Energy-conserving path-branching with the force averaging

4 Energy-conserving path-branching with the force averaging 

1 Initialization of the electron wavepacket right after branching 

We here consider only a two-state case for simple illustration, and extension to more states is rather straightforward. Suppose that at a phase space point (R(t), P t)) we have a SET path, and also the force diagonalization gives a set of Di t), D2(t) for the force eigenstates Ai(r, R(t)), A2(r, R(t)), giving rise to an electron wavepacket 

We here consider the following two propagation of the state (1) Continue the Ehrenfest d3mamics for the next short time interval At (denoted as path 0), and (2) let the path branch into two pieces (path 1 and 2). For the path-branching, along with the associated electronic state mixing, we prepare two vectors as the initial electronic states (at this time t) 

With these initial conditions, two additional SET paths are generated that are different from the SET path 0. Then at time t + At we compare the energies thus branched. 

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