Pseudo-continuum level

In a large molecule fhe vibrational and rofafional levels associated wifh any elecfronic sfafe become so exfremely congested af high vibrational energies fhaf fhey form a pseudo-continuum. This is illusfrafed for Sq, Si and fhe lowesf excited friplef sfafe T, lying below Sj,... 

Atabek, et al, (1980) have pointed out that this conclusion is incorrect when 12 l, V2- Then it would not be proper to prediagonalize the interaction between the two discrete states. Indeed level 2, after its interaction with the continuum of state 3, must be considered as a pseudo-continuum with respect... 

It is almost impossible to cover the entire range of models in Figure 25.1, and in this chapter we will limit ourselves to the different modeling approaches at the continuum level (micro-macroscopic and system-level simulations). In summary, there are computational models that are developed primarily for the lower-length scales (atomistic and mesoscopic) which do not scale to the system-level. The existing models at the macroscopic or system-level are primarily based on electrical circuit models or simple lD/pseudo-2D models [17-24]. The ID models are limited in their ability to capture spatial variations in permeability or conductivity or to handle the multidimensional structure of recent electrode and solid electrolyte materials. There have been some recent extensions to 2D [29-31], and this is still an active area of development As mentioned in a recent Materials Research Society (MRS) bulletin [6], errors arising from over-simplified macroscopic models are corrected for when the parameters in the model are fitted to real experimental data, and these models have to be improved if they are to be integrated with atomistic... 

The parallel form of F and F in [8.124] shows that the two calculations can be performed exactly in the same way, i.e., that solvent does not introduce any complication or basic modification to the procedure originally formulated for the isolated system. This is a very important characteristic of continuum BE solvation methods which can be generalized to almost any quantum mechanical level of theory. In other words, the definition of pseudo one and two-electron solvent operators assures that all the theoretical bases and the formal issues of the quantum mechanical problem remain unchanged, thus allowing a stated solution of the new system exactly as in vacuo. 

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