1
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De Santis M, Sorbelli D, Vallet V, Gomes ASP, Storchi L, Belpassi L. Frozen-Density Embedding for Including Environmental Effects in the Dirac-Kohn-Sham Theory: An Implementation Based on Density Fitting and Prototyping Techniques. J Chem Theory Comput 2022; 18:5992-6009. [PMID: 36172757 PMCID: PMC9558305 DOI: 10.1021/acs.jctc.2c00499] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Frozen density embedding (FDE) represents an embedding scheme in which environmental effects are included from first-principles calculations by considering the surrounding system explicitly by means of its electron density. In the present paper, we extend the full four-component relativistic Dirac-Kohn-Sham (DKS) method, as implemented in the BERTHA code, to include environmental and confinement effects with the FDE scheme (DKS-in-DFT FDE). The implementation, based on the auxiliary density fitting techniques, has been enormously facilitated by BERTHA's python API (PyBERTHA), which facilitates the interoperability with other FDE implementations available through the PyADF framework. The accuracy and numerical stability of this new implementation, also using different auxiliary fitting basis sets, has been demonstrated on the simple NH3-H2O system, in comparison with a reference nonrelativistic implementation. The computational performance has been evaluated on a series of gold clusters (Aun, with n = 2, 4, 8) embedded into an increasing number of water molecules (5, 10, 20, 40, and 80 water molecules). We found that the procedure scales approximately linearly both with the size of the frozen surrounding environment (consistent with the underpinnings of the FDE approach) and with the size of the active system (in line with the use of density fitting). Finally, we applied the code to a series of heavy (Rn) and super-heavy elements (Cn, Fl, Og) embedded in a C60 cage to explore the confinement effect induced by C60 on their electronic structure. We compare the results from our simulations, with respect to more-approximate models employed in the atomic physics literature. Our results indicate that the specific interactions described by FDE are able to improve upon the cruder approximations currently employed, and, thus, they provide a basis from which to generate more-realistic radial potentials for confined atoms.
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Affiliation(s)
- Matteo De Santis
- Univ. Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | - Diego Sorbelli
- Dipartimento di Chimica, Biologia e Biotecnologie, Università degli Studi di Perugia, Via Elce di Sotto 8, 06123 Perugia, Italy.,Istituto di Scienze e Tecnologie Chimiche (SCITEC), Consiglio Nazionale delle Ricerche c/o Dipartimento di Chimica, Biologia e Biotecnologie, Università degli Studi di Perugia, Via Elce di Sotto 8, 06123 Perugia, Italy
| | - Valérie Vallet
- Univ. Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | | | - Loriano Storchi
- Istituto di Scienze e Tecnologie Chimiche (SCITEC), Consiglio Nazionale delle Ricerche c/o Dipartimento di Chimica, Biologia e Biotecnologie, Università degli Studi di Perugia, Via Elce di Sotto 8, 06123 Perugia, Italy.,Dipartimento di Farmacia, Università degli Studi 'G. D'Annunzio', Via dei Vestini 31, 66100 Chieti, Italy
| | - Leonardo Belpassi
- Istituto di Scienze e Tecnologie Chimiche (SCITEC), Consiglio Nazionale delle Ricerche c/o Dipartimento di Chimica, Biologia e Biotecnologie, Università degli Studi di Perugia, Via Elce di Sotto 8, 06123 Perugia, Italy
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2
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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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3
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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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4
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Zhou C, Wu D, Gagliardi L, Truhlar DG. Calculation of the Zeeman Effect for Transition-Metal Complexes by Multiconfiguration Pair-Density Functional Theory. J Chem Theory Comput 2021; 17:5050-5063. [PMID: 34338523 DOI: 10.1021/acs.jctc.1c00208] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Spin-orbit coupling is especially critical for the description of magnetic anisotropy, electron paramagnetic resonance spectroscopy of inorganic radicals and transition-metal complexes, and intersystem crossing. Here, we show how spin-orbit coupling may be included in multiconfiguration pair-density functional theory (MC-PDFT), and we apply the resulting formulation to the calculation of magnetic g tensors (which govern the Zeeman effect) of molecules containing transition metals. MC-PDFT is an efficient method for including static and dynamic electronic correlation in the quantum mechanical treatment of molecules; here, we apply it with spin-orbit coupling by using complete active space self-consistent field (CASSCF) and complete active space configuration interaction (CASCI) wave functions and on-top density functionals. We propose a systematic CASCI scheme for the g tensor calculation of the ground state of the systems under consideration, and we show its superiority over the conventional CASSCF scheme. State interaction, which is important for degenerate and nearly degenerate states, is included by extended multi-state PDFT (XMS-PDFT). Applications are reported for the ground doublet states of 25 transition-metal complexes with d1, d5, d7, and d9 configurations. The MC-PDFT methods are shown to be both efficient and accurate as compared with complete active space second-order perturbation theory.
