The Ground State Perturbation Factor

Our next step is define the conditions in which we would expect to obtain a phosphor having a luminescent process of high quantum efficiency. We then will be able to discuss how to design a phosphor, the experimental parameters involved, and the solid state chemistry of these defect-controlled materials. 

What we have not emphasized heretofore is that only certain valence states of specific cations will be of use to us. Consider the following. 

Char first rules for the design of high efficiency phosphors are  

We find that we can dirnde the Periodic Table into two classes of cations, optically active and optically inactive. The latter possess the closed-shell electron configuration of the rare gases, i.e.- d o, as represented by the monovalent state of the alkali metals. Moreover, all of the trcuisition metals have d-electrons present. Most of these are spin-coupled, have closely spaced energy levels, and thus act as killers for luminescence. However, it is possible to find valence states where the luminescence process proceeds with high efficiency. 

A good example is Mn2+ (Sd = 6 S5/2 ). This state produces strong luminescence in many hosts while Mn +, Mn6+, Mn4+ (a special case), and Mn3+ do not. The electron configurations for these ions are d , d, d3, and d, respectively. All are spin coupled to the phonon modes of the host lattice. Note that the Mn + ion involves the half-filled electron shell which has a singlet state, S5/2. 

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Now we come, in our design of phosphors, to the choice of suitable activators. Because of the limitations imposed by the ground state perturbation factor, we are limited to certain cations in specific valence states. As we have stated before, this limits us to the electron configuration d O (i So). The following diagram shows these choices ... 

The two following lines present the results obtained later by Rerat et al. (17) the method consists in adding one more term in the expression of i) given by Eq.l4. He keeps the dipolar factor from the summation on the spectroscopic states l n)) he retains only the first one of the symmetry of interest, thus there is no extrapolation procedure on the other hand, he adds the Slater determinants l m) which contribute to the perturbation of the ground state by the operators... 

The results obtained from thermal spin equilibria indicate that AS = 1 transitions are adiabatic. The rates, therefore, depend on the coordination sphere reorganization energy, or the Franck-Condon factors. Radiationless deactivation processes are exothermic. Consequently, they can proceed more rapidly than thermally activated spin-equilibria reactions, that is, in less than nanoseconds in solution at room temperature. Evidence for this includes the observation that few transition metal complexes luminesce under these conditions. Other evidence is the very success of the photoperturbation method for studying thermal spin equilibria intersystem crossing to the ground state of the other spin isomer must be more rapid than the spin equilibrium relaxation in order for the spin equilibrium to be perturbed. 

The classical formalism quantifies the above observations by assuming that both the ground-state wave functions and the excited state wave function can be written in terms of antisymmetrized product wave functions in which the basis functions are the presumed known wave functions of the isolated molecules. The requirements of translational symmetry lead to an excited state wave function in which product wave functions representing localized excitations are combined linearly, each being modulated by a phase factor exp (ik / ,) where k is the exciton wave vector and Rt describes the location of the ith lattice site. When there are several molecules in the unit cell, the crystal symmetry imposes further transformation properties on the wave function of the excited state. Using group theory, appropriate linear combinations of the localized excitations may be found and then these are combined with the phase factor representing translational symmetry to obtain the crystal wave function for the excited state. The application of perturbation theory then leads to the E/k dependence for the exciton. It is found that the crystal absorption spectrum differs from that of the free molecule as follows ... 

Overall, protein activity is affected by four major factors a) the ground state, thermodynamic stabilization of the protein, b) active site flexibility response to solvent polarity and adsorbed water content, c) the impact of water stripping from the protein on the active conformation and d) direct solvent induced perturbation of the protein (Dordick, 1992). 

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