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Pikulová P, Misenkova D, Marek R, Komorovsky S, Novotný J. Quadratic Spin-Orbit Mechanism of the Electronic g-Tensor. J Chem Theory Comput 2023; 19:1765-1776. [PMID: 36896579 DOI: 10.1021/acs.jctc.2c01213] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/11/2023]
Abstract
Understanding how the electronic g-tensor is linked to the electronic structure is desirable for the correct interpretation of electron paramagnetic resonance spectra. For heavy-element compounds with large spin-orbit (SO) effects, this is still not completely clear. We report our investigation of quadratic SO contributions to the g-shift in heavy transition metal complexes. We implemented third-order perturbation theory in order to analyze the contributions arising from frontier molecular spin orbitals (MSOs). We show that the dominant quadratic SO term─spin-Zeeman (SO2/SZ)─generally makes a negative contribution to the g-shift, irrespective of the particular electronic configuration or molecular symmetry. We further analyze how the SO2/SZ contribution adds to or subtracts from the linear orbital-Zeeman (SO/OZ) contribution to the individual principal components of the g-tensor. Our study suggests that the SO2/SZ mechanism decreases the anisotropy of the g-tensor in early transition metal complexes and increases it in late transition metal complexes. Finally, we apply MSO analysis to the investigation of g-tensor trends in a set of closely related Ir and Rh pincer complexes and evaluate the influence of different chemical factors (the nuclear charge of the central atom and the terminal ligand) on the magnitudes of the g-shifts. We expect our conclusions to aid the understanding of spectra in magnetic resonance investigations of heavy transition metal compounds.
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Affiliation(s)
- Petra Pikulová
- CEITEC─Central European Institute of Technology, Masaryk University, Kamenice 5, Brno CZ-62500, Czechia.,Department of Chemistry, Faculty of Science, Masaryk University, Kamenice 5, Brno CZ-62500, Czechia
| | - Debora Misenkova
- Institute of Inorganic Chemistry, Slovak Academy of Science, Dúbravská cesta 9, Bratislava SK-84536, Slovakia
| | - Radek Marek
- CEITEC─Central European Institute of Technology, Masaryk University, Kamenice 5, Brno CZ-62500, Czechia.,Department of Chemistry, Faculty of Science, Masaryk University, Kamenice 5, Brno CZ-62500, Czechia
| | - Stanislav Komorovsky
- Institute of Inorganic Chemistry, Slovak Academy of Science, Dúbravská cesta 9, Bratislava SK-84536, Slovakia
| | - Jan Novotný
- CEITEC─Central European Institute of Technology, Masaryk University, Kamenice 5, Brno CZ-62500, Czechia.,Department of Chemistry, Faculty of Science, Masaryk University, Kamenice 5, Brno CZ-62500, Czechia.,Institute of Inorganic Chemistry, Slovak Academy of Science, Dúbravská cesta 9, Bratislava SK-84536, Slovakia
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2
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Lang L, Ravera E, Parigi G, Luchinat C, Neese F. Theoretical analysis of the long-distance limit of NMR chemical shieldings. J Chem Phys 2022; 156:154115. [PMID: 35459319 DOI: 10.1063/5.0088162] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022] Open
Abstract
After some years of controversy, it was recently demonstrated how to obtain the correct long-distance limit [point-dipole approximation (PDA)] of pseudo-contact nuclear magnetic resonance chemical shifts from rigorous first-principles quantum mechanics [Lang et al., J. Phys. Chem. Lett. 11, 8735 (2020)]. This result confirmed the classical Kurland-McGarvey theory. In the present contribution, we elaborate on these results. In particular, we provide a detailed derivation of the PDA both from the Van den Heuvel-Soncini equation for the chemical shielding tensor and from a spin Hamiltonian approximation. Furthermore, we discuss in detail the PDA within the approximate density functional theory and Hartree-Fock theories. In our previous work, we assumed a relatively crude effective nuclear charge approximation for the spin-orbit coupling operator. Here, we overcome this assumption by demonstrating that the derivation is also possible within the fully relativistic Dirac equation and even without the assumption of a specific form for the Hamiltonian. Crucial ingredients for the general derivation are a Hamiltonian that respects gauge invariance, the multipolar gauge, and functional derivatives of the Hamiltonian, where it is possible to identify the first functional derivative with the electron number current density operator. The present work forms an important foundation for future extensions of the Kurland-McGarvey theory beyond the PDA, including induced magnetic quadrupole and higher moments to describe the magnetic hyperfine field.
