Note that both ĤQ and |Ψ(R(t))⟩ depend parametrically on the bath configuration, R(t) ≡ {R n,ν (t)}. The nuclear DOF is updated through the classical equations of motion, with different types of forces that depend on ∇ R ( Ĥsb + Ĥb ), such as Ehrenfest dynamics (and similarly for other mean-field-like approaches) with F = jk c * j c k ∇ R ⟨j|( Ĥsb + Ĥb )|k⟩, and for the HTC Hamiltonian special case, the nuclear force is