Dynamic running

To compute the above expression, short molecular dynamics runs (with a small time step) are calculated and serve as exact trajectories. Using the exact trajectory as an initial guess for path optimization (with a large time step) we optimize a discrete Onsager-Machlup path. The variation of the action with respect to the optimal trajectory is computed and used in the above formula. 

Statistical mechanical averages in a molecular dynamics run are obtained by simply averaging an energetic or structural value over time steps. Thus if the values (xj, i are being computed in a trajectory. the statistical mechanical average is jiist... 

When the friction coefficient is set to zero, HyperChem performs regular molecular dynamics, and one should use a time step that is appropriate for a molecular dynamics run. With larger values of the friction coefficient, larger time steps can be used. This is because the solution to the Langevin equation in effect separates the motions of the atoms into two time scales the short-time (fast) motions, like bond stretches, which are approximated, and longtime (slow) motions, such as torsional motions, which are accurately evaluated. As one increases the friction coefficient, the short-time motions become more approximate, and thus it is less important to have a small timestep. 

Btamp/e Conformations of molecules like n-decane can be globally characterized by the end-to-end distance, R. In a comparison of single-molecule Brownian (Langevin) dynamics to molecular dynamics, the average end-to-end distance for n-decane from a 600 ps single-molecule Langevin dynamics run was almost identical to results from 19 ps of a 27-molecule molecular dynamics run. Both simulations were at 481K the time step and friction coeffi-... 

If the heating time t or cooling time t are non-zero, or if the run time tj. is non-zero and constant temperature is selected, velocities are adjusted (rescaled) during the molecular dynamics run to change the temperature of the system. 

To create a set of snapshots of any molecular dynamics run, press the Snapshot button of the Molecular Dynamics Options dialog box to bring up the Molecular Dynamics Snapshots dialog box for naming a snapshot file. A snapshot file contains snapshots of the coordinates and velocities of a molecular system along the trajectory. The dialog box allows you to name the file and decide at what frequency to take snapshots. For example, choosing the snapshot period to be two data steps implies that only every other time step is stored in the snapshot file. 

Focus attention on the top left-hand box. As the position and momentum of each particle in this box change, then so do the position and momentum vectors of all the image particles in all the other boxes. In particular, if the grey particle in the top left-hand box leaves its box during a dynamics run, then it is replaced by the movement of its image particle from a corresponding neighbouring box. This is a well-known technique in statistical mechanics, which acts to preserve the density. 

Figure 6. Cumulative molar concentration dynamics (--------) Run 4 simulation...

Figure 1-1. (a) Value of the dihedral angle, H(20)-C(6)-C(5)-H(21), plotted versus time for the duration of the dynamics run. (b) Histogram of the dihedral angles found in part (a). Adapted from Ref. [18]... 

We now describe a different approach which is simpler than the method of constraints and also very efficient. It does not require running a constrained simulation and can be performed entirely with a single molecular dynamics run. 

Let us illustrate this method with the three-sequence dynamic run of a Hg-Tl mixture as described in Table 1 and assume for brevity that the exponential fractionation law holds. Efficiencies are only known as relative values and we will assume that the efficiency factor of the axial cup is unity. For the best possible precision, the ratios to he measured are os-pj/ 2 T1, and TlgPTlg, "Hg/ Tlg, Hg/ Hg, and The efficiencies will he... 

The BIOGRAF program was run on a Micro VAX II conmuter equipped with an Evans and Sutherland PS390 graphics terminal. The size of coal structures evaluated, and the duration of molecular dynamics runs, were limited by the available computing speed of this system (a 5000-step, 10-ps molecular dynamics run for a 1040-atom structure, with about 75,000 van der Waals interactions per step, required about 100 hours of computation). 

Figure 14. Contour plot of the electron density at one time step during the zero-voltage molecular dynamics run. The circles indicate the simultaneous positions of those water molecules with the oxygen atom within 3 a.u. of the plane of the contour plot. From Ref. 52, by permission.

---