1
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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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2
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Harsha G, Abraham V, Zgid D. Challenges with relativistic GW calculations in solids and molecules. Faraday Discuss 2024. [PMID: 39101408 DOI: 10.1039/d4fd00043a] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/06/2024]
Abstract
For molecules and solids containing heavy elements, accurate electronic-structure calculations require accounting not only for electronic correlations but also for relativistic effects. In molecules, relativity can lead to severe changes in the ground-state description. In solids, the interplay between both correlation and relativity can change the stability of phases or it can lead to an emergence of completely new phases. Traditionally, the simplest illustration of relativistic effects can be done either by including pseudopotentials in non-relativistic calculations or alternatively by employing large all-electron basis sets in relativistic methods. By analyzing different electronic properties (band structure, equilibrium lattice constant and bulk modulus) in semiconductors and insulators, we show that capturing the interplay of relativity and electron correlation can be rather challenging in Green's function methods. For molecular problems with heavy elements, we also observe that similar problems persist. We trace these challenges to three major problems: deficiencies in pseudopotential treatment as applied to Green's function methods, the scarcity of accurate and compact all-electron basis sets that can be converged with respect to the basis-set size, and linear dependencies arising in all-electron basis sets, particularly when employing Gaussian orbitals. Our analysis provides detailed insight into these problems and opens a discussion about potential approaches to mitigate them.
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Affiliation(s)
- Gaurav Harsha
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA.
| | - Vibin Abraham
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA.
| | - Dominika Zgid
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA.
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
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3
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Yuwono SH, Li RR, Zhang T, Surjuse KA, Valeev EF, Li X, Eugene DePrince A. Relativistic Coupled Cluster with Completely Renormalized and Perturbative Triples Corrections. J Phys Chem A 2024. [PMID: 39074123 DOI: 10.1021/acs.jpca.4c02583] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/31/2024]
Abstract
We have implemented noniterative triples corrections to the energy from coupled-cluster with single and double excitations (CCSD) within the 1-electron exact two-component (1eX2C) relativistic framework. The effectiveness of both the CCSD(T) and the completely renormalized (CR) CC(2,3) approaches are demonstrated by performing all-electron computations of the potential energy curves and spectroscopic constants of copper, silver, and gold dimers in their ground electronic states. Spin-orbit coupling effects captured via the 1eX2C framework are shown to be crucial for recovering the correct shape of the potential energy curves, and the correlation effects due to triples in these systems change the dissociation energies by about 0.1-0.2 eV or about 4-7%. We also demonstrate that relativistic effects and basis set size and contraction scheme are significantly more important in Au2 than in Ag2 or Cu2.
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Affiliation(s)
- Stephen H Yuwono
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, United States
| | - Run R Li
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, United States
| | - Tianyuan Zhang
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | | | - Edward F Valeev
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - A Eugene DePrince
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, United States
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4
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Chen T, Zhang C, Cheng L, Ng KB, Malbrunot-Ettenauer S, Flambaum VV, Lasner Z, Doyle JM, Yu P, Conn CJ, Zhang C, Hutzler NR, Jayich AM, Augenbraun B, DeMille D. Relativistic Exact Two-Component Coupled-Cluster Study of Molecular Sensitivity Factors for Nuclear Schiff Moments. J Phys Chem A 2024. [PMID: 39047199 DOI: 10.1021/acs.jpca.4c02640] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/27/2024]
Abstract
Relativistic exact two-component coupled-cluster calculations of molecular sensitivity factors for nuclear Schiff moments (NSMs) are reported. We focus on molecules containing heavy nuclei, especially octupole-deformed nuclei. Analytic relativistic coupled-cluster gradient techniques are used and serve as useful tools for identifying candidate molecules that sensitively probe for physics beyond the Standard Model in the hadronic sector. Notably, these tools enable straightforward "black-box" calculations. Two competing chemical mechanisms that contribute to the NSM are analyzed, illuminating the physics of ligand effects on NSM sensitivity factors.
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Affiliation(s)
- Tianxiang Chen
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, United States
| | - 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
| | - Kia Boon Ng
- TRIUMF, 4004 Wesbrook Mall, Vancouver, BC V6T 2A3, Canada
| | - Stephan Malbrunot-Ettenauer
- TRIUMF, 4004 Wesbrook Mall, Vancouver, BC V6T 2A3, Canada
- Department of Physics, University of Toronto, Toronto M5S 1A7, Canada
| | - Victor V Flambaum
- School of Physics, University of New South Wales, Sydney 2052, Australia
| | - Zack Lasner
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, United States
- Harvard-MIT Center for Ultracold Atoms, Cambridge, Massachusetts 02138, United States
| | - John M Doyle
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, United States
- Harvard-MIT Center for Ultracold Atoms, Cambridge, Massachusetts 02138, United States
| | - Phelan Yu
- Division of Physics, Mathematics, and Astronomy, California Institute of Technology, Pasadena, California 91125, United States
| | - Chandler J Conn
- Division of Physics, Mathematics, and Astronomy, California Institute of Technology, Pasadena, California 91125, United States
| | - Chi Zhang
- Division of Physics, Mathematics, and Astronomy, California Institute of Technology, Pasadena, California 91125, United States
| | - Nicholas R Hutzler
- Division of Physics, Mathematics, and Astronomy, California Institute of Technology, Pasadena, California 91125, United States
| | - Andrew M Jayich
- Department of Physics, University of California, Santa Barbara, California 93106, United States
| | - Benjamin Augenbraun
- Department of Chemistry, Williams College, 47 Lab Campus Drive, Williamstown, Massachusetts 01267, United States
| | - David DeMille
- Department of Physics, University of Chicago, Chicago, Illinois 60637, United States
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5
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Abraham V, Harsha G, Zgid D. Relativistic Fully Self-Consistent GW for Molecules: Total Energies and Ionization Potentials. J Chem Theory Comput 2024; 20:4579-4590. [PMID: 38778459 DOI: 10.1021/acs.jctc.4c00075] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/25/2024]
Abstract
The fully self-consistent GW (scGW) method with an iterative solution of the Dyson equation provides a consistent approach for describing the ground and excited states without any dependence on the mean-field reference. In this work, we present a relativistic version of scGW for molecules containing heavy elements using the exact two-component (X2C) Coulomb approximation. We benchmark SOC-81 data set containing closed shell heavy elements for the first ionization potential using the fully self-consistent GW as well as one-shot GW. The self-consistent GW provides superior results compared to G0W0 with PBE reference and comparable results to G0W0 with PBE0 while also removing the starting point dependence. The photoelectron spectra obtained at the X2C level demonstrate very good agreement with the experimental spectra. We also observe that scGW provides very good estimation of ionization potential for the inner d-shell orbitals. Additionally, using the well-conserved total energy, we investigate the equilibrium bond length and harmonic frequencies of a few halogen dimers using scGW. Overall, our findings demonstrate the applicability of the fully self-consistent GW method for accurate ionization potential, photoelectron spectra, and total energies in finite systems with heavy elements with a reasonable computational scaling.
