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Wei Y, Debnath S, Weber JL, Mahajan A, Reichman DR, Friesner RA. Scalable Ab Initio Electronic Structure Methods with Near Chemical Accuracy for Main Group Chemistry. J Phys Chem A 2024; 128:5796-5807. [PMID: 38970826 DOI: 10.1021/acs.jpca.4c02853] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/08/2024]
Abstract
This study evaluates the precision of widely recognized quantum chemical methodologies, CCSD(T), DLPNO-CCSD(T), and localized ph-AFQMC, for determining the thermochemistry of main group elements. DLPNO-CCSD(T) and localized ph-AFQMC, which offer greater scalability compared to canonical CCSD(T), have emerged over the past decade as pivotal in producing precise benchmark chemical data. Our investigation includes closed-shell, neutral molecules, focusing on their heat of formation and atomization energy sourced from four specific small molecule data sets. First, we selected molecules from the G2 and G3 data sets, noted for their reliable experimental heat of formation data. Additionally, we incorporate molecules from the W4-11 and W4-17 sets, which provide high-level theoretical reference values for atomization energy at 0 K. Our findings reveal that both DLPNO-CCSD(T) and ph-AFQMC methods are capable of achieving a root-mean-square deviation of less than 1 kcal/mol across the combined data set, aligning with the threshold for chemical accuracy. Moreover, we make efforts to confine the maximum deviations within 2 kcal/mol, a degree of precision that significantly broadens the applicability of these methods in fields such as biology and materials science.
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Affiliation(s)
- Yujing Wei
- Department of Chemistry, Columbia University, New York, New York 10027, United States
| | - Sibali Debnath
- Department of Chemistry, Columbia University, New York, New York 10027, United States
| | - John L Weber
- Department of Chemistry, Columbia University, New York, New York 10027, United States
| | - Ankit Mahajan
- Department of Chemistry, Columbia University, New York, New York 10027, United States
| | - David R Reichman
- Department of Chemistry, Columbia University, New York, New York 10027, United States
| | - Richard A Friesner
- Department of Chemistry, Columbia University, New York, New York 10027, United States
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2
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Zangoli M, Monti F, Zanelli A, Marinelli M, Flammini S, Spallacci N, Zakrzewska A, Lanzi M, Salatelli E, Pierini F, Di Maria F. Multifunctional Photoelectroactive Materials for Optoelectronic Applications Based on Thieno[3,4-b]pyrazines and Thieno[1,2,5]thiadiazoles. Chemistry 2024; 30:e202303590. [PMID: 37983681 DOI: 10.1002/chem.202303590] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2023] [Revised: 11/17/2023] [Accepted: 11/20/2023] [Indexed: 11/22/2023]
Abstract
In this study, we introduce a novel family of symmetrical thiophene-based small molecules with a Donor-Acceptor-Donor structure. These compounds feature three different acceptor units: benzo[c][1,2,5]thiadiazole (Bz), thieno[3,4-b]pyrazine (Pz), and thieno[1,2,5]thiadiazole (Tz), coupled with electron donor units based on a carbazole-thiophene derivative. Using Density Functional Theory (DFT), we investigate how the molecular geometry and strength of the central acceptor unit impact the redox and spectroscopic properties. Notably, the incorporation of Pz and Tz moieties induces a significant redshift in the absorption and emission spectra, which extend into the near-infrared (NIR) region, simultaneously reducing their energy gaps (~1.4-1.6 eV). This shift is attributed to the increased coplanarity of the oligomeric inner core, both in the ground (S0 ) and excited (S1 ) states, due to the enhanced quinoidal character as supported by bond-length alternation (BLA) analysis. These structural changes promote better π-electron delocalization and facilitate photoinduced charge transfer processes in optoelectronic devices. Notably, we show that Pz- and Tz-containing molecules exhibit NIR electrochromic behavior and present ambivalent character in bulk heterojunction (BHJ) solar cells. Finally, theoretical calculations suggest that these molecules could serve as effective two-photon absorption (2PA) probes, further expanding their potential in optoelectronic applications.
