# 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,

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

where,

*ω*: angular frequency in units of 1/s

where,

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

*Kcal/mol*

In units of #### Energy of displacement along VGV

*KJ/mol*

In units of #### Energy of displacement along VGV

## Amber PCA eigenvalues to quasi-harmonic analysis frequencies

From equipartition theorem:

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

*λ^{amber}_{i}*: amber frequencies in units of 1/cm*λ_{i}*: amber eigenvalues in units of A^{2}- constant added to adjust Å to cm^{-1}