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Affiliation(s)
- Vibin Abraham
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Gaurav Harsha
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Dominika Zgid
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
- Department of Physics and Astronomy, University of Michigan, Ann Arbor, Michigan 48109, United States
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6
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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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7
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Zhang C, Lipparini F, Stopkowicz S, Gauss J, Cheng L. Cholesky Decomposition-Based Implementation of Relativistic Two-Component Coupled-Cluster Methods for Medium-Sized Molecules. J Chem Theory Comput 2024; 20:787-798. [PMID: 38198515 DOI: 10.1021/acs.jctc.3c01236] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2024]
Abstract
A Cholesky decomposition (CD)-based implementation of relativistic two-component coupled-cluster (CC) and equation-of-motion CC (EOM-CC) methods using an exact two-component Hamiltonian augmented with atomic-mean-field spin-orbit integrals (the X2CAMF scheme) is reported. The present CD-based implementation of X2CAMF-CC and EOM-CC methods employs atomic-orbital-based algorithms to avoid the construction of two-electron integrals and intermediates involving three and four virtual indices. Our CD-based implementation extends the applicability of X2CAMF-CC and EOM-CC methods to medium-sized molecules with the possibility to correlate around 1000 spinors. Benchmark calculations for uranium-containing small molecules were performed to assess the dependence of the CC results on the Cholesky threshold. A Cholesky threshold of 10-4 is shown to be sufficient to maintain chemical accuracy. Example calculations to illustrate the capability of the CD-based relativistic CC methods are reported for the bond-dissociation energy of the uranium hexafluoride molecule, UF6, with up to quadruple-ζ basis sets, and the lowest excitation energy in the solvated uranyl ion [UO22+(H2O)12].
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Affiliation(s)
- Chaoqun Zhang
- Department of Chemistry, the Johns Hopkins University, Baltimore, Maryland 21218, United States
| | - Filippo Lipparini
- Dipartimento di Chimica e Chimica Industriale, Università di Pisa, Via G. Moruzzi 13, Pisa I-56124, Italy
| | - Stella Stopkowicz
- Fachrichtung Chemie, Universität des Saarlandes, Saarbrücken D-66123, Germany
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033, Blindern, Oslo N-0315, Norway
| | - Jürgen Gauss
- Department Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, Mainz D-55128, Germany
| | - Lan Cheng
- Department of Chemistry, the Johns Hopkins University, Baltimore, Maryland 21218, United States
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8
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Zhang C, Zheng X, Liu J, Asthana A, Cheng L. Analytic gradients for relativistic exact-two-component equation-of-motion coupled-cluster singles and doubles method. J Chem Phys 2023; 159:244113. [PMID: 38153147 DOI: 10.1063/5.0175041] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2023] [Accepted: 11/20/2023] [Indexed: 12/29/2023] Open
Abstract
A first implementation of analytic gradients for spinor-based relativistic equation-of-motion coupled-cluster singles and doubles method using an exact two-component Hamiltonian augmented with atomic mean-field spin-orbit integrals is reported. To demonstrate its applicability, we present calculations of equilibrium structures and harmonic vibrational frequencies for the electronic ground and excited states of the radium mono-amide molecule (RaNH2) and the radium mono-methoxide molecule (RaOCH3). Spin-orbit coupling is shown to quench Jahn-Teller effects in the first excited state of RaOCH3, resulting in a C3v equilibrium structure. The calculations also show that the radium atoms in these molecules serve as efficient optical cycling centers.
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Affiliation(s)
- Chaoqun Zhang
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Xuechen Zheng
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Junzi Liu
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Ayush Asthana
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Lan Cheng
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
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9
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Zhang C, Yu P, Conn CJ, Hutzler NR, Cheng L. Relativistic coupled-cluster calculations of RaOH pertinent to spectroscopic detection and laser cooling. Phys Chem Chem Phys 2023; 25:32613-32621. [PMID: 38009218 DOI: 10.1039/d3cp04040b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2023]
Abstract
A relativistic coupled-cluster study of the low-lying electronic states in the radium monohydroxide molecule (RaOH), a radioactive polyatomic molecule of interest to laser cooling and to the search of new physics beyond the Standard Model, is reported. The level positions of the A2Π1/2 and C2Σ states have been computed with an accuracy of around 200 cm-1 to facilitate spectroscopic observation of RaOH using laser induced fluorescence spectroscopy, thereby exploiting the systematic convergence of electron-correlation and basis-set effects in relativistic coupled-cluster calculations. The energy level for the B2Δ3/2 state has also been calculated accurately to conclude that the B2Δ3/2 state lies above the A2Π1/2 state. This confirms X2Σ ↔ A2Π1/2 as a promising optical cycling transition for laser cooling RaOH.
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Affiliation(s)
- Chaoqun Zhang
- Department of Chemistry, The Johns Hopkins University, Baltimore, MD 21218, USA.
| | - Phelan Yu
- Division of Physics, Mathematics, and Astronomy, California Institute of Technology, Pasadena, CA 91125, USA.
| | - Chandler J Conn
- Division of Physics, Mathematics, and Astronomy, California Institute of Technology, Pasadena, CA 91125, USA.
| | - Nicholas R Hutzler
- Division of Physics, Mathematics, and Astronomy, California Institute of Technology, Pasadena, CA 91125, USA.
| | - Lan Cheng
- Department of Chemistry, The Johns Hopkins University, Baltimore, MD 21218, USA.
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10
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Zhang C, Hutzler NR, Cheng L. Intensity-Borrowing Mechanisms Pertinent to Laser Cooling of Linear Polyatomic Molecules. J Chem Theory Comput 2023. [PMID: 37384588 DOI: 10.1021/acs.jctc.3c00408] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/01/2023]
Abstract
A study of the intensity-borrowing mechanisms important to optical cycling transitions in laser-coolable polyatomic molecules arising from non-adiabatic coupling, contributions beyond the Franck-Condon approximation, and Fermi resonances is reported. It has been shown to be necessary to include non-adiabatic coupling to obtain computational accuracy that is sufficient to be useful for laser cooling of molecules. The predicted vibronic branching ratios using perturbation theory based on the non-adiabatic mechanisms have been demonstrated to agree well with those obtained from variational discrete variable representation calculations for representative molecules including CaOH, SrOH, and YbOH. The electron-correlation and basis-set effects on the calculated transition properties, including the vibronic coupling constants, the spin-orbit coupling matrix elements, and the transition dipole moments, and on the calculated branching ratios have been thoroughly studied. The vibronic branching ratios predicted using the present methodologies demonstrate that RaOH is a promising radioactive molecule candidate for laser cooling.
