Vertical excited state

Excited states (vertical) Solvent effects ESR Solid state dynamics Infinite systems Geminal functional theory... 

Figure Al.6.21. Bra and ket wavepacket dynamics which detennine the coherence overlap, (( ) ( ) ). Vertical arrows mark the transitions between electronic states and horizontal arrows indicate free propagation on the potential surface. Full curves are used for the ket wavepacket, while dashed curves indicate the bra wavepacket. (a) Stimulated emission, (b) Excited state (transient) absorption (from [41]).

Figure Al.6.27. Equipotential contour plots of (a) the excited- and (b), (c) ground-state potential energy surfaces. (Here a hamionic excited state is used because that is the way the first calculations were perfomied.) (a) The classical trajectory that originates from rest on the ground-state surface makes a vertical transition to the excited state, and subsequently undergoes Lissajous motion, which is shown superimposed, (b) Assuming a vertical transition down at time (position and momentum conserved) the trajectory continues to evolve on the ground-state surface and exits from chaimel 1. (c) If the transition down is at time 2 the classical trajectory exits from chaimel 2 (reprinted from [52]).

The energies of this Cl and of the other ones calculated in this work are listed in Table III. The calculated CASSCF values of the energies of the two lowest electronically states are 9.0 eV (5i, vertical) and 10.3 eV ( 2, vertical) [99]. They are considerably higher than the expenmental ones, as noted for this method by other workers [65]. In all cases, the computed conical intersections lie at much lower energies than the excited state, and are easily accessible upon excitation to Si. In the case of the H/allyl Cl, the validity confirmation process recovered the CHDN and 1,3-CHDN anchors. An attempt to approach the third anchor [BCE(I)] resulted instead in a biradical, shown in Figure 43. The bhadical may be regarded as a resonance hybrid of two allyl-type biradicals. 

Vertical ionization. A process whereby an electron is removed from a molecule, in its ground state or an excited state, so rapidly that a positive ion is produced without change in the positions or momenta of the atoms. The resultant ion is often in an excited state. 

Hydrogen transfer in excited electronic states is being intensively studied with time-resolved spectroscopy. A typical scheme of electronic terms is shown in fig. 46. A vertical optical transition, induced by a picosecond laser pulse, populates the initial well of the excited Si state. The reverse optical transition, observed as the fluorescence band Fj, is accompanied by proton transfer to the second well with lower energy. This transfer is registered as the appearance of another fluorescence band, F2, with a large anti-Stokes shift. The rate constant is inferred from the time dependence of the relative intensities of these bands in dual fluorescence. The experimental data obtained by this method have been reviewed by Barbara et al. [1989]. We only quote the example of hydrogen transfer in the excited state of... 

Fig. 13.3. Orbital correlation diagram for one ground-state ethene and one excited-state ethene. The symmetry designations apply, respectively, to the horizontal and vertical planes for two ethene molecules approaching one another in parallel planes.

In a combined experimental/computational study, the vibrational spectra of the N9H and N7H tautomers of the parent purine have been investigated [99SA(A) 2329]. Solvent effects were estimated by SCRF calculations. Vertical transitions, transition dipole moments, and permanent dipole moments of several low-lying valence states of 2-aminopurine 146 were computed using the CIS and CASSCF methods [98JPC(A)526, 00JPC(A)1930]. While the first excited state of adenine is characterized by an n n transition, it is the transition for 146. The... 

The ionization being accompanied by a vibrational excitation, the fine structure of bands can be exploited for determination of vibrational levels of an ionized system in the ground and excited states. Of course, the first (0-0) and the strongest vibrational bands are the most important because they determine adiabatic and vertical ionization potentials of radicals. 

Figure 1.3. Real-time femtosecond spectroscopy of molecules can be described in terms of optical transitions excited by ultrafast laser pulses between potential energy curves which indicate how different energy states of a molecule vary with interatomic distances. The example shown here is for the dissociation of iodine bromide (IBr). An initial pump laser excites a vertical transition from the potential curve of the lowest (ground) electronic state Vg to an excited state Vj. The fragmentation of IBr to form I + Br is described by quantum theory in terms of a wavepacket which either oscillates between the extremes of or crosses over onto the steeply repulsive potential V[ leading to dissociation, as indicated by the two arrows. These motions are monitored in the time domain by simultaneous absorption of two probe-pulse photons which, in this case, ionise the dissociating molecule.

Figure 6. Calculated potential energy curves for sextet states of FeO. The ground electronic Slate and excited states accessible by allowed electronic transitions from the ground state are shown. Points are calculated using TD-DFT at the B3LYP/6-311G(d,p) level. Sohd hnes are S states and dashed lines are II states, the vertical dashed hne indicates for the ground state. The experimental value of the dissociation energy is also diown for reference.

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],... 

The reliability of this method for the evaluation of (vertical) electronic spectra has been clearly established in the present work, and further calculations on other molecules (ethylene, vinylydene... for example) have confirmed the very promising potentialities of such an approach that avoids the possible artefacts brought in by any arbitrary truncated CIs when dealing with excited states [49]. We also emphasize that this methodology is able to give reliable splittings between states ranging from 10 keal/mol to more than 10 eV. 

Since no experimental work is available to confront the theoretical model designed to describe C3H2 excited states correctly, test calculations had to be done in a preliminary step. For that purpose, we have chosen ethylene, for which extensive calculations of the vertical spectrum as well as experimental measures are available. It is well known indeed that a correct quantitative and even qualitative description of small rr-electronsystems, is still a challenge for theoretical chemistry. The difficulties are found at each step of the computational approach ... 

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

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. 

Figure 3.13. Resonance Raman spectra of Sj excited state trans-stilbene in decane at delay times indicated. The pump wavelength was 292.9 nm and the probe wavelength was 585.8nm. The vertical dashed lines illustrated the substantial spectral evolution of the 1565 cm compared to the 1239cm band. (Reprinted with permission from reference [56]. Copyright (1993) American Chemical Society.)...

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