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Haasler M, Maier TM, Kaupp M. Toward a correct treatment of core properties with local hybrid functionals. J Comput Chem 2023; 44:2461-2477. [PMID: 37635647 DOI: 10.1002/jcc.27211] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2023] [Revised: 08/01/2023] [Accepted: 08/03/2023] [Indexed: 08/29/2023]
Abstract
In local hybrid functionals (LHs), a local mixing function (LMF) determines the position-dependent exact-exchange admixture. We report new LHs that focus on an improvement of the LMF in the core region while retaining or partly improving upon the high accuracy in the valence region exhibited by the LH20t functional. The suggested new pt-LMFs are based on a Padé form and modify the previously used ratio between von Weizsäcker and Kohn-Sham local kinetic energies by different powers of the density to enable flexibly improved approximations to the correct high-density and iso-orbital limits relevant for the innermost core region. Using TDDFT calculations for a set of K-shell core excitations of second- and third-period systems including accurate state-of-the-art relativistic orbital corrections, the core part of the LMF is optimized, while the valence part is optimized as previously reported for test sets of atomization energies and reaction barriers (Haasler et al., J Chem Theory Comput 2020, 16, 5645). The LHs are completed by a calibration function that minimizes spurious nondynamical correlation effects caused by the gauge ambiguities of exchange-energy densities, as well as by B95c meta-GGA correlation. The resulting LH23pt functional relates to the previous LH20t functional but specifically improves upon the core region.
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Affiliation(s)
- Matthias Haasler
- Technische Universität Berlin, Institute of Chemistry Theoretical Chemistry/Quantum Chemistry, Berlin, Germany
| | - Toni M Maier
- Technische Universität Braunschweig, Institute of Physical and Theoretical Chemistry, Braunschweig, Germany
| | - Martin Kaupp
- Technische Universität Berlin, Institute of Chemistry Theoretical Chemistry/Quantum Chemistry, Berlin, Germany
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2
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De Santis M, Sorbelli D, Vallet V, Gomes AS, 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] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2022] [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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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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Maier TM, Ikabata Y, Nakai H. Relativistic local hybrid functionals and their impact on 1s core orbital energies. J Chem Phys 2020; 152:214103. [DOI: 10.1063/5.0010400] [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)
- Toni M. Maier
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
- Technische Universität Berlin, Institut für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Straße des 17. Juni 135, D-10623 Berlin, Germany
| | - Yasuhiro Ikabata
- Waseda Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
| | - Hiromi Nakai
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
- Waseda Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
- Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Katsura, Kyoto 615-8520, Japan
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Maier TM, Ikabata Y, Nakai H. Restoring the iso-orbital limit of the kinetic energy density in relativistic density functional theory. J Chem Phys 2019; 151:174114. [DOI: 10.1063/1.5125634] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Toni M. Maier
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
| | - Yasuhiro Ikabata
- Waseda Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
| | - Hiromi Nakai
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
- Waseda Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
- Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Katsura, Kyoto 615-8520, Japan
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6
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Giménez CA, Maldonado AF, Aucar GA. Relativistic and electron correlation effects on NMR J-coupling of Sn and Pb containing molecules. Theor Chem Acc 2016. [DOI: 10.1007/s00214-016-1952-3] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
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7
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Brunello GF, Lee JH, Lee SG, Choi JI, Harvey D, Jang SS. Interactions of Pt nanoparticles with molecular components in polymer electrolyte membrane fuel cells: multi-scale modeling approach. RSC Adv 2016. [DOI: 10.1039/c6ra09274h] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022] Open
Abstract
Three phase model consists of Pt nanoparticles, Nafion, and graphite with oxygen, water, and hydronium.
