Vertical excitations

Figure 3, Wavepacket dynamics of the photodissociation of NOCl, shown as snapshots of the density (wavepacket amplitude squared) at various times, The coordinates, in au, are described in Figure b, and the wavepacket is initially the ground-state vibronic wave function vertically excited onto the 5i state. Increasing corresponds to chlorine dissociation. The density has been integrated over the angular coordinate. The 5i PES is ploted for the geometry, 9 = 127, the ground-state equilibrium value,...

To return to the simple picture of vertical excitation, the question remains as to how a wavepacket can be simulated using classical trajectories A classical ensemble can be specified by its distribution in phase space, Pd(p,Q), which gives the probability of finding the system of particles with momentum p and position q. In conUast, it is strictly impossible to assign simultaneously a position and momentum to a quantum particle. 

A final study that must be mentioned is a study by Haitmann et al. [249] on the ultrafast spechoscopy of the Na3p2 cluster. They derived an expression for the calculation of a pump-probe signal using a Wigner-type density mahix approach, which requires a time-dependent ensemble to be calculated after the initial excitation. This ensemble was obtained using fewest switches surface hopping, with trajectories inibally sampled from the thermalized vibronic Wigner function vertically excited onto the upper surface. 

The electron alfinity and ionization potential can be either for vertical excitations or adiabatic excitations. For adiabatic potentials, the geometry of both ions is optimized. For vertical transitions, both energies are computed for the same geometry, optimized for the starting state. 

All of the predicted excitation energies are in good agreement with the experimental values. It should also be noted that the experimental excitation energy for the third state measured the adiabatic transition rather than the vertical transition, so this value must be assumed to be somewhat lower than the true vertical excitation energy. A larger basis set is needed to produce better agreement with experiment. 

The transition energies from the ground state to the lowest 60 vertical excited states considered in this study are reported in Table 2 (30 singlets) and in Table 3 (30 triplets) where they are compared to the avalaible experimental results and to some previous theoretical calculations [45,60,65,68],... 

Table 7 Vertical excitation energies for the two lowest excited states of C2H4...

No significant improvement for the vertical excitation energy of the 2 B (3p) state was found. From these results we have decided to describe the lowest states of B and A2 symmetries with the same set of molecular orbitals, optimized for the neutral molecule within the MCSCF/ 6422 expansion. 

Our best estimation for the vertical excitation energies for states of A, symmetry are reported in Table 12. They correspond to a ground state calculated at CI( 6) level using orbitals optimized for the neutral molecule with the MCSCF/SD expansion, and excited Rydberg states calculated at the level using orbitals optimized for the positive ion... 

The vertical excited states of B2 symmetry, calculated at the Cl( level, are very high in energy. The first one, B2(3p) is already at 8.60 eV above the ground state (Table 12) with a transition moment of 0.16 a.u., probably too weak for the transition to be observed. 

Vertical excitation energies to states of B symmetry, calculated at the level using the orbitals optimized for the neutral molecule with the MCSCF/6422 expansion, are reported Table 12. The I Bi valence state and 2 B (3p) Rydberg state of C3H2 are respectively 5.2 eV and 7.5 eV above the ground state with large transition moments of... 

Table 11-1. Vertical excitation energies in eV relative to the ground state minimum of the singlet electronic excited states in the uracil...

The photophysical properties of adenine have intrigued chemists from early on. Broo studied adenine and 2-aminopurine (2AP) in order to understand their differences in photophysical properties. Adenine like all natural nucleobases has very short excited state lifetimes and low quantum yields of fluorescence, while 2AP, which differs from adenine in the position of the amino group, has long lifetimes and strong fluorescence, making it a very useful fluorescent probe. In Broo s work it was observed that the first excited state is a nn at vertical excitation but crosses with an nn state which becomes the Si state adiabatically at the minimum. The large out-of-plane distortion on the nn state opens up a deactivation channel in adenine compared to 2AP. In 2AP, on the other hand, the Si state always has a 7T7r character. 

Figure 11-12. Sj pathways for cytosine and 5M2P from vertical excitations to the sofa and twist conical intersections. Cytosine paths are shown in blue, and 5M2P are shown in green. MRCI energies are given in eV. (From Ref. [144])...

Table 11-6. Vertical excitation energy shifts in eV for uracil and thymine in aqueous phase compared to gas phase, using various levels of theory. The ordering of the states is according to the gas phase energies...

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