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Affiliation(s)
- Mattia Zangoli
- Consiglio Nazionale delle Ricerche (CNR), Istituto per la Sintesi Organica e la Fotoreattività (ISOF), via Piero Gobetti 101, 40129, Bologna, Italy
- CLAN-Center for Light Activated Nanostructures, Istituto ISOF-CNR, 40129, Bologna, Italy
| | - Filippo Monti
- Consiglio Nazionale delle Ricerche (CNR), Istituto per la Sintesi Organica e la Fotoreattività (ISOF), via Piero Gobetti 101, 40129, Bologna, Italy
| | - Alberto Zanelli
- Consiglio Nazionale delle Ricerche (CNR), Istituto per la Sintesi Organica e la Fotoreattività (ISOF), via Piero Gobetti 101, 40129, Bologna, Italy
| | - Martina Marinelli
- Department of Industrial Chemistry "Toso Montanari", University of Bologna, Viale Risorgimento 4, 40136, Bologna, Italy
| | - Soraia Flammini
- Consiglio Nazionale delle Ricerche (CNR), Istituto per la Sintesi Organica e la Fotoreattività (ISOF), via Piero Gobetti 101, 40129, Bologna, Italy
- RCCS Ospedale Policlinico San Martino, 16132, Genova, Italy
| | - Nicol Spallacci
- Consiglio Nazionale delle Ricerche (CNR), Istituto per la Sintesi Organica e la Fotoreattività (ISOF), via Piero Gobetti 101, 40129, Bologna, Italy
| | - Anna Zakrzewska
- Department of Biosystems and Soft Matter, Institute of Fundamental Technological Research, Polish Academy of Sciences, ul. Pawinskiego 5B, 02-106, Warsaw, Poland
| | - Massimiliano Lanzi
- Department of Industrial Chemistry "Toso Montanari", University of Bologna, Viale Risorgimento 4, 40136, Bologna, Italy
| | - Elisabetta Salatelli
- Department of Industrial Chemistry "Toso Montanari", University of Bologna, Viale Risorgimento 4, 40136, Bologna, Italy
| | - Filippo Pierini
- Department of Biosystems and Soft Matter, Institute of Fundamental Technological Research, Polish Academy of Sciences, ul. Pawinskiego 5B, 02-106, Warsaw, Poland
| | - Francesca Di Maria
- Consiglio Nazionale delle Ricerche (CNR), Istituto per la Sintesi Organica e la Fotoreattività (ISOF), via Piero Gobetti 101, 40129, Bologna, Italy
- CLAN-Center for Light Activated Nanostructures, Istituto ISOF-CNR, 40129, Bologna, Italy
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Chiorescu I, Krüger S, Rösch N. Single-Hydroxide Bridged Dimers of U and Np Actinyls: A Density Functional Study on Their Existence and Structure in Aqueous Solution. Inorg Chem 2023; 62:830-840. [PMID: 36585929 DOI: 10.1021/acs.inorgchem.2c03437] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Abstract
With quantum chemical calculations at the density functional theory level, we examined the structure and the stability of diactinyl monohydroxo complexes [(AnO2)2(OH)]3+/+ in aqueous solution for An = U(VI), Np(VI), and Np(V). In particular, this study contributes to understanding the hydrolysis of Np(VI) and Np(V), which is less well characterized than for U(VI). [(UO2)2(OH)]3+ is a known hydrolysis complex of U(VI) at low pH. Although not yet found in experiments, [(NpO2)2(OH)]3+ is suggested to exist due to the similarity between Np(VI) and U(VI) complexes, while [(NpO2)2(OH)]+ is a hypothetical species thus far. Our calculations suggest that the An(VI) complexes favor the parallel orientation of actinyls, whereas for the Np(V) complex a perpendicular arrangement is stabilized by hydrogen bonds between aqua ligands and the actinyl oxygen atoms. The Np(VI) complex [(NpO2)2(OH)]3+ features a structure and stability similar to its U(VI) analogue. From calculated formation constants for An(VI) diactinyl monohydroxo complexes, we find qualitative agreement with the experiment for U(VI). Both An(VI) complexes are only slightly less stable than the separate mononuclear constituents, the actinyl aqua and the monohydroxo complex. For the Np(V) species [(NpO2)2(OH)]+, we calculated a considerably lower complexation constant than for its An(VI) analogues, but it is more stable against decay into its constituents. Thus, this complex may exist at about the pH where Np(V) hydrolysis starts at not too low Np(V) concentrations.
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Affiliation(s)
- Ion Chiorescu
- Department Chemie, Technische Universität München, 85747Garching, Germany
| | - Sven Krüger
- Department Chemie, Technische Universität München, 85747Garching, Germany
| | - Notker Rösch
- Department Chemie, Technische Universität München, 85747Garching, Germany
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Rudshteyn B, Weber JL, Coskun D, Devlaminck PA, Zhang S, Reichman DR, Shee J, Friesner RA. Calculation of Metallocene Ionization Potentials via Auxiliary Field Quantum Monte Carlo: Toward Benchmark Quantum Chemistry for Transition Metals. J Chem Theory Comput 2022; 18:2845-2862. [PMID: 35377642 PMCID: PMC9123894 DOI: 10.1021/acs.jctc.1c01071] [Citation(s) in RCA: 15] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023]
Abstract
The accurate ab initio prediction of ionization energies is essential to understanding the electrochemistry of transition metal complexes in both materials science and biological applications. However, such predictions have been complicated by the scarcity of gas phase experimental data, the relatively large size of the relevant molecules, and the presence of strong electron correlation effects. In this work, we apply all-electron phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) utilizing multideterminant trial wave functions to six metallocene complexes to compare the computed adiabatic and vertical ionization energies with experimental results. We find that ph-AFQMC yields mean absolute errors (MAEs) of 1.69 ± 1.02 kcal/mol for the adiabatic energies and 2.85 ± 1.13 kcal/mol for the vertical energies. We also carry out density functional theory (DFT) calculations using a variety of functionals, which yields MAEs of 3.62-6.98 kcal/mol and 3.31-9.88 kcal/mol, as well as one variant of localized coupled cluster calculations (DLPNO-CCSD(T0) with moderate PNO cutoffs), which has MAEs of 4.96 and 6.08 kcal/mol, respectively. We also test the reliability of DLPNO-CCSD(T0) and DFT on acetylacetonate (acac) complexes for adiabatic energies measured in the same manner experimentally, and we find higher MAEs, ranging from 4.56 to 10.99 kcal/mol (with a different ordering) for DFT and 6.97 kcal/mol for DLPNO-CCSD(T0). Finally, by utilizing experimental solvation energies, we show that accurate reduction potentials in solution for the metallocene series can be obtained from the AFQMC gas phase results.
