The selective oxidation of methanol to formaldehyde occurring on titania-supported vanadate species has been analyzed theoretically with the aim of understanding why the activity of VO x /TiO 2 is ∼10 3 faster than that of VO x /SiO 2 . The active site was represented by a [(O) 3 VdO] group located at the corner of a cubic TiO x cluster, a model similar to that used successfully to describe the oxidation of methanol on isolated vanadate species supported on silica. Density functional theory was used to calculate the geometry, vibrational frequencies, and energy of all ground state and transition state structures. The equilibrium constants and rate coefficients for each elementary reaction step were calculated using statistical mechanics and absolute rate theory. Methanol oxidation to formaldehyde was taken to proceed via two key steps: the reversible adsorption of methanol across a V-O-Ti bond followed by the transfer of a hydrogen atom from an adsorbed methoxy group to a vanadyl O atom. The rate parameters and the apparent first-order rate coefficient determined for VO x /TiO 2 were found to be very similar to those reported earlier in a theoretical analysis of VO x /SiO 2 [J. Phys. Chem. C 2007, 111, 14753], indicating that the significantly higher rate of reaction seen experimentally for VO x /TiO 2 is not due to an intrinsic electronic effect of the support on the catalytic properties of the active center. Introduction of an O-vacancy adjacent to the vanadate species results in a reduction in the activation barrier for the rate-limiting step and to close agreement between the rate parameters predicted and those found experimentally. The effect of O-vacancies in the support on the rate of methanol on metal oxidesupported vanadate species is further evidenced by a strong correlation between the turnover frequency for methanol oxidation and the energy required to form an O-atom defect on metal oxide supports.

A theoretical analysis has been conducted on the selective oxidation of methanol to formaldehyde catalyzed by isolated vanadate species supported on silica. The active site was represented by a VdO group substituted for a Si-H group in the corner of silsesquioxane, Si 8 O 12 H 8 . Calculations of ground and transition states were carried out using density functional theory, whereas statistical mechanics and absolute rate theory were used to determine equilibrium constants and rate coefficients for each elementary step. The formation of formaldehyde was found to involve two key steps. The first is the reversible adsorption of methanol, which occurs by addition across one of the three V-O-Si bonds of the active site. The rate-limiting step is the transfer of a hydrogen atom from the resulting V-OCH 3 species to the VdO bond of the active center. The release of formaldehyde and water from the active center leads to a two electron reduction of the vanadium atom in the center. Rapid reoxidation of the reduced vanadium can occur via adsorption of O 2 to form a peroxide species and subsequent migration of one of the O atoms associated with the peroxide across the surface of the support. The predicted heat of adsorption and equilibrium constant for methanol adsorption are in good agreement with those found experimentally, as is the infrared spectrum of the adsorbed methanol. The apparent first-order rate coefficient and the apparent activation energy are also in very good agreement with the values determined experimentally.

Efficient identification of transition states is important for understanding reaction mechanisms. Most transition state search algorithms require long computational times and a good estimate of the transition state structure in order to converge, particularly for complex reaction systems. The growing string method (GSM) [B. Peters et al., J. Chem. Phys. 120, 7877 (2004)] does not require an initial guess of the transition state; however, the calculation is still computationally intensive due to repeated calls to the quantum mechanics code. Recent modifications to the GSM [A. Goodrow et al., J. Chem. Phys. 129, 174109 (2008)] have reduced the total computational time for converging to a transition state by a factor of 2 to 3. In this work, three transition state-finding strategies have been developed to complement the speedup of the modified-GSM: (1) a hybrid strategy, (2) an energy-weighted strategy, and (3) a substring strategy. The hybrid strategy initiates the string calculation at a low level of theory (HF/STO-3G), which is then refined at a higher level of theory (B3LYP/6-31G(*)). The energy-weighted strategy spaces points along the reaction pathway based on the energy at those points, leading to a higher density of points where the energy is highest and finer resolution of the transition state. The substring strategy is similar to the hybrid strategy, but only a portion of the low-level string is refined using a higher level of theory. These three strategies have been used with the modified-GSM and are compared in three reactions: alanine dipeptide isomerization, H-abstraction in methanol oxidation on VO(x)/SiO(2) catalysts, and C-H bond activation in the oxidative carbonylation of toluene to p-toluic acid on Rh(CO)(2)(TFA)(3) catalysts. In each of these examples, the substring strategy was proved most effective by obtaining a better estimate of the transition state structure and reducing the total computational time by a factor of 2 to 3 compared to the modified-GSM. The applicability of the substring strategy has been extended to three additional examples: cyclopropane rearrangement to propylene, isomerization of methylcyclopropane to four different stereoisomers, and the bimolecular Diels-Alder condensation of 1,3-butadiene and ethylene to cyclohexene. Thus, the substring strategy used in combination with the modified-GSM has been demonstrated to be an efficient transition state-finding strategy for a wide range of types of reactions.

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Transition state search algorithms, such as the nudged elastic band can fail, if a good initial guess of the transition state structure cannot be provided. The growing string method (GSM) [J. Chem. Phys. 120, 7877 (2004)] eliminates the need for an initial guess of the transition state. While this method only requires knowledge of the reactant and product geometries, it is computationally intensive. To alleviate the bottlenecks in the GSM, several modifications were implemented: Cartesian coordinates were replaced by internal coordinates, the steepest descent method for minimization of orthogonal forces to locate the reaction path was replaced by the conjugate gradient method, and an interpolation scheme was used to estimate the energy and gradient, thereby reducing the calls to the quantum mechanical (QM) code. These modifications were tested to measure the reduction in computational time for four cases of increasing complexity: the Muller-Brown potential energy surface, alanine dipeptide isomerization, H abstraction in methanol oxidation, and C-H bond activation in oxidative carbonylation of toluene to p-toluic acid. These examples show that the modified GSM can achieve two- to threefold speedups (measured in terms of the reduction in actual QM gradients computed) over the original version of the method without compromising accuracy of the geometry and energy of the final transition state. Additional savings in computational effort can be achieved by carrying out the initial search for the minimum energy pathway (MEP) using a lower level of theory (e.g., HF/STO-3G) and then refining the MEP using density functional theory at the B3LYP level with larger basis sets (e.g., 6-31G( *), LANL2DZ). Thus, a general strategy for determining transition state structures is to initiate the modified GSM using a low level of theory with minimal basis sets and then refining the calculation at a higher level of theory with larger basis sets.