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Affiliation(s)
- Giuseppe F. Brunello
- Computational NanoBio Technology Laboratory
- School of Materials Science and Engineering
- Georgia Institute of Technology
- Atlanta
- USA
| | - Ji Hye Lee
- Department of Organic Material Science and Engineering
- Pusan National University
- Busan 46241
- Republic of Korea
| | - Seung Geol Lee
- Department of Organic Material Science and Engineering
- Pusan National University
- Busan 46241
- Republic of Korea
| | - Ji Il Choi
- Computational NanoBio Technology Laboratory
- School of Materials Science and Engineering
- Georgia Institute of Technology
- Atlanta
- USA
| | | | - Seung Soon Jang
- Computational NanoBio Technology Laboratory
- School of Materials Science and Engineering
- Georgia Institute of Technology
- Atlanta
- USA
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8
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Zhang Z. Spin–orbit DFT with analytic gradients and applications to heavy element compounds. Theor Chem Acc 2014. [DOI: 10.1007/s00214-014-1588-0] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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9
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Alizadeh D, Jamshidi Z, Shayesteh A. Potential energy curves for the ground and low-lying excited states of CuAg. J Chem Phys 2014; 141:154301. [PMID: 25338890 DOI: 10.1063/1.4897540] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The ground and low-lying excited states of heteronuclear diatomic CuAg are examined by multi-reference configuration interaction (MRCI) method. Relativistic effects were treated and probed in two steps. Scalar terms were considered using the spin-free DKH Hamiltonian as a priori and spin-orbit coupling was calculated perturbatively via the spin-orbit terms of the Breit-Pauli Hamiltonian based on MRCI wavefunctions. Potential energy curves of the spin-free states and their corresponding Ω components correlating with the separated atom limits (2)S(Cu) + (2)S(Ag) and (2)D(Cu) + (2)S(Ag) are obtained. The results are in fine agreement with the experimental measurements and tentative conclusions for the ion-pair B0(+) state are confirmed by our theoretical calculations. Illustrative results are presented to reveal the relative importance and magnitude of the scalar and spin-orbit effects on the spectroscopic properties of this molecule. Time dependent density functional theory calculations, using the LDA, BLYP, B3LYP, and SAOP functionals have been carried out for CuAg and the accuracy of TD-DFT has been compared with ab initio results.
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Affiliation(s)
- Davood Alizadeh
- School of Chemistry, College of Science, University of Tehran, 14176 Tehran, Iran
| | - Zahra Jamshidi
- Chemistry and Chemical Engineering Research Center of Iran, 14335-186 Tehran, Iran
| | - Alireza Shayesteh
- School of Chemistry, College of Science, University of Tehran, 14176 Tehran, Iran
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10
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Maldonado AF, Aucar GA. Relativistic and electron-correlation effects on the nuclear magnetic resonance shieldings of molecules containing tin and lead atoms. J Phys Chem A 2014; 118:7863-75. [PMID: 25110942 DOI: 10.1021/jp502543m] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The reference values for NMR magnetic shieldings, σ(ref), are of the highest importance when theoretical analysis of chemical shifts are envisaged. The fact that the nonrelativistically valid relationship among spin-rotation constants and magnetic shieldings is not any longer valid for heavy atoms requires that the search for σ(ref) for such atoms needs new strategies to follow. We present here results of σ(ref) that were obtained by applying our own simple procedure which mixes accurate experimental chemical shifts (δ) and theoretical magnetic shieldings (σ). We calculated σ(Sn) and σ(Pb) in a family of heavy-halogen-containing molecules. We found out that σ(ref)[Sn;Sn(CH3)4] in gas phase should be close to 3864.11 ± 20.05 ppm (0.5%). For Pb atom, σ(ref)[Pb;Pb(CH3)4] should be close to 14475.1 ± 500.7 ppm. Such theoretical values correspond to calculations with the relativistic polarization propagator method, RelPPA, at the RPA level of approach. They are closer to experimental values as compared to those obtained applying few different functionals such as PBE0, B3LYP, BLYP, BP86, KT2, and KT3 of the density functional theory, DFT. We studied tin and lead shieldings of the XY(4-n)Z(n) (X = Sn, Pb; Y, Z = H, F, Cl, Br, I) and PbH(4-n)I(n) (n = 0, 1, 2, 3, 4) family of compounds with four-component functionals as implemented in the DIRAC code. For these systems results of calculations with RelPPA-RPA are more reliable than DFT ones. We argue about why those DFT functionals must be modified in order to obtain more accurate results of NMR magnetic shieldings within the relativistic regime: first, there is a dependence among both electron-correlation and relativistic effects that should be introduced in some way in the functionals; and second, the DIRAC code uses standard nonrelativistic functionals and the functionals B3LYP and PBE0 were parametrized only with data taken from light elements. It can explain why they are not able to properly introduce relativistic effects on nuclear magnetic shieldings. We finally show that in the analysis of magnetic shieldings for the family of compounds mentioned above, one must consider the newest and so-called heavy-atom effect on vicinal heavy atoms, HAVHA. Such effects are among the most important relativistic effects in these kind of compounds.
