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Rusakova IL, Rusakov YY. On the Utmost Importance of the Basis Set Choice for the Calculations of the Relativistic Corrections to NMR Shielding Constants. Int J Mol Sci 2023; 24:ijms24076231. [PMID: 37047204 PMCID: PMC10094374 DOI: 10.3390/ijms24076231] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/09/2023] [Revised: 03/22/2023] [Accepted: 03/23/2023] [Indexed: 03/29/2023] Open
Abstract
The investigation of the sensitivity of the relativistic corrections to the NMR shielding constants (σ) to the configuration of angular spaces of the basis sets used on the atoms of interest was carried out within the four-component density functional theory (DFT). Both types of relativistic effects were considered, namely the so-called heavy atom on light atom and heavy atom on heavy atom effects, though the main attention was paid to the former. As a main result, it was found that the dependence of the relativistic corrections to σ of light nuclei (exemplified here by 1H and 13C) located in close vicinity to a heavy atom (exemplified here by In, Sn, Sb, Te, and I) on the basis set used on the light spectator atom was very much in common with that of the Fermi-contact contribution to the corresponding nonrelativistic spin-spin coupling constant (J). In general, it has been shown that the nonrelativistic J-oriented and σ-oriented basis sets, artificially saturated in the tight s-region, provided much better accuracy than the standard nonrelativistic σ-oriented basis sets when calculating the relativistic corrections to the NMR shielding constants of light nuclei at the relativistic four-component level of the DFT theory.
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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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Abe M, Tsutsui T, Ekman J, Hada M, Das B. Accurate determination of the enhancement factor X for the nuclear Schiff moment in 205TlF molecule based on the four-component relativistic coupled-cluster theory. Mol Phys 2020. [DOI: 10.1080/00268976.2020.1767814] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Minori Abe
- Department of Chemistry, Graduate School of Science, Tokyo Metropolitan University, Tokyo, Japan
| | - Takashi Tsutsui
- Department of Chemistry, Graduate School of Science, Tokyo Metropolitan University, Tokyo, Japan
| | - Jörgen Ekman
- Department of Materials Science and Applied Mathematics, Malmö University, Malmö, Sweden
| | - Masahiko Hada
- Department of Chemistry, Graduate School of Science, Tokyo Metropolitan University, Tokyo, Japan
| | - Bhanu Das
- Department of Physics and International Education and Research Center of Science, Tokyo Institute of Technology, Tokyo, Japan
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4
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Significance of Non-Linear Terms in the Relativistic Coupled-Cluster Theory in the Determination of Molecular Properties. Symmetry (Basel) 2020. [DOI: 10.3390/sym12050811] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
The relativistic coupled-cluster (RCC) theory has been applied recently to a number of heavy molecules to determine their properties very accurately. Since it demands large computational resources, the method is often approximated to single and double excitations (RCCSD method). The effective electric fields ( E e f f ) and molecular permanent electric dipole moments (PDMs) of SrF, BaF, and mercury monohalides (HgX with X = F, Cl, Br, and I) molecules are of immense interest for probing fundamental physics. In our earlier calculations of E e f f and PDMs for the above molecules, we neglected the non-linear terms in the property evaluation expression of the RCCSD method. In this work, we demonstrate the roles of these terms in determining the above quantities and their computational time scalability with the number of processors of a computer. We also compare our results with previous calculations that employed variants of RCC theory, as well as other many-body methods and available experimental values.
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The Role of Relativistic Many-Body Theory in Electron Electric Dipole Moment Searches Using Cold Molecules. ATOMS 2019. [DOI: 10.3390/atoms7020058] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
In this review article, we survey some of our results pertaining to the search for the electric dipole moment of the electron (eEDM), using heavy polar molecules. In particular, we focus on the relativistic coupled cluster method (RCCM) and its applications to eEDM searches in YbF, HgX (X = F, Cl, Br, and I), BaF, HgA (A = Li, Na, and K), and YbOH. Our results are presented in a systematic manner, by first introducing the eEDM and its measurement using molecules, the importance of relativistic many-body theory, and finally our results, followed by future prospects.
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Cheng L, Wang F, Stanton JF, Gauss J. Perturbative treatment of spin-orbit-coupling within spin-free exact two-component theory using equation-of-motion coupled-cluster methods. J Chem Phys 2018; 148:044108. [DOI: 10.1063/1.5012041] [Citation(s) in RCA: 27] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
Affiliation(s)
- Lan Cheng
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Fan Wang
- Institute of Atomic and Molecular Physics, Key Laboratory of High Energy Density Physics and Technology, Ministry of Education, Sichuan University, Chengdu, China
| | - John F. Stanton
- Department of Chemistry, University of Florida, Gainesville, Florida 32611, USA
| | - Jürgen Gauss
- Institut für Physikalische Chemie, Universität Mainz, D-55099 Mainz, Germany
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Liu J, Shen Y, Asthana A, Cheng L. Two-component relativistic coupled-cluster methods using mean-field spin-orbit integrals. J Chem Phys 2018; 148:034106. [DOI: 10.1063/1.5009177] [Citation(s) in RCA: 34] [Impact Index Per Article: 5.7] [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
| | - Yue Shen
- 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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Lipparini F, Gauss J. Cost-Effective Treatment of Scalar Relativistic Effects for Multireference Systems: A CASSCF Implementation Based on the Spin-free Dirac–Coulomb Hamiltonian. J Chem Theory Comput 2016; 12:4284-95. [DOI: 10.1021/acs.jctc.6b00609] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Filippo Lipparini
- Institut
für Physikalische
Chemie, Universität Mainz, Duesbergweg 10-14, D-55128 Mainz, Germany
| | - Jürgen Gauss
- Institut
für Physikalische
Chemie, Universität Mainz, Duesbergweg 10-14, D-55128 Mainz, Germany
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Prasannaa VS, Vutha AC, Abe M, Das BP. Mercury monohalides: suitability for electron electric dipole moment searches. PHYSICAL REVIEW LETTERS 2015; 114:183001. [PMID: 26000997 DOI: 10.1103/physrevlett.114.183001] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/21/2014] [Indexed: 06/04/2023]
Abstract
Heavy polar diatomic molecules are the primary tools for searching for the T-violating permanent electric dipole moment of the electron (eEDM). Valence electrons in some molecules experience extremely large effective electric fields due to relativistic interactions. These large effective electric fields are crucial to the success of polar-molecule-based eEDM search experiments. Here we report on the results of relativistic ab initio calculations of the effective electric fields in a series of molecules that are highly sensitive to an eEDM, the mercury monohalides (HgF, HgCl, HgBr, and HgI). We study the influence of the halide anions on E_{eff}, and identify HgBr and HgI as attractive candidates for future electric dipole moment search experiments.