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Affiliation(s)
- Chaoqun Zhang
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, United States
| | - Nicholas R Hutzler
- Division of Physics, Mathematics, and Astronomy, California Institute of Technology, Pasadena, California 91125, United States
| | - Lan Cheng
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, United States
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11
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Liu W. Perspective: Simultaneous treatment of relativity, correlation, and
QED. WIRES COMPUTATIONAL MOLECULAR SCIENCE 2022. [DOI: 10.1002/wcms.1652] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Affiliation(s)
- Wenjian Liu
- Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science Shandong University Qingdao Shandong China
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12
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Zhang C, Cheng L. Route to Chemical Accuracy for Computational Uranium Thermochemistry. J Chem Theory Comput 2022; 18:6732-6741. [PMID: 36206308 DOI: 10.1021/acs.jctc.2c00812] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Benchmark spinor-based relativistic coupled-cluster calculations for the ionization energies of the uranium atom, the uranium monoxide molecule (UO), and the uranium dioxide molecule (UO2) and for the bond dissociation energies of UO and UO2 are reported. The accuracy of these calculations in the treatments of relativistic, electron-correlation, and basis-set effects is analyzed. The intrinsic convergence of the computed results and the favorable comparison with the experimental values demonstrate the unique applicability of the spinor representation of quantum-chemical methods to open-shell uranium-containing atomic and molecular species with uranium oxidation states ranging from U(0) to U(V).
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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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13
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Cheng L. Relativistic exact two-component coupled-cluster calculations of electronic g-factors for heavy-atom-containing molecules pertinent to search of new physics. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2113567] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/15/2022]
Affiliation(s)
- Lan Cheng
- Department of Chemistry, The Johns Hopkins University, Baltimore, MD, USA
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14
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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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15
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Yuan X, Visscher L, Gomes ASP. Assessing MP2 frozen natural orbitals in relativistic correlated electronic structure calculations. J Chem Phys 2022; 156:224108. [PMID: 35705406 DOI: 10.1063/5.0087243] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023] Open
Abstract
The high computational scaling with the basis set size and the number of correlated electrons is a bottleneck limiting applications of coupled cluster algorithms, in particular for calculations based on two- or four-component relativistic Hamiltonians, which often employ uncontracted basis sets. This problem may be alleviated by replacing canonical Hartree-Fock virtual orbitals by natural orbitals (NOs). In this paper, we describe the implementation of a module for generating NOs for correlated wavefunctions and, in particular, second order Møller-Plesset perturbation frozen natural orbitals (MP2FNOs) as a component of our novel implementation of relativistic coupled cluster theory for massively parallel architectures [Pototschnig et al. J. Chem. Theory Comput. 17, 5509, (2021)]. Our implementation can manipulate complex or quaternion density matrices, thus allowing for the generation of both Kramers-restricted and Kramers-unrestricted MP2FNOs. Furthermore, NOs are re-expressed in the parent atomic orbital (AO) basis, allowing for generating coupled cluster singles and doubles NOs in the AO basis for further analysis. By investigating the truncation errors of MP2FNOs for both the correlation energy and molecular properties-electric field gradients at the nuclei, electric dipole and quadrupole moments for hydrogen halides HX (X = F-Ts), and parity-violating energy differences for H2Z2 (Z = O-Se)-we find MP2FNOs accelerate the convergence of the correlation energy in a roughly uniform manner across the Periodic Table. It is possible to obtain reliable estimates for both energies and the molecular properties considered with virtual molecular orbital spaces truncated to about half the size of the full spaces.
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Affiliation(s)
- Xiang Yuan
- Univ. Lille, CNRS, UMR 8523 - PhLAM - Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | - Lucas Visscher
- Department of Chemistry and Pharmaceutical Sciences, Faculty of Science, Vrije Universiteit Amsterdam, de Boelelaan 1083, 1081 HV Amsterdam, The Netherlands
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16
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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: 9] [Impact Index Per Article: 4.5] [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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17
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Zheng X, Zhang C, Liu J, Cheng L. Geometry Optimizations with Spinor-Based Relativistic Coupled-Cluster Theory. J Chem Phys 2022; 156:151101. [DOI: 10.1063/5.0086281] [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
Development of analytic gradients for relativistic coupled-cluster singles and doubles augmented with a non-iterative triples [CCSD(T)] method using an all-electron exact two-component Hamiltonian with atomic mean-field spin-orbit integrals (X2CAMF) is reported. This enables efficient CC geometry optimizations with spin-orbit coupling included in orbitals. The applicability of the implementation is demonstrated using benchmark X2CAMF-CCSD(T) calculations of equilibrium structures and harmonic vibrational frequencies for methyl halides, CH3X, X=Br, I, At, as well as calculations of rotational constants and infrared spectrum for RaSH+, a radioactive molecular ion of interest to spectroscopic study.
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Affiliation(s)
- Xuechen Zheng
- Johns Hopkins University Department of Chemistry, United States of America
| | - Chaoqun Zhang
- Johns Hopkins University Department of Chemistry, United States of America
| | - Junzi Liu
- Chemistry, Johns Hopkins University Department of Chemistry, United States of America
| | - Lan Cheng
- Chemistry, Johns Hopkins University Department of Chemistry, United States of America
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18
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Liu J, Matthews DA, Cheng L. Quadratic Unitary Coupled-Cluster Singles and Doubles Scheme: Efficient Implementation, Benchmark Study, and Formulation of an Extended Version. J Chem Theory Comput 2022; 18:2281-2291. [PMID: 35312299 DOI: 10.1021/acs.jctc.1c01210] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
An efficient implementation of the quadratic unitary coupled-cluster singles and doubles (qUCCSD) scheme for calculations of electronic ground and excited states using an unrestricted molecular spin-orbital formulation and an efficient tensor contraction library is reported. The accuracy of the qUCCSD scheme and the efficiency of the present implementation are demonstrated using extensive benchmark calculations of excitation energies and an application to S0 → S1 vertical excitation energies for cis- and trans-4a,4b-dihydrotriphenylene. The qUCCSD scheme has been shown to provide improved excitation energies compared with the UCC3 scheme formulated based on perturbation theory. A UCC truncation scheme that can provide excitation energies correct through the fourth order is also presented to further improve the accuracy of the qUCCSD scheme.
