One-electron transition

Most of the free-radical mechanisms discussed thus far have involved some combination of homolytic bond dissociation, atom abstraction, and addition steps. In this section, we will discuss reactions that include discrete electron-transfer steps. Addition to or removal of one electron fi om a diamagnetic organic molecule generates a radical. Organic reactions that involve electron-transfer steps are often mediated by transition-metal ions. Many transition-metal ions have two or more relatively stable oxidation states differing by one electron. Transition-metal ions therefore firequently participate in electron-transfer processes. 

Figure 5. Ground-state conflguration and configurations corresponding formally to one-electron transitions for a system having one unpaired electron in its ground state.

Figure 10. Electron excitations in radicals (a) Collective representation of one-electron transitions of the A, B, and C types if denotes MO (b) LCI energy-level scheme (Jablonski diagram) for doublet and quartet states indicating why with radicals fluorescence (- - -) but not phosphorescence is observed. Spin-forbidden transitions are represented by dashed lines.

The photoelectric cross-section o is defined as the one-electron transition probability per unit-time, with a unit incident photon flux per area and time unit from the state to the state T en of Eq. (2). If the direction of electron emission relative to the direction of photon propagation and polarization are specified, then the differential cross-section do/dQ can be defined, given the emission probability within a solid angle element dQ into which the electron emission occurs. Emission is dependent on the angular properties of T in and Wfin therefore, in photoelectron spectrometers for which an experimental set-up exists by which the angular distribution of emission can be scanned (ARPES, see Fig. 2), important information may be collected on the angular properties of the two states. In this case, recorded emission spectra show intensities which are determined by the differential cross-section do/dQ. The total cross-section a (which is important when most of the emission in all direction is collected), is... 

The lowest transition energies of permanganate and dichromate will be ligand to metal charge transfer (LMCT) in nature. From symmetry arguments, it can be shown that the transition described by the 4—> e one-electron transition of a tetrahedral d° complex will have an Aj/Dj ratio of -0.5 (108,109). 

Fig. 45. The four one electron transitions involving the highest occupied and lowest unoccupied...

For a one-electron transition the ideal value of unity is obtained when all the molecules are transferred to the higher energy state, i.e. when the transition probability is unity. The oscillator strength can also be expressed as... 

The fact that these HOMOs and LUMOs have a two-fold degeneracy implies that there are four isoenergetic one-electron transitions to yield the first excited states this complication is however resolved by the interaction of these one-electron excitations, and this is known as configuration interaction. The concept of configuration interaction (Cl) is somewhat similar to that of the interaction of atomic orbitals to form molecular orbitals. An electron configuration defines the distribution of electrons in the available orbitals, and an actual state is a combination of any number of such electron configurations, the state wavefunction being... 

An electronic transition involves the motion of an electron from one orbital to another. In the simple model of a one-electron transition it is assumed that all other particles remain in their initial states. If the initial and final orbitals of the electron are separated in space there will be a change in dipole moment, so long as the molecule has no centre of symmetry. When this change is very large the excited state is described as a charge transfer ... 

For a one-electron transition the spin and orbital overlaps can be separated to yield... 

Of all the radiative recombinations of type A+BC -> ABCC, the reaction H+NO is the best from the spectroscopic point of view. Only one electronic transition is known, A 1A. Unlike the cases discussed up to now, the... 

Luminescence spectroscopy, whenever applicable, has the advantage that the low-temperature spectrum consists of only one electronic transition, whereas in absorption the transitions to the four spin-orbit components of g are superimposed. As a result the absorption spectrum is not as well resolved. 

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