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Affiliation(s)
- Alejandro F Maldonado
- Physics Department, Natural and Exact Science Faculty, Northeastern University of Argentina and Institute of Modelling and Innovation on Technology, IMIT , 3400 Corrientes, Argentina
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11
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Błoński P, Hafner J. Magnetic anisotropy of heteronuclear dimers in the gas phase and supported on graphene: relativistic density-functional calculations. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2014; 26:146002. [PMID: 24651700 DOI: 10.1088/0953-8984/26/14/146002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
The structural and magnetic properties of mixed PtCo, PtFe, and IrCo dimers in the gas phase and supported on a free-standing graphene layer have been calculated using density-functional theory, both in the scalar-relativistic limit and self-consistently including spin-orbit coupling. The influence of the strong magnetic moments of the 3d atoms on the spin and orbital moments of the 5d atoms, and the influence of the strong spin-orbit coupling contributed by the 5d atom on the orbital moments of the 3d atoms have been studied in detail. The magnetic anisotropy energy is found to depend very sensitively on the nature of the eigenstates in the vicinity of the Fermi level, as determined by band filling, exchange splitting and spin-orbit coupling. The large magnetic anisotropy energy of free PtCo and IrCo dimers relative to the easy direction parallel to the dimer axis is coupled to a strong anisotropy of the orbital magnetic moments of the Co atom for both dimers, and also on the Ir atom in IrCo. In contrast the PtFe dimer shows a weak perpendicular anisotropy and only small spin and orbital anisotropies of opposite sign on the two atoms. For dimers supported on graphene, the strong binding within the dimer and the stronger interaction of the 3d atom with the substrate stabilizes an upright geometry. Spin and orbital moments on the 3d atom are strongly quenched, but due to the weaker binding within the dimer the properties of the 5d atom are more free-atom-like with increased spin and orbital moments. The changes in the magnetic moment are reflected in the structure of the electronic eigenstates near the Fermi level, for all three dimers the easy magnetic direction is now parallel to the dimer axis and perpendicular to the graphene layer. The already very large magnetic anisotropy energy (MAE) of IrCo is further enhanced by the interaction with the support, the MAE of PtFe changes sign, and that of the PtCo dimer is reduced. These changes are discussed in relation to the relativistic electronic structure of free and supported dimers and it is demonstrated that the existence of a partially occupied quasi-degenerate state at the Fermi level favors the formation of a large magnetic anisotropy.
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Affiliation(s)
- Piotr Błoński
- University of Vienna, Faculty of Physics and Center for Computational Materials Science, Sensengasse 8/12, A-1090 Wien, Austria. Institute of Nuclear Physics, Polish Academy of Sciences, ul. Radzikowskiego 152, PL-31-342 Kraków, Poland
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12
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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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13
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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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15
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Bast R, Ekström U, Gao B, Helgaker T, Ruud K, Thorvaldsen AJ. The ab initio calculation of molecular electric, magnetic and geometric properties. Phys Chem Chem Phys 2011; 13:2627-51. [DOI: 10.1039/c0cp01647k] [Citation(s) in RCA: 53] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023]
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16
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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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17
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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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Franzreb K, Diez RP, Alonso JA. Observation of Zr22+, Cd22+, Hf22+, W22+, and Pt22+ in the gas phase. J Chem Phys 2009; 130:144312. [DOI: 10.1063/1.3112013] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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19
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Teng YL, Kohyama M, Haruta M, Xu Q. Infrared spectroscopic and theoretical studies on the formation of Au2NO− and AunNO (n=2–5) in solid argon. J Chem Phys 2009; 130:134511. [DOI: 10.1063/1.3109689] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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20
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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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Gourlaouen C, Gérard H, Piquemal JP, Parisel O. Understanding Lead Chemistry from Topological Insights: The Transition between Holo- and Hemidirected Structures within the [Pb(CO)n]2+ Model Series. Chemistry 2008; 14:2730-43. [DOI: 10.1002/chem.200701265] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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22
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Jiang L, Xu Q. Infrared spectra of the (AgCO)2 and AgnCO (n=2-4) molecules in rare-gas matrices. J Phys Chem A 2007; 110:11488-93. [PMID: 17020261 DOI: 10.1021/jp064129s] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
Abstract
Reactions of laser-ablated silver atoms with carbon monoxide molecules in solid argon and neon have been investigated using matrix-isolation IR spectroscopy. Small silver cluster carbonyls, (AgCO)2 and AgnCO (n=2-4), as well as mononuclear silver carbonyls, Ag(CO)2 and Ag(CO)3, are generated upon sample annealing in the argon experiments and are characterized on the basis of the isotopic substitution, the CO concentration change, and the comparison with theoretical predictions. However, these polynuclear carbonyls are absent from the neon experiments. Density functional theory calculations have been performed on these silver carbonyls and the corresponding ligand-free silver clusters, which support the identification of these silver carbonyls from the matrix IRspectrum. A terminal CO has been found in the most stable structures of (AgCO)2, Ag2CO, Ag3CO, and Ag4CO. Furthermore, a plausible reaction mechanism has been proposed to account for the formation of the (AgCO)2 and AgnCO (n=2-4) molecules.
