(a) Cut of the potential energy surfaces [CASSCF with cc-pVDZ(6,6)] for , which shows the seam of the CI between the ground and excited electronic states. (b) Sketch of the symmetric and antisymmetric allylic stretch coordinates and , and the torsion angle . (c) Initial wavefunctions of para- and ortho-fulvene, , which are the lowest vibrational and torsional eigenfunctions in the ground electronic state (see also Appendix). Here shown for as a function of and . Figures (a) and (b) are adapted from Ref. 30.
Adiabatic populations of the excited electronic state of para-fulvene [, dashed black lines] and ortho-fulvene [, solid gray lines] during and after excitation with the laser pulse , defined in Eq. (5). The pulse parameters are , (thin lines), and , (broad lines). In all cases, the maximal field strength is .
Expectation values and [panels (a) and (d)] in the excited electronic state, [panels (b) and (e)] in the electronic ground state, and [panels (c) and (d)] total expectation values for ortho-fulvene (solid gray lines) and para-fulvene (dashed black lines). The thin and broad lines represent the expectation values after excitation with a short pulse with and with a long pulse with , respectively. The pulse parameters are the same as in Fig. 2.
One-dimensional cut through the adiabatic potentials and at and , along the symmetric stretch coordinate . The initial wavefunction is shown in gray. The three vertical arrows represent the excitation with three different central laser frequencies: (a) vertical excitation, (b) excitation resonant to the vibrational ground state in , and (c) an intermediate case. The region of the CI is indicated by the circle.
Excited state expectation values and as a function of time in phase space. Here, is the momentum corresponding to the symmetric stretch coordinate . The three lines show the phase space trajectories from to for excitation with different laser pulses. The pulse parameters are (a) and (dark gray line), (c1) and (light gray line), and (c2) and (black line). For each trajectory, the end of the pulse is marked by a ×. The black cross at indicates the starting point at vertically above the minimum of the electronic ground state potential.
Differences in the adiabatic excited populations between para-fulvene and ortho-fulvene, for excitation with a single laser pulse with and (gray line); for excitation with two laser pulses with , and as before (dashed black line); and for excitation with two laser pulses with a delay time of and and (solid black line).
Maximal differences between the excited state population of ortho- and para-fulvene, , as a function of the delay times between two laser pulses. The pulse parameters are (a) and and (b) and . The data points are indicated by the gray points, the black lines show the envelope of the signal.
Expectation values and [panels (a) and (d)] in the excited electronic state [panels (b) and (e)] in the electronic ground state, and [panels (c) and (d)] total expectation values for ortho-fulvene (solid gray lines) and para-fulvene (dashed black lines) during and after a two-pulse sequence with the pulse parameters , , and a delay time .
Ground state equilibrium structure of fulvene (left panel). Since the protons and as well as and cannot be exchanged by the processes considered here, fulvene has the same MS group as the structure shown on the right, where the protons and are combined to 3 and the protons and are combined to 4.
The character table of the torsional subgroup of fulvene, which is isomorphic to .
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