关键词: 副本交换, 分子动力学, 复杂反应, 温度, 哈密顿

Abstract:

A complex reaction, such as combustion, polymerization, and zeolite synthesis, involves a large number of elementary reactions and chemical species. Given a set of elementary reactions, the apparent reaction rates, population of chemical species, and energy distribution as functions of time can be derived using deterministic or stochastic kinetic models. However, for many complex reactions, the corresponding elementary reactions are unknown. Molecular dynamics (MD) simulation, which is based on forces calculated by using either quantum mechanical methods or pre-parameterized reactive force fields, offers a possibility to probe the reaction mechanism from the first principles. Unfortunately, most reactions take place on timescales far above that of molecular simulation, which is considered to be a well-known rare event problem. The molecules may undergo numerous collisions and follow many pathways to find a favorable route to react. Often, the simulation trajectory can be trapped in a local minimum separated from others by high free-energy barriers; thus, crossing these barriers requires prohibitively long simulation times. Due to this timescale limitation, simulations are often conducted on very small systems or at unrealistically high temperatures, which might hinder their validity. In order to model complex reactions under conditions comparable with those of the experiments, enhanced sampling techniques are required. The replica exchange molecular dynamics (REMD) is one of the most popular enhance sampling techniques. By running multiple replicas of a simulation system using one or several controlling variables and exchanging the replicas according to the Metropolis acceptance rule, the phase space can be explored more efficiently. However, most published work on the REMD method focuses on the conformational changes of biological molecules or simple reactions that can be described by a reaction coordinate. The optimized parameters of such simulations may not be suitable for simulations of complex reactions, in which the energy changes are much more dramatic than those associated with conformational changes and the hundreds elementary reactions through numerous pathways are unknown prior to the simulations. Therefore, it is necessary to investigate how to use the REMD method efficiently for the simulation of complex reactions. In this work, we examined the REMD method using temperature (T-REMD) and Hamiltonian (H-REMD) as the controlling variable respectively. In order to quantitatively validate the simulation results against direct simulations and analytic solutions, we performed the study based on a simple replacement reaction (A + BC = AB + C) with variable energy barrier heights and reaction energies described using the ReaxFF functional forms. The aim was to optimize the simulation parameters including number, sequence, and swap frequency of the replicas. The T-REMD method was found to be efficient for modeling exothermic reactions of modest reaction energy (< 3 kcal∙mol^-1) or activation energy (ca. < 20 kcal∙mol^-1). The efficiency was severely impaired for reactions with high activation and reaction energies. The analysis of the simulation trajectory revealed that the problem was intrinsic and could not be solved by adjusting the simulation parameters since the phase space sampled using T-REMD was localized in the region favored by high (artificial for speed-up) temperatures, which is different from the region favored by low (experimental) temperatures. This issue was aggravated in the case of endothermic reactions. On the other hand, the H-REMD run on a series of potential surfaces having different activation energies was demonstrated to be remarkably robust. Since the energy barrier only reduces the reaction rates, while the phase space controlled by the reaction energy differences remains unchanged at a fixed temperature, excellent results were obtained with fewer replicas by using H-REMD. It is evident that H-REMD is a more suitable method for the simulation of complex reactions.

Key words: Replica exchange, Molecular dynamics, Complex reaction, Temperature, Hamilton