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Affiliation(s)
- Lucas Lang
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany
| | - Enrico Ravera
- Magnetic Resonance Center (CERM), University of Florence, and Consorzio Interuniversitario Risonanze Magnetiche di Metalloproteine (CIRMMP), Via Sacconi 6, Sesto Fiorentino 50019, Italy
| | - Giacomo Parigi
- Magnetic Resonance Center (CERM), University of Florence, and Consorzio Interuniversitario Risonanze Magnetiche di Metalloproteine (CIRMMP), Via Sacconi 6, Sesto Fiorentino 50019, Italy
| | - Claudio Luchinat
- Magnetic Resonance Center (CERM), University of Florence, and Consorzio Interuniversitario Risonanze Magnetiche di Metalloproteine (CIRMMP), Via Sacconi 6, Sesto Fiorentino 50019, Italy
| | - Frank Neese
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany
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Krivdin LB. Computational NMR of heavy nuclei involving 109Ag, 113Cd, 119Sn, 125Te, 195Pt, 199Hg, 205Tl, and 207Pb. RUSSIAN CHEMICAL REVIEWS 2021. [DOI: 10.1070/rcr4976] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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4
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Rusakova IL, Rusakov YY. Quantum chemical calculations of 77 Se and 125 Te nuclear magnetic resonance spectral parameters and their structural applications. MAGNETIC RESONANCE IN CHEMISTRY : MRC 2021; 59:359-407. [PMID: 33095923 DOI: 10.1002/mrc.5111] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/12/2020] [Revised: 09/01/2020] [Accepted: 10/07/2020] [Indexed: 06/11/2023]
Abstract
An accurate quantum chemical (QC) modeling of 77 Se and 125 Te nuclear magnetic resonance (NMR) spectra is deeply involved in the NMR structural assignment for selenium and tellurium compounds that are of utmost importance both in organic and inorganic chemistry nowadays due to their huge application potential in many fields, like biology, medicine, and metallurgy. The main interest of this review is focused on the progress in QC computations of 77 Se and 125 Te NMR chemical shifts and indirect spin-spin coupling constants involving these nuclei. Different computational methodologies that have been used to simulate the NMR spectra of selenium and tellurium compounds since the middle of the 1990s are discussed with a strong emphasis on their accuracy. A special accent is placed on the calculations resorting to the relativistic methodologies, because taking into account the relativistic effects appreciably influences the precision of NMR calculations of selenium and, especially, tellurium compounds. Stereochemical applications of quantum chemical calculations of 77 Se and 125 Te NMR parameters are discussed so as to exemplify the importance of integrated approach of experimental and computational NMR techniques.
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Affiliation(s)
- Irina L Rusakova
- A. E. Favorsky Irkutsk Institute of Chemistry, Siberian Branch of the Russian Academy of Sciences, Irkutsk, Russian Federation
| | - Yuriy Yu Rusakov
- A. E. Favorsky Irkutsk Institute of Chemistry, Siberian Branch of the Russian Academy of Sciences, Irkutsk, Russian Federation
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Lang L, Ravera E, Parigi G, Luchinat C, Neese F. Solution of a Puzzle: High-Level Quantum-Chemical Treatment of Pseudocontact Chemical Shifts Confirms Classic Semiempirical Theory. J Phys Chem Lett 2020; 11:8735-8744. [PMID: 32930598 PMCID: PMC7584370 DOI: 10.1021/acs.jpclett.0c02462] [Citation(s) in RCA: 21] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2020] [Accepted: 09/15/2020] [Indexed: 06/11/2023]
Abstract
A recently popularized approach for the calculation of pseudocontact shifts (PCSs) based on first-principles quantum chemistry (QC) leads to different results than the classic "semiempirical" equation involving the susceptibility tensor. Studies that attempted a comparison of theory and experiment led to conflicting conclusions with respect to the preferred theoretical approach. In this Letter, we show that after inclusion of previously neglected terms in the full Hamiltonian, one can deduce the semiempirical equations from a rigorous QC-based treatment. It also turns out that in the long-distance limit, one can approximate the complete A tensor in terms of the g tensor. By means of Kohn-Sham density functional theory calculations, we numerically confirm the long-distance expression for the A tensor and the theoretically predicted scaling behavior of the different terms. Our derivation suggests a computational strategy in which one calculates the susceptibility tensor and inserts it into the classic equation for the PCS.
