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Hesselmann A, Werner HJ, Knowles PJ. Thermochemical evaluation of adaptive and fixed density functional theory quadrature schemes. J Chem Phys 2022; 157:234106. [PMID: 36550055 DOI: 10.1063/5.0119622] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Abstract
A systematic study is made of the accuracy and efficiency of a number of existing quadrature schemes for molecular Kohn-Sham Density-Functional Theory (DFT) using 408 molecules and 254 chemical reactions. Included are the fixed SG-x (x = 0-3) grids of Gill et al., Dasgupta, and Herbert, the 3-zone grids of Treutler and Ahlrichs, a fixed five-zone grid implemented in Molpro, and a new adaptive grid scheme. While all methods provide a systematic reduction of errors upon extension of the grid sizes, significant differences are observed in the accuracies for similar grid sizes with various approaches. For the tests in this work, the SG-x fixed grids are less suitable to achieve high accuracies in the DFT integration, while our new adaptive grid performed best among the schemes studied in this work. The extra computational time to generate the adaptive grid scales linearly with molecular size and is negligible compared with the time needed for the self-consistent field iterations for large molecules. A comparison of the grid accuracies using various density functionals shows that meta-GGA functionals need larger integration grids than GGA functionals to reach the same degree of accuracy, confirming previous investigations of the numerical stability of meta-GGA functionals. On the other hand, the grid integration errors are almost independent of the basis set, and the basis set errors are mostly much larger than the errors caused by the numerical integrations, even when using the smallest grids tested in this work.
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Affiliation(s)
- Andreas Hesselmann
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
| | - Hans-Joachim Werner
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
| | - Peter J Knowles
- School of Chemistry, Cardiff University, Main Building, Park Place, Cardiff CF10 3AT, United Kingdom
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2
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Feller D, Stanton J, Davidson ER. Atomic Isotropic Hyperfine Properties for Second Row Elements (Al - Cl). J Chem Phys 2022; 157:126101. [DOI: 10.1063/5.0114858] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Isotropic hyperfine properties have been obtained for the second row elements Al - Cl using a systematic composite approach consisting of a sequence of core/valence correlation consistent basis sets, up through aug-cc-pCV7Z, along with configuration interaction and coupled cluster methods. The best nonrelativistic final values for the atomic ground states (in MHz) are: -1.80 27Al (2Po1/2), -24.31 29Si (3P0), 63.70 31P (4So3/2), 20.77 33S (3P2) and 35.42. 35Cl (2Po3/2). We find a large K shell contribution to the spin density at the nucleus that is almost cancelled by the L and M shell contributions. The spin density in atomic units is approximately linear with respect to atomic number.
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Affiliation(s)
- David Feller
- Department of Chemistry, Washington State University, United States of America
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Jaworski A, Hedin N. Electron correlation and vibrational effects in predictions of paramagnetic NMR shifts. Phys Chem Chem Phys 2022; 24:15230-15244. [PMID: 35703010 DOI: 10.1039/d2cp01206e] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Electronic structure calculations are fundamentally important for the interpretation of nuclear magnetic resonance (NMR) spectra from paramagnetic systems that include organometallic and inorganic compounds, catalysts, or metal-binding sites in proteins. Prediction of induced paramagnetic NMR shifts requires knowledge of electron paramagnetic resonance (EPR) parameters: the electronic g tensor, zero-field splitting D tensor, and hyperfine A tensor. The isotropic part of A, called the hyperfine coupling constant (HFCC), is one of the most troublesome properties for quantum chemistry calculations. Yet, even relatively small errors in calculations of HFCC tend to propagate into large errors in the predicted NMR shifts. The poor quality of A tensors that are currently calculated using density functional theory (DFT) constitutes a bottleneck in improving the reliability of interpretation of the NMR spectra from paramagnetic systems. In this work, electron correlation effects in calculations of HFCCs with a hierarchy of ab initio methods were assessed, and the applicability of different levels of DFT approximations and the coupled cluster singles and doubles (CCSD) method was tested. These assessments were performed for the set of selected test systems comprising an organic radical, and complexes with transition metal and rare-earth ions, for which experimental data are available. Severe deficiencies of DFT were revealed but the CCSD method was able to deliver good agreement with experimental data for all systems considered, however, at substantial computational costs. We proposed a more computationally tractable alternative, where the A was computed with the coupled cluster theory exploiting locality of electron correlation. This alternative is based on the domain-based local pair natural orbital coupled cluster singles and doubles (DLPNO-CCSD) method. In this way the robustness and reliability of the coupled cluster theory were incorporated into the modern formalism for the prediction of induced paramagnetic NMR shifts, and became applicable to systems of chemical interest. This approach was verified for the bis(cyclopentadienyl)vanadium(II) complex (Cp2V; vanadocene), and the metal-binding site of the Zn2+ → Co2+ substituted superoxide dismutase (SOD) metalloprotein. Excellent agreement with experimental NMR shifts was achieved, which represented a substantial improvement over previous theoretical attempts. The effects of vibrational corrections to orbital shielding and hyperfine tensor were evaluated and discussed within the second-order vibrational perturbation theory (VPT2) framework.
