## Adding stablizing terms to the force constant model for MD/MC purposes

## Description

The MD-simulations for systems like

- 4th order Clathrate 300K
- 6th order Ni100 surface 1000K
- 8th order BCC Ti 1000K

keep crashing due to the force constant model not being stable.

## Suggestions

This could probably be solved by simply adding one or a few extra parameters specifically for bonding purpose. For example to the 4th order clathrate model we could add a weak 8th order bonding onsite term which doesn't affect the normal dynamics much but helps stabilize the system.

Possible solutions could be

- Add high order bonding onsite term (this would break the sum rules)
- Add strongly anharmonic pair potential, as suggested by Fei, which could be fitted together with the force constant model (This will not break the sum rules since a pair potential obey sum rules.)

## Notes

We should think about how to interface this with the core of hiphive. I think it would be wise to start with absolute minimum functionality which would have to be.

- Module for giving an atoms object produce a
`fit_matrix`

(which can be appended to the fc`fit_matrix`

). - Class for ASE calculator for this new pair potential
- Unless ASE already have it, basic class for making hybrid calculators.