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Hollósy P, Jeszenszki P, Mátyus E. One-Particle Operator Representation over Two-Particle Basis Sets for Relativistic QED Computations. J Chem Theory Comput 2024; 20:5122-5132. [PMID: 38857902 DOI: 10.1021/acs.jctc.4c00270] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/12/2024]
Abstract
This work is concerned with two-spin-1/2-fermion relativistic quantum mechanics, and it is about the construction of one-particle projectors using an inherently two-particle, "explicitly correlated" basis representation necessary for good numerical convergence of the interaction energy. It is demonstrated that a faithful representation of the one-particle operators, which appear in intermediate but essential computational steps, can be constructed over a many-particle basis set by accounting for the full Hilbert space beyond the physically relevant antisymmetric subspace. Applications of this development can be foreseen for the computation of quantum-electrodynamics corrections for a correlated relativistic reference state and high-precision relativistic computations of medium-to-high-Z helium-like systems, for which other two-particle projection techniques are unreliable.
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Affiliation(s)
- Péter Hollósy
- Institute of Chemistry, ELTE, Eötvös Loránd University, Pázmány Péter Sétány 1/A, Budapest H-1117, Hungary
| | - Péter Jeszenszki
- Institute of Chemistry, ELTE, Eötvös Loránd University, Pázmány Péter Sétány 1/A, Budapest H-1117, Hungary
| | - Edit Mátyus
- Institute of Chemistry, ELTE, Eötvös Loránd University, Pázmány Péter Sétány 1/A, Budapest H-1117, Hungary
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2
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Mátyus E, Ferenc D, Jeszenszki P, Margócsy Á. The Bethe-Salpeter QED Wave Equation for Bound-State Computations of Atoms and Molecules. ACS PHYSICAL CHEMISTRY AU 2023; 3:222-240. [PMID: 37249939 PMCID: PMC10214514 DOI: 10.1021/acsphyschemau.2c00062] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/04/2022] [Revised: 01/07/2023] [Accepted: 01/09/2023] [Indexed: 05/31/2023]
Abstract
Interactions in atomic and molecular systems are dominated by electromagnetic forces and the theoretical framework must be in the quantum regime. The physical theory for the combination of quantum mechanics and electromagnetism, quantum electrodynamics has been "established" by the mid-twentieth century, primarily as a scattering theory. To describe atoms and molecules, it is important to consider bound states. In the nonrelativistic quantum mechanics framework, bound states can be efficiently computed using robust and general methodologies with systematic approximations developed for solving wave equations. With the sight of the development of a computational quantum electrodynamics framework for atomic and molecular matter, the field theoretic Bethe-Salpeter wave equation expressed in space-time coordinates, its exact equal-time variant, and emergence of a relativistic wave equation, is reviewed. A computational framework, with initial applications and future challenges in relation with precision spectroscopy, is also highlighted.
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3
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Relativistic coupled-cluster study of SrF for low-energy precision tests of fundamental physics. Theor Chem Acc 2023. [DOI: 10.1007/s00214-023-02953-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023]
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4
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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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5
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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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6
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Cruz JC, Garza J, Yanai T, Hirata S. Stochastic evaluation of four-component relativistic second-order many-body perturbation energies: A potentially quadratic-scaling correlation method. J Chem Phys 2022; 156:224102. [DOI: 10.1063/5.0091973] [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
A second-order many-body perturbation correction to the relativistic Dirac-Hartree-Fock energy is evaluated stochastically by integrating 13-dimensional products of four-component spinors and Coulomb potentials. The integration in the real space of electron coordinates is carried out by the Monte Carlo (MC) method with the Metropolis sampling, whereas the MC integration in the imaginary-time domain is performed by the inverse-CDF (cumulative distribution function) method. The computational cost to reach a given relative statistical error for spatially compact but heavy molecules is observed to be no worse than cubic and possibly quadratic with the number of electrons or basis functions. This is a vast improvement over the quintic scaling of the conventional, deterministic second-order many-body perturbation method. The algorithm is also easily and efficiently parallelized with demonstrated 92% strong scalability going from 64 to 4096 processors for a fixed job size.
