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Bruder F, Franzke YJ, Weigend F. Paramagnetic NMR Shielding Tensors Based on Scalar Exact Two-Component and Spin-Orbit Perturbation Theory. J Phys Chem A 2022; 126:5050-5069. [PMID: 35857421 DOI: 10.1021/acs.jpca.2c03579] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The temperature-dependent Fermi-contact and pseudocontact terms are important contributions to the paramagnetic NMR shielding tensor. Herein, we augment the scalar-relativistic (local) exact two-component (X2C) framework with spin-orbit perturbation theory including the screened nuclear spin-orbit correction for the EPR hyperfine coupling and g tensor to compute these temperature-dependent terms. The accuracy of this perturbative ansatz is assessed with the self-consistent spin-orbit two-component and four-component treatments serving as reference. This shows that the Fermi-contact and pseudocontact interaction is sufficiently described for paramagnetic NMR shifts; however, larger deviations are found for the EPR spectra and the principle components of the EPR properties of heavy elements. The impact of the perturbative treatment is further compared to that of the density functional approximation and the basis set. Large-scale calculations are routinely possible with the multipole-accelerated resolution of the identity approximation and the seminumerical exchange approximation, as shown for [CeTi6O3(OiPr)9(salicylate)6].
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Affiliation(s)
- Florian Bruder
- Fachbereich Chemie, Philipps-Universität Marburg, 35032 Marburg, Germany
| | - Yannick J Franzke
- Fachbereich Chemie, Philipps-Universität Marburg, 35032 Marburg, Germany
| | - Florian Weigend
- Fachbereich Chemie, Philipps-Universität Marburg, 35032 Marburg, Germany
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2
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Birnoschi L, Chilton NF. Hyperion: A New Computational Tool for Relativistic Ab Initio Hyperfine Coupling. J Chem Theory Comput 2022; 18:4719-4732. [PMID: 35776849 PMCID: PMC9367016 DOI: 10.1021/acs.jctc.2c00257] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
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Herein we describe Hyperion, a new program for computing
relativistic picture-change-corrected magnetic resonance parameters
from scalar relativistic active space wave functions, with or without
spin–orbit coupling (SOC) included a posteriori. Hyperion also includes a new orbital decomposition method
for assisting active space selection for calculations of hyperfine
coupling. For benchmarking purposes, we determine hyperfine coupling
constants of selected alkali metal, transition metal, and lanthanide
atoms, based on complete active space self-consistent field spin–orbit
calculations in OpenMolcas. Our results are in excellent agreement
with experimental data from atomic spectroscopy as well as theoretical
predictions from four-component relativistic calculations.
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Affiliation(s)
- Letitia Birnoschi
- Department of Chemistry, The University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom
| | - Nicholas F Chilton
- Department of Chemistry, The University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom
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Franzke YJ, Yu JM. Quasi-Relativistic Calculation of EPR g Tensors with Derivatives of the Decoupling Transformation, Gauge-Including Atomic Orbitals, and Magnetic Balance. J Chem Theory Comput 2022; 18:2246-2266. [PMID: 35354319 DOI: 10.1021/acs.jctc.1c01175] [Citation(s) in RCA: 12] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Abstract
We present an exact two-component (X2C) ansatz for the EPR g tensor using gauge-including atomic orbitals (GIAOs) and a magnetically balanced basis set expansion. In contrast to previous X2C and four-component relativistic ansätze for the g tensor, this implementation results in a gauge-origin-invariant formalism. Furthermore, the derivatives of the relativistic decoupling matrix are incorporated to form the complete analytical derivative of the X2C Hamiltonian. To reduce the associated computational costs, we apply the diagonal local approximation to the unitary decoupling transformation (DLU). The quasi-relativistic X2C and DLU-X2C Hamiltonians accurately reproduce the results of the parent four-component relativistic theory when accounting for two-electron picture-change effects with the modified screened nuclear spin-orbit approximation in the respective one-electron integrals and integral derivatives. According to our benchmark studies, the uncontracted Dyall and segmented-contracted Karlsruhe x2c-type basis sets perform well when compared to large even-tempered basis sets. Moreover, (range-separated) hybrid density functional approximations such as LC-ωPBE and ωB97X-D are needed to match the experimental findings. The impact of the GIAOs depends on the distribution of the spin density, and their use may change the Δg shifts by 10-50% as shown for [(C5Me5)2Y(μ-S)2Mo(μ-S)2Y(C5Me5)2]-. Routine calculations of large molecules are possible with widely available and comparably low-cost hardware as demonstrated for [Pt(C6Cl5)4]- with 3003 basis functions and three spin-(1/2) La(II) and Lu(II) compounds, for which we observe good agreement with the experimental findings.