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Affiliation(s)
- Chen Zhou
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States
| | - Dihua Wu
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States
| | - Laura Gagliardi
- Department of Chemistry, Pritzker School of Molecular Engineering, The James Franck Institute and Chicago Center for Theoretical Chemistry, The University of Chicago, Chicago, Illinois 60637, United States
| | - Donald G Truhlar
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States
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5
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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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6
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Paquier J, Giner E, Toulouse J. Relativistic short-range exchange energy functionals beyond the local-density approximation. J Chem Phys 2020; 152:214106. [DOI: 10.1063/5.0004926] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Julien Paquier
- Laboratoire de Chimie Théorique (LCT), Sorbonne Université and CNRS, F-75005 Paris, France
| | - Emmanuel Giner
- Laboratoire de Chimie Théorique (LCT), Sorbonne Université and CNRS, F-75005 Paris, France
| | - Julien Toulouse
- Laboratoire de Chimie Théorique (LCT), Sorbonne Université and CNRS, F-75005 Paris, France
- Institut Universitaire de France, F-75005 Paris, France
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7
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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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8
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Mussard B, Sharma S. One-Step Treatment of Spin–Orbit Coupling and Electron Correlation in Large Active Spaces. J Chem Theory Comput 2017; 14:154-165. [DOI: 10.1021/acs.jctc.7b01019] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Bastien Mussard
- Department of Chemistry and
Biochemistry, University of Colorado Boulder, Boulder, Colorado 80302, United States
| | - Sandeep Sharma
- Department of Chemistry and
Biochemistry, University of Colorado Boulder, Boulder, Colorado 80302, United States
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9
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Cao Z, Wang F, Yang M. Coupled-cluster method for open-shell heavy-element systems with spin-orbit coupling. J Chem Phys 2017; 146:134108. [DOI: 10.1063/1.4979491] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Zhanli Cao
- Institute of Atomic and Molecular Physics, Key Laboratory of High Energy Density Physics and Technology, Ministry of Education, Sichuan University, Chengdu 610065, 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 610065, People’s Republic of China
| | - Mingli Yang
- Institute of Atomic and Molecular Physics, Key Laboratory of High Energy Density Physics and Technology, Ministry of Education, Sichuan University, Chengdu 610065, People’s Republic of China
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10
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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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11
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Rampino S, Belpassi L, Tarantelli F, Storchi L. Full Parallel Implementation of an All-Electron Four-Component Dirac–Kohn–Sham Program. J Chem Theory Comput 2014; 10:3766-76. [DOI: 10.1021/ct500498m] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023]
Affiliation(s)
- Sergio Rampino
- Istituto
di Scienze e Tecnologie Molecolari, Consiglio Nazionale delle Ricerche
c/o Dipartimento di Chimica, Biologia e Biotecnologie, Università degli Studi di Perugia, Via Elce di Sotto 8, 06123 Perugia, Italia
| | - Leonardo Belpassi
- Istituto
di Scienze e Tecnologie Molecolari, Consiglio Nazionale delle Ricerche
c/o Dipartimento di Chimica, Biologia e Biotecnologie, Università degli Studi di Perugia, Via Elce di Sotto 8, 06123 Perugia, Italia
| | - Francesco Tarantelli
- Dipartimento
di Chimica, Biologia e Biotecnologie, Università degli Studi di Perugia, Via Elce di Sotto 8, 06123 Perugia, Italia
| | - Loriano Storchi
- Dipartimento
di Farmacia, Università degli Studi ‘G. D’Annunzio’, Via dei Vestini 31, 66100 Chieti, Italia
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12
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Hrdá M, Kulich T, Repiský M, Noga J, Malkina OL, Malkin VG. Implementation of the diagonalization-free algorithm in the self-consistent field procedure within the four-component relativistic scheme. J Comput Chem 2014; 35:1725-37. [DOI: 10.1002/jcc.23674] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/23/2014] [Revised: 06/09/2014] [Accepted: 06/10/2014] [Indexed: 01/22/2023]
Affiliation(s)
- Marcela Hrdá
