2024 Winter Molecular Simulation Seminar
Room 302, the 2nd experimental building at POSTECH
Presenter: Seungbin Hong
The principal conceptual breakthrough on which statistical mechanics is based is that of an ensemble, which refers to a collection of systems that share common macroscopic properties. Averages performed over an ensemble yield the thermodynamic quantities of a system as well as other equilibrium and dynamic properties. The examples of such ensemble are micro-canonical (NVE), canonical (NVT), isobaric (NPT), and grand-canonical (muVT) one. Although the ensemble probability distribution function (i.e.,Boltzmann distribution) corresponding to each ensemble is derived from the basic statistical postulate, there are only a handful of non-trivial, exactly soluble problems in statistical mechanics. In this sense, molecular simulations have a valuable role to play in providing essentially exact results for problems in statistical mechanics which would otherwise only be soluble by approximate methods, or might be quite intractable. One discripency in molecular simulation is that the trajectories generated by integrating the equation of motion based on classical Hamiltonian mechanics would only lead to the sampling of microcanonical ensemble due to the energy conservation. The question is now translated into the numerical algorithms to systematically control the thermodynamic variables defined in ensemble such as temperature (thermostat), pressure (barostat), and chemical potential (chemostat) to properly sample various ensembles. It should be strongly emphasized that for certain thermostats, they have been known to cause artifacts, non-quasi ergodicity, or poor dynamics in simulation. To provide a reliable route from the microscopic details of a system to macroscopic properties of experimental interest in various ensembles, therefore, understanding the theoretical background of constant ensemble simulation is not only being of academic interest, but also should be technologically useful to most of us.
Temperature control algorithms using thermostats can be divided into strong coupling methods, weak coupling methods, stochastic methods, and extended system dynamics.[1][2] Topics covered in more depth in this presentation include stochastic methods that randomly apply the new speed of each atom based on the Maxwell-Boltzmann distribution. Other methods ,velocity-rescaling method for get better dynamics. For example, Nose-Hoover chain methods applying temperature as an artificial variable rather than a random element[4]. Extended system thermostats that can explain and dynamics, strong coupling methods and weak coupling methods that can be distinguished according to the strength of interaction between each atom are discussed with formulas, and the unique strengths and weaknesses of these temperature control algorithms are discussed. In this seminar, we will dealing about each type of thermostats pros and cons based on equation and physical meaning[5]. In addition, due to problems related to the thermostat, when using the velocity rescaling technique, the motion of the center-of-mass does not take into account high-frequency motion at all, and when only one thermostat is used, the kinetic energy exchange between solvent and solute is too slow. For example, when using the Berendsen weak coupling thermostat in REMD simulation, there was also the problem of the Berendsen thermostat not being able to solve the canonical ensemble [6], which is a situation in which correct dynamics cannot be considered due to too small a temperature gradient. And in non-ergodic system , Nose-Hoover thermostat can't explore all feasible case and does not tield a canoniccal distribution in phase space [7].