Comparison of Cluster, Slab, and Analytic Potential Models for the Dimethyl Methylphosphonate (DMMP)/TiO2(110) Intermolecular Interaction

Abstract

In a previous study (J. Phys. Chem. C 2011, 115, 12403), cluster models for the TiO2 rutile(110) surface and MP2 calculations were used to develop an analytic potential energy function for dimethyl methylphosphonate (DMMP) interacting with this surface. In the work presented here, this analytic potential and MP2 cluster models are compared to DFT “slab” calculations for DMMP interacting with the TiO2(110) surface and with DFT cluster models for the TiO2(110) surface. The DFT slab calculations were performed with the PW91 and PBE functionals. The analytic potential gives DMMP/TiO2(110) potential energy curves in excellent agreement with those obtained from the slab calculations. The cluster models for the TiO2(110) surface, used for the MP2 calculations, were extended to DFT calculations with the B3LYP, PW91, and PBE functionals. These DFT calculations do not give DMMP/TiO2(110) interaction energies that agree with those from the DFT slab calculations. Analyses of the wave functions for these cluster models show that they do not accurately represent the HOMO and LUMO for the surface, which should be 2p and 3d orbitals, respectively, and the models also do not give an accurate band gap. The MP2 cluster models do not accurately represent the LUMO, and that they give accurate DMMP/TiO2(110) interaction energies is apparently fortuitous, arising from their highly inaccurate band gaps. To address this issue, accurate cluster models, consisting of 7, 10, and 15 Ti-atoms and that have the correct HOMO and LUMO properties, are proposed. The Ti7-cluster model gives a DMMP + TiO2 rutile(110) potential energy curve, determined with DFT, which is consistent with those for the MP2 cluster and DFT slab calculations and with the analytic potential energy function. DFT-D calculations, with a dispersion correction, give DMMP + TiO2 rutile(110) binding energies ∼10–15 kcal/mol stronger than those obtained from pure DFT. The DMMP + TiO2 rutile(110) binding energy is found to depend on the size of the model used to represent the TiO2(110) surface. The work presented here illustrates that care must be taken in “constructing” cluster models that accurately model surfaces.