第12页 Ch2-3

P12 the bath are weakly coupled, so that we may ignore their interaction energy.
Boltzmann distribution for a system at temperature T
P13 The relation between the Helmholtz free energy and the partition function is often more convenient to use than the relation between lnQ and the entropy.
P17 We can either compute that quantity by time averaging (the MD approach) or by ensemble averaging (the MC approach).
P25 Clearly, it would be much preferable to sample many points in the region where the region where the Boltzmann factor is large and few elsewhere. This is the basic idea behind importance sampling.
P31 We focus on Monte Carlo methods to models phenomena that do not depend on time. Dynamic Monte Carlo schemes are used to generate a numerical solution of the the master equation that is supposed to describe the time evolution of the system under study.
The prime purpose of the kind of Monte Carlo or Molecular Dynamics program that we shall be discussing is to compute equilibrium properties of classical many-body systems.
The Metropolis method was introduced as a Markov process in which a random walk is constructed in such a way that the probability of visiting a particular point is proportional to the Boltzmann factor.
P32 The boundary conditions, e.g. free or hard or periodic.
P33 Although the use of periodic boundary condition proves to be surprisingly effective method for simulating homogeneous bulk systems, one should always be aware that the use of such boundary conditions may lead to spurious correlations not present in a truly macroscopic bulk system. (not exactly isotropic)
Short-ranged means that the total potential energy of a given particle is dominated by interactions with neighboring particles that are closer than some cutoff distance.
P37 Truncate potentials: simple truncation (not for dynamics), truncation and shift (Dynamics, no discontinuities and no impulsive corrections to the pressure), minimum image convention.
P39 One should be extremely careful when applying truncated and shifted potential in models with anisotropic interactions. In that case, truncation should not be carried out at a fixed value of the distance between the molecular centers of mass but at a point where the pair potential has a fixed value, because otherwise the potential cannot be shifted to 0 at the point where it is truncated. For Monte Carlo simulations, this is not serious, but for Molecular Dynamics simulations this would be quite disastrous, as the system would no longer conserve energy, unless the impulsive forces due to the truncating and shifting are taken into account explicitly.
Minimum image convention not for dynamic.
P43 We should distinguish between trial moves that involve only the molecular centers of mass and those that change the orientation or possibly even the conformation of a molecule.