Pyrazine vibronic states

First, the S2 excitation of pyrazine under pulse train action is considered. The pyrazine vibronic structure description is that of Refs [29, [30]], that is, the Q-space (in the context of the QP-algorithm presented in Section 9.3.1) consists of the 176 states in S2 with the largest FCF to the ground vibrational state of the Sq electronic state (as discussed in Section 9.3.1). Characteristic examples of the Ps (t) populations produced by pulse trains with different parameters are... 

We are concerned with the dynamics of a molecule after optical excitation. If the state we excited is coupled only to the radation field, we will only see the exponential decay to that field by spontaneous emission, and this is too well known to warrant our interest. It is therefore necessary that the state we excite is coupled to other states. We then arrive at the conventional model for radiationless transitions a light (optical transition probability carrying) state s> coupled to a more or less dense manifold of background states fc>. In pyrazine, s> is the lBiu state and fc> is the set of vibronic states arising from the 3B3u state. In addition, the state s> may be coupled to another... 

Comparison of the results of the previous effort, where it was assumed that excitation and absorption spectrum coincided,7 with the present results shows that there is really not much of a difference. Because of the higher sensitivity, MEs belonging to P(l) are detected over a range of almost 8 GHz instead of 3.5 GHz as found previously, and in accordance with that their number has increased. We now have 35 triplet states over 7.6 GHz, which leads to a density of 140 states per cm-1. The calculated density of pyrazine triplet vibronic states around the singlet energy appears to be around 100 cm-1,13-15 but if we want a comparison, we should take into account that they are triplets (times 3) and that nuclear symmetry permits interaction only between equal symmetry species. Table II gives the nuclear spin symmetry species of pyrazine and their statistical weight. The J = 0, K = 0 has the symmetry At and therefore can only interact with Ae triplet rovibronic states, which constitute th of the triplet manifold. We therefore expect about 3 x 17/48 x 100 a 106 triplet vibronic states per cm-1 to be available for the interaction, which compares favorably to the density of 140 per cm-1 as found from the density of the ME spectrum. 

The main purpose of using the dynamics oftheKTi nn transition of pyrazine as an example is to show how to treat the effect of Cl on IC. Suzuki et al. have employed the 22-fs laser pulse for pumping in their studies of the KK nn dynamics of pyrazine. In this case, the dynamics of both population and coherence should be considered. Using the notations of bu and av to describe the vibronic states of jtjt and njt, we obtain... 

A different example of non-adiabatic effects is found in the absorption spectrum of pyrazine [171,172]. In this spectrum, the, Si state is a weak structured band, whereas the S2 state is an intense broad, fairly featureless band. Importantly, the fluorescence lifetime is seen fo dramatically decrease in fhe energy region of the 82 band. There is thus an efficient nonradiative relaxation path from this state, which results in the broad spectrum. Again, this is due to vibronic coupling between the two states [109,173,174]. 

Figure 9.33 Single vibronic level fluorescence spectra obtained by collision-lree emission Irom the zero-point level of the state of (a) pyrazine and (b) perdeuteropyrazine. (Reproduced, with permission, Ifom Udagawa, Y., Ito, M. and Suzuka, I., Chem. Phys., 46, 237, 1980)...

In at least one case, pyrazine, it is known that the ratio of the quantum yields for fluorescence and phosphorescence is comparable in the gas60 (at 1 mm) and a mixed crystal.61 However, a detailed comparison should take into account the medium-dependent vibronic interaction with states nearby to those that emit (see Sect. V). 

The additional term leads to vibronic mixing of vibrational states differing by three quanta. It has thus a relatively large effect on the position and intensity of overtones. At present, little is known about the magnitude of such nonlinear terms in actual molecules. A recent analysis (Henneker et ai, 1978b) of a pair of coupled excited states in pyrazine led to K = 1.81 and L = 0.32. The study of REPs of second overtones along with those of fundamentals would be helpful in obtaining additional data of this kind. 

The Si[ Bsu nn )] and S2[ B2u (tttt )] excited states of pyrazine represent a classic example of vibronic coupling in aromatic systems.The gas-phase absorption spectrum of pyrazine exhibits typical features of such... 

Earlier theoretical work on the excited-state dynamics of pyrazine focused on the vibronically induced anharmonic couplings in the Si state, on the interactions between gerade and ungerade rm states or on selected PE functions and electron-vibrational coupling parameters. In a series of papers the Munich group has characterized the S2 and 51-state PE surfaces in the conformational subspace relevant for the short-time photophysics following the S2 — So and 5i — So transitions.In the course of this work, the treatment has steadily improved, as regards the accuracy of the electronic-structure calculation as well as the number and description of the vibrational modes considered. The most accurate calculations are based on the CASSCE/MRCI method with a basis set of DZP quality. 

Pig. 5. Experimental (a) and calculated (b) absorption spectrum of the S f rrr ) state of pyrazine. The stick spectrum in (b) represents the vibronic energy levels and absorption intensities of the seven-mode vibronic-coupling model. The envelope has been obtained by including a phenomenological line broadening (reproduced from Ref. 112). 

Interestingly, a conical intersection very similar to that of the S i(n7r ) and S 2(7T7r ) neutral excited states has been found for the n and n hole states of the pyrazine cation.A linear vibronic-coupling model has been constructed for the and states of the pyrazine cation employing many-body Green s function methods for the calculation of the vibronic-coupling parameters. The ah initio calculated photoelectron spectrum of the Ag n ) and states is compared in Fig. 7 with the... 

Calculations of the ion yield in dependence on the pulse delay time At and on the parameters of the laser pulses have been performed in Refs. 86 and 93 for simple one-dimensional models of excited-state vibrational motion and vibronic coupling. It has been found that for the vibronic-coupling examples considered and for suitably chosen pulse parameters, the ion signal as a function of At maps very well the adiabatic electronic population probability. As an example of a molecular system comprising conical intersections. Sec. 5.1 presents a calculation of the time-resolved photoelectron spectrum of pyrazine. 

Recent experimental studies on pyrazine by Radloff and coworkers have renewed the interest in a theoretical description of the photoelectron spectroscopy of this system. In the following, we present representative results from an exact quantum-mechanical study that extends the work of Seel and Domcke in several points (i) New high-level ab initio data are employed to parameterize the model Hamiltonian, (ii) An additional vibrational mode (j/ga) is included which is known to be important for the S2 S-i internal conversion process, (iii) The vibronic coupling between the Iq and /i cation states is explicitly taken into account, (iv) To account for the relatively long probe laser pulses used in the experiment, the convolution scheme presented in Eq. (49) is employed. 

Finally, in Chap. 5 which closes Part I, an application of the tools introduced in Chaps. 2 and 4 to a quantum dynamical investigation of the photophysics of pyrazine is presented. This work focuses on the role of the low-lying dark wtt states in the non-adiabatic dynamics of the molecule after photoexcitation. Multi-reference electronic structure calculations are used to design a vibronic couping model Hamiltonian, including the four lowest electronic states and the sixteen most important vibrational modes. This model is then used to simulate the absorption spectrum and the ultrafast decay dynamics of the molecule using the MCTDH method. 

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