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Affiliation(s)
- Benjamin Rudshteyn
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
| | - John L Weber
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
| | - Dilek Coskun
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
| | - Pierre A Devlaminck
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
| | - Shiwei Zhang
- Center for Computational Quantum Physics, Flatiron Institute, 162 Fifth Avenue, New York, New York 10010, United States.,Department of Physics, College of William and Mary, Williamsburg, Virginia 23187, United States
| | - David R Reichman
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
| | - James Shee
- Department of Chemistry, University of California, Berkeley, California 94720, United States
| | - Richard A Friesner
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
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5
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Jakubowska K, Pecul M, Ruud K. Relativistic Four-Component DFT Calculations of Vibrational Frequencies. J Phys Chem A 2021; 125:10315-10320. [PMID: 34843253 PMCID: PMC8667032 DOI: 10.1021/acs.jpca.1c07398] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
![]()
We investigate the
effect of relativity on harmonic vibrational
frequencies. Density functional theory (DFT) calculations using the
four-component Dirac–Coulomb Hamiltonian have been performed
for 15 hydrides (H2X, X = O, S, Se, Te, Po; XH3, X = N, P, As, Sb, Bi; and XH4, X = C, Si, Ge, Sn, Pb)
as well as for HC≡CPbH3. The vibrational frequencies
have been calculated using finite differences of the molecular energy
with respect to geometrical distortions of the nuclei. The influences
of the choice of basis set, exchange–correlation functional,
and step length for the numerical differentiation on the calculated
harmonic vibrational frequencies have been tested, and the method
has been found to be numerically robust. Relativistic effects are
noticeable for the heavier congeners H2Te and H2Po, SbH3 and BiH3, and SnH4 and
PbH4 and are much more pronounced for the vibrational modes
with higher frequencies. Spin–orbit effects constitute a very
small fraction of the total relativistic effects, except for H2Te and H2Po. For HC≡CPbH3 we
find that only the frequencies of the modes with large contributions
from Pb displacements are significantly affected by relativity.
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Affiliation(s)
| | - Magdalena Pecul
- Faculty of Chemistry, University of Warsaw, 02-093 Warsaw, Poland
| | - Kenneth Ruud
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, UiT - The Arctic University of Norway, N-9019 Tromsø, Norway
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Gray A, Chiorescu I, Krüger S, Rösch N. Mononuclear Hydroxo Carbonato Complexes of Np(V), Np(VI), and U(VI): A Density Functional Study. Eur J Inorg Chem 2019. [DOI: 10.1002/ejic.201900759] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Affiliation(s)
- Andrew Gray
- Department Chemie Technische Universität München 85748 Garching Germany
| | - Ion Chiorescu
- Department Chemie Technische Universität München 85748 Garching Germany
| | - Sven Krüger
- Department Chemie Technische Universität München 85748 Garching Germany
| | - Notker Rösch
- Department Chemie Technische Universität München 85748 Garching Germany
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7
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Zhao L, Pan S, Holzmann N, Schwerdtfeger P, Frenking G. Chemical Bonding and Bonding Models of Main-Group Compounds. Chem Rev 2019; 119:8781-8845. [DOI: 10.1021/acs.chemrev.8b00722] [Citation(s) in RCA: 166] [Impact Index Per Article: 33.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Affiliation(s)
- Lili Zhao
- Institute of Advanced Synthesis, School of Chemistry and Molecular Engineering, Jiangsu National Synergetic Innovation Center for Advanced Materials, Nanjing Tech University, Nanjing 211816, China
| | - Sudip Pan
- Institute of Advanced Synthesis, School of Chemistry and Molecular Engineering, Jiangsu National Synergetic Innovation Center for Advanced Materials, Nanjing Tech University, Nanjing 211816, China
| | - Nicole Holzmann
- Scientific Computing Department, STFC Rutherford Appleton Laboratory, Harwell Oxford, Didcot OX11 0QX, United Kingdom
| | - Peter Schwerdtfeger
- The New Zealand Institute for Advanced Study, Massey University (Albany), 0632 Auckland, New Zealand
| | - Gernot Frenking
- Institute of Advanced Synthesis, School of Chemistry and Molecular Engineering, Jiangsu National Synergetic Innovation Center for Advanced Materials, Nanjing Tech University, Nanjing 211816, China
- Fachbereich Chemie, Philipps-Universität Marburg, Hans-Meerwein-Strasse, D-35043 Marburg, Germany
- Donostia International Physics Center (DIPC), P.K. 1072, 20080 Donostia, Euskadi, Spain
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8
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Egidi F, Goings JJ, Frisch MJ, Li X. Direct Atomic-Orbital-Based Relativistic Two-Component Linear Response Method for Calculating Excited-State Fine Structures. J Chem Theory Comput 2016; 12:3711-8. [DOI: 10.1021/acs.jctc.6b00474] [Citation(s) in RCA: 44] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Franco Egidi
- Department
of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Joshua J. Goings
- Department
of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Michael J. Frisch
- Gaussian,
Inc., 340 Quinnipiac St., Bldg. 40, Wallingford, Connecticut 06492, United States
| | - Xiaosong Li
- Department
of Chemistry, University of Washington, Seattle, Washington 98195, United States
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9
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Soini TM, Rösch N. Size-dependent properties of transition metal clusters: from molecules to crystals and surfaces--computational studies with the program ParaGauss. Phys Chem Chem Phys 2015; 17:28463-83. [PMID: 26456800 DOI: 10.1039/c5cp04281j] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023]
Abstract
In the so-called scalable regime the size-dependent behavior of the physical and chemical properties of transition metal clusters is described by scaling relationships. For most quantities this scalable regime is reached for cluster sizes between a few tens and a few hundreds of atoms, hence for systems for which an accurate treatment by density functional theory is still feasible. Thus, by invoking scaling relations one is able to obtain properties of very large nanoparticles and even the bulk limit from the results of a series of smaller cluster models. In this invited review we illustrate this strategy by exploiting results from computational studies that mostly were carried out with the density functional theory software ParaGauss. We address mainly the size-dependent behavior of the properties of transition metal clusters. To this end, we first present benchmark studies probing various approximations that are used in such density functional calculations. Subsequently we show how physical insight may be gained by exploring less understood types of systems. These applications range from bare clusters to nanoislands and nanoalloys to adsorption complexes.
