^{1,a)}and Dieter Cremer

^{2}

### Abstract

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 DFT treatment of van der Waals dispersion complexes, including full geometry optimizations and frequency calculations with analytical energy derivatives in a routine way. For this purpose, the long-range-corrected Perdew–Burke–Ernzerhof exchange functional and the one-parameter progressive correlation functional of Hirao and co-workers are combined with the Andersson–Langreth–Lundqvist (ALL) long-range correlation functional. The time-consuming self-consistent incorporation of the ALL term in the DFT iterations needed for the calculation of forces and force constants is avoided by an *a posteriori* evaluation of the ALL term and its gradient based on an effective 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 to explore the potential energy surface (PES) of the benzene dimer. The results for the binding energies and intermolecular distances agree well with coupled-cluster calculations at the complete basis-set limit. We identify 16 stationary points on the PES, which underlines the usefulness of analytical energy gradients for the investigation of the PES. Furthermore, the inclusion of analytically calculated zero point energies reveals that large-amplitude vibrations connect the eight most stable benzene dimer forms and make it difficult to identify a dominating complex form. The tilted T structure and the parallel-displaced sandwich form have the same value of 2.40 kcal/mol, which agrees perfectly with the experimental value of .

D.C. thanks the University of the Pacific for support.

I. INTRODUCTION

II. METHODOLOGY

A. Theory of the quasi-self-consistent-field dispersion-corrected-DFT method

B. Implementation of quasi-SCF-DC-DFT

III. APPLICATION TO THE BENZENE DIMER

A. Topology of the PES

IV. CONCLUSIONS AND OUTLOOK

### Key Topics

- Density functional theory
- 46.0
- Polymers
- 10.0
- Exchange correlation functionals
- 9.0
- Tensor methods
- 7.0
- Ab initio calculations
- 6.0

## Figures

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.

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.

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.

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.

(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.

(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.

## Tables

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.)

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.)

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

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

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.)

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.)

Article metrics loading...

Full text loading...

Commenting has been disabled for this content