Electronic coherence formation in the radiationless S2 decay of pyrazine: Quantum Ehrenfest simulations focused on the branching space of the conical intersection

We investigate the formation of electronic coherences in pyrazine following excitation to the S 2 1 B 2u (ππ*) state (D 2h ) and relaxation via a conical intersection (CI) to the S 1 1 B 3u (nπ*) state. In our Quantum Ehrenfest (Qu-Eh) simulations, Gaussian wavepackets (GWPs) are started in the positive and negative directions of all the selected normal modes. The GWPs moving along the derivative coupling vector cross the CI and generate coherences from time zero. The effect nevertheless cancels in the total wavefunction because the wavepackets have opposite geometric phases. Thus, our results support the theoretical conjecture which states that coherences should not be observable if the intersecting states have different Abelian point group symmetries at the Franck-Condon (FC) region. However, if initial conditions start with a small admixture of the second coupled state, in this case the S 1 1 B 3u (nπ*) state, rather than a pure S 2 state, one generates an initial gradient along either the positive or negative direction of the derivative coupling vector, thus biasing this direction so that the coherence becomes non-zero.