Brownian motion of single particles with various masses M and diameters D is studied by molecular dynamics simulations. Besides the momentum auto-correlation function of the Brownian particle the memory function and the fluctuating force which enter the generalized Langevin equation of the Brownian particle are determined and their dependence on mass and diameter are investigated for two different fluid densities. Deviations of the fluctuating force distribution from a Gaussian form are observed for small particle diameters. For heavy particles the deviations of the fluctuating force from the total force acting on the Brownian particle decrease linearly with the mass ratio m/M where m denotes the mass of a fluid particle.

Electrochemical carbon dioxide (CO 2 ) reduction is an emerging technology for efficiently recycling CO 2 into fuel, and many studies of this reaction are focused on developing advanced catalysts with high activity, selectivity, and durability. Of these catalysts, oxide-derived metal nanoparticles, which are prepared by reducing a metal oxide, have received considerable attention due to their catalytic properties. However, the mechanism of the nanoparticles' activity enhancement is not well-understood. Recently, it was discovered that the catalytic activity is quantitatively correlated to the surface density of grain boundaries (GBs), implying that GBs are mechanistically important in electrochemical CO 2 reduction. Here, using extensive density functional theory (DFT) calculations modelling the atomistic structure of GBs on the Au (111) surface, we suggest a mechanism of electrochemical CO 2 reduction to CO mediated by GBs; the broken local spatial symmetry near a GB tunes the Au metal-to-adsorbate π-backbonding ability, thereby stabilizing the key COOH intermediate. This stabilization leads to a decrease of ~200 mV in the overpotential and a change in the rate-determining step to the second reduction step, of which are consistent with previous experimental observations. The atomistic and electronic details of the mechanistic role of GBs during electrochemical CO 2 reduction presented in this work demonstrate the structure-activity relationship of atomically disordered metastable structures in catalytic applications.

Double proton transfers in formic acid dimer and formamidine dimer were studied as prototypes of multiple proton transfer. The potential energy surface (PES) for the double proton transfer was studied using ab initio quantum mechanical methods. The solvent effect on the PES was also included using the Onsager self-consistent reaction field model. In the gas phase, the transition state for the double proton transfer in the formic acid dimer complex has D 2 h symmetry, but in water it is changed to a C 2 v structure, when the Hartree−Fock (HF) level of theory is used. When the density functional theory is used, the transition state has D 2 h symmetry with and without solvent. However the barrier height depends very much on the electron correlation. The double proton transfer occurs synchronously in all the cases. For the formamidine dimer complex, the transition state has C 2 v symmetry in the gas phase, and it changes to C s symmetry in water at the HF level of theory. The C 2 v structure becomes an intermediate in water, which means that double proton transfer occurs asynchronously. In the density functional theory for the gas phase, the transition state has D 2 h symmetry, and it changes to C 2 v structure in solution. However the double proton transfer occurs synchronously in both cases. These results suggest that the correlation is very important to the PES for double proton transfer, not only in the gas phase but also in solution.

We propose a numerical integration scheme to solve stochastic differential equations driven by Poissonian white shot noise. Our formula, which is based on an integral equation, which is equivalent to the stochastic differential equation, utilizes a discrete time approximation with fixed integration time step. We show that our integration formula approaches the Euler formula if the Poissonian noise approaches the Gaussian white noise. The accuracy and efficiency of the proposed algorithm are examined by studying the dynamics of an overdamped particle driven by Poissonian white shot noise in a spatially periodic potential. We find that the accuracy of the proposed algorithm only weakly depends on the parameters characterizing the Poissonian white shot noise; this holds true even if the limit of Gaussian white noise is approached.