- Department of Theoretical Chemistry; Institute of Inorganic Chemistry; Slovak Academy of Sciences; SK-84536 Bratislava Slovakia
| | - Tomáš Kulich
- Department of Computer Science; Faculty of Mathematics, Physics and Informatics, Comenius University; SK-84248 Bratislava Slovakia
| | - Michal Repiský
- Department of Theoretical Chemistry; Institute of Inorganic Chemistry; Slovak Academy of Sciences; SK-84536 Bratislava Slovakia
- Department of Chemistry; The Centre for Theoretical and Computational Chemistry (CTCC), UiT, The Arctic University of Norway; N-9037 Tromsø Norway
| | - Jozef Noga
- Department of Theoretical Chemistry; Institute of Inorganic Chemistry; Slovak Academy of Sciences; SK-84536 Bratislava Slovakia
- Department of Inorganic Chemistry; Faculty of Natural Sciences, Comenius University; SK-84215 Bratislava Slovakia
- Computing Centre; Slovak Academy of Sciences; SK-84545 Bratislava Slovakia
| | - Olga L. Malkina
- Department of Theoretical Chemistry; Institute of Inorganic Chemistry; Slovak Academy of Sciences; SK-84536 Bratislava Slovakia
- Department of Inorganic Chemistry; Faculty of Natural Sciences, Comenius University; SK-84215 Bratislava Slovakia
| | - Vladimir G. Malkin
- Department of Theoretical Chemistry; Institute of Inorganic Chemistry; Slovak Academy of Sciences; SK-84536 Bratislava Slovakia
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14
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Chalupský J, Yanai T. Flexible nuclear screening approximation to the two-electron spin–orbit coupling based on ab initio parameterization. J Chem Phys 2013; 139:204106. [DOI: 10.1063/1.4832737] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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15
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Cuadrado R, Cerdá JI. Fully relativistic pseudopotential formalism under an atomic orbital basis: spin-orbit splittings and magnetic anisotropies. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2012; 24:086005. [PMID: 22277796 DOI: 10.1088/0953-8984/24/8/086005] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We present an efficient implementation of the spin-orbit coupling within the density functional theory based SIESTA code (2002 J. Phys.: Condens. Matter 14 2745) using the fully relativistic and totally separable pseudopotential formalism of Hemstreet et al (1993 Phys. Rev. B 47 4238). First, we obtain the spin-orbit splittings for several systems ranging from isolated atoms to bulk metals and semiconductors as well as the Au(111) surface state. Next, and after extensive tests on the accuracy of the formalism, we also demonstrate its capability to yield reliable values for the magnetic anisotropy energy in magnetic systems. In particular, we focus on the L1(0) binary alloys and on two large molecules: Mn(6)O(2)(H -sao)(6)(O(2)CH)(2)(CH(3)OH)(4) and Co(4)(hmp)(4)(CH(3)OH)(4)Cl(4). In all cases our calculated anisotropies are in good agreement with those obtained with full-potential methods, despite the latter being, in general, computationally more demanding.
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Affiliation(s)
- R Cuadrado
- Instituto de Ciencia de Materiales de Madrid ICMM-CSIC, Cantoblanco, Madrid, Spain
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16
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NAKAJIMA TAKAHITO, TSUNEDA TAKAO, NAKANO HARUYUKI, HIRAO KIMIHIKO. RECENT ADVANCES IN ELECTRONIC STRUCTURE THEORY. JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2012. [DOI: 10.1142/s0219633602000105] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Accurate quantum computational chemistry has evolved dramatically. The size of molecular systems, which can be studied accurately using molecular theory is increasing very rapidly. Theoretical chemistry has opened up a world of new possibilities. It can treat real systems with predictable accuracy. Computational chemistry is becoming an integral part of chemistry research. Theory can now make very significant contribution to chemistry. This review will focus on our recent developments in the theoretical and computational methodology for the study of molecular structure and molecular interactions. We are aiming at developing accurate molecular theory on systems containing hundreds of atoms. We continue our research in the following three directions: (i) development of new ab initio theory, particularly multireference-based perturbation theory, (ii) development of exchange and correlation functionals in density functional theory, and (iii) development of molecular theory including relativistic effects. We have enjoyed good progress in each of the above areas. We are very excited about our discoveries of new theory and new algorithms and would like to share this enthusiasm with readers.
