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

Abstract

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.

Multi-configurational short-range density functional theory can describe spin–spin coupling constants of transition metal complexes

“…than the Tamm-Dancoff approximation for the single determinant models and the generalized Tamm-Dancoff approximation for the multi-configurational models 25,69 . Similar findings of getting worse results when using TDA in the calculation of the FC term in the KS-DFT framework have been obtained by Cheng et al 70 In the remaining text, we write gTDA both for TDA and for gTDA. The gTDA is known to remove any triplet instabilities or near-instabilities, which often improves the calculation of triplet properties.…”

Visualizing and characterizing excited states from time-dependent density functional theory

“…Use of the TDA is often essential for avoiding triplet instabilities and obtaining accurate triplet excitation energies. [82][83][84][85] Triplet instabilities in the ground-state Kohn-Sham solution indicate that an unrestricted wave function would lower the energy with respect to the (unstable) closedshell solution, 86 and these instabilities manifest as negative excitation energies. 87 Triplet instabilities are common at bondstretching geometries, where singlet and triplet states become quasi-degenerate, 88,89 but may also occur near the ground-state geometry when the fraction of Hartree-Fock exchange is large, [90][91][92][93][94][95] or for large values of the range separation parameter in RSH or LRC functionals.…”

A comparison of methods for theoretical photochemistry: Applications, successes and challenges

“…Moreover, CIS can also give significantly improved estimations of triplet excitation energies compared to TD-HF. 33…”