Instantaneous excitation

As it stands, the picture of dynamics from Eq. (29) is derived from the interaction of molecules with a continuous light source, that is, the system is at equilibrium with the oscillating light field. It is also valid if the light source is an infinitely short laser pulse, as here all frequencies are instantaneously excited. 

The wavepacket /(t), on the other hand, is constructed in a completely different way. In view of (4.4), the initial state multiplied by the transition dipole function is instantaneously promoted to the excited electronic state. It can be regarded as the state created by an infinitely short light pulse. This picture is essentially classical (Franck principle) the electronic excitation induced by the external field does not change the coordinate and the momentum distributions of the parent molecule. As a consequence of the instantaneous excitation process, the wavepacket /(t) contains the stationary wavefunctions for all energies Ef, weighted by the amplitudes t(Ef,n) [see Equations (4.3) and (4.5)]. When the wavepacket attains the excited state, it immediately begins to move under the influence of the intramolecular forces. The time dependence of the excitation of the molecule due to the external perturbation and the evolution of the nuclear wavepacket /(t) on the excited-state PES must not be confused (Rama Krishna and Coalson 1988 Williams and Imre 1988a,b)... 

After instantaneous excitation of A, the normalized decay of A is given by R(t) = NA(t)/NA0). According to (3.10), its Laplace transformation, related to the lifetime xA, defines the relative quantum yield of luminescence ... 

Turning back to geminate recombination after weak and instantaneous excitation, we simply have to omit the bimolecular terms in Eqs. (3.357) ... 

Hence, both the IET and Markovian theory provide the lowest-order approximation for the fluorescence quantum yield with respect to acceptor concentration. This approximation is the only limitation of the validity of IET. Because of this limitation, IET is unable to describe properly the long-time asymptote of the system response to instantaneous excitation (Fig. 3.56) and the nonlinearity of the Stern-Volmer law at high concentrations (Fig. 3.61). On... 

The initial condition for N is prepared by instantaneous excitation, after which the annihilation rate constant k/(t) decreases with time, approaching its stationary (Markovian) value kt as t —> oo. The non-Markovian generalization of another equation, (3.761), became possible only in the framework of the unified theory, where it takes the integral form. Unfortunately, the system response to the light pulses of finite duration or permanent illumination remains a problem for either UT or DET. The convolution recipes such as (3.5) or (3.437) are inapplicable to annihilation, which is bilinear in N. Therefore we will start from IET, which is solely capable of consistent consideration of stationary absorbtion and conductivity [199]. Then we will turn to UT and the Markovian theories applied to the relaxation of the instantaneously excited system described in Ref. 275. 

In the discussion so far, instantaneous excitation or deexcitation by a 8 function pulse has been assumed to transfer wave packets from one electronic state to another state. For realistic pulses, the wave packets may be obtained by numerically integrating Eqs. (25) and (30). 

Instantaneous excitation of spins is possible, allowing complex systems to be simplified using two-dimensional techniques. 

Figure 2.30 shows the accumulated instantaneous excited state lifetime (t) and cis trans conversion ratio (p) for 1 and Im computed at the CASSCF/3-21G level of theory. For each individual series of calculations, the computed observables reach a limiting value after 50 trajectories. The swarm seems to be already of reasonable size to draw qualitative conclusions. For example, one has confidence in the conclusion that the methylation of the model chromophore reduces (by 20 to 60%) the efficiency of the conversion and extends (by about 40 to 50 fs) the lifetime of the excited state. 

We saw that the soliton in the ground state of an odd-site chain is either neutral with spin-1/2 for the undoped chain (5°), or charged with spin 0 for the singly doped chain S ). We now discuss the types of solitons present in the excited states of an even-site chain. Suppose that an even-site chain is instantaneously excited from the ground state to the or 2Ag states. This is a vertical transition, with the soliton-antisoliton separation initially zero. Within a time 27r/o o a soliton-antisoliton pair is created and separates a distance Their... 

The denominator in this expression is the total fluorescence generated by an instantaneous excitation pulse, which for a single-exponential decay is just t. The convolution integral in the numerator can be evaluated straightforwardly ... 

If the fluorescence response to an instantaneous excitation pulse is multiexponential,... 

Fig. 7.2 Variation of the concentration of the excited species A as a function of time. Following an ideally instantaneous excitation, A is formed at f = 0 (dashed line). Then, the concentration of A decays exponentially, in accordance with a first order kinetics (continuous line). After a lifetime t = t2-t the excited state concentration is reduced by an e factor ([ A]2 = [ A]i/e)...

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