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Affiliation(s)
- Junzi Liu
- School of Chemistry and Biological Engineering, University of Science and Technology Beijing, Beijing, 100083, China
| | - Devin A Matthews
- Department of Chemistry, Southern Methodist University, Dallas, Texas 75275, United States
| | - Lan Cheng
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, United States
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19
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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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20
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Guo M, Wang Z, Lu Y, Wang F. Energy correction and analytic energy gradients due to triples in CCSD(T) with spin–orbit coupling on graphic processing units using single-precision data. Mol Phys 2021. [DOI: 10.1080/00268976.2021.1974591] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Minggang Guo
- Institute of Atomic and Molecular Physics, Key Laboratory of High Energy Density Physics and Technology, Ministry of Education, Sichuan University, Chengdu, People’s Republic of China
| | - Zhifan Wang
- College of Chemistry and Life Science, Chengdu Normal University, Chengdu, People’s Republic of China
- School of Electronic Engineering, Chengdu Technological University, Chengdu, People’s Republic of China
| | - Yanzhao Lu
- Institute of Atomic and Molecular Physics, Key Laboratory of High Energy Density Physics and Technology, Ministry of Education, Sichuan University, Chengdu, People’s Republic of China
| | - Fan Wang
- Institute of Atomic and Molecular Physics, Key Laboratory of High Energy Density Physics and Technology, Ministry of Education, Sichuan University, Chengdu, People’s Republic of China
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21
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Liu J, Cheng L. Unitary coupled-cluster based self-consistent polarization propagator theory: A quadratic unitary coupled-cluster singles and doubles scheme. J Chem Phys 2021; 155:174102. [PMID: 34742195 DOI: 10.1063/5.0062090] [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
The development of a quadratic unitary coupled-cluster singles and doubles (qUCCSD) based self-consistent polarization propagator method is reported. We present a simple strategy for truncating the commutator expansion of the unitary version of coupled-cluster transformed Hamiltonian H̄. The qUCCSD method for the electronic ground state includes up to double commutators for the amplitude equations and up to cubic commutators for the energy expression. The qUCCSD excited-state eigenvalue equations include up to double commutators for the singles-singles block of H̄, single commutators for the singles-doubles and doubles-singles blocks, and the bare Hamiltonian for the doubles-doubles block. Benchmark qUCCSD calculations of the ground-state properties and excitation energies for representative molecules demonstrate significant improvement of the accuracy and robustness over the previous UCC3 scheme derived using Møller-Plesset perturbation theory.
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Affiliation(s)
- Junzi Liu
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Lan Cheng
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
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22
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Barzakh A, Andreyev AN, Raison C, Cubiss JG, Van Duppen P, Péru S, Hilaire S, Goriely S, Andel B, Antalic S, Al Monthery M, Berengut JC, Bieroń J, Bissell ML, Borschevsky A, Chrysalidis K, Cocolios TE, Day Goodacre T, Dognon JP, Elantkowska M, Eliav E, Farooq-Smith GJ, Fedorov DV, Fedosseev VN, Gaffney LP, Garcia Ruiz RF, Godefroid M, Granados C, Harding RD, Heinke R, Huyse M, Karls J, Larmonier P, Li JG, Lynch KM, Maison DE, Marsh BA, Molkanov P, Mosat P, Oleynichenko AV, Panteleev V, Pyykkö P, Reitsma ML, Rezynkina K, Rossel RE, Rothe S, Ruczkowski J, Schiffmann S, Seiffert C, Seliverstov MD, Sels S, Skripnikov LV, Stryjczyk M, Studer D, Verlinde M, Wilman S, Zaitsevskii AV. Large Shape Staggering in Neutron-Deficient Bi Isotopes. PHYSICAL REVIEW LETTERS 2021; 127:192501. [PMID: 34797155 DOI: 10.1103/physrevlett.127.192501] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/19/2021] [Revised: 10/01/2021] [Accepted: 10/08/2021] [Indexed: 06/13/2023]
Abstract
The changes in the mean-square charge radius (relative to ^{209}Bi), magnetic dipole, and electric quadrupole moments of ^{187,188,189,191}Bi were measured using the in-source resonance-ionization spectroscopy technique at ISOLDE (CERN). A large staggering in radii was found in ^{187,188,189}Bi^{g}, manifested by a sharp radius increase for the ground state of ^{188}Bi relative to the neighboring ^{187,189}Bi^{g}. A large isomer shift was also observed for ^{188}Bi^{m}. Both effects happen at the same neutron number, N=105, where the shape staggering and a similar isomer shift were observed in the mercury isotopes. Experimental results are reproduced by mean-field calculations where the ground or isomeric states were identified by the blocked quasiparticle configuration compatible with the observed spin, parity, and magnetic moment.
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Affiliation(s)
- A Barzakh
- Petersburg Nuclear Physics Institute, NRC Kurchatov Institute, 188300 Gatchina, Russia
| | - A N Andreyev
- Department of Physics, University of York, York YO10 5DD, United Kingdom
- Advanced Science Research Center, Japan Atomic Energy Agency, Tokai-mura, Ibaraki 319-1195, Japan
| | - C Raison
- Department of Physics, University of York, York YO10 5DD, United Kingdom
| | - J G Cubiss
- Department of Physics, University of York, York YO10 5DD, United Kingdom
| | - P Van Duppen
- KU Leuven, Instituut voor Kern- en Stralingsfysica, B-3001 Leuven, Belgium
| | - S Péru
- Université Paris-Saclay, CEA, LMCE, 91680 Bruyères-le-Châtel, France
| | - S Hilaire
- Université Paris-Saclay, CEA, LMCE, 91680 Bruyères-le-Châtel, France
| | - S Goriely
- Institut d'Astronomie et d'Astrophysique, CP-226, Université Libre de Bruxelles, 1050 Brussels, Belgium
| | - B Andel
- Department of Nuclear Physics and Biophysics, Comenius University in Bratislava, 84248 Bratislava, Slovakia
| | - S Antalic
- Department of Nuclear Physics and Biophysics, Comenius University in Bratislava, 84248 Bratislava, Slovakia
| | - M Al Monthery
- Department of Physics, University of York, York YO10 5DD, United Kingdom
| | - J C Berengut
- School of Physics, University of New South Wales, Sydney NSW 2052, Australia
| | - J Bieroń
