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How are class II force field cross-terms derived?

Physics Asked by Emerson P L on October 20, 2020

In some class II force fields, there are cross-terms that characterize bond-bond, bond-angle interactions and others. Example of equations below:

$$sum_{bond-bond}^{}k_{bb}(b-b_{0})(b^{‘}-b^{‘}_{0})$$
$$sum_{bond-angle}^{}k_{ba}(b-b_{0})(theta^{‘}-theta^{‘}_{0})$$

My question is: how do I get the $k_{bb}$ and $k_{ba}$ values?

I thought of two possibilities:

  1. $k_{bb}$ must be obtained by some combination rule (e.g., Lorentz-Berthelot) that involves two $k_{b}$ values (of the bonds of interest). A similar procedure could be done for $k_{ba}$.

  2. Or $k_{bb}$ and $k_{ba}$ are adjusted as a total energy of the molecule of interest (e.g., I take the force field and adjust the "global" equation for various geometric configurations, where the energy values are obtained by quantum chemistry).

If "1." approach exists, could someone kindly provide me with an article that reports the existing combination rules for that purpose (i.e., if you face it)?

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