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Affiliation(s)
- Ling Jiang
- National Institute of Advanced Industrial Science and Technology (AIST), Ikeda, Osaka 563-8577, Japan
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23
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Sarpe-Tudoran C, Fricke B, Anton J, Persina V. Adsorption of superheavy elements on metal surfaces. J Chem Phys 2007; 126:174702. [PMID: 17492874 DOI: 10.1063/1.2727447] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Fully relativistic four-component density functional theory with the general gradient approximation calculations have been performed to determine the adsorption energy and position of the superheavy element 112 on a Au surface. Extended cluster as well as embedded cluster calculations were used to simulate the surface which allow for the top, bridge, and hollow adsorption sites without losing the advantage of symmetry considerations. Comparison with analogous calculations of the adsorption of the homologue element Hg allows to predict the adsorption of element 112 at a bridge site with a binding energy of 0.67 eV.
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Kullie O, Zhang H, Kolb J, Kolb D. Relativistic density functional calculations using two-spinor minimax finite-element method and linear combination of atomic orbitals for ZnO, CdO, HgO, UubO and Cu2, Ag2, Au2, Rg2. J Chem Phys 2006; 125:244303. [PMID: 17199347 DOI: 10.1063/1.2409288] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In previous work the authors have presented a highly accurate two-spinor fully relativistic solution of the two-center Coulomb problem utilizing the finite-element method (FEM) and furthermore developed a relativistic minimax two-spinor linear combination of atomic orbitals (LCAO). In the present paper the authors present Dirac-Fock-Slater (DFS-) density functional calculations for two-atomic molecules up to super heavy systems using the fully nonlinear minimax FEM and the minimax LCAO in its linearized approximation (linear approximation to relativistic minimax). The FEM gives highly accurate benchmark results for the DFS functional. Especially considering molecules with up to super heavy atoms such as UubO and Rg2, the authors found that LCAO fails to give the correct systematic trends. The accurate FEM results shed a new light on the quality of the DFS-density functional.
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Affiliation(s)
- O Kullie
- Department of Natural Science, University of Kassel, D-34132 Kassel, Germany.
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25
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Gourlaouen C, Gérard H, Parisel O. Exploring the Hydration of Pb2+: Ab Initio Studies and First-Principles Molecular Dynamics. Chemistry 2006; 12:5024-32. [PMID: 16642524 DOI: 10.1002/chem.200600045] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Abstract
Even though lead is a well-known toxicant widely scattered throughout the world since antiquity, its chemistry is poorly documented at the molecular level. Here we investigate the hydration of the Pb(2+) ion by means of first-principles molecular dynamics (Car-Parrinello molecular dynamics, CPMD). We found that the hydrated cation is heptacoordinated in a dynamically holodirected arrangement roughly corresponding to a fluxional distorted pentagonal bipyramid. The time-averaged Pb-O bond length is especially large and amounts to 2.70 A with an associated root-mean-square deviation of 0.26 A. This results from a dynamic exchange between short (<2.6 A), intermediate (2.6-3.0 A) and long (>3.0 A) Pb-O bonds. The latter very long Pb-O distance implies that the determination of the coordination number n(c) from experimental work may not necessarily yield values directly comparable to the theoretical value of n(c)=7, since not all experimental techniques would recognize such a long distance as a bond to the metal cation. Pronounced disorders are evidenced in the second shell, characteristic of a chaotropic cation, and exchanges between the first and second shells cannot be excluded on a timescale of a few tens of picoseconds.