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Affiliation(s)
- Lucas Lang
- Max-Planck-Institut
für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany
| | - Enrico Ravera
- Magnetic
Resonance Center (CERM), University of Florence,
and Consorzio Interuniversitario Risonanze Magnetiche di Metalloproteine
(CIRMMP), via Sacconi
6, Sesto Fiorentino 50019, Italy
- Department
of Chemistry “Ugo Schiff”, University of Florence, via della Lastruccia 3, Sesto Fiorentino 50019, Italy
| | - Giacomo Parigi
- Magnetic
Resonance Center (CERM), University of Florence,
and Consorzio Interuniversitario Risonanze Magnetiche di Metalloproteine
(CIRMMP), via Sacconi
6, Sesto Fiorentino 50019, Italy
- Department
of Chemistry “Ugo Schiff”, University of Florence, via della Lastruccia 3, Sesto Fiorentino 50019, Italy
| | - Claudio Luchinat
- Magnetic
Resonance Center (CERM), University of Florence,
and Consorzio Interuniversitario Risonanze Magnetiche di Metalloproteine
(CIRMMP), via Sacconi
6, Sesto Fiorentino 50019, Italy
- Department
of Chemistry “Ugo Schiff”, University of Florence, via della Lastruccia 3, Sesto Fiorentino 50019, Italy
| | - Frank Neese
- Max-Planck-Institut
für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany
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6
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On the development of the exact two-component relativistic method for calculating indirect NMR spin-spin coupling constants. Chem Phys 2019. [DOI: 10.1016/j.chemphys.2018.09.039] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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7
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Relativistic effects in the NMR spectra of compounds containing heavy chalcogens. MENDELEEV COMMUNICATIONS 2018. [DOI: 10.1016/j.mencom.2018.01.001] [Citation(s) in RCA: 40] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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8
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Jaszuński M, Antušek A, Demissie TB, Komorovsky S, Repisky M, Ruud K. Indirect NMR spin–spin coupling constants in diatomic alkali halides. J Chem Phys 2016; 145:244308. [DOI: 10.1063/1.4972892] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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9
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Wodyński A, Malkina OL, Pecul M. The Relativistic Effects on the Carbon-Carbon Coupling Constants Mediated by a Heavy Atom. J Phys Chem A 2016; 120:5624-34. [PMID: 27177252 DOI: 10.1021/acs.jpca.5b10258] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The (2)JCC, (3)JCC, and (4)JCC spin-spin coupling constants in the systems with a heavy atom (Cd, In, Sn, Sb, Te, Hg, Tl, Pb, Bi, and Po) in the coupling path have been calculated by means of density functional theory. The main goal was to estimate the relativistic effects on spin-spin coupling constants and to explore the factors which may influence them, including the nature of the heavy atom and carbon hybridization. The methods applied range, in order of reduced complexity, from the Dirac-Kohn-Sham (DKS) method (density functional theory with four-component Dirac-Coulomb Hamiltonian), through DFT with two- and one-component zeroth-order regular approximation (ZORA) Hamiltonians, to scalar effective core potentials (ECPs) with the nonrelativistic Hamiltonian. The use of DKS and ZORA methods leads to very similar results, and small-core ECPs of the MDF and MWB variety reproduce correctly the scalar relativistic effects. Scalar relativistic effects usually are larger than the spin-orbit coupling effects. The latter tend to influence the most the coupling constants of the sp(3)-hybridized carbon atoms and in compounds of the p-block heavy atoms. Large spin-orbit coupling contributions for the Po compounds are probably connected with the inverse of the lowest triplet excitation energy.
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Affiliation(s)
- Artur Wodyński
- Faculty of Chemistry, University of Warsaw , ul. Pasteura 1, 02-093 Warszawa, Poland
| | - Olga L Malkina
- Institute of Inorganic Chemistry, Slovak Academy of Sciences , Dubravska cesta 9, SK-84536 Bratislava, Slovak Republic.,Department of Inorganic Chemistry, Faculty of Natural Sciences, Comenius University , SK-84215 Bratislava, Slovakia
| | - Magdalena Pecul
- Faculty of Chemistry, University of Warsaw , ul. Pasteura 1, 02-093 Warszawa, Poland
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10
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Rusakova IL, Rusakov YY, Krivdin LB. Indirect relativistic bridge and substituent effects from the 'heavy' environment on the one-bond and two-bond (13)C-(1)H spin-spin coupling constants. MAGNETIC RESONANCE IN CHEMISTRY : MRC 2016; 54:39-45. [PMID: 26352434 DOI: 10.1002/mrc.4313] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/17/2015] [Accepted: 07/18/2015] [Indexed: 06/05/2023]
Abstract
Indirect relativistic bridge effect (IRBE) and indirect relativistic substituent effect (IRSE) induced by the 'heavy' environment of the IV-th, V-th and VI-th main group elements on the one-bond and geminal (13)C-(1)H spin-spin coupling constants are observed, and spin-orbit parts of these two effects were interpreted in terms of the third-order Rayleigh-Schrödinger perturbation theory. Both effects, IRBE and IRSE, rapidly increase with the total atomic charge of the substituents at the coupled carbon. The accumulation of IRSE for geminal coupling constants is not linear with respect to the number of substituents in contrast to the one-bond couplings where IRSE is an essentially additive quantity.