- Instytut Fizyki Teoretycznej, Uniwersytet Jagielloński, ul. prof. Stanisława Łojasiewicza 11, Kraków, Poland
| | - M L Bissell
- School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom
| | - A Borschevsky
- Van Swinderen Institute, University of Groningen, 9747 Groningen, Netherlands
| | - K Chrysalidis
- CERN, Esplanade des Particules 1, 1211 Geneva 23, Switzerland
- Institut für Physik, Johannes Gutenberg-Universität, Mainz, D-55128 Mainz, Germany
| | - T E Cocolios
- KU Leuven, Instituut voor Kern- en Stralingsfysica, B-3001 Leuven, Belgium
| | - T Day Goodacre
- School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom
- CERN, Esplanade des Particules 1, 1211 Geneva 23, Switzerland
- TRIUMF, 4004 Wesbrook Mall, Vancouver British Columbia V6T 2A3, Canada
| | - J-P Dognon
- NIMBE, CEA, CNRS, Universiteé Paris-Saclay, CEA Saclay, 91190 Gif-sur-Yvette, France
| | - M Elantkowska
- Poznan University of Technology, Piotrowo 3, Poznan 60-965, Poland
| | - E Eliav
- School of Chemistry, Tel Aviv University, 69978 Tel Aviv, Israel
| | - G J Farooq-Smith
- KU Leuven, Instituut voor Kern- en Stralingsfysica, B-3001 Leuven, Belgium
| | - D V Fedorov
- Petersburg Nuclear Physics Institute, NRC Kurchatov Institute, 188300 Gatchina, Russia
| | - V N Fedosseev
- CERN, Esplanade des Particules 1, 1211 Geneva 23, Switzerland
| | - L P Gaffney
- School of Engineering and Computing, University of the West of Scotland, Paisley PA1 2BE, United Kingdom
| | - R F Garcia Ruiz
- School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom
| | - M Godefroid
- SQUARES, CP160/09, Université libre de Bruxelles, Av. F.D. Roosevelt 50, 1050 Brussels, Belgium
| | - C Granados
- KU Leuven, Instituut voor Kern- en Stralingsfysica, B-3001 Leuven, Belgium
- CERN, Esplanade des Particules 1, 1211 Geneva 23, Switzerland
| | - R D Harding
- Department of Physics, University of York, York YO10 5DD, United Kingdom
- CERN, Esplanade des Particules 1, 1211 Geneva 23, Switzerland
| | - R Heinke
- Institut für Physik, Johannes Gutenberg-Universität, Mainz, D-55128 Mainz, Germany
| | - M Huyse
- KU Leuven, Instituut voor Kern- en Stralingsfysica, B-3001 Leuven, Belgium
| | - J Karls
- CERN, Esplanade des Particules 1, 1211 Geneva 23, Switzerland
- Department of Physics, University of Gothenburg, SE-412 96 Gothenburg, Sweden
| | - P Larmonier
- CERN, Esplanade des Particules 1, 1211 Geneva 23, Switzerland
| | - J G Li
- Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
| | - K M Lynch
- CERN, Esplanade des Particules 1, 1211 Geneva 23, Switzerland
| | - D E Maison
- Petersburg Nuclear Physics Institute, NRC Kurchatov Institute, 188300 Gatchina, Russia
- Saint Petersburg State University, 7/9 Universitetskaya nab., St. Petersburg, 199034 Russia
| | - B A Marsh
- CERN, Esplanade des Particules 1, 1211 Geneva 23, Switzerland
| | - P Molkanov
- Petersburg Nuclear Physics Institute, NRC Kurchatov Institute, 188300 Gatchina, Russia
| | - P Mosat
- Department of Nuclear Physics and Biophysics, Comenius University in Bratislava, 84248 Bratislava, Slovakia
| | - A V Oleynichenko
- Petersburg Nuclear Physics Institute, NRC Kurchatov Institute, 188300 Gatchina, Russia
- Department of Chemistry, M. V. Lomonosov Moscow State University, Leninskie gory 1/3, Moscow, 119991 Russia
| | - V Panteleev
- Petersburg Nuclear Physics Institute, NRC Kurchatov Institute, 188300 Gatchina, Russia
| | - P Pyykkö
- Department of Chemistry, University of Helsinki, P.O. Box 55 (A. I. Virtasen aukio 1), FIN-00014 Helsinki, Finland
| | - M L Reitsma
- Van Swinderen Institute, University of Groningen, 9747 Groningen, Netherlands
| | - K Rezynkina
- KU Leuven, Instituut voor Kern- en Stralingsfysica, B-3001 Leuven, Belgium
| | - R E Rossel
- CERN, Esplanade des Particules 1, 1211 Geneva 23, Switzerland
| | - S Rothe
- CERN, Esplanade des Particules 1, 1211 Geneva 23, Switzerland
| | - J Ruczkowski
- Poznan University of Technology, Piotrowo 3, Poznan 60-965, Poland
| | - S Schiffmann
- SQUARES, CP160/09, Université libre de Bruxelles, Av. F.D. Roosevelt 50, 1050 Brussels, Belgium
| | - C Seiffert
- CERN, Esplanade des Particules 1, 1211 Geneva 23, Switzerland
| | - M D Seliverstov
- Petersburg Nuclear Physics Institute, NRC Kurchatov Institute, 188300 Gatchina, Russia
| | - S Sels
- KU Leuven, Instituut voor Kern- en Stralingsfysica, B-3001 Leuven, Belgium
| | - L V Skripnikov
- Petersburg Nuclear Physics Institute, NRC Kurchatov Institute, 188300 Gatchina, Russia
- Saint Petersburg State University, 7/9 Universitetskaya nab., St. Petersburg, 199034 Russia
| | - M Stryjczyk
- KU Leuven, Instituut voor Kern- en Stralingsfysica, B-3001 Leuven, Belgium
- University of Jyväskylä, Department of Physics, P.O. Box 35, FI-40014 Jyväskylä, Finland
| | - D Studer
- Institut für Physik, Johannes Gutenberg-Universität, Mainz, D-55128 Mainz, Germany
| | - M Verlinde
- KU Leuven, Instituut voor Kern- en Stralingsfysica, B-3001 Leuven, Belgium
| | - S Wilman
- Poznan University of Technology, Piotrowo 3, Poznan 60-965, Poland
| | - A V Zaitsevskii
- Petersburg Nuclear Physics Institute, NRC Kurchatov Institute, 188300 Gatchina, Russia
- Department of Chemistry, M. V. Lomonosov Moscow State University, Leninskie gory 1/3, Moscow, 119991 Russia
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23
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Babin MC, DeWitt M, DeVine JA, McDonald DC, Ard SG, Shuman NS, Viggiano AA, Cheng L, Neumark DM. Electronic structure of NdO via slow photoelectron velocity-map imaging spectroscopy of NdO --. J Chem Phys 2021; 155:114305. [PMID: 34551540 DOI: 10.1063/5.0063307] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Electronically excited NdO is a possible product of the chemistry associated with the release of Nd into the ionosphere, and emission from these states may contribute to the observations following such experiments. To better characterize the energetics and spectroscopy of NdO, we report a combined experimental and theoretical study using slow photoelectron velocity-map imaging spectroscopy of cryogenically cooled NdO- anions (cryo-SEVI) supplemented by wave function-based quantum-chemical calculations. Using cryo-SEVI, we measure the electron affinity of NdO to be 1.0091(7) eV and resolve numerous transitions to low-lying electronic and vibrational states of NdO that are assigned with the aid of the electronic structure calculations. Additionally, temperature-dependent data suggest contributions from the (2)4.5 state of NdO- residing 2350 cm-1 above the ground anion state. Photodetachment to higher-lying excited states of NdO is also reported, which may help to clarify observations from prior release experiments.