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Affiliation(s)
- Christophe Gourlaouen
- Université Pierre et Marie Curie - Paris 6, Laboratoire de Chimie Théorique, UMR 7616, CC 137, 4 place Jussieu, 75252 Paris Cedex 05, France
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26
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Gourlaouen C, Piquemal JP, Parisel O. [Pb(H2O)]2+ and [Pb(OH)]+: Four-component density functional theory calculations, correlated scalar relativistic constrained-space orbital variation energy decompositions, and topological analysis. J Chem Phys 2006; 124:174311. [PMID: 16689575 DOI: 10.1063/1.2186994] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022] Open
Abstract
Within the scope of studying the molecular implications of the Pb(2+) cation in environmental and polluting processes, this paper reports Hartree-Fock and density functional theory (B3LYP) four-component relativistic calculations using an all-electron basis set applied to [Pb(H(2)O)](2+) and [Pb(OH)](+), two complexes expected to be found in the terrestrial atmosphere. It is shown that full-relativistic calculations validate the use of scalar relativistic approaches within the framework of density functional theory. [Pb(H(2)O)](2+) is found C(2v) at any level of calculations whereas [Pb(OH)](+) can be found bent or linear depending of the computational methodology used. When C(s) is found the barrier to inversion through the C(infinityv) structure is very low, and can be overcome at high enough temperature, making the molecule floppy. In order to get a better understanding of the bonding occurring between the Pb(2+) cation and the H(2)O and OH(-) ligands, natural bond orbital and atoms-in-molecule calculations have been performed. These approaches are supplemented by a topological analysis of the electron localization function. Finally, the description of these complexes is refined using constrained-space orbital variation complexation energy decompositions.
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Affiliation(s)
- Christophe Gourlaouen
- Laboratoire de Chimie Théorique-UMR 7616 CNRS/UPMC, Université Pierre et Marie Curie-Paris 6, Case Courrier 137-4, place Jussieu, F. 75252 Paris Cedex 05, France
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27
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Tian WQ, Ge M, Gu F, Yamada T, Aoki Y. Binary Clusters AuPt and Au6Pt: Structure and Reactivity within Density Functional Theory. J Phys Chem A 2006; 110:6285-93. [PMID: 16686464 DOI: 10.1021/jp055506o] [Citation(s) in RCA: 61] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Within density functional theory with the general gradient approximation for the exchange and correlation, the bimetallic clusters AuPt and Au(6)Pt have been studied for their structure and reactivity. The bond strength of AuPt lies between those of Au(2) and Pt(2), and it is closer to that of Au(2). The Pt atom is the reactive center in both AuPt and AuPt(+) according to electronic structure analysis. AuPt(+) is more stable than AuPt. Au(6)Pt prefers electronic states with low multiplicity. The most stable conformation of Au(6)Pt is a singlet and has quasi-planar hexagonal frame with Pt lying at the hexagonal center. The doping of Pt in Au cluster enhances the chemical regioselectivity of the Au cluster. The Pt atom essentially serves as electron donor and the Au atoms bonded to the Pt atom acts as electron acceptor in Au(6)Pt. The lowest triplet of edge-capped rhombus Au(6)Pt clusters is readily accessible with very small singlet-triplet energy gap (0.32 eV). O(2) prefers to adsorb on Au and CO prefers to adsorb on Pt. O(2) and CO have stronger adsorption on AuPt than they do on Au(6)Pt. CO has a much stronger adsorption on AuPt bimetallic cluster than O(2) does. The adsorption of CO on Pt modifies the geometry of AuPt bimetallic clusters.
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Affiliation(s)
- Wei Quan Tian
- State Key Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun 130023, China.
