On the time-dependent Lagrangian approach in quantum chemistry

We formulate the time-dependent variational principle in the form of the Euler-Lagrange equations, and demonstrate that standard variational as well as nonvariational wave functions may be obtained from these. We also demonstrate how inherently real expectation values of Hermitian operators can be constructed for nonvariational wave functions by using the time-dependent Hellmann-Feynman theorem which, in turn, is a simple consequence of the Euler-Lagrange equations. The procedure is illustrated by derivation of time-dependent Hartree-Fock and of time-dependent coupled cluster theory. Finally we give the fundamental equations for molecular dynamics within semiclassical electron nuclear dynamics (END) with a classical description of the nuclei and coupled cluster description of the electrons. © 1998 American Institute of Physics