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Affiliation(s)
- Irina L Rusakova
- A. E. Favorsky Irkutsk Institute of Chemistry, Siberian Branch of the Russian Academy of Sciences, Irkutsk, Russia
| | - Yury Yu Rusakov
- A. E. Favorsky Irkutsk Institute of Chemistry, Siberian Branch of the Russian Academy of Sciences, Irkutsk, Russia
| | - Leonid B Krivdin
- A. E. Favorsky Irkutsk Institute of Chemistry, Siberian Branch of the Russian Academy of Sciences, Irkutsk, Russia
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11
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Zarycz MNC, Provasi PF, Sauer SPA. On the truncation of the number of excited states in density functional theory sum-over-states calculations of indirect spin spin coupling constants. J Chem Phys 2015; 143:244107. [PMID: 26723651 DOI: 10.1063/1.4937572] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
It is investigated, whether the number of excited (pseudo)states can be truncated in the sum-over-states expression for indirect spin-spin coupling constants (SSCCs), which is used in the Contributions from Localized Orbitals within the Polarization Propagator Approach and Inner Projections of the Polarization Propagator (IPPP-CLOPPA) approach to analyzing SSCCs in terms of localized orbitals. As a test set we have studied the nine simple compounds, CH4, NH3, H2O, SiH4, PH3, SH2, C2H2, C2H4, and C2H6. The excited (pseudo)states were obtained from time-dependent density functional theory (TD-DFT) calculations with the B3LYP exchange-correlation functional and the specialized core-property basis set, aug-cc-pVTZ-J. We investigated both how the calculated coupling constants depend on the number of (pseudo)states included in the summation and whether the summation can be truncated in a systematic way at a smaller number of states and extrapolated to the total number of (pseudo)states for the given one-electron basis set. We find that this is possible and that for some of the couplings it is sufficient to include only about 30% of the excited (pseudo)states.
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Affiliation(s)
- M Natalia C Zarycz
- Department of Physics, University of Northeastern - CONICET, Av. Libertad 5500, Corrientes W3404AAS, Argentina
| | - Patricio F Provasi
- Department of Physics, University of Northeastern - CONICET, Av. Libertad 5500, Corrientes W3404AAS, Argentina
| | - Stephan P A Sauer
- Department of Chemistry, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark
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12
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Wodyński A, Pecul M. The influence of a presence of a heavy atom on the spin-spin coupling constants between two light nuclei in organometallic compounds and halogen derivatives. J Chem Phys 2014; 140:024319. [DOI: 10.1063/1.4858466] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [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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Demissie TB, Repisky M, Komorovsky S, Isaksson J, Svendsen JS, Dodziuk H, Ruud K. Four-component relativistic chemical shift calculations of halogenated organic compounds. J PHYS ORG CHEM 2013. [DOI: 10.1002/poc.3157] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Affiliation(s)
- Taye B. Demissie
- Institute of Physical Chemistry; Polish Academy of Sciences; Kasprzaka 44/52 Warsaw Poland
- Centre for Theoretical and Computational Chemistry, Department of Chemistry; University of Tromsø; N-9037 Tromsø Norway
| | - Michal Repisky
- Centre for Theoretical and Computational Chemistry, Department of Chemistry; University of Tromsø; N-9037 Tromsø Norway
| | - Stanislav Komorovsky
- Centre for Theoretical and Computational Chemistry, Department of Chemistry; University of Tromsø; N-9037 Tromsø Norway
| | - Johan Isaksson
- Centre for Research-based Innovation on Marine Bioactivities and Drug Discovery (MABCENT); University of Tromsø; N-9037 Tromsø Norway
| | - John S. Svendsen
- Centre for Research-based Innovation on Marine Bioactivities and Drug Discovery (MABCENT); University of Tromsø; N-9037 Tromsø Norway
| | - Helena Dodziuk
- Institute of Physical Chemistry; Polish Academy of Sciences; Kasprzaka 44/52 Warsaw Poland
| | - Kenneth Ruud
- Centre for Theoretical and Computational Chemistry, Department of Chemistry; University of Tromsø; N-9037 Tromsø Norway
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14
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Wodyński A, Repiský M, Pecul M. A comparison of two-component and four-component approaches for calculations of spin-spin coupling constants and NMR shielding constants of transition metal cyanides. J Chem Phys 2012; 137:014311. [DOI: 10.1063/1.4730944] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.6] [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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Rusakov YY, Krivdin LB, Potapov VA, Penzik MV, Amosova SV. Conformational analysis and diastereotopic assignments in the series of selenium-containing heterocycles by means of 77Se-1H spin-spin coupling constants: a combined theoretical and experimental study. MAGNETIC RESONANCE IN CHEMISTRY : MRC 2011; 49:389-398. [PMID: 21452352 DOI: 10.1002/mrc.2760] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/27/2010] [Revised: 02/25/2011] [Accepted: 03/01/2011] [Indexed: 05/30/2023]
Abstract
A combined theoretical and experimental study on the stereochemical behavior of (77)Se-(1)H spin-spin coupling constants has been performed at the second-order polarization propagator approach level together with heteronuclear multiple-bond correlation technique in the series of selenium-containing four-, five- and six-membered heterocycles including the derivatives of thiaselenetane, selenasilole, thiaselenole, thiaselenolane and dihydrothiaselenine. Geminal and vicinal (77)Se-(1)H spin-spin couplings were shown to have the pronounced stereochemical dependences in respect with the topology of the coupling pathway, internal rotation of the side-chain substituents and ring inversion providing a straightforward tool for the conformational analysis and diastereotopic assignments in the chiral organoselenium compounds.
