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Molecular properties in the Tamm–Dancoff approximation: indirect nuclear spin–spin coupling constants

Cheng, Chi Y.; Ryley, Matthew S.; Peach, Michael J.G.; Tozer, David J.; Helgaker, Trygve; Teale, Andrew M.

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Chi Y. Cheng

Matthew S. Ryley

Michael J.G. Peach

David J. Tozer

Trygve Helgaker

Professor of Computational and Theoretical Chemistry


The Tamm-Dancoff approximation (TDA) can be applied to the computation of excitation energies using time-dependent Hartree-Fock (TD-HF) and time-dependent density-functional theory (TD-DFT). In addition to simplifying the resulting response equations, the TDA has been shown to significantly improve the calculation of triplet excitation energies in these theories, largely overcoming issues associated with triplet instabilities of the underlying reference wave functions. Here, we examine the application of the TDA to the calculation of another response property involving triplet perturbations, namely the indirect nuclear spin-spin coupling constant. Particular attention is paid to the accuracy of the triplet spin-dipole and Fermi-contact components. The application of the TDA in HF calculations leads to vastly improved results. For DFT calculations, the TDA delivers improved stability with respect to geometrical variations but does not deliver higher accuracy close to equilibrium geometries. These observations are rationalized in terms of the ground- and excited-state potential energy surfaces and, in particular, the severity of the triplet instabilities associated with each method. A notable feature of the DFT results within the TDA is their similarity across a wide range of different functionals. The uniformity of the TDA results suggests that some conventional evaluations may exploit error cancellations between approximations in the functional forms and those arising from triplet instabilities. The importance of an accurate treatment of correlation for evaluating spin-spin coupling constants is highlighted by this comparison.

Journal Article Type Article
Acceptance Date Jan 26, 2015
Online Publication Date Mar 27, 2015
Publication Date Jul 18, 2015
Deposit Date Dec 16, 2015
Publicly Available Date Dec 16, 2015
Journal Molecular Physics
Print ISSN 0026-8976
Electronic ISSN 1362-3028
Publisher Taylor & Francis Open
Peer Reviewed Peer Reviewed
Volume 113
Issue 13-14
Pages 1937-1951
Keywords nuclear magnetic resonance, spin–spin coupling constants, Hartree–Fock theory, density–functional theory, coupled-cluster theory
Public URL
Publisher URL
Additional Information This is an Accepted Manuscript of an article published by Taylor & Francis in Molecular Physics on 27/03/2015, available online:


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