Theory

Spring constant

Adaptations used to calculate cavity flexibility from Amber mass-weighted eigenvalues.

$\omega = \lambda_{amber} c \ 10^{8} \ 10^{3}$

where,

$\omega = 2\pi \nu$

where,

$\omega^{2} = \frac{\lambda_{NMA}}{m}$

where,

$\lambda_{NMA} = 4 \pi^{2} c^{2} 4.184E^{-22} \lambda_{Amber}^{2}$

$k_{VGV} = \frac{1}{108.591^{2}} \sum_{i=1}^{3N-6} c_{i}^{2} \lambda_{i \ Amber}^{2}$

$\lambda_{NMA} = 4 \pi^{2} c^{2} E^{-22} \lambda_{Amber}^{2}$

$k_{VGV} = \frac{1}{53.088^{2}} \sum_{i=1}^{3N-6} c_{i}^{2} \lambda_{i \ Amber}^{2}$

From equipartition theorem:

$\omega_{i} = \sqrt{\frac{K_{B}T}{\lambda_{PCA \ i}}}$

In Amber from angstroms^2 to cm^-1 in Kcal/mol, at 300K:

$\lambda_{i \ amber} = 108.587 \sqrt{\frac{0.6}{\lambda_{PCA \ i}}}$