An efficient algorithm for the density-functional theory treatmentof dispersion interactions

摘要

The quasi-self-consistent-field dispersion-corrected density-functional theory formalism(QSCF-DC-DFT) is developed and presented as an efficient and reliable scheme for the DFTtreatment of van der Waals dispersion complexes, including full geometry optimizations andfrequency calculations with analytical energy derivatives in a routine way. For this purpose, thelong-range-corrected Perdew–Burke–Ernzerhof exchange functional and the one-parameterprogressive correlation functional of Hirao and co-workers are combined with the Andersson-Langreth–Lundqvist (ALL) long-range correlation functional. The time-consuming self-consistentincorporation of the ALL term in the DFT iterations needed for the calculation of forces and forceconstants is avoided by an a posteriori evaluation of the ALL term and its gradient based on aneffective partitioning of the coordinate space into global and intramonomer coordinates.QSCF-DC-DFT is substantially faster than SCF-DC-DFT would be. QSCF-DC-DFT is used toexplore the potential energy surface (PES) of the benzene dimer. The results for the binding energiesand intermolecular distances agree well with coupled-cluster calculations at the complete basis-setlimit. We identify 16 stationary points on the PES, which underlines the usefulness of analyticalenergy gradients for the investigation of the PES. Furthermore, the inclusion of analyticallycalculated zero point energies reveals that large-amplitude vibrations connect the eight most stablebenzene dimer forms and make it difficult to identify a dominating complex form. The tilted Tstructure and the parallel-displaced sandwich form have the same D_0 value of 2.40 kcal/mol, whichagrees perfectly with the experimental value of 2.40 ± 0.40 kcal/mol.