Electronic State Populations and Decay Mechanism

It is well known from previous experimental [9-12] and theoretical works [13, 21, 24-26] that after excitation to the bright B2u t t ) state, pyrazine undergoes an ultrafast radiationless decay process in a few tens of femtoseconds. This process was directly observed recently by TRPES using sub-20 fs pulses [11, 12]. In this section, we present quantum dynamics simulations of the excited state dynamics of pyrazine triggered by a 14 fs sine-squared shaped laser pulse resonant with the transition from the ground to the B2u Tnr ) state. Specifically, the total Hamiltonian operator reads 

Our results were analyzed in term of diabatic and adiabatic electronic state populations. In what follows, the diabatic electronic states are labeled by Greek letters whereas the adiabatic electronic states are labeled by Latin letters. The diabatic population for the state a is simply the norm of the corresponding wavefunction component 

The adiabatic populations are more difficult to obtain. Consider the transformation matrix V(Q) that diagonalizes the diabatic potential matrix W(g) of Eq.(5.3) 

The adiabatic population of the state a) is obtained as the expectation value of the corresponding projection operator 

The diabatic and adiabatic electronic state populations obtained with the three-state model are shown in full lines in Fig. 5.5a, b, respectively. The diabatic populations obtained with the four-state model are also shown in dashed lines in Fig. 5.5a. The comparison of the diabatic populations for the three- and four-state models confirms that the inclusion of the B2g mr ) state in the simulations has a minor effect on the non-adiabatic decay dynamics of the molecule after excitation to the B2u (tttt ) state. Only a very small amount of population is transfered to the B2g mr ) state, with a maximum of less than 0.02 at 11 fs. In addition, the populations of the B uinn ), Auimr ) and B2 (7r7r ) states are similar in the three- and four-state models. The population of the B2 (7r7r ) state reaches a maximum of nearly 0.6 at 11 fs, and then quickly decays to almost zero at 50 fs. A recurrence is then seen at 95 fs, as in the simulation with the two-state model. Between 0 and 20fs, both the Bsuinn ) and Auimr ) state populations rise quickly and reach approximately 0.15 at 20fs. Then, between 20 and 40 fs, the B uinir ) state population continues to rise and reaches a 

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