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28
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Davis WB, Hefferlin R. An atlas of forecasted molecular data. 2. Vibration frequencies of main-group and transition-metal neutral gas-phase diatomic molecules in the ground state. J Chem Inf Model 2006; 46:820-5. [PMID: 16563013 DOI: 10.1021/ci050439g] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
This atlas of diatomic-molecular vibration frequencies parallels the previously offered Atlas of Internuclear Separations. The Atlas was produced by mining the data from Huber and Herzberg and training neural network software to forecast new data. New protocols were employed with the powerful software, which was originally designed for forecasting the financial markets. The Atlas presents 1920 additional vibration frequencies for use until critical tables are available to fill the needs more precisely. The precision of the predictions is characterized by the average fractional 1% confidence limit, that is, 10.66%. The accuracies of the predictions are determined in two ways. First, 221 of the 224 Huber and Herzberg data values used for training and validation fall within the prediction confidence limits or fall outside by less than 10% of the Huber and Herzberg values, and 181 values agree (within the limits). Second, 87 of 101 comparison data values, consisting of literature data and some additional Huber and Herzberg values, fall within the prediction confidence limits or fall outside by less than half the prediction values, and 44 of the 101 values agree (within the limits).
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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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31
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Dai D, Whangbo MH, Ugrinov A, Sevov SC, Wang F, Li L, Villesuzanne A, Alekseyev AB, Liebermann HP, Buenker RJ. Analysis of the Effect of Spin−Orbit Coupling on the Electronic Structure and Excitation Spectrum of the Bi22- Anion in (K-crypt)2Bi2 on the Basis of Relativistic Electronic Structure Calculations. J Phys Chem A 2005; 109:1675-83. [PMID: 16833492 DOI: 10.1021/jp044675q] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The Bi2(2-) anions that have been characterized in (K-crypt)2Bi2 are isoelectronic with O2 but are diamagnetic and EPR-silent, unlike O2. The UV-vis spectrum measured for (K-crypt)2Bi2 shows two broad absorption peaks located at 2.05 and 2.85 eV, but no absorption at lower energies down to 0.62 eV. To account for these observations, the electronic structures of the isoelectronic diatomic dianions Q2(2-) (Q = N, P, As, Sb, Bi) were compared on the basis of relativistic density functional theory calculations, and the electronic excitations of Bi2(2-) were analyzed on the basis of relativistic configuration interaction calculations. The extent of spin-orbit coupling, brought about by the relativistic effect, increases steadily in the order N < P < As < Sb < Bi such that the "closed-shell" state is more stable than the "open-shell" state for Bi2(2-), while the opposite is the case for N2(2-), P2(2-), As2(2-), and Sb2(2-). The nature of the electronic excitations of Bi2(2-) was assigned and discussed from the viewpoint of molecular orbitals in the absence of spin-orbit coupling.
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Affiliation(s)
- Dadi Dai
- Department of Chemistry, North Carolina State University, Raleigh, North Carolina 27695-8204, USA
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32
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Jiang L, Xu Q. Reactions of Gold Atoms and Small Clusters with CO: Infrared Spectroscopic and Theoretical Characterization of AunCO (n = 1−5) and Aun(CO)2 (n = 1, 2) in Solid Argon. J Phys Chem A 2005; 109:1026-32. [PMID: 16833410 DOI: 10.1021/jp045681p] [Citation(s) in RCA: 59] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Laser-ablated Au atoms have been co-deposited with CO molecules in solid argon to produce gold carbonyls. In addition to the previously reported Au(CO)n (n = 1, 2) and Au2(CO)2 molecules, small gold cluster monocarbonyls Au(n)CO (n = 2-5) are formed on sample annealing and characterized using infrared spectroscopy on the basis of the results of the isotopic substitution and CO concentration change and comparison with theoretical predictions. Of particular interest is that the mononuclear gold carbonyls, Au(CO)n (n = 1, 2), are favored under the experimental conditions of higher CO concentration and lower laser energy, whereas the yields of the gold cluster carbonyls, Au(n)CO (n = 2-5) and Au2(CO)2, remarkably increase with lower CO concentration and higher laser power. Density functional theory (DFT) calculations have been performed on these molecules and the corresponding small naked gold clusters. The identities of these gold carbonyls Au(n)CO (n = 1-5) and Au(n)(CO)2 (n = 1, 2) are confirmed by the good agreement between the experimental and calculated vibrational frequencies, relative absorption intensities, and isotopic shifts.
