Intermolecular potentials of the methane dimer calculated with Møller-Plesset perturbation theory and density functional theory

Abstract

We have calculated the intermolecular interaction potentials of the methane dimer at the minimum-energy D(3d) conformation using the Hartree-Fock (HF) self-consistent theory, the correlation-corrected second-order Møller-Plesset (MP2) perturbation theory, and the density functional theory (DFT) with the Perdew-Wang (PW91) functional as the exchange or the correlation part. The HF calculations yield unbound potentials largely due to the exchange-repulsion interaction. In the MP2 calculations, the basis set effects on the repulsion exponent, the equilibrium bond length, the binding energy, and the asymptotic behavior of the calculated intermolecular potentials have been thoroughly studied. We have employed basis sets from the Slater-type orbitals fitted with Gaussian functions (STO-nG) (n=3-6) [Quantum Theory of Molecular and Solids: The Self-Consistent Field for Molecular and Solids (McGraw-Hill, New York, 1974), Vol. 4], Pople's medium size basis sets of Krishnan et al. [J. Chem. Phys. 72, 650 (1980)] [up to 6-311++G(3df,3pd)] to Dunning's correlation consistent basis sets [J. Chem. Phys. 90, 1007 (1989)] (cc-pVXZ and aug-cc-pVXZ) (X=D, T, and Q). With increasing basis size, the repulsion exponent and the equilibrium bond length converge at the 6-31G** basis set and the 6-311++G(2d,2p) basis set, respectively, while a large basis set (aug-cc-pVTZ) is required to converge the binding energy at a chemical accuracy (approximately 0.01 kcal/mol). Up to the largest basis set used, the asymptotic dispersion coefficient has not converged to the destined C6 value from molecular polarizability calculations. The slow convergence could indicate the inefficacy of using the MP2 calculations with Gaussian-type functions to model the asymptotic behavior. Both the basis set superposition error (BSSE) corrected and uncorrected results are presented to emphasize the importance of including such corrections. Only the BSSE corrected results systematically converge to the destined potential curve with increasing basis size. The DFT calculations generate a wide range of interaction patterns, from purely unbound to strongly bound, underestimating or overestimating the binding energy. The binding energy calculated using the PW91PW91 functional and the equilibrium bond length calculated using the PW91VP86 functional are close to the MP2 results at the basis set limit.

Steric and Chain Length Effects in the (${\sqrt {(3)} }$×${\sqrt {(3)} }$)R30° Structures of Alkanethiol Self‐Assembled Monolayers on Au(111)

“…Similar conclusions were found for the equilibrium structures of alkane dimers. [32,64,65] 2. Alkanethiols on Unreconstructed Au (111) We begin our the studies of thiol SAMs on unreconstructed, relaxed Au(111) surfaces with a ( ffiffiffiffiffiffi ffi ð3Þ p ffiffiffiffiffiffi ffi ð3Þ p )R308 lattice.…”

“…DFT calculations using the generalized gradient approximation (GGA) systematically underestimate dispersion interactions. [32,66] Recent DFT studies of SAMs have described the van der Waals interaction using a C 6 term. [12] However, a quantum mechanics/molecular mechanics study of SAMs reported that the van der Waals chain-chain interactions are negligible for short-chain alkanethiols.…”

“…[30] The exchange-correlation functional was the GGA by Perdew and Wang (PW91), [46] which partly recovers the van der Waals attraction. [32,66] The electronic wave function was described by a plane-wave basis set with a kinetic energy cutoff of 450 eV and the projector augmented-wave (PAW) method. [8,31] The surfaces were modeled by a 3D-periodic ( ffiffiffiffiffiffi ffi ð3Þ p ffiffiffiffiffiffi ffi ð3Þ p )R308 supercell consisting of a slab of four layers of gold atoms in the (111) direction and ten layers of vacuum to avoid spurious self-interactions.…”

“…For n a adatoms (n v vacancies) the energy of bulk gold atoms, E bulk , is added (subtracted). As dispersion interactions are systematically underestimated by DFT, [32,66] the chain-chain nonbonded interactions have been analyzed by comparing PW91 density functional and MP2 energies. The latter method gives accurate interaction energies for alkane dimers.…”

“…The latter method gives accurate interaction energies for alkane dimers. [32,64,65] Hence, pairs of alkane molecules (C n H 2n + 2 , n = 2-6) with orientations and distances corresponding to the SAM structure were used to evaluate the dispersion interactions between alkane chains. The chain-chain interaction energy in the SAM was approximated as the sum over nearest-neighbor pair interactions and the difference between MP2 and PW91 energies was used to correct the DFT binding energies for the corresponding thiol SAM [Eq.…”