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Affiliation(s)
- J. César Cruz
- Universidad Autónoma Metropolitana-Iztapalapa, Mexico
| | - Jorge Garza
- Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, Mexico
| | - Takeshi Yanai
- Institute of Transformative Bio-Molecules, Nagoya University, Japan
| | - So Hirata
- Department of Chemistry, University of Illinois at Urbana-Champaign, United States of America
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7
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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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8
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Lu L, Hu H, Jenkins AJ, Li X. Exact-Two-Component Relativistic Multireference Second-Order Perturbation Theory. J Chem Theory Comput 2022; 18:2983-2992. [PMID: 35481362 DOI: 10.1021/acs.jctc.2c00171] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
As the relativistic corrections become stronger for late-row elements, the fully perturbative treatment of spin-orbit coupling and dynamic correlation may become inadequate for accurate descriptions of chemical properties. In this work, we introduce a determinant-based Kramers-unrestricted exact-two-component multireference second-order perturbation (X2C-MRPT2) method which variationally includes relativistic corrections with a perturbative dynamic correlation. The restricted active space partitioning scheme is employed to provide an adjustable correlation space for the second-order perturbation treatment. The multistate perturbation theory is also developed to improve the descriptions of ground and excited states. Benchmark studies of atomic fine-structure splittings and spectroscopic constants of molecular monohydrides using X2C-MRPT2 are compared to the other perturbative and variational approaches. The results suggest that X2C-MRPT2 is a highly accurate alternative to the fully variational multireference configuration interaction method at only a small fraction of the computational cost.
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Affiliation(s)
- Lixin Lu
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Hang Hu
- 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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9
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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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10
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Zhang N, Xiao Y, Liu W. SOiCI and iCISO: combining iterative configuration interaction with spin-orbit coupling in two ways. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:224007. [PMID: 35287124 DOI: 10.1088/1361-648x/ac5db4] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2022] [Accepted: 03/14/2022] [Indexed: 06/14/2023]
Abstract
The near-exact iCIPT2 approach for strongly correlated systems of electrons, which stems from the combination of iterative configuration interaction (iCI, an exact solver of full CI) with configuration selection for static correlation and second-order perturbation theory (PT2) for dynamic correlation, is extended to the relativistic domain. In the spirit of spin separation, relativistic effects are treated in two steps: scalar relativity is treated by the infinite-order, spin-free part of the exact two-component (X2C) relativistic Hamiltonian, whereas spin-orbit coupling (SOC) is treated by the first-order, Douglas-Kroll-Hess-like SOC operator derived from the same X2C Hamiltonian. Two possible combinations of iCIPT2 with SOC are considered, i.e., SOiCI and iCISO. The former treats SOC and electron correlation on an equal footing, whereas the latter treats SOC in the spirit of state interaction, by constructing and diagonalizing an effective spin-orbit Hamiltonian matrix in a small number of correlated scalar states. Both double group and time reversal symmetries are incorporated to simplify the computation. Pilot applications reveal that SOiCI is very accurate for the spin-orbit splitting (SOS) of heavy atoms, whereas the computationally very cheap iCISO can safely be applied to the SOS of light atoms and even of systems containing heavy atoms when SOC is largely quenched by ligand fields.
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Affiliation(s)
- Ning Zhang
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, People's Republic of China
| | - Yunlong Xiao
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, People's Republic of China
| | - Wenjian Liu
- Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao, Shandong 266237, People's Republic of China
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11
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Ferenc D, Jeszenszki P, Mátyus E. On the Breit interaction in an explicitly correlated variational Dirac–Coulomb framework. J Chem Phys 2022; 156:084110. [DOI: 10.1063/5.0075097] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The Breit interaction is implemented in the no-pair variational Dirac–Coulomb (DC) framework using an explicitly correlated Gaussian basis reported in the previous paper [P. Jeszenszki, D. Ferenc, and E. Mátyus, J. Chem. Phys. 156, 084111 (2022)]. Both a perturbative and a fully variational inclusion of the Breit term are considered. The no-pair DC plus perturbative Breit and the no-pair DC–Breit energies are compared with perturbation theory results including the Breit–Pauli Hamiltonian and leading-order non-radiative quantum electrodynamics corrections for low Z values. Possible reasons for the observed deviations are discussed.