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Affiliation(s)
- Thomas M Soini
- Department Chemie and Catalysis Research Center, Technische Universität München, 85747 Garching, Germany.
| | - Notker Rösch
- Department Chemie and Catalysis Research Center, Technische Universität München, 85747 Garching, Germany. and Institute of High Performance Computing, Agency for Science, Technology and Research, 1 Fusionopolis Way, Connexis #16-16, Singapore 138632, Singapore
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10
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Peralta JE, Hod O, Scuseria GE. Magnetization Dynamics from Time-Dependent Noncollinear Spin Density Functional Theory Calculations. J Chem Theory Comput 2015; 11:3661-8. [DOI: 10.1021/acs.jctc.5b00494] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Juan E. Peralta
- Department
of Physics, Central Michigan University, Mt. Pleasant, Michigan 48859, United States
| | - Oded Hod
- Department
of Chemical Physics, School of Chemistry, Raymond and Beverly Sackler
Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 6997801, Israel
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11
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Knecht S, Legeza Ö, Reiher M. Communication: Four-component density matrix renormalization group. J Chem Phys 2014; 140:041101. [DOI: 10.1063/1.4862495] [Citation(s) in RCA: 67] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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13
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Wang F, Liu W. Comparison of Different Polarization Schemes in Open-shell Relativistic Density Functional Calculations. J CHIN CHEM SOC-TAIP 2013. [DOI: 10.1002/jccs.200300087] [Citation(s) in RCA: 66] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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14
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Zeng Q, Shi J, Jiang G, Yang M, Wang F, Chen J. Structures and optical absorptions of PbSe clusters from ab initio calculations. J Chem Phys 2013; 139:094305. [DOI: 10.1063/1.4819695] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.2] [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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Ganyushin D, Neese F. A fully variational spin-orbit coupled complete active space self-consistent field approach: application to electron paramagnetic resonance g-tensors. J Chem Phys 2013; 138:104113. [PMID: 23514471 DOI: 10.1063/1.4793736] [Citation(s) in RCA: 87] [Impact Index Per Article: 7.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
In this work, a relativistic version of the state-averaged complete active space self-consistent field method is developed (spin-orbit coupled state-averaged complete active space self-consistent field; CAS-SOC). The program follows a "one-step strategy" and treats the spin-orbit interaction (SOC) on the same footing as the electron-electron interaction. As opposed to other existing approaches, the program employs an intermediate coupling scheme in which spin and space symmetry adapted configuration space functions are allowed to interact via SOC. This adds to the transparency and computational efficiency of the procedure. The approach requires the utilization of complex-valued configuration interaction coefficients, but the molecular orbital coefficients can be kept real-valued without loss of generality. Hence, expensive arithmetic associated with evaluation of complex-valued transformed molecular integrals is completely avoided. In order to investigate the quality of the calculated wave function, we extended the method to the calculation of electronic g-tensors. As the SOC is already treated to all orders in the SA-CASSCF process, first order perturbation theory with the Zeeman operator is sufficient to accomplish this task. As a test-set, we calculated g-tensors of a set of diatomics, a set of d(1) transition metal complexes MOX4(n-), and a set of 5f(1) actinide complexes AnX6(n-). These calculations reveal that the effect of the wavefunction relaxation due to variation inclusion of SOC is of the same order of magnitude as the effect of inclusion of dynamic correlation and hence cannot be neglected for the accurate prediction of electronic g-tensors.
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Affiliation(s)
- Dmitry Ganyushin
- Max-Planck-Institut für Chemische Energiekonversion, Stiftstrasse 34-36, Mülheim an der Ruhr, D-45470, Germany
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16
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Baldes A, Weigend F. Efficient two-component self-consistent field procedures and gradients: implementation in TURBOMOLE and application to. Mol Phys 2013. [DOI: 10.1080/00268976.2013.802037] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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17
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Yoshizawa T, Sakaki S. NMR shielding constants of CuX, AgX, and AuX (X = F, Cl, Br, and I) investigated by density functional theory based on the Douglas-Kroll-Hess Hamiltonian. J Comput Chem 2013; 34:1013-23. [DOI: 10.1002/jcc.23224] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/01/2012] [Revised: 12/11/2012] [Accepted: 12/13/2012] [Indexed: 11/11/2022]
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18
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Laury ML, Wilson AK. Examining the heavyp-block with a pseudopotential-based composite method: Atomic and molecular applications of rp-ccCA. J Chem Phys 2012; 137:214111. [DOI: 10.1063/1.4768420] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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20
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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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21
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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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22
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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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23
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Reiher M. Relativistic Douglas–Kroll–Hess theory. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2011. [DOI: 10.1002/wcms.67] [Citation(s) in RCA: 97] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Affiliation(s)
- Markus Reiher
- Laboratorium für Physikalische Chemie, ETH Zurich, Zurich, Switzerland
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24
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Zeng T, Fedorov DG, Schmidt MW, Klobukowski M. Two-component natural spinors from two-step spin-orbit coupled wave functions. J Chem Phys 2011; 134:214107. [DOI: 10.1063/1.3592780] [Citation(s) in RCA: 38] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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25
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Affiliation(s)
- Wenjian Liu
- a Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, State Key Laboratory of Rare Earth Materials Chemistry and Applications, College of Chemistry and Molecular Engineering, and Center for Computational Science and Engineering , Peking University , Beijing 100871, People's Republic of China
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Wüllen CV. A Quasirelativistic Two-component Density Functional and Hartree-Fock Program. ACTA ACUST UNITED AC 2010. [DOI: 10.1524/zpch.2010.6114] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
Abstract
Abstract
This work describes the implementation of an efficient two-component quasirelativistic density functional and Hartree-Fock program. The fact that the basis functions are real can be exploited if a special internal representation of operators and density matrices is used. This also leads to a considerable reduction of the effort in the closed shell case. While in most applications to open shell molecules, the noncollinear approach to define a relativistic spin density is preferable, the collinear approach finds its application in the calculation of magnetic anisotropy energies. Linear algebra steps in the SCF procedure have a higher relative weight compared to the nonrelativistic case, therefore some care was necessary to make them fast when parallelizing the code. The quasirelativistic Hamiltonians that have been implemented are the ´zeroth-order regular approximation´ (ZORA) Hamiltonian, the Douglas-Kroll-Hess Hamiltonian up to the sixth order, together with an accurate approximation to treat the picture change effect of the electron interaction, and effective core potential (ECP) matrix elements. Geometry gradients are available for the ZORA and ECP methods.