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Affiliation(s)
- Mark C Babin
- Department of Chemistry, University of California, Berkeley, Berkeley, California 94720, USA
| | - Martin DeWitt
- Department of Chemistry, University of California, Berkeley, Berkeley, California 94720, USA
| | - Jessalyn A DeVine
- Department of Chemistry, University of California, Berkeley, Berkeley, California 94720, USA
| | - David C McDonald
- NRC Postdoc at Air Force Research Laboratory, Space Vehicles Directorate, Kirtland Air Force Base, Albuquerque, New Mexico 87117, USA
| | - Shaun G Ard
- Air Force Research Laboratory, Space Vehicles Directorate, Kirtland Air Force Base, Albuquerque, New Mexico 87117, USA
| | - Nicholas S Shuman
- Air Force Research Laboratory, Space Vehicles Directorate, Kirtland Air Force Base, Albuquerque, New Mexico 87117, USA
| | - Albert A Viggiano
- Air Force Research Laboratory, Space Vehicles Directorate, Kirtland Air Force Base, Albuquerque, New Mexico 87117, USA
| | - Lan Cheng
- Department of Chemistry, Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Daniel M Neumark
- Department of Chemistry, University of California, Berkeley, Berkeley, California 94720, USA
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24
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Thomas S, Hampe F, Stopkowicz S, Gauss J. Complex ground-state and excitation energies in coupled-cluster theory. Mol Phys 2021. [DOI: 10.1080/00268976.2021.1968056] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Simon Thomas
- Department Chemie, Johannes Gutenberg-Universität Mainz, Mainz, Germany
| | - Florian Hampe
- Department Chemie, Johannes Gutenberg-Universität Mainz, Mainz, Germany
| | - Stella Stopkowicz
- Department Chemie, Johannes Gutenberg-Universität Mainz, Mainz, Germany
| | - Jürgen Gauss
- Department Chemie, Johannes Gutenberg-Universität Mainz, Mainz, Germany
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25
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Pokhilko P, Iskakov S, Yeh CN, Zgid D. Evaluation of two-particle properties within finite-temperature self-consistent one-particle Green's function methods: Theory and application to GW and GF2. J Chem Phys 2021; 155:024119. [PMID: 34266259 DOI: 10.1063/5.0054661] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
Abstract
One-particle Green's function methods can model molecular and solid spectra at zero or non-zero temperatures. One-particle Green's functions directly provide electronic energies and one-particle properties, such as dipole moment. However, the evaluation of two-particle properties, such as ⟨S2⟩ and ⟨N2⟩, can be challenging because they require a solution of the computationally expensive Bethe-Salpeter equation to find two-particle Green's functions. We demonstrate that the solution of the Bethe-Salpeter equation can be completely avoided. Applying the thermodynamic Hellmann-Feynman theorem to self-consistent one-particle Green's function methods, we derive expressions for two-particle density matrices in a general case and provide explicit expressions for GF2 and GW methods. Such density matrices can be decomposed into an antisymmetrized product of correlated one-electron density matrices and the two-particle electronic cumulant of the density matrix. Cumulant expressions reveal a deviation from ensemble representability for GW, explaining its known deficiencies. We analyze the temperature dependence of ⟨S2⟩ and ⟨N2⟩ for a set of small closed-shell systems. Interestingly, both GF2 and GW show a non-zero spin contamination and a non-zero fluctuation of the number of particles for closed-shell systems at the zero-temperature limit.
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Affiliation(s)
- Pavel Pokhilko
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Sergei Iskakov
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Chia-Nan Yeh
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Dominika Zgid
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
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26
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Halbert L, Vidal ML, Shee A, Coriani S, Severo Pereira Gomes A. Relativistic EOM-CCSD for Core-Excited and Core-Ionized State Energies Based on the Four-Component Dirac-Coulomb(-Gaunt) Hamiltonian. J Chem Theory Comput 2021; 17:3583-3598. [PMID: 33944570 DOI: 10.1021/acs.jctc.0c01203] [Citation(s) in RCA: 27] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Abstract
We report an implementation of the core-valence separation approach to the four-component relativistic Hamiltonian-based equation-of-motion coupled-cluster with singles and doubles theory (CVS-EOM-CCSD) for the calculation of relativistic core-ionization potentials and core-excitation energies. With this implementation, which is capable of exploiting double group symmetry, we investigate the effects of the different CVS-EOM-CCSD variants and the use of different Hamiltonians based on the exact two-component (X2C) framework on the energies of different core-ionized and -excited states in halogen- (CH3I, HX, and X-, X = Cl-At) and xenon-containing (Xe, XeF2) species. Our results show that the X2C molecular mean-field approach [Sikkema, J.; J. Chem. Phys. 2009, 131, 124116], based on four-component Dirac-Coulomb mean-field calculations (2DCM), is capable of providing core excitations and ionization energies that are nearly indistinguishable from the reference four-component energies for up to and including fifth-row elements. We observe that two-electron integrals over the small-component basis sets lead to non-negligible contributions to core binding energies for the K and L edges for atoms such as iodine or astatine and that the approach based on Dirac-Coulomb-Gaunt mean-field calculations (2DCGM) are significantly more accurate than X2C calculations for which screened two-electron spin-orbit interactions are included via atomic mean-field integrals.
