Single electron transitions

Vibrational transitions accompanying an electronic transition are referred to as vibronic transitions. These vibronic transitions, with their accompanying rotational or, strictly, rovibronic transitions, give rise to bands in the spectrum, and the set of bands associated with a single electronic transition is called an electronic band system. This terminology is usually adhered to in high-resolution electronic spectroscopy but, in low-resolution work, particularly in the liquid phase, vibrational structure may not be resolved and the whole band system is often referred to as an electronic band. 

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 Dipole-Dipole Coupling Mechanism. In this model, two absorbing groups have a single electronic transition. 

The Kossel model (146) of single-electron transitions to unoccupied states has been applied to the interpretation of the absorption-edge structure of isolated atoms (inert gases) as well as to molecules and solids, in which case use is made of band-model calculations, including the possible existence of quasi-stationary bound states as exciton states. Parratt (229), who has carried out the first careful analysis of the absorption spectrum of an inert gas, assumed that dipole selection rules govern the transition possibilities, with allowed transitions being Is - np. 

It was quantitatively interpreted (Rice et al., 1977) as originating from bond alternation phase oscillations (in contrast to the bond alternation amplitude oscillations mentioned in subsection 4.8.2D). The vibrational absorption lines labeled 2 to 10 are directly related to the Ag Raman lines of TCNQ. The broad peak above 1600 cm originates from the single electron transition across the gap, and the indented line shape of mode 2 is a consequence of Fano interference between the single electron continuum and the phonon mode. The line intensities are determined by the respective electron - vibration coupling constants. 

The electronic structure of Cr +lAljO, has also been studied by a number of workers using density-functional theory. Attention has been focused on the so-called R peak and C/band, corresponding roughly to the single-electron transitions (spin flip) and (crystal field),... 

The theoretical considerations that were developed in Section 3 for one- and two-dimensional NLO-phores merely required the incorporation of donor and acceptor groups coupled to each other. No assumptions were made concerning the structural molecular equivalent of the LCAO couphng parameter, c, between donor and acceptor. In the one-dimensional molecules to be dealt with first, a single donor-acceptor pair is present. For this case, the consequences of the different extent of couphng on molecular polarizabilities were calculated on the basis of a single electronic transition with charge-transfer character (p. 139). The crucial parameters and AE g... 

The existence of a unique value for Xc does not imply that a single electronic transition causes the observed rotation, for the sum rule derivable from the theory of optical rotation. 

If two or more transitions overlap, the quantitative interpretation of the MCD spectrum becomes much more difficult and computational curve fitting that requires simple band shapes is needed. Often, the vibrational structure of the MCD spectrum, which will in general be different from the one in the absorption spectrum, will be so pronounced that this assumption is not fulfilled. Although uncommon, there are some cases known where some sections of the vibrational envelope associated with a single electronic transition are positive and some negative. Thus, the appearance of both positive and negative MCD peaks in a spectral region does not necessarily mean that... 

In the case of (8aS)-(+)-l,8a-dihydroazulene 10,15 the composition of the apparent CD and UV bands was rather simple, because each of the apparent bands was composed of a single electronic transition. The case of chiral troponoid spiro compounds (15aS)-(-)-14 and (18a5)-(-)-15 was also simple because of their Ci symmetrical structures. 16 On the other hand, the Ji-electron chromophores of the twisted naphthalene-diene systems 22-26 are complex and have no symmetric character.18 Therefore, to clarify the applicability of the 7i-electron SCF-CI-DV MO method to such complicated systems, it is important to analyze the composition of the apparent CD and UV bands theoretically obtained. As illustrated in Figure... 

Molecular spectra are not solely derived from single electronic transitions between the ground and excited states. Quantised transitions do occur between vibrational states within each electronic state and between rotational sublevels. As we have seen, the wavelength of each absorption is dependent on the difference between the energy levels. Some transitions require less energy and consequently appear at longer wavelengths. 

In terms of the frontier-orbital approach, the two radical bands , C and D, are related to the single-electron transitions HOMO - SOMO and SOMO -> LUMO, which correspond to the two first excited configurations, the electronic occupation of HOMO, SOMO and LUMO being two, one and zero respectively (Ballester et al, 1982a). 

Consider an electronic transition coupled to both the relatively sharp vibron transitions and the broad spectrum of phonons. The vibrons will split the single-electron transitions characterized by the quantum number n into a series of lines characterized by the vibrational quantum number j. Each vibron level is split further into closely spaced phonon lines, which we represent by a set of quantum numbers /, representing the phonon modes. Thus, in our simple representation a state can be given by the three quantum numbers (in order of decreasing energy) (n,j, /). However, the number of phonon modes is so large that experimentally, at high temperatures, one measures only an unresolved band. 

---