NMR AND DFT STUDY OF Co-C BOND ACTIVATION MECHANISM IN VITAMIN B_(12) COMPOUNDS

This report focuses on a theoretical study of the cobalt-cabon bond activation mechanism in Vitamin B12, its co enzyme complexes, and model compounds such as cobalamins (Cbl), cobaloximes and cobalt porphyrins. In particular, emphasis is placed on the nucleotide loop and its role in the base on and base off mechanism.     

Learning Theory Estimates via Integral Operators and Their Approximations

The regression problem in learning theory is investigated with least square Tikhonov regularization schemes in reproducing kernel Hilbert spaces (RKHS). We follow our previous work and apply the sampling operator to the error analysis in both the RKHS norm and the L² norm. The tool for estimating the sample error is a Bennet inequality for random variables with values in Hilbert spaces. By taking the Hilbert space to be the one consisting of Hilbert-Schmidt operators in the RKHS, we improve the error bounds in the L² metric, motivated by an idea of Caponnetto and de Vito. The error bounds we derive in the RKHS norm, together with a Tsybakov function we discuss here, yield interesting applications to the error analysis of the (binary) classification problem, since the RKHS metric controls the one for the uniform convergence.     

F+H2→HF+H反应的全量子态分辨的散射动力学研究

利用高灵敏度的氢原子里德堡飞渡时间谱方法研究了 F H_2→HF H 反应碰撞能在5.02kJ/mol 下的交叉分子束反应态态散射动力学.所有在时间飞渡谱中被观测到的谱峰可以归属为 HF 产物的振转态结构.还观测到了明显的 HF(v’=3)前向散射,以及少许的 HF(v’=2)前向散射.     

Modeling Language Evolution

We describe a model for the evolution of the languages used by the agents of a society. Our main result proves convergence of these languages to a common one under certain conditions. A few special cases are elaborated in more depth.     

Lattice path combinatorics and asymptotics of multiplicities of weights in tensor powers

We give asymptotic formulas for the multiplicities of weights and irreducible summands in high-tensor powers V_λ^⊗N of an irreducible representation V_λ of a compact connected Lie group G. The weights are allowed to depend on N, and we obtain several regimes of pointwise asymptotics, ranging from a central limit region to a large deviations region. We use a complex steepest descent method that applies to general asymptotic counting problems for lattice paths with steps in a convex polytope.     

Rate constants from the reaction path Hamiltonian. I. Reactive flux simulations for dynamically correct rates

As ab initio electronic structure calculations become more accurate, inherent sources of error in classical transition state theory such as barrier recrossing and tunneling may become major sources of error in calculating rate constants. This paper introduces a general method for diabatically constructing the transverse eigensystem of a reaction path Hamiltonian in systems with many degenerate transverse frequencies. The diabatically constructed reaction path Hamiltonian yields smoothly varying coupling constants that, in turn, facilitate reactive flux calculations. As an example we compute the dynamically corrected rate constant for the chair to boat interconversion of cyclohexane, a system with 48 degrees of freedom and a number of degenerate frequencies. The transmission coefficients obtained from the reactive flux simulations agree with previous results that have been calculated using an empirical potential. Furthermore, the calculated rate constants agree with experimental values. Comparison to variational transition state theory shows that, despite finding the true bottleneck along the reaction pathway, variational transition state theory only accounts for half of the rate constant reduction due to recrossing trajectories.