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Affiliation(s)
- Dávid Ferenc
- ELTE, Eötvös Loránd University, Institute of Chemistry, Pázmány Péter sétány 1/A, Budapest, H-1117, Hungary
| | - Péter Jeszenszki
- ELTE, Eötvös Loránd University, Institute of Chemistry, Pázmány Péter sétány 1/A, Budapest, H-1117, Hungary
| | - Edit Mátyus
- ELTE, Eötvös Loránd University, Institute of Chemistry, Pázmány Péter sétány 1/A, Budapest, H-1117, Hungary
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12
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Jeszenszki P, Ferenc D, Mátyus E. Variational Dirac–Coulomb explicitly correlated computations for atoms and molecules. J Chem Phys 2022; 156:084111. [DOI: 10.1063/5.0075096] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The Dirac–Coulomb equation with positive-energy projection is solved using explicitly correlated Gaussian functions. The algorithm and computational procedure aims for a parts-per-billion convergence of the energy to provide a starting point for further comparison and further developments in relation with high-resolution atomic and molecular spectroscopy. Besides a detailed discussion of the implementation of the fundamental spinor structure, permutation, and point-group symmetries, various options for the positive-energy projection procedure are presented. The no-pair Dirac–Coulomb energy converged to a parts-per-billion precision is compared with perturbative results for atomic and molecular systems with small nuclear charge numbers. Paper II [D. Ferenc, P. Jeszenszki, and E. Mátyus, J. Chem. Phys. 156, 084110 (2022).] describes the implementation of the Breit interaction in this framework.
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Affiliation(s)
- Péter Jeszenszki
- ELTE, Eötvös Loránd University, Institute of Chemistry, Pázmány Péter sétány 1/A, Budapest H-1117, Hungary
| | - Dávid Ferenc
- ELTE, Eötvös Loránd University, Institute of Chemistry, Pázmány Péter sétány 1/A, Budapest H-1117, Hungary
| | - Edit Mátyus
- ELTE, Eötvös Loránd University, Institute of Chemistry, Pázmány Péter sétány 1/A, Budapest H-1117, Hungary
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13
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Eskridge B, Krakauer H, Shi H, Zhang S. Ab initio calculations in atoms, molecules, and solids, treating spin-orbit coupling and electron interaction on an equal footing. J Chem Phys 2022; 156:014107. [PMID: 34998316 DOI: 10.1063/5.0075900] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
Abstract
We incorporate explicit, non-perturbative treatment of spin-orbit coupling into ab initio auxiliary-field quantum Monte Carlo (AFQMC) calculations. The approach allows a general computational framework for molecular and bulk systems in which material specificity, electron correlation, and spin-orbit coupling effects can be captured accurately and on an equal footing, with favorable computational scaling vs system size. We adopt relativistic effective-core potentials that have been obtained by fitting to fully relativistic data and that have demonstrated a high degree of reliability and transferability in molecular systems. This results in a two-component spin-coupled Hamiltonian, which is then treated by generalizing the ab initio AFQMC approach. We demonstrate the method by computing the electron affinity in Pb, the bond dissociation energy in Br2 and I2, and solid Bi.
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Affiliation(s)
- Brandon Eskridge
- Department of Physics, College of William and Mary, Williamsburg, Virginia 23187, USA
| | - Henry Krakauer
- Department of Physics, College of William and Mary, Williamsburg, Virginia 23187, USA
| | - Hao Shi
- Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, USA
| | - Shiwei Zhang
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA
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14
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Jenkins AJ, Hu H, Lu L, Frisch MJ, Li X. Two-Component Multireference Restricted Active Space Configuration Interaction for the Computation of L-Edge X-ray Absorption Spectra. J Chem Theory Comput 2021; 18:141-150. [PMID: 34908414 DOI: 10.1021/acs.jctc.1c00564] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
X-ray absorption spectroscopy is a powerful probe of local electronic and nuclear structures, providing insights into chemical processes. The theoretical prediction and interpretation of metal L-edge X-ray absorption spectra are complicated by both relativistic effects, including spin-orbit coupling and the multiconfigurational nature of the states involved. This work details an exact two-component multireference restricted active space (RAS) configuration interaction scheme that uses an exact two-component state-averaged complete active space self-consistent-field method, which includes the spin-orbit coupling in a variational manner, for the accurate description of the electronic structure before using a RAS configuration interaction method to describe the core excited states of the X-ray spectrum. Benchmark calculations are presented for a series of iron-containing complexes, with results showing key features of the spectrum being reproduced, including ligand-to-metal charge transfer and shake-up excitations.
