Virial pressure calculation in Cassandra: Tensors versus dot_product

Hello,

This is strictly a question, and not about an issue I have found in Cassandra. As far as I can tell it accurately calculates pressure.

Cassandra calculates the virial contribution to pressure by calculating stress tensors, which is fine, although a lot of effort. Is there a reason for this method? Towhee also uses tensors for the molecular virial, which makes me feel like there may be a necessity to do this.

Isn't it simpler to calculate the force between atom 'a' of molecule 1 and atom 'b' of molecule 2 (fab), and then project this force onto the vector between the two molecules centers of mass (r12) by taking the dot_product(r12,fab) to get the molecular virial contribution from atoms 1a and 2b, and then sum over all atom interactions? Is this method less accurate than stress tensors?

Cassandra's method is more elaborate, and I am just curious if it was out of a necessity that I should know about (perhaps pertaining to complicated molecules)?

Thanks,

Braden