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Affiliation(s)
- Yannick J Franzke
- Fachbereich Chemie, Philipps-Universität Marburg, 35032 Marburg, Germany
| | - Jason M Yu
- Department of Chemistry, University of California─Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
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Franzke YJ, Yu JM. Hyperfine Coupling Constants in Local Exact Two-Component Theory. J Chem Theory Comput 2021; 18:323-343. [PMID: 34928142 DOI: 10.1021/acs.jctc.1c01027] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
We present a highly efficient implementation of the electron-nucleus hyperfine coupling matrix within the one-electron exact two-component (X2C) theory. The complete derivative of the X2C Hamiltonian is formed, that is, the derivatives of the unitary decoupling transformation are considered. This requires the solution of the response and Sylvester equations, consequently increasing the computational costs. Therefore, we apply the diagonal local approximation to the unitary decoupling transformation (DLU). The finite nucleus model is employed for both the scalar potential and the vector potential. Two-electron picture-change effects are modeled with the (modified) screened nuclear spin-orbit approach. Our implementation is fully integral direct and OpenMP-parallelized. An extensive benchmark study regarding the Hamiltonian, the basis set, and the density functional approximation is carried out for a set of 12-17 transition-metal compounds. The error introduced by DLU is negligible, and the DLU-X2C Hamiltonian accurately reproduces its four-component "fully" relativistic parent results. Functionals with a large amount of Hartree-Fock exchange such as CAM-QTP-02 and ωB97X-D are generally favorable. The pure density functional r2SCAN performs remarkably and even outperforms the common hybrid functionals TPSSh and CAM-B3LYP. Fully uncontracted basis sets or contracted quadruple-ζ bases are required for accurate results. The capability of our implementation is demonstrated for [Pt(C6Cl5)4]- with more than 4700 primitive basis functions and four rare-earth single-molecule magnets: [La(OAr*)3]-, [Lu(NR2)3]-, [Lu(OAr*)3]-, and [TbPc2]-. Here, the results with the spin-orbit DLU-X2C Hamiltonian are in an excellent agreement with the experimental findings of all Pt, La, Lu, and Tb molecules.
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Affiliation(s)
- Yannick J Franzke
- Fachbereich Chemie, Philipps-Universität Marburg, Hans-Meerwein-Straße 4, 35032 Marburg, Germany
| | - Jason M Yu
- Department of Chemistry, University of California, Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, United States
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Rouf SA, Mareš J, Vaara J. Relativistic Approximations to Paramagnetic NMR Chemical Shift and Shielding Anisotropy in Transition Metal Systems. J Chem Theory Comput 2017. [DOI: 10.1021/acs.jctc.7b00168] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Syed Awais Rouf
- NMR Research Unit, University of Oulu, P.O.
Box 3000, Oulu FIN-90014, Finland
| | - Jiří Mareš
- NMR Research Unit, University of Oulu, P.O.
Box 3000, Oulu FIN-90014, Finland
| | - Juha Vaara
- NMR Research Unit, University of Oulu, P.O.
Box 3000, Oulu FIN-90014, Finland
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6
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Bučinský L, Jayatilaka D, Grabowsky S. Importance of Relativistic Effects and Electron Correlation in Structure Factors and Electron Density of Diphenyl Mercury and Triphenyl Bismuth. J Phys Chem A 2016; 120:6650-69. [PMID: 27434184 DOI: 10.1021/acs.jpca.6b05769] [Citation(s) in RCA: 48] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
This study investigates the possibility of detecting relativistic effects and electron correlation in single-crystal X-ray diffraction experiments using the examples of diphenyl mercury (HgPh2) and triphenyl bismuth (BiPh3). In detail, the importance of electron correlation (ECORR), relativistic effects (REL) [distinguishing between total, scalar and spin-orbit (SO) coupling relativistic effects] and picture change error (PCE) on the theoretical electron density, its topology and its Laplacian using infinite order two component (IOTC) wave functions is discussed. This is to develop an understanding of the order of magnitude and shape of these different effects as they manifest in the electron density. Subsequently, the same effects are considered for the theoretical structure factors. It becomes clear that SO and PCE are negligible, but ECORR and scalar REL are important in low- and medium-order reflections on absolute and relative scales-not in the high-order region. As a further step, Hirshfeld atom refinement (HAR) and subsequent X-ray constrained wavefunction (XCW) fitting have been performed for the compound HgPh2 with various relativistic and nonrelativistic wave functions against the experimental structure factors. IOTC calculations of theoretical structure factors and relativistic HAR as well as relativistic XCW fitting are presented for the first time, accounting for both scalar and spin-orbit relativistic effects.
