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An efficient algorithm for the density-functional theory treatment of dispersion interactions
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Image of FIG. 1.
FIG. 1.

Forces between the benzene monomers for the T-AoA form of the benzene dimer (see Fig. 2) in dependence of the interfragment distance as calculated with vdW forces excluded (dotted lines), calculated numerically (dashed line), and calculated analytically (solid line). For the definition of , see Fig. 2. Calculations done with the functional; for details of the calculation, see Sec. II B. Numeric forces calculated with a step width for of 0.02 Å.

Image of FIG. 2.
FIG. 2.

Ball and stick representations of the 16 benzene dimer forms calculated in this work. For each form, the appropriate notation and the symmetry are given. Dashed lines indicate distances between geometrical centers of the monomers and possible sideward shifts. Some geometrical parameters are given that are not included in Table II. Distances in Å and angles in degrees.

Image of FIG. 3.
FIG. 3.

(a) Schematic description of the PES region hosting the PD forms. For reasons of simplification only the carbon rings are shown, the one on the top in blue in the online version, gray in the print version and the one at the bottom in black using apart from the two exceptions on the right side the top view. (b) Schematic description of the PES region hosting the T and EoP forms. The proper notation, symmetry, values, and the character of the stationary point are given.


Generic image for table
Table I.

Energies, thermochemistry, and characterization of calculated stationary points for the different forms of the benzene dimer. (Calculations were done with the functional and the aug-cc-pVDZ basis for C atoms and cc-pVDZ basis set for H atoms of Dunning (Ref. 110). See Fig. 2 for the structure and geometry of the dimers. Monomer: and . All energies are in and wave numbers in . The notation of the various forms is described in the text and uses the following abbreviations: PD, parallel displaced; T, T form; SW, sandwich form; AoA, atom over atom; AoB, atom over bond; BoB, bond over bond; til, tilted; rot, rotated; I, intermediate. M, SP1, SP2, and SP3 denote minimum, first order, second order, and third order saddle points.)

Generic image for table
Table II.

Comparison of QSCF-DC-DFT with SAPT(DFT) and PBE(CCSD(T)) geometries for the benzene dimer.a

Generic image for table
Table III.

Comparison of dissociation energies obtained for the benzene dimer with different methods. ( values in kcal/mol. For the notation of stationary points see Fig. 2 and text. The characterizations as M2, M1, T, and S8 are taken from Ref. 33.)


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: An efficient algorithm for the density-functional theory treatment of dispersion interactions