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Affiliation(s)
- Andrew J Jenkins
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Hang Hu
- Molecular Engineering and Sciences Institute, University of Washington, Seattle, Washington 98195, United States
| | - Lixin Lu
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Michael J Frisch
- Gaussian Inc., 340 Quinnipiac Street, Building 40, Wallingford, Connecticut 06492, United States
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
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15
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Jeszenszki P, Ferenc D, Mátyus E. All-order explicitly correlated relativistic computations for atoms and molecules. J Chem Phys 2021; 154:224110. [PMID: 34241227 DOI: 10.1063/5.0051237] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A variational solution procedure is reported for the many-particle no-pair Dirac-Coulomb and Dirac-Coulomb-Breit Hamiltonians aiming at a parts-per-billion (ppb) convergence of the atomic and molecular energies, described within the fixed nuclei approximation. The procedure is tested for nuclear charge numbers from Z = 1 (hydrogen) to 28 (iron). Already for the lowest Z values, a significant difference is observed from leading-order Foldy-Woythusen perturbation theory, but the observed deviations are smaller than the estimated self-energy and vacuum polarization corrections.
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Affiliation(s)
- Péter Jeszenszki
- Institute of Chemistry, ELTE, Eötvös Loránd University, Pázmány Péter sétány 1/A, Budapest H-1117, Hungary
| | - Dávid Ferenc
- Institute of Chemistry, ELTE, Eötvös Loránd University, Pázmány Péter sétány 1/A, Budapest H-1117, Hungary
| | - Edit Mátyus
- Institute of Chemistry, ELTE, Eötvös Loránd University, Pázmány Péter sétány 1/A, Budapest H-1117, Hungary
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16
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Anderson RJ, Booth GH. Four-component full configuration interaction quantum Monte Carlo for relativistic correlated electron problems. J Chem Phys 2020; 153:184103. [DOI: 10.1063/5.0029863] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Robert J. Anderson
- Department of Physics, King’s College London, Strand, London WC2R 2LS, United Kingdom
| | - George H. Booth
- Department of Physics, King’s College London, Strand, London WC2R 2LS, United Kingdom
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17
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Talukdar K, Nayak MK, Vaval N, Pal S. Electronic structure parameter of nuclear magnetic quadrupole moment interaction in metal monofluorides. J Chem Phys 2020; 153:184306. [PMID: 33187446 DOI: 10.1063/5.0028669] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The electronic structure parameter (WM) of the nuclear magnetic quadrupole moment (MQM) interaction in numerous open-shell metal monofluorides (viz., MgF, CaF, SrF, BaF, RaF, and PbF) is computed in the fully relativistic coupled-cluster framework. The electron-correlation effects are found to be very important for the precise calculation of WM in the studied molecular systems. The molecular MQM interaction parameter scales nearly as Z2 in the alkaline earth metal monofluorides, where Z is the nuclear charge of metal. Our study identifies 223RaF as a good candidate for the experimental search of the nuclear MQM, which can help unravel the physics beyond the standard model in the hadron sector of matter.
