Travel

To continue the idea of representing a normal mode as a simple harmonic oscillator, the distance the atoms move through can be represented as the distance the idealized mass moves through. This can be calculated knowing the energy of the mode and the force constant:

$\begin{displaymath}E = \frac{1}{2}kx^2. \end{displaymath}$

Here k is the force-constant for the mode, and is given by

$\begin{displaymath}k = <\psi\vert Hessian\vert\psi>; \end{displaymath}$

E is the energy of the mode.

From this, the distance, x, which the system moves through, can be calculated from

$\begin{displaymath}x =\sqrt{\frac{2\times 1.196266\times 10^8 \times 1000 \times 10^8 \nu}{N k}}, \end{displaymath}$

where 1.196266x10⁸ is the conversion factor from cm^-1 to ergs, 1000 converts from millidynes to dynes, 10⁸ converts from cm to Å, and N converts from moles to molecules.

The travel can also be calculated using the DRC, by depositing one quantum of energy into a vibrational mode. For a system at a stationary point, the relevant keywords would be IRC=1 DRC t=1m. For larger systems, the time may need to be increased. At least one coordinate must have an optimization flag set to 1. This is required in order to instruct the DRC to print the turning points.