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Affiliation(s)
- Ling Jiang
- National Institute of Advanced Industrial Science and Technology (AIST), Ikeda, Osaka 563-8577, Japan
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33
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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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Affiliation(s)
- Li Xiao
- Department of Chemistry and Biochemistry, Southern Illinois University, Carbondale, Illinois 62901
| | - Lichang Wang
- Department of Chemistry and Biochemistry, Southern Illinois University, Carbondale, Illinois 62901
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35
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Tian WQ, Ge M, Sahu BR, Wang D, Yamada T, Mashiko S. Geometrical and Electronic Structure of the Pt7 Cluster: A Density Functional Study. J Phys Chem A 2004. [DOI: 10.1021/jp0498365] [Citation(s) in RCA: 48] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Affiliation(s)
- Wei Quan Tian
- Department of Chemistry, University of British Columbia, 2036 Main Mall, Vancouver, BC, Canada, V6T 1Z1, Center of Molecular Science, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100080, P. R. China, Department of Physics, University of Texas at Austin, Austin, Texas 78712-0264, and Communications Research Laboratory, Kansai Advanced Research Center, 588-2 Iwaoka, Kobe 651-2942, Japan
| | - Maofa Ge
- Department of Chemistry, University of British Columbia, 2036 Main Mall, Vancouver, BC, Canada, V6T 1Z1, Center of Molecular Science, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100080, P. R. China, Department of Physics, University of Texas at Austin, Austin, Texas 78712-0264, and Communications Research Laboratory, Kansai Advanced Research Center, 588-2 Iwaoka, Kobe 651-2942, Japan
| | - B. R. Sahu
- Department of Chemistry, University of British Columbia, 2036 Main Mall, Vancouver, BC, Canada, V6T 1Z1, Center of Molecular Science, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100080, P. R. China, Department of Physics, University of Texas at Austin, Austin, Texas 78712-0264, and Communications Research Laboratory, Kansai Advanced Research Center, 588-2 Iwaoka, Kobe 651-2942, Japan
| | - Dianxun Wang
- Department of Chemistry, University of British Columbia, 2036 Main Mall, Vancouver, BC, Canada, V6T 1Z1, Center of Molecular Science, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100080, P. R. China, Department of Physics, University of Texas at Austin, Austin, Texas 78712-0264, and Communications Research Laboratory, Kansai Advanced Research Center, 588-2 Iwaoka, Kobe 651-2942, Japan
| | - Toshiki Yamada
- Department of Chemistry, University of British Columbia, 2036 Main Mall, Vancouver, BC, Canada, V6T 1Z1, Center of Molecular Science, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100080, P. R. China, Department of Physics, University of Texas at Austin, Austin, Texas 78712-0264, and Communications Research Laboratory, Kansai Advanced Research Center, 588-2 Iwaoka, Kobe 651-2942, Japan
| | - Shinro Mashiko
- Department of Chemistry, University of British Columbia, 2036 Main Mall, Vancouver, BC, Canada, V6T 1Z1, Center of Molecular Science, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100080, P. R. China, Department of Physics, University of Texas at Austin, Austin, Texas 78712-0264, and Communications Research Laboratory, Kansai Advanced Research Center, 588-2 Iwaoka, Kobe 651-2942, Japan
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36
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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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37
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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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38
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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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39
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Anton J, Jacob T, Fricke B, Engel E. Relativistic density functional calculations for Pt2. PHYSICAL REVIEW LETTERS 2002; 89:213001. [PMID: 12443406 DOI: 10.1103/physrevlett.89.213001] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/19/2002] [Indexed: 05/24/2023]
Abstract
First full-relativistic density functional calculations with the extension of the spin-polarization functional for the relativistic density functional theory in their collinear and noncollinear form are presented here for the molecular system Pt2. The agreement with experiment is very good.