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Affiliation(s)
- TAKAHITO NAKAJIMA
- Department of Applied Chemistry, School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan
| | - TAKAO TSUNEDA
- Department of Applied Chemistry, School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan
| | - HARUYUKI NAKANO
- Department of Applied Chemistry, School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan
| | - KIMIHIKO HIRAO
- Department of Applied Chemistry, School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan
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17
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Liu W, Wang F, Li L. The Beijing Density Functional (BDF) Program Package: Methodologies and Applications. JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2011. [DOI: 10.1142/s0219633603000471] [Citation(s) in RCA: 115] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
The Beijing Density Functional (BDF) program package is such a code that can perform nonrelativistic, one-, two-, and four-component relativistic density functional calculations on medium-sized molecular systems with various functionals in most compact and yet sufficient basis set expansions. The mergence of different approaches in a single code facilitates direct and systematic comparisons between different Hamiltonians, since they share all the same numerical and technical issues. In this account, the methodologies adopted in the code will be discussed in great detail and some applications of the code will be briefly presented.
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Affiliation(s)
- Wenjian Liu
- Institute of Theoretical and Computational Chemistry and State Key, Laboratory of Rare Earth Materials Chemistry and Applications, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, P. R. China
| | - Fan Wang
- Institute of Theoretical and Computational Chemistry and State Key, Laboratory of Rare Earth Materials Chemistry and Applications, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, P. R. China
| | - Lemin Li
- Institute of Theoretical and Computational Chemistry and State Key, Laboratory of Rare Earth Materials Chemistry and Applications, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, P. R. China
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18
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Anderson JSM, Ayers PW. Quantum Theory of Atoms in Molecules: Results for the SR-ZORA Hamiltonian. J Phys Chem A 2011; 115:13001-6. [DOI: 10.1021/jp204558n] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- James S. M. Anderson
- Department of Physics, University of Tokyo, Hongo, Bunkyo-ku, Tokyo, Japan 113-0033
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario, Canada L8S 4M1
| | - Paul W. Ayers
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario, Canada L8S 4M1
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19
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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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20
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Affiliation(s)
- Takahito Nakajima
- Computational Molecular Science Research Team, Advanced Institute for Computational Science, RIKEN, 7-1-26 Minatojima-minami, Cyuo, Kobe, Hyogo 650-0047, Japan
| | - Kimihiko Hirao
- Director, Advanced Institute for Computational Science, RIKEN, 7-1-26 Minatojima-minami, Cyuo, Kobe, Hyogo 650-0047, Japan
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21
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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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22
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Belpassi L, Storchi L, Quiney HM, Tarantelli F. Recent advances and perspectives in four-component Dirac–Kohn–Sham calculations. Phys Chem Chem Phys 2011; 13:12368-94. [DOI: 10.1039/c1cp20569b] [Citation(s) in RCA: 55] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023]
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23
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Nataraj HS, Kállay M, Visscher L. General implementation of the relativistic coupled-cluster method. J Chem Phys 2010; 133:234109. [DOI: 10.1063/1.3518712] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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24
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Storchi L, Belpassi L, Tarantelli F, Sgamellotti A, Quiney HM. An Efficient Parallel All-Electron Four-Component Dirac−Kohn−Sham Program Using a Distributed Matrix Approach. J Chem Theory Comput 2010; 6:384-94. [DOI: 10.1021/ct900539m] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Affiliation(s)
- Loriano Storchi
- Dipartimento di Chimica and I.S.T.M.—C.N.R., Università di Perugia, 06123, Italy, and ARC Centre of Excellence for Coherent X-ray Science School of Physics, The University of Melbourne, Victoria, 3010, Australia
| | - Leonardo Belpassi
- Dipartimento di Chimica and I.S.T.M.—C.N.R., Università di Perugia, 06123, Italy, and ARC Centre of Excellence for Coherent X-ray Science School of Physics, The University of Melbourne, Victoria, 3010, Australia
