1.1 高分子的基本概念 1.2 高分子化合物的基本特征 1.4 高分子化合物的命名和分类 1.5 聚合反应

Approaches to Asymmetric Catalysis Organometallic catalysis Broad scope Ligand control Inert conditions -Cost and toxicity Bioorganic catalysis Highly selective High rate of reaction Limited scope

How to analyse the errors of simulation results? Sustematic errors: Possible sources. 'poor equilibration; bad random number generator; 'system size effect. Practical method for detecting systematic errors: -longer simulation, different initial configurations; test random number generator, use different generators; simulation with larger systems

Application of MR2T2 algorithm in statistical mechanics Canonical ensemble: Distribution function: p(rN)=exp(-E(rN)/KT)/Q Q= JdrN exp(-E(rN)/kT) Different states of the Markov chain: In the application of Metropolis algorithm to a simulation of molecular system, the states of the Markov chain correspond to different configurations of the molecular system

Monte Carlo Integration Hit and miss method:Algorithm: （ 1) generate N uniform random numbers, (i=1, 2,..., N), on(a,b) and N uniform random numbers, (i=1, 2,..., N), on (0,c); （2) calculate g() and count the number of cases, Nhit for whichg() （3)I can be estimated by

What is a Monte Carlo simulation? Monte Carlo simulation is numerical method based on the extensive use of random numbers for solving different problems. Remark: Monte Carlo simulation can be used tostudy not only stochastic problems (e.g., diffusion) but also non stochastic ones (Monte Carlo

Molecular dynamics for continuous potentials Short history: The first MD simulation for a system interacting with a continuous potential (Lennard-Jones potential) was carried out by A. Rahman in1964. A. Rahman, Phys. Rev. 136, A405, (1964). Main differences between MD with continuous poentials and

How to start up? Initial configuration: Criteria for choosing initial configuration: quick relaxation to the equilibrium state. Random initial configuration: Advantage: liquid-like, easy to generate. Drawback: substantial overlaps at high densities. Use: Monte-Carlo for systems without hard-core interactions. Not suitable for hard-core interactions and MD at high densities

Necessary Background of Statistical Physics (2) when the velocity of the center of mass is fixed to zeroKinetic energy

Why one needs statistics for describing physical phenomena? Any measurable macroscopic property is an average over a very huge number of microscopic configurations. Time scale of thermal fluctuations and basic relaxations~fs(femto second, 10-15 second). During the time interval necessary for realizing a measurement, a macroscopic system undergoes the change of its microscopic configuration for many many times!