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Affiliation(s)
- Lukáš Bučinský
- Institute of Physical Chemistry and Chemical Physics FCHPT, Slovak University of Technology , Radlinskeho 9, Bratislava SK-812 37, Slovakia
| | - Dylan Jayatilaka
- School of Chemistry and Biochemistry, The University of Western Australia , 35 Stirling Highway, Perth WA 6009, Australia
| | - Simon Grabowsky
- Fachbereich 2 - Biologie/Chemie, Universität Bremen , Leobener Straβe NW2, 28359 Bremen, Germany
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Martin B, Autschbach J. Temperature dependence of contact and dipolar NMR chemical shifts in paramagnetic molecules. J Chem Phys 2015; 142:054108. [PMID: 25662637 DOI: 10.1063/1.4906318] [Citation(s) in RCA: 61] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Using a recently proposed equation for NMR nuclear magnetic shielding for molecules with unpaired electrons [A. Soncini and W. Van den Heuvel, J. Chem. Phys. 138, 021103 (2013)], equations for the temperature (T) dependent isotropic shielding for multiplets with an effective spin S equal to 1/2, 1, 3/2, 2, and 5/2 in terms of electron paramagnetic resonance spin Hamiltonian parameters are derived and then expanded in powers of 1/T. One simplifying assumption used is that a matrix derived from the zero-field splitting (ZFS) tensor and the Zeeman coupling matrix (g-tensor) share the same principal axis system. The influence of the rhombic ZFS parameter E is only investigated for S = 1. Expressions for paramagnetic contact shielding (from the isotropic part of the hyperfine coupling matrix) and pseudo-contact or dipolar shielding (from the anisotropic part of the hyperfine coupling matrix) are considered separately. The leading order is always 1/T. A temperature dependence of the contact shielding as 1/T and of the dipolar shielding as 1/T(2), which is sometimes assumed in the assignment of paramagnetic chemical shifts, is shown to arise only if S ≥ 1 and zero-field splitting is appreciable, and only if the Zeeman coupling matrix is nearly isotropic (Δg = 0). In such situations, an assignment of contact versus dipolar shifts may be possible based only on linear and quadratic fits of measured variable-temperature chemical shifts versus 1/T. Numerical data are provided for nickelocene (S = 1). Even under the assumption of Δg = 0, a different leading order of contact and dipolar shifts in powers of 1/T is not obtained for S = 3/2. When Δg is not very small, dipolar and contact shifts both depend in leading order in 1/T in all cases, with sizable contributions in order 1/T(n) with n = 2 and higher.
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Affiliation(s)
- Bob Martin
- Department of Chemistry, University at Buffalo, State University of New York, Buffalo, New York 14260-3000, USA
| | - Jochen Autschbach
- Department of Chemistry, University at Buffalo, State University of New York, Buffalo, New York 14260-3000, USA
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Křístková A, Komorovsky S, Repisky M, Malkin VG, Malkina OL. Relativistic four-component calculations of indirect nuclear spin-spin couplings with efficient evaluation of the exchange-correlation response kernel. J Chem Phys 2015; 142:114102. [DOI: 10.1063/1.4913639] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Anežka Křístková
- Institute of Inorganic Chemistry, Slovak Academy of Sciences, Dúbravská cesta 9, SK-84536 Bratislava, Slovakia
| | - Stanislav Komorovsky
- Centre for Theoretical and Computational Chemistry, University of Tromsø - The Arctic University of Norway, N-9037 Tromsø, Norway
| | - Michal Repisky
- Centre for Theoretical and Computational Chemistry, University of Tromsø - The Arctic University of Norway, N-9037 Tromsø, Norway
| | - Vladimir G. Malkin
- Institute of Inorganic Chemistry, Slovak Academy of Sciences, Dúbravská cesta 9, SK-84536 Bratislava, Slovakia
| | - Olga L. Malkina
- Institute of Inorganic Chemistry, Slovak Academy of Sciences, Dúbravská cesta 9, SK-84536 Bratislava, Slovakia
- Department of Inorganic Chemistry, Comenius University, Bratislava, Slovakia
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Autschbach J. Relativistic calculations of magnetic resonance parameters: background and some recent developments. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2014; 372:20120489. [PMID: 24516182 DOI: 10.1098/rsta.2012.0489] [Citation(s) in RCA: 51] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
This article outlines some basic concepts of relativistic quantum chemistry and recent developments of relativistic methods for the calculation of the molecular properties that define the basic parameters of magnetic resonance spectroscopic techniques, i.e. nuclear magnetic resonance shielding, indirect nuclear spin-spin coupling and electric field gradients (nuclear quadrupole coupling), as well as with electron paramagnetic resonance g-factors and electron-nucleus hyperfine coupling. Density functional theory (DFT) has been very successful in molecular property calculations, despite a number of problems related to approximations in the functionals. In particular, for heavy-element systems, the large electron count and the need for a relativistic treatment often render the application of correlated wave function ab initio methods impracticable. Selected applications of DFT in relativistic calculation of magnetic resonance parameters are reviewed.
