Excitation, one-electron

In principle, one molecule of a chemiluminescent reactant can react to form one electronically excited molecule, which in turn can emit one photon of light. Thus one mole of reactant can generate Avogadro s number of photons defined as one einstein (ein). Light yields can therefore be defined in the same terms as chemical product yields, in units of einsteins of light emitted per mole of chemiluminescent reactant. This is the chemiluminescence quantum yield which can be as high as 1 ein/mol or 100%. 

When both electron donor (D) and acceptor (A) groups are attached to a w-electron system it is not possible to consider the transition in terms of the excitation of one electron since it is a composite of several different one-electron excitation types. An example of a molecule which has electronic transitions of this type is Michler s ketone ... 

Expressions have been given by Sohn, Hendrickson, and Gray (48) for the excitation energies of the three spin-allowed one-electron d-d transitions, and for the corresponding spin-forbidden transitions. Since these partial results already include all the singly excited states for d6, Cocv, systems, the use of the full matrices (Table 5) will usually have only a minor effect on the fitting parameters. It should be noted that the one-electron excitation... 

One-Electron Excitation d, 2EXg(a 2g e2g eXg) Ground States dS,3A2g(a ge24e g) rf9, et )... 

Much like the porphyrin and TPP complexes, the observed MCD of the Q band of the TAP and Pc complexes is relatively straightforward to reproduce. TDDFT calculations find that this transition is dominated by the alu—>eg one-electron excitation (136,151-153) and the calculated Aj parameters are large and positive. 

The second major absorption feature in Mo2(02 CCH3)4 was a strong band near 34,000 cm with an oscillator strength of about 0.2 that was considered to be consistent with an N- V type transition, such as the one-electron excitation 8(2b2g) - S (2Z>, u), which would be localized on the metals. 

Figure 3.2 Ground state (gs) and excited electronic states. The displacement of one electron is a one-electron excitation (l-ees) that of two electrons is 2-ees...

Electronic States of a Diatomic Molecule. In the picture of orbitals a one-electron excited state is described by the initial and final orbitals and by the multiplicity of the excited state. In an unsaturated molecule like ethylene (ethene) there will therefore be excited states labelled 3 (tt-tt ), 1 (xr—zr8 6), 3(7T-cr ), etc. in order of increasing energy. Two- or more electron excitations would require two or more such labels, but in practice the number of accessible excited states is quite small. For the purposes of photophysics and photochemistry it is almost always sufficient to consider one-electron excitations. 

Figure 3.15 In a polyatomic molecule one-electron excitations are described by the labels of the orbitals involved in the transition from the ground state (G). When these orbitals are localized in different zones of space the transition implies a charge transfer...

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... 

Thus far, consideration has only been given the reactivity of the lowest LF state arising from a n-d - a type excitation. In a complex such as Cr(NH3)5Cl2+ the direct population of a higher LF state may result in the population of the o y(dx2 y2) orbital rather than the af(dz2) orbital. In such a case loss of an equatorial NH3 would be expected if such a process can compete with internal conversion to the lowest LF state which would populate the o dz 2). However in a series of Cr(NH3)s X + complexes the reaction and quantum yields are independent of which one-electron excitation is achieved.21 This result implicates fast internal conversion and provides little information concerning the reactivity of the upper LF states. 

Turning now to other non-0H complexes where a correlation may exist between one-electron excited state configurations and the stereochemistry of photosubstitution we can consider the Rh(III) and Ir(III) homologues of Co(III)-ammines and Co(III)-cyanides. Literature data for Rh(CN)s(X)3- and Ir(CN)s(X)3- is meager but do show, at least, that for X < < CN in LF strength that X undergoes substitu-... 

We have utilized the fermion creation and annihilation operators denoted a a, and apa, respectively. These operators act on the electron in the pth orbital with the projected spin a. The set 0p(r)) represents the molecular orbitals and the last term, hauc, in Eq- (13-3) is the nuclear repulsion energy. We use the following definitions of the one-electron excitation operator... 

State One electron excitation in the principal configuration CASSCF3 MR-CCr With averaged coupled pair 1 functional3 CASPT2b CASSCF/CCI0 ... 

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