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Affiliation(s)
- Kaushik Talukdar
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
| | - Malaya K Nayak
- Theoretical Chemistry Section, Bhabha Atomic Research Centre, Trombay, Mumbai 400085, India
| | - Nayana Vaval
- Electronic Structure Theory Group, Physical Chemistry Division, CSIR-National Chemical Laboratory, Pune 411008, India
| | - Sourav Pal
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
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18
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Charge Conjugation Symmetry in the Finite Basis Approximation of the Dirac Equation. Symmetry (Basel) 2020. [DOI: 10.3390/sym12071121] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023] Open
Abstract
Four-component relativistic atomic and molecular calculations are typically performed within the no-pair approximation where negative-energy solutions are discarded. These states are, however, needed in QED calculations, wherein, furthermore, charge conjugation symmetry, which connects electronic and positronic solutions, becomes an issue. In this work, we shall discuss the realization of charge conjugation symmetry of the Dirac equation in a central field within the finite basis approximation. Three schemes for basis set construction are considered: restricted, inverse, and dual kinetic balance. We find that charge conjugation symmetry can be realized within the restricted and inverse kinetic balance prescriptions, but only with a special form of basis functions that does not obey the right boundary conditions of the radial wavefunctions. The dual kinetic balance prescription is, on the other hand, compatible with charge conjugation symmetry without restricting the form of the radial basis functions. However, since charge conjugation relates solutions of opposite value of the quantum number κ , this requires the use of basis sets chosen according to total angular momentum j rather than orbital angular momentum ℓ. As a special case, we consider the free-particle Dirac equation, where opposite energy solutions are related by charge conjugation symmetry. We show that there is additional symmetry in that solutions of the same value of κ come in pairs of opposite energy.
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19
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Paquier J, Giner E, Toulouse J. Relativistic short-range exchange energy functionals beyond the local-density approximation. J Chem Phys 2020; 152:214106. [DOI: 10.1063/5.0004926] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Julien Paquier
- Laboratoire de Chimie Théorique (LCT), Sorbonne Université and CNRS, F-75005 Paris, France
| | - Emmanuel Giner
- Laboratoire de Chimie Théorique (LCT), Sorbonne Université and CNRS, F-75005 Paris, France
| | - Julien Toulouse
- Laboratoire de Chimie Théorique (LCT), Sorbonne Université and CNRS, F-75005 Paris, France
- Institut Universitaire de France, F-75005 Paris, France
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20
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Nakashima H, Nakatsuji H. Inverse Hamiltonian method assisted by the complex scaling technique for solving the Dirac-Coulomb equation: Helium isoelectronic atoms. Chem Phys Lett 2020. [DOI: 10.1016/j.cplett.2020.137447] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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21
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Saue T, Bast R, Gomes ASP, Jensen HJA, Visscher L, Aucar IA, Di Remigio R, Dyall KG, Eliav E, Fasshauer E, Fleig T, Halbert L, Hedegård ED, Helmich-Paris B, Iliaš M, Jacob CR, Knecht S, Laerdahl JK, Vidal ML, Nayak MK, Olejniczak M, Olsen JMH, Pernpointner M, Senjean B, Shee A, Sunaga A, van Stralen JNP. The DIRAC code for relativistic molecular calculations. J Chem Phys 2020; 152:204104. [PMID: 32486677 DOI: 10.1063/5.0004844] [Citation(s) in RCA: 103] [Impact Index Per Article: 25.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
DIRAC is a freely distributed general-purpose program system for one-, two-, and four-component relativistic molecular calculations at the level of Hartree-Fock, Kohn-Sham (including range-separated theory), multiconfigurational self-consistent-field, multireference configuration interaction, electron propagator, and various flavors of coupled cluster theory. At the self-consistent-field level, a highly original scheme, based on quaternion algebra, is implemented for the treatment of both spatial and time reversal symmetry. DIRAC features a very general module for the calculation of molecular properties that to a large extent may be defined by the user and further analyzed through a powerful visualization module. It allows for the inclusion of environmental effects through three different classes of increasingly sophisticated embedding approaches: the implicit solvation polarizable continuum model, the explicit polarizable embedding model, and the frozen density embedding model.
