Excited States Ordering

The symmetry of each excited state must be used when matching up predicted and observed states. You cannot simply assume that the theoretical excited state ordering corresponds to the experimental. In most cases, Gaussian will identify the symmetry for each excited state. In those relatively rare instances when it cannot —as will be true for benzene—you will need to determine it by examining the transition wavefiinction coefficients and molecular orbitals. 

The excited-state ordering is expected to play an important role in governing the photophysical and photochemical modes of deactivation of DPB following electro-... 

The spectroscopic investigations do not provide sufficient information to elucidate the excited state ordering for all the uranate centres. The ordering appears to be A2(Tig) < E (T ig) in the (UO5 Vp) centre. In a recent paper, Runciman and Wong reported on the absorption and laser excited fluorescence of hexavalent uranium in LiF l. As in the NaF—U system, the relative intensities of various emission line-series in LiF—U depend strongly on the excitation wavelength. The results from temperature dependent decay measurements show that the LiF—U system in this respect also resembles the NaF—U system. 

Although the electronic properties of oligothiophenes have already been reviewed [29, 30], the picture of the nature and ordering of the electronic states in the solid state is still diffuse and incoherent. Therefore we will cover recent results on the optical properties especially in the soUd state and the outcome may lead to a clearer picture of the excited state ordering. This may even contribute to a better understanding of the electronic states for other rigid-rod-like conjugated materials. 

However, if the zeroth-order ground-state energy is well separated from low lying excited states, the diagonal... 

This expression may be interpreted in a very similar spirit to tliat given above for one-photon processes. Now there is a second interaction with the electric field and the subsequent evolution is taken to be on a third surface, with Hamiltonian H. In general, there is also a second-order interaction with the electric field through which returns a portion of the excited-state amplitude to surface a, with subsequent evolution on surface a. The Feymnan diagram for this second-order interaction is shown in figure Al.6.9. 

Second-order effects include experiments designed to clock chemical reactions, pioneered by Zewail and coworkers [25]. The experiments are shown schematically in figure Al.6.10. An initial 100-150 fs pulse moves population from the bound ground state to the dissociative first excited state in ICN. A second pulse, time delayed from the first then moves population from the first excited state to the second excited state, which is also dissociative. By noting the frequency of light absorbed from tlie second pulse, Zewail can estimate the distance between the two excited-state surfaces and thus infer the motion of the initially prepared wavepacket on the first excited state (figure Al.6.10 ). 

In words, equation (Al.6.89) is saying that the second-order wavefunction is obtained by propagating the initial wavefunction on the ground-state surface until time t", at which time it is excited up to the excited state, upon which it evolves until it is returned to the ground state at time t, where it propagates until time t. NRT stands for non-resonant tenn it is obtained by and cOj -f-> -cOg, and its physical interpretation is... 

For two Bom-Oppenlieimer surfaces (the ground state and a single electronic excited state), the total photodissociation cross section for the system to absorb a photon of energy ai, given that it is initially at a state x) with energy can be shown, by simple application of second-order perturbation theory, to be [89]... 

In this chapter, we discussed the significance of the GP effect in chemical reactions, that is, the influence of the upper electronic state(s) on the reactive and nonreactive transition probabilities of the ground adiabatic state. In order to include this effect, the ordinary BO equations are extended either by using a HLH phase or by deriving them from first principles. Considering the HLH phase due to the presence of a conical intersection between the ground and the first excited state, the general fomi of the vector potential, hence the effective... 

In the excited states for the same potential, the log modulus contains higher order terms mx(x, x, etc.) with coefficients that depend on time. Each term can again be decomposed (arbitrarily) into parts analytic in the t half-planes, but from elementary inspection of the solutions in [261,262] it turns out that every term except the lowest [shown in Eq. (59)] splits up equally (i.e., the/ s are just 1 /2) and there is no contribution to the phases from these temis. Potentials other than the harmonic can be treated in essentially identical ways. 

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