Constrained reaction coordinate dynamics

Carter E A, Ciccotti G, Hynes J T and Kapral R 1989 Constrained reaction coordinate dynamics for the simulation of rare events Chem. Phys. Lett. 156 472-7... 

I. Coluzza, M. Sprik, and G. Ciccotti (2003) Constrained reaction coordinate dynamics for systems with constraints. Mol. Phys. 101, p. 2885... 

E. A, Carter, G. Ciccotti, J. T. Hynes, and R. Kapral, Chem. Phys. Lett., 156, 472 (1989). Constrained Reaction Coordinate Dynamics for the Simulation of Rare Events. 

T. Mosell, G. Schrimpf, and J. Brickmann, J. Phys. Chem. B, 101, 9476 (1997). Diffusion of Aromatic Molecules in Zeolite NaY. 1. Constrained Reaction Coordinate Dynamics. 

Ciccotti, G. Kapral, R. Vanden-Eijnden, E., Blue moon sampling, vectorial reaction coordinates, and unbiased constrained dynamics, Chem. Phys. Chem. 2005, 6, 1809-1814... 

In this section we discuss first in general the techniques used to simulate the chemical reactions with relatively high activation barriers. After that we provide a more detailed discussion of the constrained dynamics approach. Special emphasis will be put on MD along the intrinsic reaction coordinate (IRC), illustrated by a few simple examples.33... 

The idea of constrained dynamics performed for a set of points along such a reaction path , i.e. for a set of fixed values of the reaction coordinate, A, is not specific to MD. Similar approaches have been commonly used in computational studies based on static quantum-chemical calculations. Such approaches are known as linear transit calculations, reaction path scans, etc. A set of constrained geometry optimizations with the constraint driving the system from reactants to products is a popular way to bracket a transition state, for instance. 

Lo et al. used plane wave calculations to examine methanol coupling near a protonated site in chabazite.286,287 Constrained Car-Parrinello molecular dynamics were used to probe potential reaction coordinates for the reaction. These calculations suggest a reaction path that proceeds via formation of stable intermediates of methane and formaldehyde. A novel feature of this work was the use of transition path sampling, a technique to efficiently search for transition states that requires little a priori information regarding the configuration of the final products of a reaction. Methanol coupling in ferrierite (FER) has been examined with periodic DFT calculations by Govind et al.2SS... 

It is clear that the funnel shape with a vast number of chain conformations in the unfolded state makes a difficult sampling target for calculations of the dynamics. We therefore prefer to work in a tube, which is more accessible to simulations. Hence, we do not require absolute equilibrium in the direction perpendicular to the reaction coordinate. We are satisfied with a local equilibrium in a tube that follows the milestones (sampling is always constrained in time and space and it is assumed that it is appropriate for the problem at hand) (Figure 13.4). Obviously, this picture is not a complete view of the funnel. Nevertheless, it allows for the sampling of a group of reactive trajectories of special properties and of interest. 

The particular model used in the original simulation i- of this reaction was that of a Cl + CI2 like reaction as modeled by a LEPS potential energy surface. The barrier for this symmetric reaction was normally taken to be 20 kcal/mol (—33 kT at room temperature). Other simulations used 10 and 5 kcal/mol barriers. The reactants were placed in either a 50 or 100 atom solvent (Ar in the earliest simulations Ar, He, or Xe in the later work) with periodic truncated octahedron boundary conditions. To sample the rare reactive events, as described previously, this system was equilibrated with the Cl—Cl—Cl reaction coordinate constrained at its value at the transition state dividing surface (specifically, the value of the antisymmetric stretch coordinate was set equal to zero). From symmetry arguments, this constraint is the appropriate one (except in the rare case where the solvent stabilizes the transition state sufficiently such that a well is created at the top of the gas phase barrier). For each initial configuration, velocities were chosen for all coordinates from a Boltzmann distribution and molecular dynamics run for 1 ps both forward and backward in time. 

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