Theoretical investigation

The simplest, qualitative, theoretical understanding of the nature of oxirene is provided by Breslow s concept of antiaromaticity. Whatever criticisms may be levelled at this notion (78JA6920), it does correctly predict that oxirene should be unusually unstable. 

Neither ground-state ethynol (hydroxyacetylene) (80) nor carbenaoxirane (81) appears to be a viable point of ingress to the oxirene-methanoylcarbene system, as both can isomerize to ketene by lower-energy pathways. The limited experimental information available on carbenaoxirane (Section 5.05.6.3.4(f/)) indicates that it is indeed largely isolated from the oxirene-methanoylcarbene manifold (but note the photolysis of ketene in Section 5.5.6.3.4(ff)) appropriate labelling experiments with (the unknown) ethynol have not been performed. 

In this section we discuss theoretical investigations that help us to understand the structures, electronic spectra, and reactions of aromatic and heteroaromatic diazonium ions. 

Klasinc and Schulte-Frohlinde (1968), who also used HMO for the investigation of substituted benzene diazonium ions, were the first to realize that the remarkable distortion of bond lengths and angles of the benzene ring by the diazonio group (Sec. 4.2) has a significant influence on its reactivity. They found that the sp2-hybridization at the carbon atoms of the benzene ring varied from 1.75 for C(l) to 2.16 for C(2). 

Sukigara and Kikuchi interpreted these experimental data by carrying out Pariser-Parr (PP) calculations on the benzenediazonium ion. On the basis of Romming s X-ray structure of the benzenediazonium ion (1963), with fixed bond integrals for the CC and CN bonds (/ Cc and / CN), but an adjustable bond integral / NN, they were able to ascribe the 259 nm and 295 nm bands to the lAx — xAi and transi- 

Bagal (1974) studied the influence of substituents on the ground and first excited states of arenediazonium ions. With regard to compounds in which mesomeric structures such as 4.1b are important, these authors are skeptical about the validity of the PP method. Later, Bagal et al. (1982) used CNDO/2. The calculated 7r-electron densities at all the nitrogen and carbon atoms were similar to those in the earlier PP results. 

The investigation by Mustroph et al. (1981) was made using SCF-CI with the PPP approximation to calculate the influence of substituents on the longest wavelength band. This study is interesting because the authors come to the conclusion that 591 nm is the theoretical limit that can be obtained with substituted benzenediazo-nium ions. As far as we are aware, that limit had not been reached by the early 1990s. 

Values are averaged over all isomers with this number of bond alterations. 

Number of newly formed double bonds in five-membered rings. 

MNDO or ab initio calculations (Table 5.3). Further confirmation for the preference of 1,2-addition was established by ab initio calculation of the C-H bond energy in hydrogenated fullerenes [35]. Hybrid density functional theory using the B3LYP functional with the 6-31 G(d,p) basis set leads to the bond energies shown in Table 5.3. The most stable bond is found in 1,2 adducts with a bond energy of 2.86 eV, followed by a bond energy of 2.69 eV in 1,4-adducts. All the other addition patterns such as 1,3 addition or addition to a [5,6] bond lead to less stable C-H bonds (Table 5.3). 

If tetrahydro[60]fullerene (C5QH4) is formed by additions to two [6,6] double bonds, which are two 1,2-additions with respect to the cyclohexatriene units in C q, then eight regioisomers are possible [37, 38] (see Chapter 10). This very plausible assumption is corroborated by the theoretical investigations of multiple additions to C50 in a 1,2- and a 1,4-mode. These investigations predict 1,2-additions to be favorable over 1,4-additions up to the formation of CjqHj2 (see also Table 5.5 below) 

One isomer that does not derive exclusively from 1,2-additions - the isomer 1,2,4,15 - is calculated to be more stable than all of the other mentioned isomers except the cis-Tisomer (Table 5.4) [33], Nevertheless, the three isomers, which are calculated as the most stable 1,2-addition-products, are the major isomers in the reductions with either borane or hydrazine (ds-l-isomer, see Sections 5.2.1 and 5.2.3) or with the Zn/Cu-couple trans-3 and e-isomer, see Section 5.2.2), whereas the 1,2-1,4-addition product (1,2,4,15-isomer) was not observed as a main product in a reduction. 