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Affiliation(s)
- J Anton
- Universität Kassel, Fachbereich Physik, D-34109 Kassel, Germany
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40
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Pershina V, Bastug T, Jacob T, Fricke B, Varga S. Intermetallic compounds of the heaviest elements: the electronic structure and bonding of dimers of element 112 and its homolog Hg. Chem Phys Lett 2002. [DOI: 10.1016/s0009-2614(02)01428-8] [Citation(s) in RCA: 32] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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41
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Quiney HM, Belanzoni P. Relativistic density functional theory using Gaussian basis sets. J Chem Phys 2002. [DOI: 10.1063/1.1502245] [Citation(s) in RCA: 45] [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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42
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Wang F, Li L. Analytical energy gradient evaluation in relativistic and nonrelativistic density functional calculations. J Comput Chem 2002; 23:920-7. [PMID: 11984853 DOI: 10.1002/jcc.10082] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
The expressions of analytical energy gradients in density functional theory and their implementation in programs are reported. The evaluation of analytical energy gradients can be carried out in the fully 4-component relativistic, approximate relativistic, and nonrelativistic density functional calculations under local density approximation or general gradient approximation with or without frozen core approximation using different basis sets in our programs. The translational invariance condition and the fact that the one-center terms do not contribute to the energy gradients are utilized to improve the calculation accuracy and to reduce the computational effort. The calculated results of energy gradients and optimized geometry as well as atomization energies of some molecules by the analytical gradient method are in very good agreement with results obtained by the numerical derivative method.
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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, China
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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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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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45
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Van Wüllen C. Spin densities in two-component relativistic density functional calculations: noncollinear versus collinear approach. J Comput Chem 2002; 23:779-85. [PMID: 12012354 DOI: 10.1002/jcc.10043] [Citation(s) in RCA: 135] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
With present day exchange-correlation functionals, accurate results in nonrelativistic open shell density functional calculations can only be obtained if one uses functionals that do not only depend on the electron density but also on the spin density. We consider the common case where such functionals are applied in relativistic density functional calculations. In scalar-relativistic calculations, the spin density can be defined conventionally, but if spin-orbit coupling is taken into account, spin is no longer a good quantum number and it is not clear what the "spin density" is. In many applications, a fixed quantization axis is used to define the spin density ("collinear approach"), but one can also use the length of the local spin magnetization vector without any reference to an external axis ("noncollinear approach"). These two possibilities are compared in this work both by formal analysis and numerical experiments. It is shown that the (nonrelativistic) exchange-correlation functional should be invariant with respect to rotations in spin space, and this only holds for the noncollinear approach. Total energies of open shell species are higher in the collinear approach because less exchange energy is assigned to a given Kohn-Sham reference function. More importantly, the collinear approach breaks rotational symmetry, that is, in molecular calculations one may find different energies for different orientations of the molecule. Data for the first ionization potentials of Tl, Pb, element 113, and element 114, and for the orientation dependence of the total energy of I+2 and PbF indicate that the error introduced by the collinear approximation is approximately 0.1 eV for valence ionization potentials, but can be much larger if highly ionized open shell states are considered. Rotational invariance is broken by the same amount. This clearly indicates that the collinear approach should not be used, as the full treatment is easily implemented and does not introduce much more computational effort.
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Affiliation(s)
- Christoph Van Wüllen
- Technische Universität Berlin, Sekr. C3, Strasse des 17. Juni 115, D-10623 Berlin, Germany.
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46
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Visscher L. The Dirac equation in quantum chemistry: strategies to overcome the current computational problems. J Comput Chem 2002; 23:759-66. [PMID: 12012352 DOI: 10.1002/jcc.10036] [Citation(s) in RCA: 42] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Abstract
A perspective on the use of the relativistic Dirac equation in quantum chemistry is given. It is demonstrated that many of the computational problems that plague the current implementations of the different electronic structure methods can be overcome by utilizing the locality of the small component wave function and density. Possible applications of such new and more efficient formulations are discussed.
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Affiliation(s)
- Lucas Visscher
- Department of Theoretical Chemistry, Faculty of Sciences, Vrije Universiteit Amsterdam, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands.
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47
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Liu W, van Wüllen C, Wang F, Li L. Spectroscopic constants of MH and M2 (M=Tl, E113, Bi, E115): Direct comparisons of four- and two-component approaches in the framework of relativistic density functional theory. J Chem Phys 2002. [DOI: 10.1063/1.1446026] [Citation(s) in RCA: 56] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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48
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49
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Chapter 3 Relativistic self-consistent fields. ACTA ACUST UNITED AC 2002. [DOI: 10.1016/s1380-7323(02)80029-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
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Yanai T, Iikura H, Nakajima T, Ishikawa Y, Hirao K. A new implementation of four-component relativistic density functional method for heavy-atom polyatomic systems. J Chem Phys 2001. [DOI: 10.1063/1.1412252] [Citation(s) in RCA: 63] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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