# Theory

#### Disclaimer: this section is for ANA's developers reference. It does not contain relevant information for the users.

## Spring constant

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

where,

*Î½*: frequency in units of 1/s*Î»^{amber}*: amber frequencies in units of 1/cm*c*: speed of light- constants added to adjust
*cm*to*angstroms*and*Kg*to*g*

where,

*Ï‰*: angular frequency in units of 1/s

where,

*Î»^{NMA}*: spring constant*k*for a NMA vector*m*: mass (doesn't matter as long as units are correct)

### In units of *Kcal/mol*

#### Rigidity constant

### In units of *KJ/mol*

#### Rigidity constant

## Amber PCA eigenvalues to quasi-harmonic analysis frequencies

From equipartition theorem:

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

*Î»_{amber i}*: amber frequencies in units of 1/cm*Î»_{PCA i}*: amber PCA eigenvalues in units of Ã…^{2}- constant added to adjust Ã… to cm^{-1}