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Affiliation(s)
- Trond Saue
- Laboratoire de Chimie et Physique Quantique, UMR 5626 CNRS-Université Toulouse III-Paul Sabatier, 118 Route de Narbonne, F-31062 Toulouse, France
| | - Radovan Bast
- Department of Information Technology, UiT The Arctic University of Norway, N-9037 Tromsø, Norway
| | - André Severo Pereira Gomes
- Université de Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers, Atomes et Molécules, F-59000 Lille, France
| | - Hans Jørgen Aa Jensen
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, DK-5230 Odense M, Denmark
| | - Lucas Visscher
- Department of Chemistry and Pharmaceutical Sciences, Vrije Universiteit Amsterdam, NL-1081HV Amsterdam, The Netherlands
| | - Ignacio Agustín Aucar
- Instituto de Modelado e Innovación Tecnológica, CONICET, and Departamento de Física-Facultad de Ciencias Exactas y Naturales, UNNE, Avda. Libertad 5460, W3404AAS Corrientes, Argentina
| | - Roberto Di Remigio
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, N-9037 Tromsø, Norway
| | - Kenneth G Dyall
- Dirac Solutions, 10527 NW Lost Park Drive, Portland, Oregon 97229, USA
| | - Ephraim Eliav
- School of Chemistry, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel
| | - Elke Fasshauer
- Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, 8000 Aarhus, Denmark
| | - Timo Fleig
- Laboratoire de Chimie et Physique Quantique, UMR 5626 CNRS-Université Toulouse III-Paul Sabatier, 118 Route de Narbonne, F-31062 Toulouse, France
| | - Loïc Halbert
- Université de Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers, Atomes et Molécules, F-59000 Lille, France
| | - Erik Donovan Hedegård
- Division of Theoretical Chemistry, Lund University, Chemical Centre, P.O. Box 124, SE-221 00 Lund, Sweden
| | - Benjamin Helmich-Paris
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany
| | - Miroslav Iliaš
- Department of Chemistry, Faculty of Natural Sciences, Matej Bel University, Tajovského 40, 974 01 Banská Bystrica, Slovakia
| | - Christoph R Jacob
- Technische Universität Braunschweig, Institute of Physical and Theoretical Chemistry, Gaußstr. 17, 38106 Braunschweig, Germany
| | - Stefan Knecht
- ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Jon K Laerdahl
- Department of Microbiology, Oslo University Hospital, Oslo, Norway
| | - Marta L Vidal
- Department of Chemistry, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark
| | - Malaya K Nayak
- Theoretical Chemistry Section, Bhabha Atomic Research Centre, Trombay, Mumbai 400085, India
| | - Małgorzata Olejniczak
- Centre of New Technologies, University of Warsaw, S. Banacha 2c, 02-097 Warsaw, Poland
| | - Jógvan Magnus Haugaard Olsen
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, N-9037 Tromsø, Norway
| | | | - Bruno Senjean
- Department of Chemistry and Pharmaceutical Sciences, Vrije Universiteit Amsterdam, NL-1081HV Amsterdam, The Netherlands
| | - Avijit Shee
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Ayaki Sunaga
- Department of Chemistry, Tokyo Metropolitan University, 1-1 Minami-Osawa, Hachioji-city, Tokyo 192-0397, Japan
| | - Joost N P van Stralen
- Department of Chemistry and Pharmaceutical Sciences, Vrije Universiteit Amsterdam, NL-1081HV Amsterdam, The Netherlands
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22
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Affiliation(s)
- Wenjian Liu
- Qingdao Institute for Theoretical and Computational Sciences, Shandong University, Qingdao, Shandong 266237, People’s Republic of China
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23
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Hu H, Jenkins AJ, Liu H, Kasper JM, Frisch MJ, Li X. Relativistic Two-Component Multireference Configuration Interaction Method with Tunable Correlation Space. J Chem Theory Comput 2020; 16:2975-2984. [DOI: 10.1021/acs.jctc.9b01290] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Hang Hu
- Molecular Engineering and Sciences Institute, University of Washington, Seattle, Washington 98195, United States
| | - Andrew J. Jenkins
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Hongbin Liu
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Joseph M. Kasper
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Michael J. Frisch
- Gaussian Inc., 340 Quinnipiac Street, Building 40, Wallingford, Connecticut 06492, United States
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
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24