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Affiliation(s)
- Yury Yu Rusakov
- A. E. Favorsky Irkutsk Institute of Chemistry, Siberian Branch of the Russian Academy of Sciences, Irkutsk, Russia
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Rusakov YY, Krivdin LB, Sauer SPA, Levanova EP, Levkovskaya GG. Structural trends of 77Se-1H spin-spin coupling constants and conformational behavior of 2-substituted selenophenes. MAGNETIC RESONANCE IN CHEMISTRY : MRC 2010; 48:44-52. [PMID: 19877126 DOI: 10.1002/mrc.2537] [Citation(s) in RCA: 38] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
Experimental measurements and second-order polarization propagator approach (SOPPA) calculations of (77)Se-(1)H spin-spin coupling constants together with theoretical energy-based conformational analysis in the series of 2-substituted selenophenes have been carried out. A new basis set optimized for the calculation of (77)Se-(1)H spin-spin coupling constants has been introduced by extending the aug-cc-pVTZ-J basis for selenium. Most of the spin-spin coupling constants under study, especially vicinal (77)Se-(1)H couplings, demonstrated a remarkable stereochemical behavior with respect to the internal rotation of the substituent in the 2-position of the selenophene ring, which is of major importance in the stereochemical studies of the related organoselenium compounds.
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Affiliation(s)
- Yury Yu Rusakov
- A. E. Favorsky Irkutsk Institute of Chemistry, Siberian Branch of the Russian Academy of Sciences, Favorsky St. 1, 664033 Irkutsk, Russia
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Kupka T. H2O, H2, HF, F2 and F2O nuclear magnetic shielding constants and indirect nuclear spin-spin coupling constants (SSCCs) in the BHandH/pcJ-n and BHandH/XZP Kohn-Sham limits. MAGNETIC RESONANCE IN CHEMISTRY : MRC 2009; 47:959-970. [PMID: 19681101 DOI: 10.1002/mrc.2500] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
Good performance of segmented contracted basis sets XZP, where X = D, T, Q and 5, for obtaining H(2)O, H(2), HF, F(2) and F(2)O nuclear isotropic shielding constants in the BHandH Kohn-Sham basis set limit was shown. The results of two- and three-parameter complete basis set limit extrapolation schemes were compared with experimental results, earlier literature data and benchmark ab initio results. Similar convergence patterns of shieldings obtained from calculations using general purpose XZP basis sets and from polarization-consistent basis sets pcS-n and pcJ-n, where n = 0, 1, 2, 3 and 4, designed to accurately predict magnetic properties were observed. On the contrary, the SSCCs were more sensitive to the XZP basis set size and generally less accurate than those estimated using pcJ-n basis set family. The BHandH density functional markedly outperforms B3LYP method in predicting heavy atom shieldings and SSCCs values in the studied systems.
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Affiliation(s)
- Teobald Kupka
- Department of Chemistry, University of Opole, 48, Oleska Street, 45-052 Opole, Poland.
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18
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Olejniczak M, Pecul M. Spin-Spin Coupling Constants Transmitted through IrH⋅⋅⋅HN Dihydrogen Bonds. Chemphyschem 2009; 10:1247-59. [DOI: 10.1002/cphc.200800817] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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19
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Kupka T. Prediction of water's isotropic nuclear shieldings and indirect nuclear spin-spin coupling constants (SSCCs) using correlation-consistent and polarization-consistent basis sets in the Kohn-Sham basis set limit. MAGNETIC RESONANCE IN CHEMISTRY : MRC 2009; 47:210-221. [PMID: 19086009 DOI: 10.1002/mrc.2369] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
Density functional theory (DFT) was used to estimate water's isotropic nuclear shieldings and indirect nuclear spin-spin coupling constants (SSCCs) in the Kohn-Sham (KS) complete basis set (CBS) limit. Correlation-consistent cc-pVxZ and cc-pCVxZ (x = D, T, Q, 5, and 6), and their modified versions (ccJ-pVxZ, unc-ccJ-pVxZ, and aug-cc-pVTZ-J) and polarization-consistent pc-n and pcJ-n (n = 0, 1, 2, 3, and 4) basis sets were used, and the results fitted with a simple mathematical formula. The performance of over 20 studied density functionals was assessed from comparison with the experiment. The agreement between the CBS DFT-predicted isotropic shieldings, spin-spin values, and the experimental values was good and similar for the modified correlation-consistent and polarization-consistent basis sets. The BHandH method predicted the most accurate (1)H, (17)O isotropic shieldings and (1)J(OH) coupling constant (deviations from experiment of about -0.2 and -1 ppm and 0.6 Hz, respectively). The performance of BHandH for predicting water isotropic shieldings and (1)J(OH) is similar to the more advanced methods, second-order polarization propagator approximation (SOPPA) and SOPPA(CCSD), in the basis set limit.