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Affiliation(s)
- Jochen Autschbach
- Department of Chemistry, State University of New York at Buffalo, , Buffalo, NY 14260-3000, USA
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Affiliation(s)
- Michał Jaszuński
- a Institute of Organic Chemistry , Polish Academy of Sciences , Warszawa , 01-224 , Kasprzaka 44, Poland
| | - Małgorzata Olejniczak
- b Faculty of Chemistry , University of Warsaw , Pasteura 1, Laboratoire de Chimie et Physique Quantiques (UMR 5626), CNRS and Université de Toulouse 3 (Paul Sabatier), 118 Route de Narbonne, F-31062 Toulouse, France, Warsaw , 02-093 , Poland
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Abstract
This perspective article discusses some broadly-known and some less broadly-known consequences of Einstein's special relativity in quantum chemistry, and provides a brief outline of the theoretical methods currently in use, along with a discussion of recent developments and selected applications. The treatment of the electron correlation problem in relativistic quantum chemistry methods, and expanding the reach of the available relativistic methods to calculate all kinds of energy derivative properties, in particular spectroscopic and magnetic properties, requires on-going efforts.
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Affiliation(s)
- Jochen Autschbach
- Department of Chemistry, State University of New York at Buffalo, New York 14260-3000, USA.
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12
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Pritchard B, Autschbach J. Theoretical Investigation of Paramagnetic NMR Shifts in Transition Metal Acetylacetonato Complexes: Analysis of Signs, Magnitudes, and the Role of the Covalency of Ligand–Metal Bonding. Inorg Chem 2012; 51:8340-51. [DOI: 10.1021/ic300868v] [Citation(s) in RCA: 51] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- 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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Aquino F, Pritchard B, Autschbach J. Scalar Relativistic Computations and Localized Orbital Analyses of Nuclear Hyperfine Coupling and Paramagnetic NMR Chemical Shifts. J Chem Theory Comput 2012; 8:598-609. [DOI: 10.1021/ct2008507] [Citation(s) in RCA: 73] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023]
Affiliation(s)
- Fredy Aquino
- Department
of Chemistry, University at Buffalo, State
University of New York, Buffalo, New York 14260−3000
| | - Ben Pritchard
- Department
of Chemistry, University at Buffalo, State
University of New York, Buffalo, New York 14260−3000
| | - Jochen Autschbach
- Department
of Chemistry, University at Buffalo, State
University of New York, Buffalo, New York 14260−3000
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Aquino F, Govind N, Autschbach J. Scalar Relativistic Computations of Nuclear Magnetic Shielding and g-Shifts with the Zeroth-Order Regular Approximation and Range-Separated Hybrid Density Functionals. J Chem Theory Comput 2011; 7:3278-92. [DOI: 10.1021/ct200408j] [Citation(s) in RCA: 38] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023]
Affiliation(s)
- Fredy Aquino
- Department of Chemistry, State University of New York at Buffalo, Buffalo, New York 14260-3000
| | - Niranjan Govind
- William R. Wiley Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, 902 Battelle Blvd, P.O. Box 999, Mail Stop K8-91 Richland, Washington 99352, United States
| | - Jochen Autschbach
- Department of Chemistry, State University of New York at Buffalo, Buffalo, New York 14260-3000
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Autschbach J, Pritchard B. Calculation of molecular g-tensors using the zeroth-order regular approximation and density functional theory: expectation value versus linear response approaches. Theor Chem Acc 2011. [DOI: 10.1007/s00214-010-0880-x] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
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