The synergistic effect of graphene and MoS2 was investigated by using density functional theory (DFT) calculations on the enhanced photocatalytic H2 production activity of TiO2/graphene/MoS2 ternary nanoparticles. Our results indicate that it can form a weak covalent bond between the Ti atom of TiO2 nanocluster and the nearest C atom on graphene, which not only makes the original degenerate C(2p) orbital level of the graphene (part of the conduction band energy level) split, resulting in the production of a lower level of C(2p) that makes it easier to accept the excited electron from the Ti(3d) orbital, but also forms a +/- sequence electric field in the interface between them. It is conclusive that the electron moves from the TiO2 cluster to the graphene. In addition, we also find that the band gap of the TiO2 cluster can be doped by the graphene and MoS2, and the conduction band consists predominantly of C(2p), S(3p) and Mo(4d) orbital energy level near the Fermi level. These results illustrate that the excited electron will eventually accumulate in the graphene or MoS2 film, which can effectively enhance the separation between the excited electrons and the holes in the TiO2 clusters, thereby increasing the efficiency of hydrogen evolution. Our results are consistent with the experimental results, and can provide some valuable information for the design of photocatalytic composites.

In this work, a valence bond type multireference density functional theory (MRDFT) method, called the Hamiltonian matrix correction based density functional valence bond method (hc-DFVB), is presented. In hc-DFVB, the static electronic correlation is considered by the valence bond self-consistent field (VBSCF) strategy, while the dynamic correlation energy is taken into account by Kohn-Sham density functional theory (KS-DFT). Different from our previous version of DFVB (J. Chem. Theory Comput. 2012, 8, 1608), hc-DFVB corrects the dynamic correlation energy with a Hamiltonian correction matrix, improving the functional adaptability and computational accuracy. The method was tested for various physical and chemical properties, including spectroscopic constants, bond dissociation energies, reaction barriers, and singlet-triplet gaps. The accuracy of hc-DFVB matches that of KS-DFT and high level molecular orbital (MO) methods quite well. Furthermore, hc-DFVB keeps the advantages of VB methods, which are able to provide clear interpretations and chemical insights with compact wave functions.

The Cholesky decomposition (CD) technique, used to approximate the two-electron repulsion integrals (ERIs), is applied to the valence bond self-consistent field (VBSCF) method. Test calculations on ethylene, C2 n H2 n +2 , and C2 n H4 n -2 molecules (n = 1-7) show that the performance of the VBSCF method is much improved using the CD technique, and thus, the integral transformation from basis functions to VB orbitals is no longer the bottleneck in VBSCF calculations. The errors of the CD-based ERIs and of the total energy are controlled by the CD threshold, for which a value of 10(-6) ensures to control the total energy error within 10(-6) Hartree. © 2016 Wiley Periodicals, Inc.