Excited states contribution

The knowledge of the excited state contributions to a and P is of importance not only for understanding the origin of the responses but also for computational purposes. Indeed, for medium-size molecules like / -nitroaniline or small molecules studied with extended basis sets, the full configuration space becomes rapidly very huge and out of reach for a complete ab initio treatment. Therefore, if one needs to tmncate the configuration space, one has to ensure that the most contributing excited states are present and correctly reproduced. 

The second aspect of our nitroaniline investigation concerns the analysis of (a) and Pvec in terms of the excited states contributions. The N-dependence of (a(0 0) is very similar for the three compounds and saturates for N = 20 (Fig. 9). Moreover, at most 10 excited states contribute significantly. For Pvec(0 0, 0), the On graphs (Figs. 10-12) exhibit some differences among the isomers. For -NA, 3 states present a dominant Oni state 3 (On = 0.96), state 6 (On = 0.62) and state 13 (On = -0.47). For the two other... 

The identity of the excited states contributing to the collision-induced dissociation in other systems studied, particularly N, is not as well known, however, and more than one reactant ion state may be present. Parenthetically, it may be noted that the identity of states producing... 

Starting with (t = 0), the evolution of with time can be calculated to high accuracy. The most important components that determine the excited state potential are the excited state distortions, i.e. the position of the potential minimum along the configurational coordinates of the vibrational modes involved. Only modes with a displacement in the excited state contribute to vibronic structure in an allowed transition and therefore only these modes need to be considered in our calculation. 

The first numerical terms C = P2 1 + p) j / (l20(kT)2) are often referred to as Bleaney s factors and their relative values (scaled to Coy = -100) have been tabulated at 300 K for any 4f configurations including excited states contributions (table 3, Bleaney et al. (1972)). Finally, the introduction of the geometrical factors defined by eqs. (30), (31) together with C into eq. (41) gives the classical eq. (42) for the pseudo-contact shifts according to Bleaney s approach (Forsberg, 1996)... 

Optical properties are usually related to the interaction of a material with electromagnetic radiation in the frequency range from IR to UV. As far as the linear optical response is concerned, the electronic and vibrational structure is included in the real and imaginary parts of the dielectric function i(uj) or refractive index n(oj). However, these only provide information about states that can be reached from the ground state via one-photon transitions. Two-photon states, dark and spin forbidden states (e.g., triplet) do not contribute to n(u>). In addition little knowledge is obtained about relaxation processes in the material. A full characterization requires us to go beyond the linear approximation, considering higher terms in the expansion of h us) as a function of the electric field, since these terms contain the excited state contribution. 

Similar equations serve as a basis for semi-empirical quantum chemical computations by the sum-over-states (SOS) method (Dirk etal., 1986 Kanis et al., 1992, 1994 Tomonari et al., 1997). Quite often, however, only very few excited states contribute to the observed NLO response (Tomonari et al., 1993). This is especially true for the one-dimensional NLO-phores to be dealt with in the next section, where to a good approximation only one excited state needs to be taken into account. 

Figure 2 Experimental arrangement for measurements of the Fe nuclear resonance at the Advanced Photon Source (APS). In the standard fill pattern, electron bunches with a duration of 100 ps are separated by 153 ns. X-ray pulses are generated when alternating magnetic fields in the undulator accelerate these electron bunches. The spectral bandwidth of the X-rays is reduced to 1 eV by the heat-load monochromator and to 1 meV by the high-resolution monochromator. At the sample, the flux of the beam is about 10 photons/s. APD indicates the avalanche photodiode used to detect emitted X-rays. The lower right inset illustrates that counting is enabled only for times weU-separated from the X-ray pulse, so that only delayed photon emission resulting from decay of the nuclear excited state contributes to the experimental signal...

The absorption around 750 nm, red-shifted to the ground state, is considered to be due to the non-solvated excited state, not to the "hot" ground state, since absorption due to Sq- S2 is observed around 340 nm in equilibrium and the sum of the energy of 640 nm and 750 nm corresponds to 340 nm. This fact suggests a possibility that the growth of absorption due to some new "state" from the non-solvated excited state, probably the solvated excited state, contributes partially to the fast component of the bleach recovery near the absorption maximum... 

The ground and excited electronic states are discussed in detail by Massey ( ). No excited state contributions are included in this calculation. 

An extension of the Hohenberg-Kohn theorems to an arbitrary excited electronic state has not been possible till date. It has been possible only for the lowest state of a given symmetry [45] and for the ensemble of states [46], It may be anticipated from the principles of maximum hardness and minimum polarizability that a system would become softer and more polarizable on electronic excitation since it is generally more reactive in its excited state than in the ground state. Global softness, polarizability, and several local reactivity parameters p(r, t), Vp, —V2p,/(r), electrostatic potential, and quantum potential have been calculated [25] for different atoms, ions, and molecules for the lowest energy state of a particular symmetry and various complexions of a two-state ensemble. It has been observed that a system is harder and less polarizable in its ground state than in its excited states, and an increase in the excited state contribution in a two-state ensemble makes the system softer and more polarizable. Surface plots of different local quantities reveal an increase in reactivity with electronic excitation. 

Accordingly, we identify 12.4 eV as the value of Eg from our bonding model. This closely agrees with Eg = 12.2 eV, found from the dielectric constant. Table 5.6 contains comparisons of the same kind for ionic compounds. The agreement is surprisingly good, since the excited states contributing to the polarizability need not be the same as the lowest excited states in the UV spectrum. 

Excited state contributions described by Pi have a key characteristic in that they increase with increased reaction asymmetry AG])xn decreased reorganization energy Eg [5]. Eurthermore, the isotopic disparity pu< also increases with these trends, resulting in an increase in significance of the third difference in Eq. (10.55) with increased AGrxn 3tid decreased Eg [5]. 

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