Trajectory averages

HyperChem run s the molecular dynain ics trajectory, averaging and analyzing a trajectory and creating the Cartesian coordinates and velocities, fhe period for reporting these coordinates and velocities is th e data collection period. At-2. It is a m iiltiplc of the basic time step. At = ii At], and is also referred to as a data step. The value 1I2 is set in the Molecular Dynamics options dialog box. 

For the purposes of the present treatment, we wish to rewrite this trajectory average as an average over the initial, equilibrium distribution. If the system evolves according to deterministic (e.g., Hamiltonian) dynamics, each trajectory is uniquely determined by its initial point, and (8.46) can be written without modification as an average over the canonical phase space distribution. 

In terms of a trajectory average, the time correlation function can be written as... 

Generally, MD is performed to simulate a continuous phase trajectory in the microcanonical N,E,V) ensemble, while in MC method, individual phase points of an (N,V,T) ensemble are simulated. As far as the equilibrium properties are concerned, the trajectory average of MD and the configurational average of MC are equivalent (Allen and Tildesley, 1987). Recently, MD simulation of other types of ensembles also have been achieved. In the N,E,V) simulations, volume and total energy are held constant and the temperature and pressure are allowed to fluctuate. Andersen (1980) suggested methods for simulation of isobaric-isoenthalpic and isobaric-isothermal (A, P,7) ensembles. A... 

One situation in which we would expect different initial conditions to yield different trajectory averages is if the energy surface has several connected components. 

As we discussed in the Background chapter, to prove that integrating this set of differential equations does indeed simulate a model system with chemical potentials and pressures equal in both boxes, we have to show that the trajectory averages calculated by integrating Eqs. (4) are the corresponding thermodynamic averages. 

The GEMD trajectory average of a property A, which depends on the coordinates and momenta of the atoms constituting the... 

A comparison between the trajectory average product energies and those found by the above dynamical model are shown in Table 8 for random activation calculations on surface lA with J equal zero. Trajectory results at the exit-channel barrier are used to evaluate equations (19) and (20). There is excellent agreement between the two sets of energies. The dynamical model correctly predicts an increase in the fraction of available energy partitioned to CC vibration as the total energy in HCC is raised. 

We have now presented two averages for macroscopic properties 1. The trajectory average over consecutive time points ... 

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