Excitations of single electrons

Optical transitions occur between stationary states involving many electrons and cannot in general be described by the excitation of single electrons that change orbitals. The selection rules determine the intensities of the optical transitions and these rules are a simple consequence of the symmetries of the initial and final states. 

The corresponding fiinctions i-, Xj etc. then define what are known as the normal coordinates of vibration, and the Hamiltonian can be written in tenns of these in precisely the fonn given by equation (AT 1.69). witli the caveat that each tenn refers not to the coordinates of a single particle, but rather to independent coordinates that involve the collective motion of many particles. An additional distinction is that treatment of the vibrational problem does not involve the complications of antisymmetry associated with identical fennions and the Pauli exclusion prmciple. Products of the nonnal coordinate fiinctions neveitlieless describe all vibrational states of the molecule (both ground and excited) in very much the same way that the product states of single-electron fiinctions describe the electronic states, although it must be emphasized that one model is based on independent motion and the other on collective motion, which are qualitatively very different. Neither model faithfully represents reality, but each serves as an extremely usefiil conceptual model and a basis for more accurate calculations. 

Consider a diatomic molecule A2 in which there is a single a bond. Excitation of an electron to the a state gives rise to an absorption at 15,000 cm-1. The binding energy of an electron in the valence shell of atom A is -9.5 eV. 

Figure 9.2 Schematic representation of a photon being absorbed by a single molecule of chromophore. The photon causes excitation of an electron (depicted by a vertical arrow) from the HOMO to the LUMO...

The oxidation of 3,6-dehydrohomoadamantane (52) with NO+BF4, photo-excited tetracyanobenzene, and under anodic conditions has been found to involve a common radical cation intermediate. The study has shown that the activation of propellane cTc-c bonds with strong oxidizing electrophiles occurs by a sequence of single-electron transfer steps. These findings are supported by ab initio computations showing that the isomeric radical cations can equilibrate with low barriers and lead to a common product. ... 

In the case of PN the origin of the absorption band at 350 nm is the excitation of an electron from the lone pair orbital on nitrogen (nz) to the singly occupied nitrogen 2p orbital that lies in the molecular plane (py). In the case of PN two transitions (To -> T3, To T4) contribute to the absorption band around 300 nm, one of which is the same in nature as in the case of PN. It is reasonable to assume that the same situation will be found with the substituted phenylnitrenes. Therefore, we can predict that the influence of the substituents on the maxima of the intensive absorption bands of substituted singlet and triplet phenylnitrenes will be similar. Indeed, Fig. 5... 

The second reason for delocalization of energy losses is the collective nature of excited states. This collectivity may exist even for excited electronic states of a single molecule. The simplest example is the excitation of zr-electron states, which are delocalized along the molecule. When a fast electron excites such a molecule, it transfers its energy to the whole ensemble of tt electrons. As a result, the energy absorption is delocalized along the molecule, and the latter can be a long (e.g., a polymer molecule). 

In a dl octahedral complex like [Ti(H20)6]3+ excitation of an electron from t2g to eg gives a single absorption band at an energy equal to the ligand field splitting D0. The theory is more complicated for... 

In terms of single electron configurations, the ground and first excited electronic states of LiO may be written... 

Quintet states on a single molecule require the simultaneous excitation of two electrons and are, therefore, energetically inaccessible (at least in aromatics in the solid phase). This is the reason for which the quintet states in the final products of reactions (80) and (81) have been omitted. Any of the nine pair states is formed with equal probability since the individual triplet exci-tons are in thermal equilibrium. Thus the rate of formation of each of the nine l states is (1/9) K, and K 1 Cg, and C T are the rate transitions to energetically accessible final... 

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