Semi-empirical models overview

Dipole moments for hypervalent molecules calculated from semi-empirical models are generally larger than experimental values (sometimes by a factor of two or more), suggesting descriptions which are too ionic. Figure 10-11 provides an overview for the PM3 model. Semi-empirical models should not be used. 

Recently, Pallares and Johnsson [106] presented an overview of the macroscopic semi-empirical models used for the description of the fluid dynamics of circulating fluidized bed combustion units. They summarized the basic modeling concepts and assumptions made for each model together with the major advantages and drawbacks. In order to make a structured analysis of the processes involved, the CFBC unit is often divided into 6 fluid dynamical zones like the bottom bed, freeboard, exit zone, exit duct, cyclone and downcomer and particle seal, which have been shown to exhibit different fluid dynamical behavior. 

In this section we aim to introduce some of the main theoretical ideas which underlie the strategies for modelling liquid crystal molecules. It is clear that there are a very wide range of methods available and we will not attempt to be comprehensive. Instead, we will begin with a brief overview of traditional semi-empirical approaches and then progress to concentrate on treating fully predictive parameter-free calculations of molecular electronic structure and properties in some depth. 

In this work the use of molecular electrostatic potential (MEP) maps for similarity studies is reviewed in light of the latest results. First, methods of obtaining MEP maps is overviewed. The methodology, reliability and the efficiency of calculations based on semi-empirical as well as ab initio methods are discussed in detail. Point-charge models and multipole expansion methods which provide MEP maps of satisfactory quality are evaluated critically. Later on, similarity indices of various kinds are analyzed, compared and examples of their use are shown. Finally, the last section lists and summarizes software packages capable of calculating MEP map based similarity indices. 

There is an already impressive literature on the application of various first principles and semi-empirical approaches to aspects of zeolite chemistry (see, e.g., [104-107]). Even a cursory overview of this aspect of zeolite modeling and simulation would be beyond the scope of the present paper. However, two recent development areas are noted. 

Let us remind that while the number of six-index combinatimis from a set of 36 indices (30 molecular coimectivity indices plus five empirical indices, plus M) entails many millions of combinations, the number of greedy combinations entails only hundreds of combinations to find out a six-index descriptor. In the present chapter an overview will also be given on the model quality of semi-random combinations, i.e., multilinear descriptors made of graph-theoretical and experimental indices plus random indices. These last t5rpe of indices were chosen from two sets of 38 different subsets of random indices, and in some cases they show an interesting model quafity. 

---