Geometry optimisations with a nonlocal density-functional theory method based on a double Hirshfeld partitioning

: Energy gradients have been derived for the nonlocal density-functional theory (NLDFT) method from Heselmann [J. Chem. Theory Comput. 9, 273 (2013)]. It is shown that the derivative of the NLDFT functional can easily be obtained analytically due to the fact that the inherent Hirshfeld weights are described in terms of analytic expressions of the atomic densities determined by Slater's rules. The accuracy of the NLDFT gradient has been tested by performing geometry optimisations for a range of 76 tripeptide molecules and a number of small noncovalently bonded dimer systems for which high level coupled cluster reference structures are accessible. It was found that the resulting optimised structures are in good agreement with corresponding structures optimised using second-order Moller-Plesset or coupled cluster wave function electron correlation methods. Moreover, conformer energies as well as intermolecular interaction energies are shown to be in fair agreement with corresponding density-functional theory methods employing pairwise atom-atom dispersion models.