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27
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Fedorov DG, Klobukowski M. Multireference study of spin-orbit coupling in the hydrides of the 6p-block elements using the model core potential method. J Chem Phys 2010; 132:074102. [DOI: 10.1063/1.3297887] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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28
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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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Pershina V. Electronic Structure and Chemistry of the Heaviest Elements. CHALLENGES AND ADVANCES IN COMPUTATIONAL CHEMISTRY AND PHYSICS 2010. [DOI: 10.1007/978-1-4020-9975-5_11] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/30/2023]
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Cramer CJ, Truhlar DG. Density functional theory for transition metals and transition metal chemistry. Phys Chem Chem Phys 2009; 11:10757-816. [PMID: 19924312 DOI: 10.1039/b907148b] [Citation(s) in RCA: 1063] [Impact Index Per Article: 70.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Abstract
We introduce density functional theory and review recent progress in its application to transition metal chemistry. Topics covered include local, meta, hybrid, hybrid meta, and range-separated functionals, band theory, software, validation tests, and applications to spin states, magnetic exchange coupling, spectra, structure, reactivity, and catalysis, including molecules, clusters, nanoparticles, surfaces, and solids.
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Affiliation(s)
- Christopher J Cramer
- Department of Chemistry and Supercomputing Institute, University of Minnesota, Minneapolis, MN 55455-0431, USA.
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31
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van Wüllen C. Magnetic anisotropy from density functional calculations. Comparison of different approaches: Mn12O12 acetate as a test case. J Chem Phys 2009; 130:194109. [PMID: 19466823 DOI: 10.1063/1.3134430] [Citation(s) in RCA: 62] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Magnetic anisotropy is the capability of a system in a triplet or higher spin state to store magnetic information. Although the source of the magnetic anisotropy is the zero-field splitting of the ground state of the system, there is a difference between these two quantities that has to be fully rationalized before one makes comparisons. This is especially important for small spins such as triplets, where the magnetic anisotropy energy is only half of the zero-field splitting. Density functional calculations of magnetic anisotropy energies correspond to a high-field limit where the spins are aligned by the external magnetic field. Data are presented for the well-studied molecular magnet Mn(12)O(12) acetate. Both perturbative and self-consistent treatments, different quasirelativistic Hamiltonians (zeroth order regular approximation, Douglas-Kroll, effective core potentials) and exchange-correlation functionals are compared. It is shown that some effects usually considered minor, such as the inclusion of the exchange-correlation potential in the effective one-particle spin-orbit operator, lead to sizable differences when computing magnetic anisotropy energies. Higher-order contributions, that is, the difference between self-consistent and perturbative results, increase the magnetic anisotropy energy somewhat but do not introduce sizeable quartic terms or an in-plane anisotropy. In numerical experiments, on can switch off and on spin-orbit coupling at individual atomic sites. This procedure yields single-site contributions to the overall magnetic anisotropy energy that could be used as parameters in phenomenological spin Hamiltonians. If ferrimagnetic systems are treated with broken symmetry density functional methods where the Kohn-Sham reference function is not a spin eigenfunction, corrections are needed which depend on the size of the exchange couplings in the system and must therefore be evaluated case by case.
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Affiliation(s)
- Christoph van Wüllen
- Fachbereich Chemie, Technische Universität Kaiserslautern, 67663 Kaiserslautern, Germany.
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32
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Kremleva A, Krüger S, Rösch N. Role of aliphatic and phenolic hydroxyl groups in uranyl complexation by humic substances. Inorganica Chim Acta 2009. [DOI: 10.1016/j.ica.2008.11.021] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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33
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Neese F. Spin-Hamiltonian Parameters from First Principle Calculations: Theory and Application. HIGH RESOLUTION EPR 2009. [DOI: 10.1007/978-0-387-84856-3_5] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
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34
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Assadollahzadeh B, Schwerdtfeger P. A systematic search for minimum structures of small gold clusters Au[sub n] (n=2–20) and their electronic properties. J Chem Phys 2009; 131:064306. [PMID: 19691387 DOI: 10.1063/1.3204488] [Citation(s) in RCA: 175] [Impact Index Per Article: 11.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Behnam Assadollahzadeh
- Centre for Theoretical Chemistry and Physics, New Zealand Institute for Advanced Study, Massey University (Albany), Private Bag 102904, North Shore MSC, 0745 Auckland, New Zealand.