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Affiliation(s)
- Aleksander Jaworski
- Department of Materials and Environmental Chemistry, Stockholm University, SE-106 91 Stockholm, Sweden.
| | - Niklas Hedin
- Department of Materials and Environmental Chemistry, Stockholm University, SE-106 91 Stockholm, Sweden.
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Feller D, Stanton JF, Davidson ER. Atomic isotropic hyperfine properties for first row elements (B–F) revisited. J Chem Phys 2022; 156:034304. [DOI: 10.1063/5.0080155] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- David Feller
- Department of Chemistry, Washington State University, Pullman, Washington 99164-4630, USA and University of Alabama, Tuscaloosa, Alabama 35487-0336, USA
| | - John F. Stanton
- Quantum Theory Project, Department of Chemistry, University of Florida, Gainesville, Florida 32611, USA
| | - Ernest R. Davidson
- Department of Chemistry, University of Washington, Seattle, Washington 98195-1700, USA
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Ghassemi Tabrizi S, Arbuznikov AV, Jiménez-Hoyos CA, Kaupp M. Hyperfine-Coupling Tensors from Projected Hartree-Fock Theory. J Chem Theory Comput 2020; 16:6222-6235. [PMID: 32841008 DOI: 10.1021/acs.jctc.0c00617] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Abstract
We assess the calculation of hyperfine coupling (HFC) tensors by different variants of Projected Hartree-Fock (PHF) theory. For a set of small main-group S = 1/2 radicals (BO, CO+, CN, AlO, vinyl, methyl, ethynyl), spin-symmetry as well as complex-conjugation and point-group symmetry are first broken in a reference determinant, and then variationally restored, in the frame of the modern formulation of PHF theory. Historically, PHF theory was basically restricted to the restoration of spin symmetry from an unrestricted HF determinant (conserving Sz symmetry). This afforded unsatisfactory HFCs. We obtain far better results for isotropic (and anisotropic) HFCs when the variational energy is further lowered by working with generalized determinants that completely break spin symmetry, and when additional symmetries are used. Specifically, complex-conjugation projection recovers a substantial fraction of the dynamical correlation energy in small molecules, and the detailed equations for combined complex-conjugation, spin- and point-group projection in the density-matrix/diagonalization formulation of PHF theory are here reported for the first time. The compact representation of the PHF wave function allows for a straightforward evaluation of the spin-density matrix and of HFC tensors with little effort. The promising performance of PHF theory may motivate the application of post-PHF methods to the calculation of HFC tensors.