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Affiliation(s)
- V S Prasannaa
- Indian Institute of Astrophysics, II Block, Koramangala, Bangalore 560 034, India
- Department of Physics, Calicut University, Calicut, Malappuram, Kerala 673 635, India
| | - A C Vutha
- Department of Physics and Astronomy, York University, Toronto, Ontario M3J 1P3, Canada
| | - M Abe
- Tokyo Metropolitan University, 1-1, Minami-Osawa, Hachioji-city, Tokyo 192-0397, Japan
- JST, CREST, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan
| | - B P Das
- Indian Institute of Astrophysics, II Block, Koramangala, Bangalore 560 034, India
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Cheng L, Gauss J. Analytical evaluation of first-order electrical properties based on the spin-free Dirac-Coulomb Hamiltonian. J Chem Phys 2011; 134:244112. [DOI: 10.1063/1.3601056] [Citation(s) in RCA: 37] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023] Open
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Mizukami W, Nakajima T, Hirao K, Yanai T. A dual-level approach to four-component relativistic density-functional theory. Chem Phys Lett 2011. [DOI: 10.1016/j.cplett.2011.04.031] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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Abe M, Suzuki T, Fujii Y, Hada M, Hirao K. Ligand effect on uranium isotope fractionations caused by nuclear volume effects: An ab initio relativistic molecular orbital study. J Chem Phys 2010; 133:044309. [PMID: 20687652 DOI: 10.1063/1.3463797] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We have calculated the nuclear volume term (ln K(nv)) of the isotope fractionation coefficient (epsilon) between (235)U-(238)U isotope pairs by considering the effect of ligand coordination in a U(IV)-U(VI) reaction system. The reactants were modeled as [UO(2)Cl(3)](-) and [UO(2)Cl(4)](2-) for U(VI), and UCl(4) for U(IV). We adopted the Dirac-Coulomb Hartree-Fock method with the Gaussian-type finite nucleus model. The result obtained was ln K(nv)=0.001 90 at 308 K, while the experimentally estimated value of ln K(nv) is 0.002 24. We also discuss how the ligand affects the value of ln K(nv), especially for the various structures of different compounds, and different ligands within the halogen ion series (F, Cl, and Br).
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Affiliation(s)
- Minori Abe
- Department of Chemistry, Graduate School of Science, Tokyo Metropolitan University, 1-1 Minami-Osawa, Hachioji-shi, Tokyo 192-0397, Japan.
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Hisashima TA, Matsushita T, Asada T, Koseki S, Toyota A. Tetra-hydrides of the third-row transition elements: spin–orbit coupling effects on geometrical deformation in WH4 and OsH4. Theor Chem Acc 2007. [DOI: 10.1007/s00214-007-0302-x] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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14
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Abe M, Nakajima T, Hirao K. The relativistic complete active-space second-order perturbation theory with the four-component Dirac Hamiltonian. J Chem Phys 2006; 125:234110. [PMID: 17190550 DOI: 10.1063/1.2404666] [Citation(s) in RCA: 40] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The relativistic complete active-space second-order perturbation theory (CASPT2) is developed for the four-component relativistic Hamiltonian. The present method can describe the near-degenerated and dissociated electronic states of molecules involving atoms of heavy elements. The present approach is less expensive than the relativistic multireference configuration interaction method. The ground and low-lying excited states of TlH, Tl(2), and PtH molecules are calculated with the Dirac-Coulomb (DC) CASPT2 method and their spectroscopic constants are obtained. These spectroscopic constants are compared with experimental findings and previous theoretical work. For all the molecules, the spectroscopic constants of DC-CASPT2 show good agreement with the experimental or previous theoretical spectroscopic constants. The present theory provides accurate descriptions of bonding or dissociation states and of ground and excited states in a well-balanced way.
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Affiliation(s)
- Minori Abe
- Department of Applied Chemistry, School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan
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van Stralen JN, Visscher L, Larsen CV, Jensen HJA. First-order MP2 molecular properties in a relativistic framework. Chem Phys 2005. [DOI: 10.1016/j.chemphys.2004.10.018] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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Abe M, Mori S, Nakajima T, Hirao K. Electronic structures of PtCu, PtAg, and PtAu molecules: a Dirac four-component relativistic study. Chem Phys 2005. [DOI: 10.1016/j.chemphys.2004.09.035] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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