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Pašteka LF, Helgaker T, Saue T, Sundholm D, Werner HJ, Hasanbulli M, Major J, Schwerdtfeger P. Atoms and molecules in soft confinement potentials. Mol Phys 2020. [DOI: 10.1080/00268976.2020.1730989] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- L. F. Pašteka
- Centre for Advanced Study (CAS) at the Norwegian Academy of Science and Letters, Oslo, Norway
- Department of Physical and Theoretical Chemistry & Laboratory for Advanced Materials, Faculty of Natural Sciences, Comenius University, Bratislava, Slovakia
| | - T. Helgaker
- Centre for Advanced Study (CAS) at the Norwegian Academy of Science and Letters, Oslo, Norway
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, Oslo, Norway
| | - T. Saue
- Centre for Advanced Study (CAS) at the Norwegian Academy of Science and Letters, Oslo, Norway
- Laboratoire de Chimie et Physique Quantiques, UMR 5626 CNRS – Universitè Toulouse III (Paul Sabatier), Toulouse Cedex 09, France
| | - D. Sundholm
- Centre for Advanced Study (CAS) at the Norwegian Academy of Science and Letters, Oslo, Norway
- Department of Chemistry, University of Helsinki, Helsinki, Finland
| | - H.-J. Werner
- Centre for Advanced Study (CAS) at the Norwegian Academy of Science and Letters, Oslo, Norway
- Institute for Theoretical Chemistry, University of Stuttgart, Stuttgart, Germany
| | - M. Hasanbulli
- Centre for Theoretical Chemistry and Physics, The New Zealand Institute for Advanced Study, Massey University Auckland, Auckland, New Zealand
| | - J. Major
- Centre for Theoretical Chemistry and Physics, The New Zealand Institute for Advanced Study, Massey University Auckland, Auckland, New Zealand
| | - P. Schwerdtfeger
- Centre for Advanced Study (CAS) at the Norwegian Academy of Science and Letters, Oslo, Norway
- Centre for Theoretical Chemistry and Physics, The New Zealand Institute for Advanced Study, Massey University Auckland, Auckland, New Zealand
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25
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Yamamoto S, Tatewaki H. The ground and first excited states of HoS studied by four-component relativistic KR-MCSCF and KRCI. Theor Chem Acc 2020. [DOI: 10.1007/s00214-020-2586-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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26
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Jenkins AJ, Liu H, Kasper JM, Frisch MJ, Li X. Variational Relativistic Two-Component Complete-Active-Space Self-Consistent Field Method. J Chem Theory Comput 2019; 15:2974-2982. [DOI: 10.1021/acs.jctc.9b00011] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Andrew J. Jenkins
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Hongbin Liu
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Joseph M. Kasper
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Michael J. Frisch
- Gaussian Inc., 340 Quinnipiac Street, Building 40, Wallingford, Connecticut 06492, United States
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
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27
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Talukdar K, Nayak MK, Vaval N, Pal S. Relativistic coupled-cluster investigation of parity (P) and time-reversal (T ) symmetry violations in HgF. J Chem Phys 2019; 150:084304. [PMID: 30823771 DOI: 10.1063/1.5083000] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We employ the Z-vector method in the four-component relativistic coupled-cluster framework to calculate the parity (P) and time-reversal (T ) symmetry violating scalar-pseudoscalar nucleus-electron interaction constant (Ws), the effective electric field (Eeff) experienced by the unpaired electron, and the nuclear magnetic quadrupole moment-electron interaction constant (WM) in the open-shell ground electronic state of HgF. The molecular frame dipole moment and the magnetic hyperfine structure (HFS) constant of the molecule are also calculated at the same level of theory. The outcome of our study is that HgF has a high value of Eeff (115.9 GV/cm), Ws (266.4 kHz), and WM (3.59 × 1033 Hz/e cm2), which shows that it can be a possible candidate for the search of new physics beyond the standard model. Our results are in good agreement with the available literature values. Furthermore, we investigate the effect of the basis set and the virtual energy functions on the computed properties. The role of the high-energy virtual spinors is found to be significant in the calculation of the HFS constant and the P,T-odd interaction coefficients.