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Affiliation(s)
- Loïc Halbert
- CNRS, UMR 8523-PhLAM-Physique des Lasers, Atomes et Molécules, Université de Lille, F-59000 Lille, France
| | - Marta L Vidal
- DTU Chemistry-Department of Chemistry, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark
| | - Avijit Shee
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Sonia Coriani
- DTU Chemistry-Department of Chemistry, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark
| | - André Severo Pereira Gomes
- CNRS, UMR 8523-PhLAM-Physique des Lasers, Atomes et Molécules, Université de Lille, F-59000 Lille, France
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27
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Liu J, Cheng L. Relativistic coupled‐cluster and equation‐of‐motion coupled‐cluster methods. WIRES COMPUTATIONAL MOLECULAR SCIENCE 2021. [DOI: 10.1002/wcms.1536] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Affiliation(s)
- Junzi Liu
- Department of Chemistry The Johns Hopkins University Baltimore Maryland USA
| | - Lan Cheng
- Department of Chemistry The Johns Hopkins University Baltimore Maryland USA
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28
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Liu J, Zheng X, Asthana A, Zhang C, Cheng L. Analytic evaluation of energy first derivatives for spin-orbit coupled-cluster singles and doubles augmented with noniterative triples method: General formulation and an implementation for first-order properties. J Chem Phys 2021; 154:064110. [PMID: 33588557 DOI: 10.1063/5.0038779] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A formulation of analytic energy first derivatives for the coupled-cluster singles and doubles augmented with noniterative triples [CCSD(T)] method with spin-orbit coupling included at the orbital level and an implementation for evaluation of first-order properties are reported. The standard density-matrix formulation for analytic CC gradient theory adapted to complex algebra has been used. The orbital-relaxation contributions from frozen core, occupied, virtual, and frozen virtual orbitals to analytic spin-orbit CCSD(T) gradients are fully taken into account and treated efficiently, which is of importance to calculations of heavy elements. Benchmark calculations of first-order properties including dipole moments and electric-field gradients using the corresponding exact two-component property integrals are presented for heavy-element containing molecules to demonstrate the applicability and usefulness of the present analytic scheme.
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Affiliation(s)
- Junzi Liu
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Xuechen Zheng
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Ayush Asthana
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Chaoqun Zhang
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Lan Cheng
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
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29
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Zhang C, Korslund H, Wu Y, Ding S, Cheng L. Towards accurate prediction for laser-coolable molecules: relativistic coupled-cluster calculations for yttrium monoxide and prospects for improving its laser cooling efficiencies. Phys Chem Chem Phys 2020; 22:26167-26177. [PMID: 33188674 DOI: 10.1039/d0cp04608f] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Benchmark relativistic coupled-cluster calculations for yttrium monoxide (YO) with accurate treatment of relativistic and electron correlation effects are reported. The spin-orbit mixing of 2Π and 2Δ is found to be an order of magnitude smaller than previously reported in the literature. Together with the measurement of the lifetime of the A'2Δ3/2 state, it implies an enhanced capability of a narrow-line cooling scheme to bring YO to sub-recoil temperature. The computed electronic transition properties also support a four-photon scheme to close the leakage of the A2Π1/2 ↔ X2Σ1/2+ cycle through the A'2Δ3/2 state by repumping the A'2Δ3/2 state to the B2Σ1/2+ state, which subsequently decays back to X2Σ1/2+. Relativistic coupled-cluster methods, capable of providing accurate spectroscopic parameters that characterize the local potential curves and hence of providing accurate Franck-Condon factors, appear to be promising candidates for accurate calculation of properties for laser-coolable molecules.
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Affiliation(s)
- Chaoqun Zhang
- Department of Chemistry, The Johns Hopkins University, Baltimore, MD 21218, USA.
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30
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Barker JR, Stanton JF, Nguyen TL. Semiclassical transition state theory/master equation kinetics of HO + CO: Performance evaluation. INT J CHEM KINET 2020. [DOI: 10.1002/kin.21420] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Affiliation(s)
- John R. Barker
- Climate and Space Sciences & Engineering University of Michigan Ann Arbor Michigan
| | - John F. Stanton
- Quantum Theory Project Department of Chemistry University of Florida Gainesville Florida
| | - Thanh Lam Nguyen
- Quantum Theory Project Department of Chemistry University of Florida Gainesville Florida
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31
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Matthews DA, Cheng L, Harding ME, Lipparini F, Stopkowicz S, Jagau TC, Szalay PG, Gauss J, Stanton JF. Coupled-cluster techniques for computational chemistry: The CFOUR program package. J Chem Phys 2020; 152:214108. [DOI: 10.1063/5.0004837] [Citation(s) in RCA: 214] [Impact Index Per Article: 53.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
Affiliation(s)
- Devin A. Matthews
- Department of Chemistry, Southern Methodist University, Dallas, Texas 75275, USA
| | - Lan Cheng
- Department of Chemistry, Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Michael E. Harding
- Institut für Physikalische Chemie, Karlsruher Institut für Technologie (KIT), Kaiserstr. 12, D-76131 Karlsruhe, Germany
| | - Filippo Lipparini
- Dipartimento di Chimica e Chimica Industriale, Università di Pisa, Via G. Moruzzi 13, I-56124 Pisa, Italy
| | - Stella Stopkowicz
- Department Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, D-55128 Mainz, Germany
| | - Thomas-C. Jagau
- Department of Chemistry, University of Munich (LMU), Butenandtstr. 5-13, D-81377 Munich, Germany
| | - Péter G. Szalay
- ELTE Eötvös Loránd University, Institute of Chemistry, Pázmány Péter sétány 1/A, H-1117 Budapest, Hungary
| | - Jürgen Gauss
- Department Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, D-55128 Mainz, Germany
| | - John F. Stanton
- Quantum Theory Project, Departments of Chemistry and Physics, University of Florida, Gainesville, Florida 32611, USA
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Meitei OR, Houck SE, Mayhall NJ. Spin–Orbit Matrix Elements for a Combined Spin-Flip and IP/EA approach. J Chem Theory Comput 2020; 16:3597-3606. [DOI: 10.1021/acs.jctc.0c00103] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Oinam Romesh Meitei
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Shannon E. Houck
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Nicholas J. Mayhall
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
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33
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Cheng L. A study of non-iterative triples contributions in relativistic equation-of-motion coupled-cluster calculations using an exact two-component Hamiltonian with atomic mean-field spin-orbit integrals: Application to uranyl and other heavy-element compounds. J Chem Phys 2019; 151:104103. [DOI: 10.1063/1.5113796] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Lan Cheng
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
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34
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Pokhilko P, Epifanovsky E, Krylov AI. General framework for calculating spin-orbit couplings using spinless one-particle density matrices: Theory and application to the equation-of-motion coupled-cluster wave functions. J Chem Phys 2019; 151:034106. [PMID: 31325926 DOI: 10.1063/1.5108762] [Citation(s) in RCA: 31] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
Abstract
Standard implementations of nonrelativistic excited-state calculations compute only one component of spin multiplets (i.e., Ms = 0 triplets); however, matrix elements for all components are necessary for deriving spin-dependent experimental observables. Wigner-Eckart's theorem allows one to circumvent explicit calculations of all multiplet components. We generate all other spin-orbit matrix elements by applying Wigner-Eckart's theorem to a reduced one-particle transition density matrix computed for a single multiplet component. In addition to computational efficiency, this approach also resolves the phase issue arising within Born-Oppenheimer's separation of nuclear and electronic degrees of freedom. A general formalism and its application to the calculation of spin-orbit couplings using equation-of-motion coupled-cluster wave functions are presented. The two-electron contributions are included via the mean-field spin-orbit treatment. Intrinsic issues of constructing spin-orbit mean-field operators for open-shell references are discussed, and a resolution is proposed. The method is benchmarked by using several radicals and diradicals. The merits of the approach are illustrated by a calculation of the barrier for spin inversion in a high-spin tris(pyrrolylmethyl)amine Fe(II) complex.