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35
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Peralta JE, Barone V. Magnetic exchange couplings from noncollinear spin density functional perturbation theory. J Chem Phys 2008; 129:194107. [DOI: 10.1063/1.3013602] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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36
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Jackson VE, Craciun R, Dixon DA, Peterson KA, de Jong WA. Prediction of Vibrational Frequencies of UO22+ at the CCSD(T) Level. J Phys Chem A 2008; 112:4095-9. [DOI: 10.1021/jp710334b] [Citation(s) in RCA: 44] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Virgil E. Jackson
- Department of Chemistry, University of Alabama, Tuscaloosa, Alabama 35487-0336
| | - Raluca Craciun
- Department of Chemistry, University of Alabama, Tuscaloosa, Alabama 35487-0336
| | - David A. Dixon
- Department of Chemistry, University of Alabama, Tuscaloosa, Alabama 35487-0336
| | - Kirk A. Peterson
- Department of Chemistry, Washington State University, Pullman, Washington 99164-4630
| | - Wibe A. de Jong
- Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, P.O. Box 999, Richland, Washington 99352
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37
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Armbruster MK, Weigend F, van Wüllen C, Klopper W. Self-consistent treatment of spin-orbit interactions with efficient Hartree-Fock and density functional methods. Phys Chem Chem Phys 2008; 10:1748-56. [PMID: 18350180 DOI: 10.1039/b717719d] [Citation(s) in RCA: 120] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Efficient self-consistent field (SCF) schemes including both scalar relativistic effects and spin-orbit (SO) interactions at Hartree-Fock (HF) and density functional (DFT) levels are presented. SO interactions require the extension of standard procedures to two-component formalisms. Efficiency is achieved by using effective core potentials (ECPs) and by employing the resolution-of-the-identity approximation for the Coulomb part (RI-J) in pure DFT calculations as well as also for the HF-exchange part (RI-JK) in the case of HF or hybrid-DFT treatments. The procedures were implemented in the program system TURBOMOLE; efficiency is demonstrated for comparably large systems, such as Pb54. Relevance of SO effects for electronic structure and stability is illustrated by treatments of small Pb and Po clusters with and without accounting for SO effects.
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Affiliation(s)
- Markus K Armbruster
- Forschungszentrum Karlsruhe GmbH, Institut für Nanotechnologie, P. O. Box 3640, D-76021, Karlsruhe, Germany
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38
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Di Valentin C, Neyman KM, Risse T, Sterrer M, Fischbach E, Freund HJ, Nasluzov VA, Pacchioni G, Rösch N. Density-functional model cluster studies of EPR g tensors of Fs+ centers on the surface of MgO. J Chem Phys 2007; 124:044708. [PMID: 16460201 DOI: 10.1063/1.2161190] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We report g tensors of surface color centers, so-called F(s) (+) centers, of MgO calculated with two density-functional approaches using accurately embedded cluster models. In line with recent UHV measurements on single-crystalline MgO film, we determined only small g-tensor anisotropies and negative shifts Deltag identical with g-g(e) for all F(s) (+) sites considered, namely, (001)-terrace, step, edge, and corner sites. The g values are very sensitive to the local structure of the defect: relaxation reverses the sign of Deltag. However, accounting for the spin-orbit interaction either self-consistently or perturbatively yields very similar results. In addition to the values of the tensor components, their direction with respect to the surface was determined. In contrast to edges, significant deviations from ideal C(2v) symmetry were found for F(s) (+) centers at steps. Recent data on single-crystalline thin films are reevaluated in the light of these results.
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Affiliation(s)
- Cristiana Di Valentin
- Dipartimento di Scienza dei Materiali, Università degli Studi Milano-Bicocca, 20125 Milano, Italy
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39
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Neese F. Importance of direct spin-spin coupling and spin-flip excitations for the zero-field splittings of transition metal complexes: a case study. J Am Chem Soc 2007; 128:10213-22. [PMID: 16881651 DOI: 10.1021/ja061798a] [Citation(s) in RCA: 385] [Impact Index Per Article: 22.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
This work reports the evaluation of several theoretical approaches to the zero-field splitting (ZFS) in transition metal complexes. The experimentally well-known complex [Mn(acac)3] is taken as an example. The direct spin-spin contributions to the ZFS have been calculated on the basis of density functional theory (DFT) or complete active space self-consistent field (CASSCF) wave functions and have been found to be much more important than previously assumed. The contributions of the direct term may exceed approximately 1 cm(-1) in magnitude and therefore cannot be neglected in any treatment that aims at a realistic quantitative modeling of the ZFS. In the DFT framework, two different variants to treat the spin-orbit coupling (SOC) term have been evaluated. The first approach is based on previous work by Pederson, Khanna, and Kortus, and the second is based on a "quasi-restricted" DFT treatment which is rooted in our previous work on ZFS. Both approaches provide very similar results and underestimate the SOC contribution to the ZFS by a factor of 2 or more. The SOC is represented by an accurate multicenter spin-orbit mean-field (SOMF) approximation which is compared to the popular effective DFT potential-derived SOC operator. In addition to the DFT results, direct "infinite order" ab initio calculations of the SOC contribution to the ZFS based on CASSCF wave functions, the spectroscopy-oriented configuration interaction (SORCI), and the difference-dedicated CI (DDCI) approach are reported. In general, the multireference ab initio results provide a more realistic description of the ZFS in [Mn(acac)3]. The conclusions likely carry over to many other systems. This is attributed to the explicit treatment of the multiplet effects which are of dominant importance, since the calculations demonstrate that, even in the high-spin d4 system MnIII, the spin-flip excitations make the largest contribution to the SOC. It is demonstrated that the ab initio methods can be used even for somewhat larger molecules (the present calculations were done with more than 500 basis functions) in a reasonable time frame. Much more economical but still fairly reasonable results have been achieved with the INDO/S treatment based on CASSCF and SOC-CI wave functions.
