We present a Gaussian-basis implementation of orbital-free density-functional theory (OF-DFT) in which the trust-region image method (TRIM) is used for optimization. This second-order optimization scheme has been constructed to provide benchmark all-electron results with very tight convergence of the particle-number constraint, associated chemical potential, and electron density. It is demonstrated that, by preserving the saddle-point nature of the optimization and simultaneously optimizing the density and chemical potential, an order of magnitude reduction in the number of iterations required for convergence is obtained. The approach is compared and contrasted with a new implementation of the nested optimization scheme put forward by Chan, Cohen, and Handy. Our implementation allows for semilocal kinetic-energy (and exchange−correlation) functionals to be handled self-consistently in all-electron calculations. The all-electron Gaussian-basis setting for these calculations will enable direct comparison with a wide range of standard high-accuracy quantum-chemical methods as well as with Kohn−Sham density-functional theory. We expect that the present implementation will provide a useful tool for analyzing the performance of approximate kinetic-energy functionals in finite systems.

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.

A recently proposed variation principle [N. I. Gidopoulos, Phys. Rev. A 83, 040502(R) (2011)] for the determination of Kohn-Sham effective potentials is examined and extended to arbitrary electron-interaction strengths and to mixed states. Comparisons are drawn with Lieb's convex-conjugate functional, which allows for the determination of a potential associated with a given electron density by maximization, yielding the Kohn-Sham potential for a non-interacting system. The mathematical structure of the two functionals is shown to be intrinsically related; the variation principle put forward by Gidopoulos may be expressed in terms of the Lieb functional. The equivalence between the information obtained from the two approaches is illustrated numerically by their implementation in a common framework.