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Affiliation(s)
- Kaushik Talukdar
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
| | - Malaya K Nayak
- Theoretical Chemistry Section, Bhabha Atomic Research Centre, Trombay, Mumbai 400085, India
| | - Nayana Vaval
- Electronic Structure Theory Group, Physical Chemistry Division, CSIR-National Chemical Laboratory, Pune 411008, India
| | - Sourav Pal
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
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28
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Paquier J, Toulouse J. Four-component relativistic range-separated density-functional theory: Short-range exchange local-density approximation. J Chem Phys 2018; 149:174110. [DOI: 10.1063/1.5049773] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
Affiliation(s)
- Julien Paquier
- Laboratoire de Chimie Théorique (LCT), Sorbonne Université and CNRS, F-75005 Paris, France
| | - Julien Toulouse
- Laboratoire de Chimie Théorique (LCT), Sorbonne Université and CNRS, F-75005 Paris, France
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29
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Mussard B, Sharma S. One-Step Treatment of Spin–Orbit Coupling and Electron Correlation in Large Active Spaces. J Chem Theory Comput 2017; 14:154-165. [DOI: 10.1021/acs.jctc.7b01019] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Bastien Mussard
- Department of Chemistry and
Biochemistry, University of Colorado Boulder, Boulder, Colorado 80302, United States
| | - Sandeep Sharma
- Department of Chemistry and
Biochemistry, University of Colorado Boulder, Boulder, Colorado 80302, United States
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30
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Lipparini F, Kirsch T, Köhn A, Gauss J. Internally Contracted Multireference Coupled Cluster Calculations with a Spin-Free Dirac–Coulomb Hamiltonian: Application to the Monoxides of Titanium, Zirconium, and Hafnium. J Chem Theory Comput 2017; 13:3171-3184. [DOI: 10.1021/acs.jctc.7b00110] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Filippo Lipparini
- Institut
für Physikalische Chemie, Universität Mainz, Duesbergweg 10-14, D-55128 Mainz, Germany
| | - Till Kirsch
- Institut
für Physikalische Chemie, Universität Mainz, Duesbergweg 10-14, D-55128 Mainz, Germany
| | - Andreas Köhn
- Institut
für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring
55, D-70569 Stuttgart, Germany
| | - Jürgen Gauss
- Institut
für Physikalische Chemie, Universität Mainz, Duesbergweg 10-14, D-55128 Mainz, Germany
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31
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Sasmal S, Talukdar K, Nayak MK, Vaval N, Pal S. Electron–nucleus scalar–pseudoscalar interaction in PbF: Z-vector study in the relativistic coupled-cluster framework. Mol Phys 2017. [DOI: 10.1080/00268976.2017.1332396] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Sudip Sasmal
- Electronic Structure Theory Group, Physical Chemistry Division, CSIR-National Chemical Laboratory, Pune, India
| | - Kaushik Talukdar
- Department of Chemistry, Indian Institute of Technology Bombay, Mumbai, India
| | - Malaya K. Nayak
- Theoretical Chemistry Section, Bhabha Atomic Research Centre, Mumbai, India
| | - Nayana Vaval
- Electronic Structure Theory Group, Physical Chemistry Division, CSIR-National Chemical Laboratory, Pune, India
| | - Sourav Pal
- Department of Chemistry, Indian Institute of Technology Bombay, Mumbai, India
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32
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Shee A, Visscher L, Saue T. Analytic one-electron properties at the 4-component relativistic coupled cluster level with inclusion of spin-orbit coupling. J Chem Phys 2016; 145:184107. [DOI: 10.1063/1.4966643] [Citation(s) in RCA: 42] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Affiliation(s)
- Avijit Shee
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), CNRS/Université Toulouse III - Paul Sabatier, 118 Route de Narbonne, F-31062 Toulouse Cedex, France
| | - Lucas Visscher
- Department of Theoretical Chemistry, Faculty of Sciences, Vrije Universiteit Amsterdam, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands
| | - Trond Saue
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), CNRS/Université Toulouse III - Paul Sabatier, 118 Route de Narbonne, F-31062 Toulouse Cedex, France
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