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Affiliation(s)
- Pavel Pokhilko
- Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482, USA
| | - Evgeny Epifanovsky
- Q-Chem, Inc., 6601 Owens Drive, Suite 105, Pleasanton, California 94588, USA
| | - Anna I Krylov
- Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482, USA and Institut für Physikalische Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, D-55128 Mainz, Germany
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35
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Wodyński A, Kaupp M. Density Functional Calculations of Electron Paramagnetic Resonance g- and Hyperfine-Coupling Tensors Using the Exact Two-Component (X2C) Transformation and Efficient Approximations to the Two-Electron Spin-Orbit Terms. J Phys Chem A 2019; 123:5660-5672. [PMID: 31184482 DOI: 10.1021/acs.jpca.9b03979] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
Abstract
A two-component quasirelativistic density functional theory implementation of the computation of hyperfine and g-tensors at exact two-component (X2C) and Douglas-Kroll-Hess method (DKH) levels in the Turbomole code is reported and tested for a series of smaller 3d1, 4d1, and 5d1 complexes, as well as for some larger 5d7 Ir and Pt systems in comparison with earlier four-component matrix-Dirac-Kohn-Sham results. A main emphasis is placed on efficient approximations to the two-electron spin-orbit contributions, comparing an existing implementation of two variants of Boettger's "scaled nuclear spin-orbit" (SNSO) approximation in the code with a newly implemented atomic mean-field spin-orbit (AMFSO) approximation. The different variants perform overall comparably well with the four-component data. The AMFSO approximation has the added advantage of being able to include the spin-other-orbit contributions arising from the Gaunt term of relativistic electron-electron interactions. These are of comparably larger importance for the 3d complexes than for their heavier homologues. The excellent agreement between X2C and four-component electron paramagnetic resonance parameter results provides the opportunity to treat large systems efficiently and accurately with the computationally more expedient two-component quasirelativistic methodology.
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Affiliation(s)
- Artur Wodyński
- Technische Universität Berlin , Institut für Chemie, Theoretische Chemie/Quantenchemie , Sekr. C7, Straße des 17. Juni 135, D-10623 , Berlin , Germany
| | - Martin Kaupp
- Technische Universität Berlin , Institut für Chemie, Theoretische Chemie/Quantenchemie , Sekr. C7, Straße des 17. Juni 135, D-10623 , Berlin , Germany
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36
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Zhou X, Cao Z, Wang F. Analytical energy gradients for ionized states using equation-of-motion coupled-cluster theory with spin-orbit coupling. J Chem Phys 2019; 150:154114. [PMID: 31005096 DOI: 10.1063/1.5088639] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Spin-orbit coupling (SOC) may have a significant effect on the structure and harmonic frequencies of particularly heavy p-block element compounds. However, reports on analytical energy gradients with SOC are scarce, especially for excited states. In this work, we implemented analytical energy gradients for ionized states using the equation-of-motion coupled-cluster (CC) theory at the CC singles and doubles level (EOM-IP-CCSD) with SOC. Effects of SOC on structure and harmonic frequencies as well as properties for both the ground and some excited states of open-shell compounds with one unpaired electron can be investigated efficiently with the present implementation. A closed-shell reference is required in the calculations, and SOC is included in post-Hartree-Fock treatment. Relativistic effective core potentials are employed in dealing with both scalar relativistic effects and SOC, and we treat perturbations that are even under time reversal in this work. Both time-reversal symmetry and double point group symmetry for D2h * and its subgroups are exploited in the implementation. The method is applicable to states which can be reached by removing one electron from a closed-shell reference state. The results of some open-shell cations indicate the importance of SOC on structures and harmonic frequencies of heavy element compounds.
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Affiliation(s)
- Xiaojun Zhou
- Institute of Atomic and Molecular Physics, Key Laboratory of High Energy Density Physics and Technology, Ministry of Education, Sichuan University, Chengdu, People's Republic of China
| | - Zhanli Cao
- School of Science, Xi'an University of Posts and Telecommunications, Xi'an 710121, People's Republic of China
| | - Fan Wang
- Institute of Atomic and Molecular Physics, Key Laboratory of High Energy Density Physics and Technology, Ministry of Education, Sichuan University, Chengdu, People's Republic of China
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Asthana A, Liu J, Cheng L. Exact two-component equation-of-motion coupled-cluster singles and doubles method using atomic mean-field spin-orbit integrals. J Chem Phys 2019; 150:074102. [DOI: 10.1063/1.5081715] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Affiliation(s)
- Ayush Asthana
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Junzi Liu
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Lan Cheng
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
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38
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Nguyen DT, Steimle T, Linton C, Cheng L. Optical Stark and Zeeman Spectroscopy of Thorium Fluoride (ThF) and Thorium Chloride (ThCl). J Phys Chem A 2019; 123:1423-1433. [DOI: 10.1021/acs.jpca.8b11853] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Duc-Trung Nguyen
- School of Molecular Sciences, Arizona State University Tempe, Arizona 85287-1604, United States
| | - Timothy Steimle
- School of Molecular Sciences, Arizona State University Tempe, Arizona 85287-1604, United States
| | - Colan Linton
- Physics Department, University of New Brunswick, 8 Bailey Drive, Fredericton, New Brunswick E3B5A3, Canada
| | - Lan Cheng
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, United States
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39
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Liu J, Asthana A, Cheng L, Mukherjee D. Unitary coupled-cluster based self-consistent polarization propagator theory: A third-order formulation and pilot applications. J Chem Phys 2018; 148:244110. [DOI: 10.1063/1.5030344] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Junzi Liu
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Ayush Asthana
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Lan Cheng
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Debashis Mukherjee
- Raman Center for Atomic, Molecular and Optical Sciences, Indian Association for the Cultivation of Science, Kolkata 700-032, India
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40
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Liu J, Cheng L. An atomic mean-field spin-orbit approach within exact two-component theory for a non-perturbative treatment of spin-orbit coupling. J Chem Phys 2018; 148:144108. [DOI: 10.1063/1.5023750] [Citation(s) in RCA: 41] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Junzi Liu
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Lan Cheng
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
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