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Affiliation(s)
- Shadan Ghassemi Tabrizi
- Institut für Chemie, Theoretische Chemie, Technische Universität Berlin, Sekr. C7, Strasse des 17. Juni 135, 10623 Berlin, Germany
| | - Alexei V Arbuznikov
- Institut für Chemie, Theoretische Chemie, Technische Universität Berlin, Sekr. C7, Strasse des 17. Juni 135, 10623 Berlin, Germany
| | - Carlos A Jiménez-Hoyos
- Department of Chemistry, Wesleyan University, Middletown, Connecticut 06459, United States
| | - Martin Kaupp
- Institut für Chemie, Theoretische Chemie, Technische Universität Berlin, Sekr. C7, Strasse des 17. Juni 135, 10623 Berlin, Germany
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Witwicki M, Walencik PK, Jezierska J. How accurate is density functional theory in predicting spin density? An insight from the prediction of hyperfine coupling constants. J Mol Model 2019; 26:10. [PMID: 31834497 DOI: 10.1007/s00894-019-4268-0] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2019] [Accepted: 11/25/2019] [Indexed: 01/30/2023]
Abstract
Electron paramagnetic resonance (EPR) spectroscopy has been proven to be an important technique for studying paramagnetic systems. Probably, the most accessible EPR parameter and the one that provides a significant amount of information about molecular structure and spin density is the hyperfine coupling constant (HFCC). Hence, accurate quantum-chemical modeling of HFCCs is frequently essential to the adequate interpretation of EPR spectra. It requires the precise spin density, which is the difference between the densities of α- and β-electrons, and thus, its quality is expected to reflect the quality of the total electron density. The question of which approximate exchange-correlation density functional yields sufficiently accurate HFCCs, and thus, the spin density remains open. To assess the performance of well-established density functionals for calculating HFCCs, we used a series of 26 small paramagnetic species and compared the obtained results to the CCSD reference values. The performance of DFT was also tested on EPR-studied o-semiquinone radical interacting with water molecules and Mg2+ cation. The HFCCs were additionally calculated by the DLPNO-CCSD method, and this wave function-based technique was found superior to all functionals we tested. Although some functionals were found, on average, to be fairly efficient, we found that the most accurate functional is system-dependent, and therefore, the DLPNO-CCSD method should be preferred for theoretical investigations of the HFCCs and spin density.
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Affiliation(s)
- Maciej Witwicki
- Faculty of Chemistry, Wrocław University, ul. F. Joliot-Curie 14, 50-383, Wrocław, Poland.
| | - Paulina K Walencik
- Faculty of Chemistry, Wrocław University, ul. F. Joliot-Curie 14, 50-383, Wrocław, Poland
| | - Julia Jezierska
- Faculty of Chemistry, Wrocław University, ul. F. Joliot-Curie 14, 50-383, Wrocław, Poland
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Datta D, Gauss J. Accurate Prediction of Hyperfine Coupling Tensors for Main Group Elements Using a Unitary Group Based Rigorously Spin-Adapted Coupled-Cluster Theory. J Chem Theory Comput 2019; 15:1572-1592. [PMID: 30698956 DOI: 10.1021/acs.jctc.8b01048] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We present the development of a perturbative triples correction scheme for the previously reported unitary group based spin-adapted combinatoric open-shell coupled-cluster (CC) singles and doubles (COS-CCSD) approach and report on the applications of the newly developed method, termed "COS-CCSD(T)", to the calculation of hyperfine coupling (HFC) tensors for radicals consisting of hydrogen, second- and third-row elements. The COS-CCSD(T) method involves a single noniterative step with [Formula: see text] scaling of the computational cost for the calculation of triples corrections to the energy. The key feature of this development is the use of spatial semicanonical orbitals generated from standard restricted open-shell Hartree-Fock (ROHF) orbitals, which allows the unperturbed Hamiltonian operator to be defined in terms of a diagonal spin-free Fock operator. The HFC tensors are computed as a first-order property via implementation of an analytic derivative scheme. The required one-particle spin density matrix is computed by using one- and two-particle spin-free density matrices that are obtained from the analytic derivative implementation, in this way avoiding the use of any spin-dependent operator and maintaining spin adaptation of the CC wavefunction. Benchmark calculations of HFC tensors for a set of 21 radicals indicate reasonably good agreement of the COS-CCSD(T) results with experiment and a consistent improvement over the COS-CCSD method. We demonstrate that the accuracies of the isotropic hyperfine coupling constants obtained in unrestricted HF (UHF) reference based spin-orbital CCSD(T) calculations deteriorate when spin contamination in the UHF wavefunction is large, and the results may even become qualitatively incorrect when spin polarization is the driving mechanism. Within a similar noniterative perturbative treatment of triple excitations, the spin-adapted COS-CCSD(T) approach produces accurate results, thus ensuring cost-effectiveness together with reliability.