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Affiliation(s)
- Teobald Kupka
- Institute of Chemistry, University of Opole, 45-052 Opole, Poland.
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20
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Restricted magnetically balanced basis applied for relativistic calculations of indirect nuclear spin–spin coupling tensors in the matrix Dirac–Kohn–Sham framework. Chem Phys 2009. [DOI: 10.1016/j.chemphys.2008.10.037] [Citation(s) in RCA: 52] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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21
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22
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Antušek A, Ke¸dziera D, Jackowski K, Jaszuński M, Makulski W. Indirect spin–spin coupling constants in CH4, SiH4 and GeH4 – Gas-phase NMR experiment and ab initio calculations. Chem Phys 2008. [DOI: 10.1016/j.chemphys.2008.07.002] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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San Fabián J, Díez E, García de la Vega JM, Suardíaz R. Approximating correlation effects in multiconfigurational self-consistent field calculations of spin-spin coupling constants. J Chem Phys 2008; 128:084108. [PMID: 18315034 DOI: 10.1063/1.2834210] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- J San Fabián
- Departamento de Química Física Aplicada, Facultad de Ciencias, Universidad Autónoma de Madrid, E-28049 Madrid, Spain.
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Lantto P, Romero RH, Gómez SS, Aucar GA, Vaara J. Relativistic heavy-atom effects on heavy-atom nuclear shieldings. J Chem Phys 2006; 125:184113. [PMID: 17115744 DOI: 10.1063/1.2378737] [Citation(s) in RCA: 44] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The principal relativistic heavy-atom effects on the nuclear magnetic resonance (NMR) shielding tensor of the heavy atom itself (HAHA effects) are calculated using ab initio methods at the level of the Breit-Pauli Hamiltonian. This is the first systematic study of the main HAHA effects on nuclear shielding and chemical shift by perturbational relativistic approach. The dependence of the HAHA effects on the chemical environment of the heavy atom is investigated for the closed-shell X(2+), X(4+), XH(2), and XH(3) (-) (X=Si-Pb) as well as X(3+), XH(3), and XF(3) (X=P-Bi) systems. Fully relativistic Dirac-Hartree-Fock calculations are carried out for comparison. It is necessary in the Breit-Pauli approach to include the second-order magnetic-field-dependent spin-orbit (SO) shielding contribution as it is the larger SO term in XH(3) (-), XH(3), and XF(3), and is equally large in XH(2) as the conventional, third-order field-independent spin-orbit contribution. Considering the chemical shift, the third-order SO mechanism contributes two-thirds of the difference of approximately 1500 ppm between BiH(3) and BiF(3). The second-order SO mechanism and the numerically largest relativistic effect, which arises from the cross-term contribution of the Fermi contact hyperfine interaction and the relativistically modified spin-Zeeman interaction (FC/SZ-KE), are isotropic and practically independent of electron correlation effects as well as the chemical environment of the heavy atom. The third-order SO terms depend on these factors and contribute both to heavy-atom shielding anisotropy and NMR chemical shifts. While a qualitative picture of heavy-atom chemical shifts is already obtained at the nonrelativistic level of theory, reliable shifts may be expected after including the third-order SO contributions only, especially when calculations are carried out at correlated level. The FC/SZ-KE contribution to shielding is almost completely produced in the s orbitals of the heavy atom, with values diminishing with the principal quantum number. The relative contributions converge to universal fractions for the core and subvalence ns shells. The valence shell contribution is negligible, which explains the HAHA characteristics of the FC/SZ-KE term. Although the nonrelativistic theory gives correct chemical shift trends in present systems, the third-order SO-I terms are necessary for more reliable predictions. All of the presently considered relativistic corrections provide significant HAHA contributions to absolute shielding in heavy atoms.
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Affiliation(s)
- Perttu Lantto
- NMR Research Group, Department of Physical Sciences, University of Oulu, P.O. Box 3000, FIN-90014 Oulu, Finland.
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Oprea CI, Rinkevicius Z, Vahtras O, Agren H, Ruud K. Density functional theory study of indirect nuclear spin-spin coupling constants with spin-orbit corrections. J Chem Phys 2005; 123:014101. [PMID: 16035827 DOI: 10.1063/1.1947190] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
This work outlines the calculation of indirect nuclear spin-spin coupling constants with spin-orbit corrections using density functional response theory. The nonrelativistic indirect nuclear spin-spin couplings are evaluated using the linear response method, whereas the relativistic spin-orbit corrections are computed using quadratic response theory. The formalism is applied to the homologous systems H2X (X=O,S,Se,Te) and XH4 (X=C,Si,Ge,Sn,Pb) to calculate the indirect nuclear spin-spin coupling constants between the protons. The results confirm that spin-orbit corrections are important for compounds of the H2X series, for which the electronic structure allows for an efficient coupling between the nuclei mediated by the spin-orbit interaction, whereas in the case of the XH4 series the opposite situation is encountered and the spin-orbit corrections are negligible for all compounds of this series. In addition we analyze the performance of the density functional theory in the calculations of nonrelativistic indirect nuclear spin-spin coupling constants.
