Four-level molecular model

A molecular fluorescence model is presented which is particularly appropriate for short pulse excitation. The frozen excitation model treats the two rotational levels which are directly excited by the laser as an isolated system with constant total number density. Consider the four level molecular model illustrated in Fig. 1. The four level model was solved by Berg and Shackleford (5 ) for the case where steady state is established throughout all molecular levels. Levels le and 2e are the single... 

Figure 1. Four-level molecular model. QiS is the collisional-transfer rate constant from level i to level j, TV is the sum of the electronic quenching and spontaneous emission rate constants, W,t is the absorption rate constant, and Wlt is the stimulated emission rate constant. WIt and WtI are proportional to the laser power PL. The dashed vertical line separates levels le and 2e, which are treated as an isolated system, from those levels not affected directly by the laser radiation.

The electron-spm echo envelope modulation (ESEEM) phenomenon [37, 38] is of primary interest in pulsed EPR of solids, where anisotropic hyperfme and nuclear quadnipole interactions persist. The effect can be observed as modulations of the echo intensity in two-pulse and three-pulse experiments in which x or J is varied. In liquids the modulations are averaged to zero by rapid molecular tumbling. The physical origin of ESEEM can be understood in tenns of the four-level spin energy diagram for the S = I = model system... 

In general QSAR models can be constructed from any combination of the four levels of structure calculation. We are currently developing a software package to compute the different classes of molecular descriptors and to construct action models. This software package is being called "A Hierarchal QSAR Molecular Structure Calculator". 

The relative energy levels of the four diastereomers were determined by molecular modeling calculations [32, 33]. Figure 19 demonstrates as examples the complex conformers of four zirconocene(propylene)(isobutyl) species. In Fig. 20, the relative energies of four diastereomers (I-IV) are compared for four zirconocenes - each differently substituted at the Cp ring. 

Whole-chain motions, A much more elaborate model is required for any further interpretation of overall chain motions. Its derivation is well beyond the scope of this chapter, but may be followed in [11]. The authors of this review concentrate on the Doi-Edwards reptation model [12] for tangled polymer chains, either in relatively concentrated solutions or in mobile bulk states. Such a chain portion is represented in a simplified way in Figure 4.6. There are essentially four levels of angular motion available to the chain. The normal modes of molecular vibration constitute the most rapid motions, but their angular extent, a few degrees, is insufficient to contribute significantly and directly to the correlation function. 

In the following model, a simplified four-level scheme of the molecular photoisomerization (Fig. 3.9) is applied. We suppose that the x is contributed only by trans molecules and the first hyperpolarizability of trans molecule has only one nonzero component = Paaa, where zl is a given direction in the (x y) plane of the film. 

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