The effects of bonding to a platinum atom are calculated for the reduction of oxygen to water. The electron-correlation corrected MP2 method is used, and the electrode potential is modeled by variations in values for the electron affinities of the reaction centers. Potential-dependent transition state structures and activation energies are reported for the one-electron reactions Pt-O 2 ϩ H ϩ (aq) ϩ e Ϫ (U) r Pt-OOH [i ] Pt-OOH ϩ H ϩ (aq) ϩ e Ϫ (U) r Pt-(OHOH) [ii] Pt-(OHOH) ϩ H ϩ (aq) ϩ e Ϫ (U) r Pt-OH ϩ H 2 O [ iii ] Pt-OH ϩ H ϩ (aq) ϩ e Ϫ (U) r Pt-OH 2 [iv] This is the predicted lowest energy pathway. An alternative, where step (ii) is replaced by Pt-OOH ϩ H ϩ (aq) ϩ e Ϫ (U) r Pt-O ϩ H 2 O [ v ] is excluded by the high activation energy calculated for it, though reduction of Pt-O to Pt-OH Pt-O ϩ H ϩ (aq) ϩ e Ϫ (U) r Pt-OH [vi] has a very low activation energy. Compared to uncatalyzed outer-Helmholtz-plane values, bonding to the Pt has the effect of decreasing the calculated high reduction activation energies for O 2 and H 2 O 2. Bonding to Pt also decreases the HOOи and increases the HOи activation energy values. The reverse reaction, oxidation of H 2 O to O 2 , is also discussed in light of these results. The issues of potential-dependent double-layer potential drops and adsorbate bond polarizations are discussed, and it is pointed out that the results of this study can be used to estimate the effects of such potential drops.

We observed ring expansion of 1-methylcyclobutylfluorocarbene at 8 kelvin, a reaction that involves carbon tunneling. The measured rate constants were 4.0 x 10(-6) per second in nitrogen and 4 x 10(-5) per second in argon. Calculations indicated that at this temperature the reaction proceeds from a single quantum state of the reactant so that the computed rate constant has achieved a temperature-independent limit. According to calculations, the tunneling contribution to the rate is 152 orders of magnitude greater than the contribution from passage over the barrier. We discuss environmental effects of the solid-state inert-gas matrix on the reaction rate.

The outer-sphere reduction of oxygen to water according to O2(g) + 4H+(aq) + 4e- → 2H2O(l) (1) and its reverse reaction are analyzed using self-consistent ab initio MP2/6-31G** calculations over the electrode potential range of U = 0−2 V (H+/H2). Activation energies are calculated for each of the four one-electron steps:  O2 + H+ + e-(U) → HOO• (2); HOO• + H+ + e-(U) → H2O2 (3); H2O2 + H+ + e-(U) → HO• + H2O (4); and HO• + H+ + e-(U) → H2O (5). In the calculational model H+ is a hydronium ion with two water molecules hydrogen bonded to it. The electrode potential is given by U/V = φ/eV − φH + /H 2 /eV (6) where φ and φH + /H 2 are the thermodynamic work functions of the electrode surface and of the standard hydrogen electrode surface, respectively. Electron transfer is assumed to occur when the electron affinity, EA, of the reaction complex equals the ionization potential, IP, of the electrode and there is an equilibrium so that φ = IP = EA. The electron transfers to an RO···H+···OH2(OH2) orbital that is H+···OH2 antibonding and RO···H+ bonding and this orbital is greatly stabilized by the electric field due to the positive charge. Over the potential range considered, activation energies for the reduction reactions decrease in the sequence (4) > (2) > (3) > (5). For the reverse reactions the activation energies decrease according to (5) > (4) ≃ (3) > (2). It is found that calculated reversible potentials, U°, as determined simply from reaction energies for reactions 1, 4, 5, 2 + 3 and reactions 4 + 5 differ from the measured values by a constant.

Multiconfiguration molecular mechanics (MCMM) is an extension of molecular mechanics to chemically reactive systems. This dual-level method combines molecular mechanics potentials for the reactant and product configurations with electronic structure Hessians at the saddle point and a small number of nonstationary points to model the potential energy surface in the reaction swath region between reactants and products where neither molecular mechanics potential is valid. The resulting semiglobal potential energy surface is used as input for dynamics calculations of tunneling probabilities and variational transition state theory rate constants. In this paper, we present a standard strategy for applying MCMM to calculate rate constants for atom transfer reactions. In particular, we propose a general procedure for determining where to calculate the electronic structure Hessians. We tested this strategy for a diverse test suite of six reactions involving hydrogenatom transfer. It yields reasonably accurate rate constants as compared to direct dynamics using an uninterpolated full potential energy surface at the same electronic structure level. Furthermore, the rate constants at each of several successively more demanding levels of dynamical theory are also predicted accurately, which indicates that the MCMM potential energy surface accurately predicts many different details of the potential energy surface with a limited number of electronic structure Hessians.

a The rate constant including tunneling is then given by k CVT/MT = κ MT k CVT , where κ MT is the transmission coefficient (denoted κ CVT/MT in Ref. 1 ), and MT is ZCT, SCT, LCT(0), LCT, or µOMT. The definition for the transmission coefficient is given in Ref. 1 . See Section 2.3 of text for MCMM notation.b With n max = 0, where n max is the highest vibrational quantum number included in LCT calculations; for direct dynamics, it is the number of energetically allowed final states.c With n max = 0; the n max for MCMM is determined according to the protocol described in Section 3.2 of text. Note that in direct dynamics and MCMM, the potential energy surfaces and reaction paths are not identical, and thus the energetically allowed highest excited states are not necessarily the same.d With n max = 0. e With n max = 1.