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Affiliation(s)
- Frank Neese
- Institut für Physikalische und Theoretische Chemie, Universität Bonn, Wegelerstrasse 12, 53115 Bonn, Germany.
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40
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Reiher M, Wolf A. Exact decoupling of the Dirac Hamiltonian. II. The generalized Douglas-Kroll-Hess transformation up to arbitrary order. J Chem Phys 2006; 121:10945-56. [PMID: 15634044 DOI: 10.1063/1.1818681] [Citation(s) in RCA: 488] [Impact Index Per Article: 27.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In order to achieve exact decoupling of the Dirac Hamiltonian within a unitary transformation scheme, we have discussed in part I of this series that either a purely numerical iterative technique (the Barysz-Sadlej-Snijders method) or a stepwise analytic approach (the Douglas-Kroll-Hess method) are possible. For the evaluation of Douglas-Kroll-Hess Hamiltonians up to a pre-defined order it was shown that a symbolic scheme has to be employed. In this work, an algorithm for this analytic derivation of Douglas-Kroll-Hess Hamiltonians up to any arbitrary order in the external potential is presented. We discuss how an estimate for the necessary order for exact decoupling (within machine precision) for a given system can be determined from the convergence behavior of the Douglas-Kroll-Hess expansion prior to a quantum chemical calculation. Once this maximum order has been accomplished, the spectrum of the positive-energy part of the decoupled Hamiltonian, e.g., for electronic bound states, cannot be distinguished from the corresponding part of the spectrum of the Dirac operator. An efficient scalar-relativistic implementation of the symbolic operations for the evaluation of the positive-energy part of the block-diagonal Hamiltonian is presented, and its accuracy is tested for ground-state energies of one-electron ions over the whole periodic table. Furthermore, the first many-electron calculations employing sixth up to fourteenth order DKH Hamiltonians are presented.
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Affiliation(s)
- Markus Reiher
- Lehrstuhl für Theoretische Chemie, Universität Bonn, Wegelerstrasse 12, D-53115 Bonn, Germany.
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41
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Armbruster MK, Klopper W, Weigend F. Basis-set extensions for two-component spin-orbit treatments of heavy elements. Phys Chem Chem Phys 2006; 8:4862-5. [PMID: 17066175 DOI: 10.1039/b610211e] [Citation(s) in RCA: 60] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The accuracy of standard basis sets of quadruple-zeta and lower quality for the use in two-component self-consistent field procedures including spin-orbit coupling is investigated for the elements In-I and Au-At. Spin-orbit coupling leads to energetic and spatial splittings of inner shells, which are not described accurately with standard basis sets optimized for scalar relativistic calculations. This results in large errors in total atomic energies and significant errors in atomization energies of compounds containing these atoms. We show how these errors can be corrected by adding just a few steep sets of basis functions and demonstrate the quality of the resulting extended basis sets.
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Affiliation(s)
- Markus K Armbruster
- Center for Functional Nanostructures (CFN) and Lehrstuhl für Theoretische Chemie, Institut für Physikalische Chemie, Universität Karlsruhe (TH), D-76128 Karlsruhe, Germany
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42
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Komorovský S, Repiský M, Malkina OL, Malkin VG, Malkin I, Kaupp M. Resolution of identity Dirac-Kohn-Sham method using the large component only: Calculations of g-tensor and hyperfine tensor. J Chem Phys 2006; 124:084108. [PMID: 16512709 DOI: 10.1063/1.2173995] [Citation(s) in RCA: 37] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A new relativistic two-component density functional approach, based on the Dirac-Kohn-Sham method and an extensive use of the technique of resolution of identity (RI), has been developed and is termed the DKS2-RI method. It has been applied to relativistic calculations of g and hyperfine tensors of coinage-metal atoms and some mercury complexes. The DKS2-RI method solves the Dirac-Kohn-Sham equations in a two-component framework using explicitly a basis for the large component only, but it retains all contributions coming from the small component. The DKS2-RI results converge to those of the four-component Dirac-Kohn-Sham with an increasing basis set since the error associated with the use of RI will approach zero. The RI approximation provides a basis for a very efficient implementation by avoiding problems associated with complicated integrals otherwise arising from the elimination of the small component. The approach has been implemented in an unrestricted noncollinear two-component density functional framework. DKS2-RI is related to Dyall's [J. Chem. Phys. 106, 9618 (1997)] unnormalized elimination of the small component method (which was formulated at the Hartree-Fock level and applied to one-electron systems only), but it takes advantage of the local Kohn-Sham exchange-correlation operators (as, e.g., arising from local or gradient-corrected functionals). The DKS2-RI method provides an attractive alternative to existing approximate two-component methods with transformed Hamiltonians (such as Douglas-Kroll-Hess [Ann. Phys. 82, 89 (1974); Phys. Rev. A 33, 3742 (1986)] method, zero-order regular approximation, or related approaches) for relativistic calculations of the structure and properties of heavy-atom systems. In particular, no picture-change effects arise in the property calculations.
