Hellmann-Feynman theorem and the definition of forces in quantum time-dependent and transport problems

The conventional Hellmann-Feynman theorem for the definition of forces on nuclei is not directly applicable to quantum time-dependent and transport problems. We present a rigorous derivation of a general Hellmann-Feynman-like theorem that applies to all quantum mechanical systems and reduces to well-known results for ground-state problems. It provides a rigorous definition of forces in time-dependent and transport problems. Explicit forms of Pulay-like forces are derived and the conditions for them to be zero are identified. A practical scheme fur nb initio calculations of current-induced forces is described and the study of the transfer of a Si atom between two electrodes is presented as an example.