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Affiliation(s)
- Corneliu I Oprea
- Laboratory of Theoretical Chemistry, The Royal Institute of Technology, SCFAB, SE-10691 Stockholm, Sweden
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Manninen P, Vaara J, Ruud K. Perturbational relativistic theory of electron spin resonance g-tensor. J Chem Phys 2004; 121:1258-65. [PMID: 15260666 DOI: 10.1063/1.1759321] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We carry out a complete treatment of the leading-order relativistic one-electron contributions, arising from the Breit-Pauli Hamiltonian, to the g-tensor of electron spin resonance spectroscopy. We classify the different terms and discuss their interpretation as well as give numerical ab initio estimates for the F2(-), Cl2(-), Br2(-), and I2(-) series, using analytical response theory calculations with a multiconfigurational self-consistent field reference state. The results are compared to available experimental data. (c) 2004 American Institute of Physics
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Affiliation(s)
- Pekka Manninen
- Laboratory of Physical Chemistry, Department of Chemistry, P.O. Box 55 (A.I. Virtasen aukio 1), FIN-00014 University of Helsinki, Helsinki, Finland
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Arbuznikov AV, Vaara J, Kaupp M. Relativistic spin-orbit effects on hyperfine coupling tensors by density-functional theory. J Chem Phys 2004; 120:2127-39. [PMID: 15268351 DOI: 10.1063/1.1636720] [Citation(s) in RCA: 80] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
A second-order perturbation theory treatment of spin-orbit corrections to hyperfine coupling tensors has been implemented within a density-functional framework. The method uses the all-electron atomic mean-field approximation and/or spin-orbit pseudopotentials in incorporating one- and two-electron spin-orbit interaction within a first-principles framework. Validation of the approach on a set of main-group radicals and transition metal complexes indicates good agreement between all-electron and pseudopotential results for hyperfine coupling constants of the lighter nuclei in the system, except for cases in which scalar relativistic effects become important. The nonrelativistic Fermi contact part of the isotropic hyperfine coupling constants is not always accurately reproduced by the exchange-correlation functionals employed, particularly for the triplet and pi-type doublet radicals in the present work. For this reason, ab initio coupled-cluster singles and doubles with perturbative triples results for the first-order contributions have been combined in the validation calculations with the density-functional results for the second-order spin-orbit contributions. In the cases where spin-orbit corrections are of significant magnitude relative to the nonrelativistic first-order terms, they improve the agreement with experiment. Antisymmetric contributions to the hyperfine tensor arise from the spin-orbit contributions and are discussed for the IO2 radical, whereas rovibrational effects have been evaluated for RhC, NBr, and NI.
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Affiliation(s)
- Alexei V Arbuznikov
- Institut fur Anorganische Chemie, Universitat Wurzburg, Am Hubland, D-97074 Wurzburg, Germany.
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Manninen P, Lantto P, Vaara J, Ruud K. Perturbationalab initiocalculations of relativistic contributions to nuclear magnetic resonance shielding tensors. J Chem Phys 2003. [DOI: 10.1063/1.1586912] [Citation(s) in RCA: 112] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Bryce DL, Wasylishen RE. Interpretation of indirect nuclear spin-spin coupling tensors for polyatomic xenon fluorides and group 17 fluorides: results from relativistic density-functional calculations. Inorg Chem 2002; 41:3091-101. [PMID: 12054987 DOI: 10.1021/ic020025u] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Significant improvements have been made recently in the calculation of NMR indirect nuclear spin-spin coupling tensors (J). In particular, the relativistic zeroth-order regular approximation density-functional theory (ZORA-DFT) approach holds great promise for the calculation of spin-spin coupling constants for a variety of chemical systems containing heavy nuclei. In the present work, the ZORA-DFT method is applied to the calculation of the complete reduced coupling tensors, K, for a range of chlorine-, bromine-, iodine-, and xenon-containing species: K(Cl,F) for ClF(2)(+), ClF(3), ClF(4)(+), ClF(5), ClF(6)(-), and ClF(6)(+); K(Br,F) for BrF(3), BrF(6)(-), and BrF(6)(+); K(I,F) for IF(4)(+) and IF(6)(+); K(Xe,F) for XeF(+), XeF(2), XeF(3)(+), XeF(4), XeF(5)(-), XeF(5)(+), and XeF(7)(+). These species represent a wide variety of geometrical bonding arrangements. Agreement between the calculated coupling constants and available experimental data is excellent, and the absolute sign of the coupling constants is provided. It is shown that (1)K(iso) may be positive or negative even within the same molecule, e.g., K(Cl,F)(iso) may be of either sign, depending on the local environment. Periodic trends in (1)K(iso) for isovalent and isostructural molecules are evident. The spin-spin coupling anisotropies, Delta K, and the orientations of the K tensors are also determined. The success of the calculations is a direct result of employing reliable geometries and considering both scalar and spin-orbit relativistic effects. The dependence of K(Cl,F)(iso) and K(Xe,F)(iso) on the local molecular and electronic structure is discussed in terms of the paramagnetic spin-orbit (PSO) and combined Fermi-contact spin-dipolar (FC+SD) coupling mechanisms. The PSO term depends strongly on the number of valence shell electron lone pairs on the central heavy atom, and the FC+SD contribution increases with the Cl[bond]F or Xe[bond]F bond length for a given series of compounds. This interpretation allows for the successful rationalization of the existing experimental data.
