Geometry Optimizations in a Subsystem Density Functional Theory Formalism: A Benchmark Study.

We present a benchmark study on equilibrium structures optimized with subsystem density functional theory (sDFT) employing a new analytical gradient implementation in the program SERENITY. Geometry optimizations are performed on all complexes of the S22 [Jurečka et al. Phys. Chem. Chem. Phys. 2006, 8, 1985-1993] and A24 [Řezáč and Hobza. J. Chem. Theory Comput. 2013, 9, 2151-2155] test sets. While some combinations of approximate exchange-correlation (XC) and nonadditive kinetic-energy functionals (e.g., LDA/Thomas-Fermi or PW91/PW91k) more or less successfully mimic the effect of medium-range dispersion in these complexes, we also include the combination of BP86/LLP91. This functional reproduces the dispersion problem of the corresponding BP86 Kohn-Sham (KS-)DFT calculations and can hence successfully be corrected by empirical dispersion corrections developed for KS-DFT. We propose this as a robust and accurate strategy for sDFT geometry optimizations, which appears to be preferable over the previously used strategy relying on error cancellation between XC and nonadditive kinetic-energy functionals. In fact, the best results in our benchmark are obtained from BP86/LLP91 together with a D3-type dispersion correction. We also discuss the difference between our Gaussian-type orbital implementation in SERENITY and a Slater-type orbital based implementation in the Amsterdam density functional (ADF) program but only find small differences in most cases.