| | - Francesco Tarantelli
- Dipartimento di Chimica and I.S.T.M.—C.N.R., Università di Perugia, 06123, Italy, and ARC Centre of Excellence for Coherent X-ray Science School of Physics, The University of Melbourne, Victoria, 3010, Australia
| | - Antonio Sgamellotti
- Dipartimento di Chimica and I.S.T.M.—C.N.R., Università di Perugia, 06123, Italy, and ARC Centre of Excellence for Coherent X-ray Science School of Physics, The University of Melbourne, Victoria, 3010, Australia
| | - Harry M. Quiney
- Dipartimento di Chimica and I.S.T.M.—C.N.R., Università di Perugia, 06123, Italy, and ARC Centre of Excellence for Coherent X-ray Science School of Physics, The University of Melbourne, Victoria, 3010, Australia
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25
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Four-Component Electronic Structure Methods. CHALLENGES AND ADVANCES IN COMPUTATIONAL CHEMISTRY AND PHYSICS 2010. [DOI: 10.1007/978-1-4020-9975-5_7] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
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van Wüllen C. Relativistic Density Functional Theory. CHALLENGES AND ADVANCES IN COMPUTATIONAL CHEMISTRY AND PHYSICS 2010. [DOI: 10.1007/978-1-4020-9975-5_5] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
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27
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Belpassi L, Tarantelli F, Sgamellotti A, Quiney HM. Poisson-transformed density fitting in relativistic four-component Dirac–Kohn–Sham theory. J Chem Phys 2008; 128:124108. [DOI: 10.1063/1.2868770] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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28
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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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29
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Tymczak CJ, Challacombe M. Linear scaling computation of the Fock matrix. VII. Periodic density functional theory at the Gamma point. J Chem Phys 2006; 122:134102. [PMID: 15847450 DOI: 10.1063/1.1853374] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Linear scaling quantum chemical methods for density functional theory are extended to the condensed phase at the Gamma point. For the two-electron Coulomb matrix, this is achieved with a tree-code algorithm for fast Coulomb summation [M. Challacombe and E. Schwegler, J. Chem. Phys. 106, 5526 (1997)], together with multipole representation of the crystal field [M. Challacombe, C. White, and M. Head-Gordon, J. Chem. Phys. 107, 10131 (1997)]. A periodic version of the hierarchical cubature algorithm [M. Challacombe, J. Chem. Phys. 113, 10037 (2000)], which builds a telescoping adaptive grid for numerical integration of the exchange-correlation matrix, is shown to be efficient when the problem is posed as integration over the unit cell. Commonalities between the Coulomb and exchange-correlation algorithms are discussed, with an emphasis on achieving linear scaling through the use of modern data structures. With these developments, convergence of the Gamma-point supercell approximation to the k-space integration limit is demonstrated for MgO and NaCl. Linear scaling construction of the Fockian and control of error is demonstrated for RBLYP6-21G* diamond up to 512 atoms.
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Affiliation(s)
- C J Tymczak
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA.
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Belpassi L, Tarantelli F, Sgamellotti A, Quiney HM. Electron density fitting for the Coulomb problem in relativistic density-functional theory. J Chem Phys 2006; 124:124104. [PMID: 16599659 DOI: 10.1063/1.2179420] [Citation(s) in RCA: 35] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A density fitting approach for the Coulomb matrix representation within the four-component formulation of relativistic density-functional theory is presented. Our implementation, which uses G-spinor basis sets, shares all the advantages of those found in nonrelativistic quantum chemistry. We show that very accurate Coulomb energies may be obtained using a modest number of scalar auxiliary basis functions for molecules containing heavy atoms. The efficiency of this new implementation is demonstrated in a detailed study of the spectroscopic properties of the gold dimer, and its scaling behavior has been tested by calculations of some closed-shell gold clusters (Au2, Au3+, Au4, Au5+). The algorithm is found to scale as O(N3), just as it does in the nonrelativistic case, and represents a dramatic improvement in efficiency over the conventional approach in the calculation of the Coulomb matrix, with computation times that are reduced to less than 3% for Au2 and up to 1% in the case of Au5+.
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Affiliation(s)
- Leonardo Belpassi
- Dipartimento di Chimica e I.S.T.M.-C.N.R., Università di Perugia, Perugia 06123, Italy.
