependent density functional theory (4c-DR-TDDFT) calculates spectra directly for a selected frequency region while including the relativistic effects variationally, making the method well suited for X-ray applications. In this work, we show that accurate X-ray absorption spectra near L2,3- and M4,5-edges of closed-shell transition metal and actinide compounds with different central atoms, ligands, and oxidation states can be obtained by means of 4c-DR-TDDFT. While the main absorption lines do not change noticeably with the basis set and geometry, the exchange-correlation functional has a strong influence with hybrid functionals performing the best. The energy shift compared to the experiment is shown to depend linearly on the amount of Hartee-Fock exchange with the optimal value being 60% for spectral regions above 1000 eV, providing relative errors below 0.2% and 2% for edge energies and SO splittings, respectively. Finally, the methodology calibrated in this work is used to reproduce the experimental L2,3-edge X-ray absorption spectra of [RuCl2(DMSO)2(Im)2] and [WCl4(PMePh2)2], and resolve the broad bands into separated lines, allowing an interpretation based on ligand field theory and double point groups. These results support 4c-DR-TDDFT as a reliable method for calculating and analyzing X-ray absorption spectra of chemically interesting systems, advance the accuracy of state-of-the art relativistic DFT approaches, and provide a reference for benchmarking more approximate techniques.
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Affiliation(s)
- Lukas Konecny
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, University of Tromsø − The Arctic University
of Norway, 9037 Tromsø, Norway
| | - Jan Vicha
- Centre
of Polymer Systems, Tomas Bata University, tř. Tomáše
Bati 5678, 760 01 Zlín, Czech Republic
| | - Stanislav Komorovsky
- Institute
of Inorganic Chemistry, Slovak Academy of
Sciences, Dúbravská cesta 9, SK-84536 Bratislava, Slovakia
| | - Kenneth Ruud
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, University of Tromsø − The Arctic University
of Norway, 9037 Tromsø, Norway
| | - Michal Repisky
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, University of Tromsø − The Arctic University
of Norway, 9037 Tromsø, Norway
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21
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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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