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Affiliation(s)
- David L Bryce
- Department of Chemistry, University of Alberta, Edmonton, Alberta, Canada T6G 2G2
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Bryce DL, Wasylishen RE, Autschbach J, Ziegler T. Periodic trends in indirect nuclear spin-spin coupling tensors: relativistic density functional calculations for interhalogen diatomics. J Am Chem Soc 2002; 124:4894-900. [PMID: 11971740 DOI: 10.1021/ja012596b] [Citation(s) in RCA: 46] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
There have been significant advances in the calculation and interpretation of indirect nuclear spin-spin coupling (J) tensors during the past few years; however, much work remains to be done, especially for molecules containing heavy atoms where relativistic effects may play an important role. Many J tensors cannot be explained based solely on a nonrelativistic Fermi-contact mechanism. In the present work, the relativistic zeroth-order regular approximation density-functional (ZORA-DFT) implementation for the calculation of J has been applied to the complete series of homonuclear and heteronuclear diatomic halogen molecules: F(2), Cl(2), Br(2), I(2), At(2), ClF, BrF, IF, ClBr, ClI, and BrI. For all of these compounds, the reduced isotropic coupling constant (K(iso)) is positive and the reduced anisotropic coupling constant (DeltaK) is negative. With the exception of molecular fluorine, the magnitudes of K(iso) and DeltaK are shown to increase linearly with the product of the atomic numbers of the coupled nuclei. ZORA-DFT calculations of J for F(2) and ClF are in excellent agreement with the results obtained from multiconfigurational self-consistent-field calculations. The relative importance of the various coupling mechanisms is approximately constant for all of the compounds, with the paramagnetic spin-orbit term being the dominant contributor to K(iso), at approximately 70-80%. Available experimental stimulated resonant Raman spectroscopy data are exploited to extract the complete J((127)I,(127)I) tensor for iodine in two rotational states. The dependence of K(iso) and DeltaK on bond length and rovibrational state is investigated by using calculated results in combination with available experimental data. In addition to providing new insights into periodic trends for J coupling tensors, this work further demonstrates the utility of the ZORA-DFT method and emphasizes the necessity of spin-orbit relativistic corrections for J calculations involving heavy nuclei.
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Affiliation(s)
- David L Bryce
- Department of Chemistry, Dalhousie University, Halifax, Nova Scotia, Canada
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Ab initio characterization of through-space indirect nuclear spin–spin coupling tensors for fluorine-X (X=F, C, H) spin pairs. J Mol Struct 2002. [DOI: 10.1016/s0022-2860(01)00725-6] [Citation(s) in RCA: 36] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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Vaara J, Malkina OL, Stoll H, Malkin VG, Kaupp M. Study of relativistic effects on nuclear shieldings using density-functional theory and spin–orbit pseudopotentials. J Chem Phys 2001. [DOI: 10.1063/1.1330208] [Citation(s) in RCA: 92] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Barone V, Peralta JE, Contreras RH. NMR3J(C1,H3) couplings in 1-X-bicyclo[1.1.1]pentanes. FPT-DFT and NBO studies of hyperconjugative interactions and heavy atom substituent effects. J Comput Chem 2001. [DOI: 10.1002/jcc.1117] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Kirtman B, Champagne B, Luis JM. Efficient treatment of the effect of vibrations on electrical, magnetic, and spectroscopic properties. J Comput Chem 2000. [DOI: 10.1002/1096-987x(200012)21:16<1572::aid-jcc14>3.0.co;2-8] [Citation(s) in RCA: 47] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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36
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Ruud K, Schimmelpfennig B, Ågren H. Internal and external heavy-atom effects on phosphorescence radiative lifetimes calculated using a mean-field spin–orbit Hamiltonian. Chem Phys Lett 1999. [DOI: 10.1016/s0009-2614(99)00712-5] [Citation(s) in RCA: 56] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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