Reference structure, choice

The main difficulty with the RE concept is the hypothetical nature of the reference structure, its choice being somewhat arbitrary. There are many ways of defining RE (M. Dewar, C. F. Wilcox, and others). Here we shall briefly examine the topological resonance energy (TRE). TRE is a nonparametric index which is directly related to the topology of a molecule and is of great practical value in predicting the aromatic stability of an arbitrary jt-network. 

So far, we have been assuming that the choice of a suitable reference structure is obvious. There is no problem as long as the distortions from some symmetrical struc-... 

The choice of a symmetric reference structure Dq implies /, = fn. The mixed element/) 2 says that changing both bond lengths in the same sense does not require the same deformation energy as increasing one and decreasing the other. In matrix representation we obtain... 

The main difficulty with the RE concept is the hypothetical nature of the reference structure its choice being somewhat arbitrary. The RE index of conjugated hydrocarbons, calculated in the standard way. 

Classification of surrounding rock stability is important reference to choice supporting methods in deep mining. Classifications of rock mass structure reflect geological characteristics, which can evaluate rock mass stability and be used in a wide range of practice. RMR classification and... 

Now it is clear why sums of covalent radii cannot represent adequately the variety of polar bonds. Optimizing the radii can only tune the system to a certain range of polarities. The r values will vary depending on the choice of the reference structures and the optimization procedure, especially when metal atoms (with low ENs) are involved. Thus, Slater s atomic radii of the most electronegative elements (F, O, N) are underestimated. However, a simple additive model can work where all atoms happen to be of similar EN, as in many organic molecules. 

The choice of a reference structure is more or less arbitrary. Classically, the RE is defined as... 

It will be seen that the choice of reference structure turns out to be crucial to the success of Dewar s computation of resonance energy. We show the predicted order of aromaticity of the set of 11 small conjugated hydrocarbons in Figure 6 using various reference structures. Readers may wish first to make their own rankings of these 11 for comparison with the results below. The annulenes, (CH) , will also be examined. 

Column 4 of Figure 6 shows the predicted order of aromaticity of our set of 11 compounds using the simple Hiickel energy calculation but with the Hess— Schaad reference structure. Thus, the only difference between the results in column 1 and column 4 is the choice of reference structure. This difference has a large consequence, and it seems to us that while the computed order of aromaticity in column 1 is poor, the order in column 4 is quite satisfactory. Benzene is at the top followed by naphthalene. Calicene and azulene are predicted to be more weakly aromatic, followed by the nonaromatics, butadiene, fulvene, and heptalene. The antiaromatics pentalene, benzocyclo-butadiene, and fulvalene follow with cyclobutadiene, the most antiaromatic, at the bottom. 

As seen in this example, the syntax of each resonance structure specification (STR... END) is very similar to that of a SCHOOSE keylist (see NBO Manual, p. B-77ff). Such SNRTSTR keylist may be included in the input file (after the usual NBO... SEND keylist) to dictate the choice of reference structures for NRT analysis. 

A comparison of our results to the preferred coordination numbers determined by Brown [35] in 1985 cf. Fig. 13) based on the smaller set of reference structures available at that time shows that for high Ac, the values determined by the approach presented here tend to be higher than those reported by Brown. This is mainly an expected result of the different approach in defining the boundary of the first coordination shell. For lower Ac the results of both studies are not significantly different, as the clear gap between the bond lengths of nearest and second-nearest neighboring shells of anions around a cation make the detailed choice of the threshold value less relevant. 

As shown by the first prompt there are four types of search, of which we will discuss two exact and substructure (SSS). In an exact search, only information regarding exactly the stracture given will be retrieved, but even so there may well be several answers, because CA treats stereoisomers and isotopically substituted compounds as separate answers. At the conclusion of the search the system gives the number of answers, (e.g., 4). We may now look at the four answers by using the display command. As in the CA File, there is a choice of display formats, but if we choose SUB we will get (1) the Registry Number, (2) the approved CA index name, (3) other names that have appeared in CA for that compound, (4) a structural formula, and (5) the number of CA references since 1967, along with a notation as to... 

In this simplified situation, can we really consider that the mean flame structure and thickness are steady, after certain delay and distance from initiation, and then the "turbulent flame speed" is a well-defined intrinsic quantity Indeed, with the present state of knowledge, there is no certainty in any answer to this question. Of course, it is hardly possible to build an experiment with nondecaying turbulence without external stirring. In deca)dng turbulence, the independence of the turbulent flame speed on the choice of reference values of progress variable has been verified in neither experiment nor theory. 

---