Shake transition

In the present example a change of 6p to np with different principal quantum numbers n is possible. Hence, shake-modified spectator transitions or resonance shake transitions can occur, and if) and (g) are examples of shake-up and shake-off resonance double Auger processes, respectively. (If there is a lower unoccupied orbital, shake-down is also possible). 

In principle, one can extract from G(ti)) the complete series of the primary (one-hole, Ih) and excited (shake-up) states of the cation. In practice, one usually restricts the portion of shake-up space to be spanned to the 2h-lp (two-hole, one-particle) states defined by a single-electron transition, neglecting therefore excitations of higher rank (3h-2p, 4h-3p. ..) in the ionized system. In the so-called ADC[3] scheme (22), elertronic correlation effects in the reference ground state are included through third-order. In this scheme, multistate 2h-lp/2h-lp configuration interactions are also accounted for to first-order, whereas the couplings of the Ih and 2h-lp excitation manifolds are of second-order in electronic correlation. 

The selection rules appropriate for a shake-up transition are of the monopole type2, 76. The intensity of a shake-up peak depends on the overlap integral between the lower state molecular orbital from which the electron is excited (in the neutral molecule) and the upper state molecular orbital to which the electron is excited (in the core-ionized molecule). Consequently one expects transitions of the type au au, ag " ag> 7T nu, and irg - ng with g u and u - g transitions forbidden. 

As a first, trivial, example of the application of the overlap criterion, let us consider the possibility of a shake-up peak associated with the C Is ionization of the terminal carbon atom in nitroethane and the v - v transition of the nitro group in that molecule. In this case the core ionization occurs in a region of the... 

The core ionization of an atom stabilizes all the valence electrons in the atom. Depending on whether the electronic transition shifts electron density to or from an atom, the energy separation for a shake-up peak of that atom will be less than or greater than the energy of the neutral molecule ionization81. As an illustration of these effects, let us consider the shake-up spectra of formamide, H2NCH082. The principal transitions involved are the vl - n3 and 7r2 - 7r3 transitions. The tTj... 

Because of the l/r dependence, the exchange interaction rapidly decreases with an increase in the difference between the principal quantum numbers of the impaired electrons and the core vacancy. Thus multiplet splitting is negligible in the Is spectra of paramagnetic transition metal compounds. On the other hand, shake-up intensity is essentially independent of the core level involved. Hence one can distinguish between shake-up and multiplet satellites by changing the principal quantum number of the core electron ionized76. ... 

The use of transition metal nitrato compounds can be of value. For example, tetranitratozirconium(IV), Zr(N03)4, on shaking with quinoline at room temperature, gives a 90% yield of almost pure 7-nitroquinoline (74JCS(Pl)175l). 

Fig. 42. Relationship between relaxation energies, Koopmans Theorem and the relative intensities of direct photoionization and shake up and shake off transitions...

Table 5. Core level binding energies, and transition energies and intensities for low energy shake up structures in poly para-substituted styrenes...

Comparison of the UV spectrum of polystyrene in the 2600 A region with that of toluene shows a close relationship in terms of both extinction coefficients and vibronic fine structure. The effect of para substituents is most conveniently characterized by the shift in the band corresponding to the a0-o transition. The comparison of substituent effects on the electronic excited states of thepara substituted polystyrenes parallels those for the corresponding para substituted toluenes. Such a correlation would only be expected if the tr - n transitions were effectively localized within a given pendant group of the polymer system. This conclusion is reinforced by the observation that polystyrene and toluene show similar shake up structure in their ESC A spectra with respect to both band profiles and intensities (when due... 

In a review such as this it is inappropriate to present a detailed theoretical interpretation of the results since this is available elsewhere 36 Suffice it to say that it may readily be shown that the it- it shake up transitions involve the highest occupied and lowest unoccupied virtual orbitals of the pendant group. 

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