Calculations, structural features

Apart from finding structures that give energy minima, most molecular mechanics packages will calculate structural features such as the surface area or the molecular volume. Quantities such as these are often used to investigate relationships between molecular structure and pharmacological activity. This field of human endeavour is called QSAR (quantitative structure and activity relations). 

We have previously reviewed ( 1, 2) the methods used to calculate structural features of copolymers and terpolymers from monomer reactivity ratios, monomer feed compositions and conversions, and have written a program for calculating structural features of copolymers from either terminal model or penultimate model reactivity ratios (3). This program has been distributed widely and is in general use. A listing of an instructive program for calculating structural features of instantaneous terpolymers from monomer feed compositions and terminal model reactivity ratios was appended to one of our earlier reviews (.1). 

This program was written to calculate structural features of terpolymers prepared via the following propagation reactions from radicals AA, BA, CA, B and C and from monomers A, B and C. Reactivity ratios utilized by this program are also defined in the following scheme ... 

Mathematical procedures for calculating structural features of cyclocopolymers and of copolymers derived from them are proposed and are used in studies on the 1H-NMR spectra of styrene-methyl methacrylate copolymers derived from styrene-(methacrylic anhydride) copolymers. Reactivity ratios and cycliza-tion constants for styrene-methacrylic anhydride copolymerization were determined from structural features of the derived styrene-methyl methacrylate copolymers. The amount of uncyclized methacrylic anhydride units present in styrene-methacrylic anhydride copolymers having high styrene contents is considerably less than that predicted by these copolymerization parameters. The methoxy proton resonances of the derived copolymers are more intense in the highest field methoxy proton resonance area than would be expected if such resonance were due only to cosyndiotactic SMS triads. Possible explanations for these discrepancies are proposed. 

Table 1. X-ray Crystallographic Data and Calculated Structural Features of 1,2,4-Triazines...

Conditional probabilities can then be used to calculate structural features of the copolymers or to evaluate statistical features of the copolymerization mechanism. If terms such as P(A), P(AA), and P(ABA) are used to represent unconditional probabilities of finding monomer xmits, dyads, triads, etc. in the polymer chain, and if terms such as P(A/A), P(A/AB) and P(b/BBB) are used to represent conditional probabilities that A or B xmits follow other monomer xmits or monomer sequences in the copolymer chain, a copolymer can be considered to obey Bernoullian statistics if P(a) = P(A/a) =... 

Table 5.7 Comparison of the Calculated Structural Features and the Experimental Data Around the Central Boron Atom in the Compound Triethyiammonium-6,7-benzo-3-o-hydroxyphenyi-1,4-diphenyi-2,8,9-trioxa-4-phospha-1-boratricycio(3.3.1) nonane (CSD refcode JiNSUU) as Shown in Figure 5.11...

It is possible to identify particular spectral features in the modulated reflectivity spectra to band structure features. For example, in a direct band gap the joint density of states must resemble that of critical point. One of the first applications of the empirical pseudopotential method was to calculate reflectivity spectra for a given energy band. Differences between the calculated and measured reflectivity spectra could be assigned to errors in the energy band... 

Caleulations by the more rigorous proeedure yield, in MM3, a sum of (a) bond energies, (b) steric energy, (c) vibrational zero point and thermal energies, and (d) structural features POP and TORS. Energies (a), (b), and (d) are calculated as before. Bond energy parameters appear to be quite different from those of the default MM3 calculations canied out so far because zero point and thermal energies are not included in the parameters but are added later. 

The first widely used molecular mechanics pro gram was developed by Professor N L Allinger of the University of Georgia and was known in its various versions as MM2 MM3 and so on They have been re fined to the extent that many structural features can be calculated more easily and more accurately than they can be measured experimentally... 

Calculations at several levels of theory (AMI, 6-31G, and MP2/6-31G ) find lower activation energies for the transition state leading to the observed product. The transition-state calculations presumably reflect the same structural features as the frontier orbital approach. The greatest transition-state stabilization should arise from the most favorable orbital interactions. As discussed earlier for Diels-Alder reactions, the-HSAB theory can also be applied to interpretation of the regiochemistry of 1,3-dipolar cycloaddi-... 

According to these data, which structural features provide stabilization of radial centers Determine the level of agreement between these data and the radical stabilization energies given in Table 12.7 if the standard C—H bond dissociation energy is taken to be 98.8 kcal/mol. (Compare the calculated and observed bond dissociation energies for the benzyl, allyl, and vinyl systems.)... 

These differences have been attributed to various factors caused by the introduction of new structural features. Thus isopentane has a tertiary carbon whose C—H bond does not have exactly the same amount of s character as the C—H bond in pentane, which for that matter contains secondary carbons not possessed by methane. It is known that D values, which can be measured, are not the same for primary, secondary, and tertiary C—H bonds (see Table 5.3). There is also the steric factor. Hence, it is certainly not correct to use the value of 99.5 kcal mol (416 kJ mol ) from methane as the E value for all C—H bonds. Several empirical equations have been devised that account for these factors the total energy can be computed if the proper set of parameters (one for each structural feature) is inserted. Of course these parameters are originally calculated from the known total energies of some molecules that contain the structural feature. 

It seems reasonable to believe that this problem could be overcome by studying more coordinating ligands with the same structural features. Very recently, it has been demonstrated [56] that the use of iminobis(oxazolines) (Fig. 18) leads to better enantioselectivities and recoverable catalysts, both with laponite and nalion-silica supports (Table 8). Theoretical calculations are consistent with the stronger coordinating ability of iminobis(oxazolines) being the origin of these results [57]. 

Single slab. A number of recent calculations of surface electronic structures have shown that the essential electronic and structural features of the bulk material are recovered only a few atomic layers beneath a metal surface. Thus, it is possible to model a surface by a single slab consisting of 5-15 atomic layers with two-dimensional translational symmetry parallel to the surface and vacuum above and below the slab. Using the two-dimensional periodicity of the slab (or thin film), a band-structure approach with two-dimensional periodic boundary conditions can be applied to the surface electronic structure. 

Similarity searching requires the specification of an entire molecule, called the target structure or reference structure, rather than the partial structure that is required for substructure searching. The target molecule is characterized by a set of structural features, and this set is compared with the corresponding sets of features for each of the database structures. Each such comparison enables the calculation of a measure of similarity between the... 

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