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31
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Systematically convergent basis sets for transition metals. II. Pseudopotential-based correlation consistent basis sets for the group 11 (Cu, Ag, Au) and 12 (Zn, Cd, Hg) elements. Theor Chem Acc 2005. [DOI: 10.1007/s00214-005-0681-9] [Citation(s) in RCA: 955] [Impact Index Per Article: 50.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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32
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Belpassi L, Tarantelli F, Sgamellotti A, Quiney HM. Computational strategies for a four-component Dirac–Kohn–Sham program: Implementation and first applications. J Chem Phys 2005; 122:184109. [PMID: 15918696 DOI: 10.1063/1.1897383] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
An implementation of the generalized gradient approximation within the four-component formulation of relativistic density-functional theory using G-spinor basis sets is presented. This approach is based on the direct evaluation of the relativistic density and its gradient from the G-spinor amplitudes and gradients without explicit reference to the total density matrix. This proves to be a particularly efficient scheme, with an intrinsic computational cost that scales linearly with the number of G-spinor basis functions. In order to validate this new implementation, incorporated in the parallel version of the program BERTHA, a detailed study of the diatomic system CsAu is also reported. The spectroscopic constants D(e),r(e),omega(e), and x(e)omega(e) and the dipole moment mu have been calculated and compared with the best available theoretical and experimental data. The sensitivity of our results to the details of the numerical schemes used to evaluate the matrix elements is analyzed in detail. Also presented is a comparative study of molecular properties in the alkali auride series which have been obtained using several standard non-relativistic density functionals.
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Affiliation(s)
- Leonardo Belpassi
- Dipartimento di Chimica e Istituto Consiglio Nazionale delle Ricerche (CNR) di Scienze e Tecnologie Molecolari (ISTM), Università di Perugia, Perugia 06123, Italy.
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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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35
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Gao J, Liu W, Song B, Liu C. Time-dependent four-component relativistic density functional theory for excitation energies. J Chem Phys 2004; 121:6658-66. [PMID: 15473721 DOI: 10.1063/1.1788655] [Citation(s) in RCA: 72] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Time-dependent four-component relativistic density functional theory within the linear response regime is developed for calculating excitation energies of heavy element containing systems. Since spin is no longer a good quantum number in this context, we resort to time-reversal adapted Kramers basis when deriving the coupled Dirac-Kohn-Sham equation. The particular implementation of the formalism into the Beijing density functional program package utilizes the multipolar expansion of the induced density to facilitate the construction of the induced Coulomb potential. As the first application, pilot calculations on the valence excitation energies and fine structures of the rare gas (Ne to Rn) and Group 12 (Zn to Hg) atoms are reported. To the best of our knowledge, it is the first time to be able to account for spin-orbit coupling within time-dependent density functional theory for excitation energies.
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Affiliation(s)
- Jun Gao
- Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, People's Republic of China
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37
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Nakajima T, Hirao K. Pseudospectral approach to relativistic molecular theory. J Chem Phys 2004; 121:3438-45. [PMID: 15303907 DOI: 10.1063/1.1775791] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The efficient relativistic Dirac-Hartree-Fock (DHF) and Dirac-Kohn-Sham (DKS) methods are proposed by an application of the pseudospectral (PS) approach. The present PS-DHF/DKS method is a relativistic extension of the PS-HF/KS method of Friesner, though we aim at higher numerical accuracy by elimination of superfluous arbitrariness. The relativistic PS-DHF/DKS method is implemented into our REL4D programs. Several PS applications to molecular systems show that the relativistic PS-DHF/DKS approach is more efficient than the traditional approach without a loss of accuracy. The present PS-DKS method successfully assigns and predicts the photoelectron spectra of hexacarbonyl complexes of tungsten and seaborgium theoretically.
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Affiliation(s)
- Takahito Nakajima
- Department of Applied Chemistry, Graduate School of Engineering, The University of Tokyo, Tokyo, Japan
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Rösch N, Matveev A, Nasluzov VA, Neyman KM, Moskaleva L, Krüger S. Quantum chemistry with the Douglas-Kroll-Hess approach to relativistic density functional theory: Efficient methods for molecules and materials. THEORETICAL AND COMPUTATIONAL CHEMISTRY 2004. [DOI: 10.1016/s1380-7323(04)80038-4] [Citation(s) in RCA: 32] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
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40
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Wang F, Li L. Numerical examination of performance of some exchange-correlation functionals for molecules containing heavy elements. J Comput Chem 2004; 25:669-77. [PMID: 14978710 DOI: 10.1002/jcc.10421] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Abstract
The performance of 17 exchange-correlation functionals for molecules containing heavy elements are numerically examined through four-component relativistic density DFT calculations. The examined functionals show the similar accuracy as they do for the molecules containing light elements only except for bond lengths. LDA and OP86 produce good results for bond lengths and frequencies but bad bond energies. Different functionals do not show much different performance for bond energies except LDA. BP86 and GP86 produce results with average accuracy while LYP does not perform well. Although encouraging results are obtained with functional B97GGA-1, other heavily parameterized and meta-GGA functionals do not produce impressive results.