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Affiliation(s)
- Dipayan Datta
- Institut für Physikalische Chemie , Johannes Gutenberg-Universität Mainz , Duesbergweg 10-14 , 55128 Mainz , Germany
| | - Jürgen Gauss
- Institut für Physikalische Chemie , Johannes Gutenberg-Universität Mainz , Duesbergweg 10-14 , 55128 Mainz , Germany
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Schattenberg CJ, Maier TM, Kaupp M. Lessons from the Spin-Polarization/Spin-Contamination Dilemma of Transition-Metal Hyperfine Couplings for the Construction of Exchange-Correlation Functionals. J Chem Theory Comput 2018; 14:5653-5672. [DOI: 10.1021/acs.jctc.8b00597] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Caspar J. Schattenberg
- Institut für Chemie, Technische Universität Berlin, Theoretische Chemie/Quantenchemie, Sekr. C7, Straße des 17. Juni 135, D-10623 Berlin, Germany
| | - 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
| | - Martin Kaupp
- Institut für Chemie, Technische Universität Berlin, Theoretische Chemie/Quantenchemie, Sekr. C7, Straße des 17. Juni 135, D-10623 Berlin, Germany
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Maier TM, Arbuznikov AV, Kaupp M. Local hybrid functionals: Theory, implementation, and performance of an emerging new tool in quantum chemistry and beyond. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2018. [DOI: 10.1002/wcms.1378] [Citation(s) in RCA: 65] [Impact Index Per Article: 10.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Affiliation(s)
- Toni M. Maier
- Institut für Chemie Theoretische Chemie/Quantenchemie Technische Universität Berlin Berlin Germany
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering Waseda University Tokyo Japan
| | - Alexei V. Arbuznikov
- Institut für Chemie Theoretische Chemie/Quantenchemie Technische Universität Berlin Berlin Germany
| | - Martin Kaupp
- Institut für Chemie Theoretische Chemie/Quantenchemie Technische Universität Berlin Berlin Germany
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Sharkas K, Pritchard B, Autschbach J. Effects from Spin–Orbit Coupling on Electron–Nucleus Hyperfine Coupling Calculated at the Restricted Active Space Level for Kramers Doublets. J Chem Theory Comput 2015; 11:538-49. [DOI: 10.1021/ct500988h] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
Affiliation(s)
- Kamal Sharkas
- Department of Chemistry, State University of New York at Buffalo, Buffalo, New York 14260-3000, United States
| | - Ben Pritchard
- Department of Chemistry, State University of New York at Buffalo, Buffalo, New York 14260-3000, United States
| | - Jochen Autschbach
- Department of Chemistry, State University of New York at Buffalo, Buffalo, New York 14260-3000, United States
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Lan TN, Kurashige Y, Yanai T. Toward Reliable Prediction of Hyperfine Coupling Constants Using Ab Initio Density Matrix Renormalization Group Method: Diatomic 2Σ and Vinyl Radicals as Test Cases. J Chem Theory Comput 2014; 10:1953-67. [DOI: 10.1021/ct400978j] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Tran Nguyen Lan
- The Graduate University for Advanced Studies, Myodaiji, Okazaki, Aichi 444-8585, Japan
| | - Yuki Kurashige
- The Graduate University for Advanced Studies, Myodaiji, Okazaki, Aichi 444-8585, Japan
- Department
of Theoretical and Computational Molecular Science, Institute for Molecular Science, Okazaki, Aichi 444-8585, Japan
| | - Takeshi Yanai
- The Graduate University for Advanced Studies, Myodaiji, Okazaki, Aichi 444-8585, Japan
- Department
of Theoretical and Computational Molecular Science, Institute for Molecular Science, Okazaki, Aichi 444-8585, Japan
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