Which theorem arose from Feynman's MIT thesis, 'Forces in Molecules'?

The theorem associated with Feynman's “Forces in Molecules” work is the Hellmann–Feynman theorem.

In quantum mechanics, the theorem connects the derivative of a system's energy with respect to a parameter to the expectation value of the Hamiltonian's derivative with respect to that parameter. When the parameter is a nuclear coordinate, the result provides a powerful way to calculate forces inside molecules from the electronic wavefunction.

Feynman presented his contribution in the 1939 paper “Forces in Molecules,” written while he was completing his doctoral work at Princeton. The name is shared with physicist Hans Hellmann, whose work appeared earlier; related results had also been obtained independently by Paul Güttinger and Wolfgang Pauli. Thus, Feynman was not the theorem's sole originator.

The question's reference to an “MIT thesis” is a historical slip: Feynman studied at MIT as an undergraduate, but his doctorate and the “Forces in Molecules” work belong to Princeton. That wording does not change the canonical answer, which is the Hellmann–Feynman theorem.