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Affiliation(s)
- Fan Wang
- State Key Laboratory of Rare Earth Materials Chemistry and Applications, College of Chemistry, and Molecular Engineering, Peking University, Beijing 100871, People's Republic of China
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41
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van Wüllen C. Relativistic Density Functional Calculations on Small Molecules. THEORETICAL AND COMPUTATIONAL CHEMISTRY 2004. [DOI: 10.1016/s1380-7323(04)80037-2] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
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42
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Nakajima T, Hirao K. Extended Douglas–Kroll transformations applied to the relativistic many-electron Hamiltonian. J Chem Phys 2003. [DOI: 10.1063/1.1594173] [Citation(s) in RCA: 75] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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43
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Fossgaard O, Gropen O, Valero MC, Saue T. On the performance of four-component relativistic density functional theory: Spectroscopic constants and dipole moments of the diatomics HX and XY (X,Y=F, Cl, Br, and I). J Chem Phys 2003. [DOI: 10.1063/1.1574317] [Citation(s) in RCA: 42] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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45
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Saue T, Jensen HJA. Linear response at the 4-component relativistic level: Application to the frequency-dependent dipole polarizabilities of the coinage metal dimers. J Chem Phys 2003. [DOI: 10.1063/1.1522407] [Citation(s) in RCA: 102] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Saue T, Visscher L. Four-Component Electronic Structure Methods for Molecules. THEORETICAL CHEMISTRY AND PHYSICS OF HEAVY AND SUPERHEAVY ELEMENTS 2003. [DOI: 10.1007/978-94-017-0105-1_6] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/24/2023]
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48
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Yanai T, Nakajima T, Ishikawa Y, Hirao K. A highly efficient algorithm for electron repulsion integrals over relativistic four-component Gaussian-type spinors. J Chem Phys 2002. [DOI: 10.1063/1.1479351] [Citation(s) in RCA: 48] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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49
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Abstract
A four-component relativistic implementation of Kohn-Sham theory for molecular systems is presented. The implementation is based on a nonredundant exponential parametrization of the Kohn-Sham energy, well suited to studies of molecular static and dynamic properties as well as of total electronic energies. Calculations are presented of the bond lengths and the harmonic and anharmonic vibrational frequencies of Au(2), Hg(2+)(2), HgAu(+), HgPt, and AuH. All calculations are based on the full four-component Dirac-Coulomb Hamiltonian, employing nonrelativistic local, gradient-corrected, and hybrid density functionals. The relevance of the Coulomb and Breit operators for the construction of relativistic functionals is discussed; it is argued that, at the relativistic level of density-functional theory and in the absence of a vector potential, the neglect of current functionals follows from the neglect of the Breit operator.
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Affiliation(s)
- Trond Saue
- UMR 7551 CNRS/Université Louis Pasteur, Laboratoire de Chimie Quantique et Modélisation Moléculaire, 4 rue Blaise Pascal, F-67000 Strasbourg, France
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50
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Abstract
The theoretical and technical foundations are presented for the efficient relativistic electronic structure theories to treat heavy-atomic molecular systems. This review contains two surveys of four-component and two-component quasi-relativistic approaches. First, we review our highly efficient computational scheme for four-component relativistic ab initio molecular orbital (MO) methods over generally contracted spherical harmonic Gaussian-type spinors (GTSs). Illustrative calculations, which are performed with a new four-component relativistic ab initio molecular orbital program package REL4D, clearly show the efficiency of our computational scheme by the Dirac-Hartree-Fock (DHF) and Dirac-Hartree-Fock (DKS) methods. Next, in the two-component quasi-relativistic framework, two relativistic Hamiltonians, RESC and higher order Douglas-Kroll (DK) Hamiltonians, are introduced, and several illustrative calculations are shown. Numerical results for several systems show that good accuracy can be obtained with our third-order DK (DK3) Hamiltonian.
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Affiliation(s)
- Takahito Nakajima
- Department of Applied Chemistry, Graduate School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan
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