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Affiliation(s)
- Stanislav Komorovský
- Institute of Inorganic Chemistry, Slovak Academy of Sciences, Dúbravská cesta 9, SK-84536 Bratislava, Slovak Republic
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43
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Di Valentin C, Neyman KM, Risse T, Sterrer M, Fischbach E, Freund HJ, Nasluzov VA, Pacchioni G, Rösch N. Density-functional model cluster studies of EPR g tensors of Fs+ centers on the surface of MgO. J Chem Phys 2006. [DOI: 10.1063/1.2161190 10.1063/1.2161190] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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44
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Melo JI, Ruiz de Azúa MC, Peralta JE, Scuseria GE. Relativistic calculation of indirect NMR spin-spin couplings using the Douglas-Kroll-Hess approximation. J Chem Phys 2005; 123:204112. [PMID: 16351245 DOI: 10.1063/1.2133730] [Citation(s) in RCA: 43] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We have employed the Douglas-Kroll-Hess approximation to derive the perturbative Hamiltonians involved in the calculation of NMR spin-spin couplings in molecules containing heavy elements. We have applied this two-component quasirelativistic approach using finite perturbation theory in combination with a generalized Kohn-Sham code that includes the spin-orbit interaction self-consistently and works with Hartree-Fock and both pure and hybrid density functionals. We present numerical results for one-bond spin-spin couplings in the series of tetrahydrides CH(4), SiH(4), GeH(4), and SnH(4). Our two-component Hartree-Fock results are in good agreement with four-component Dirac-Hartree-Fock calculations, although a density-functional treatment better reproduces the available experimental data.
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Affiliation(s)
- Juan I Melo
- Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón 1, 1428 Buenos Aires, Argentina
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van Wüllen C, Michauk C. Accurate and efficient treatment of two-electron contributions in quasirelativistic high-order Douglas-Kroll density-functional calculations. J Chem Phys 2005; 123:204113. [PMID: 16351246 DOI: 10.1063/1.2133731] [Citation(s) in RCA: 84] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Two-component quasirelativistic approaches are in principle capable of reproducing results from fully relativistic calculations based on the four-component Dirac equation (with fixed particle number). For one-electron systems, this also holds in practice, but in many-electron systems one has to transform the two-electron interaction, which is necessary because a picture change occurs when going from the Dirac equation to a two-component method. For one-electron properties, one can take full account of picture change in a manageable way, but for the electron interaction, this would spoil the computational advantages which are the main reason to perform quasirelativistic calculations. Exploiting those picture change effects are largest in the atomic cores, which in molecular applications do not differ too much from the cores of isolated neutral atoms, we propose an elegant, efficient, and accurate approximation to the two-electron picture change problem. The new approach, called the "model potential" approach because it makes use of atomic (four- and two-component) data to estimate picture change effects in molecules, shares with the nuclear-only approach that the Douglas-Kroll operator needs to be constructed only once (not in each self-consistent-field iteration) and that no time-consuming multicenter relativistic two-electron integrals need to be calculated. The new approach correctly describes the screening of both the nearest nucleus and distant nuclei, for the scalar-relativistic as well as the spin-orbit parts of the Hamiltonian. The approach is tested on atomic and molecular-orbital energies as well as spectroscopic constants of the lead dimer.
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Affiliation(s)
- Christoph van Wüllen
- Institute of Chemistry, Technical University Berlin, Strasse des 17. Juni 135, D-10623 Berlin, Germany.
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Matveev AV, Majumder S, Rösch N. Efficient treatment of the Hartree interaction in the relativistic Kohn-Sham problem. J Chem Phys 2005; 123:164104. [PMID: 16268678 DOI: 10.1063/1.2079907] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We elaborate the two-component Douglas-Kroll reduction of the Dirac-Kohn-Sham problem of relativistic density-functional theory as introduced by Matveev and Rosch [J. Chem. Phys. 118, 3997 (2003)]. That method retains corrections to the Coulomb self-interaction (or Hartree) term of the energy functional that are due to the picture change. Using analytic expressions for the matrix elements, one is able to abandon the resolution of the identity approach for a crucial step of the relativistic transformation. Thus, a major source of uncertainties of the method is eliminated because basis sets no longer have to be extended by functions of higher angular momentum, previously required to ensure kinetic balance. This approach also relies on the electron charge-density fitting scheme via an auxiliary basis set. An efficient approximate implementation results if one restricts the relativistic transformation to the spherically symmetric atom-centered auxiliary functions. It provides accurate results while simplifying greatly the expressions for the matrix elements of the relativistically transformed operators and significantly reducing the computational effort. We demonstrate the performance of the method for the fine structure of one-electron levels of the Hg atom, the g-tensor shifts of NO2, and the properties of the diatomic molecules Bi2, Pb2, PbO, and TlH.
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Affiliation(s)
- Alexei V Matveev
- Department Chemie, Theoretische Chemie, Technische Universität München, 85747 Garching, Germany
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48
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van Wüllen C. Sixth-order Douglas–Kroll: two-component reference data for one-electron ions from through. Chem Phys 2005. [DOI: 10.1016/j.chemphys.2004.10.010] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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49
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50
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Peralta JE, Uddin J, Scuseria GE. Scalar relativistic all-electron density functional calculations on periodic systems. J Chem Phys 2005; 122:84108. [PMID: 15836021 DOI: 10.1063/1.1851973] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Scalar relativistic effects are included in periodic boundary conditions calculations with Gaussian orbitals. This approach is based on the third-order Douglas-Kroll-Hess approximation, allowing the treatment of all electrons on an equal footing. With this methodology, we are able to perform relativistic all-electron density functional calculations using the traditional local spin-density and generalized gradient approximations (GGA), as well as meta-GGA and hybrid density functionals. We present benchmark results for the bulk metals Pd, Ag, Pt, and Au, and the large band gap semiconductors AgF and AgCl.
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Affiliation(s)
- Juan E Peralta
- Department of Chemistry, Rice University, Houston, TX 77005-1892, USA
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