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Viswanathan R, Thompson D L and Raff L M 1984 Theoretical investigations of elementary processes in the chemical vapor deposition of silicon from silane. Unimolecular decomposition of SiH J. Chem. Phys. 80 4230 0... 

Properties and Reactions. Amine boranes are usually colodess, crystalline compounds, which exhibit sharp melting points and thermal stability when pure. Primary and secondary amine boranes are generally soHds at ambient temperatures. With the exception of trimetbylamine borane, the ahphatic /-amine boranes are Hquids. The nature of the bonding in amine boranes has been the subject of theoretical investigations (21—23). 

Some theoretical investigations have attempted to follow reactions of diazirines, among them reactions of 3-chloro- and 3-fluoro-diazirines. 

Figure 1 A flow chart of experimental information about drug-receptor interaction. The objects of experimental and theoretical investigation are boxed, and the experimental information is circled.

Figure 2 A flow chart of theoretical modeling drug-receptor interaction and relation to experiment. The objects of theoretical investigation are m rectangles, and the experimental information IS m the ovals.

BW Beck. Theoretical Investigations of h on-Sulfur Proteins. Ph.D. thesis. Pullman, WA Washington State University, 1997. 

Vacancy chromatography has some quite unique properties and a number of potentially useful applications. Vacancy chromatography can be theoretically investigated using the equations derived from the plate theory for the elution of... 

Poz, M.. Y. 1993. Theoretical investigation and practical applications of non-isothermic jets for the purpose of ventilating rooms. ASHRAE Transactions, vol. 99, no. 1, pp. 950-9.39. Prandtl, L. 1942. Bemerkungen zur theorie der freien turbulenz. Z. fiir Angeivandie Math,. 

Bloor, and D.B. Ingham. Theoretical Investigations of the Flow in a Conical Cyclone. 

Theoretical investigations of quenched-annealed systems have been initiated with success by Madden and Glandt [15,16] these authors have presented exact Mayer cluster expansions of correlation functions for the case when the matrix subsystem is generated by quenching from an equihbrium distribution, as well as for the case of arbitrary distribution of obstacles. However, their integral equations for the correlation functions... 

The rates of most reactions are sensitive functions of temperature, and an understanding of the molecular basis for this dependence is an essential goal in theoretical investigations of kinetics. Experimentally it has been found that the rate constant... 

Cambridge) and J. H. van Vleck (Harvard) fundamental theoretical investigations of the electronic structure of magnetic and disordered systems. 

Great progress has been made in the experimental and theoretical investigation of tautomerism of five-membered ring systems since 1975, and a number of reviews dealing partly or entirely with this subject have appeared since then. In Table I some pertinent references are given. 

Although azafulvalenes as yet comprise a small class of cyclic cross-conjugated compounds, they have been the subject of a variety of theoretical investigations spanning a range from the Hiickel (HMO) theory to the... 

Most studies concerning pyrimidines originate from biochemical questions. Since these systems are dominated by hydrogen-bonding and/or dispersion contributions, methods beyond the Hartree-Fock level are mandatory. The success of quantum chemical studies in this field is impressive and many effects could be explained on the basis of these theoretical investigations. 

In a combined experimental and theoretical investigation it was found that the / -alkyl group in the dienophile gave a steric interaction in the transition-state structure which supported the asynchronous transition-state structure for the Lewis acid-catalyzed carbo- and hetero-Diels-Alder reactions. The calculated transition-state energies were of similar magnitude as obtained in other studies of these BF3-catalyzed carbo-Diels-Alder reactions. 

The number of theoretical investigations of hetero-Diels-Alder reaction is very limited. The few papers dealing with this class of reactions have shown that the influence of the Lewis acid on the reaction course can to a high extent be compared to those found the carbo-Diels-Alder reactions. At the present stage of investigations, however, more work is needed if we are to understand the influence and control of selectivity in Lewis acid-catalyzed hetero-Diels-Alder reaction - we are probably at the beginning of a new era in this field. 

The theoretical investigations of Lewis acid-catalyzed 1,3-dipolar cycloaddition reactions are also very limited and only papers dealing with cycloaddition reactions of nitrones with alkenes have been investigated. The Influence of the Lewis acid catalyst on these reactions are very similar to what has been calculated for the carbo- and hetero-Diels-Alder reactions. The FMOs are perturbed by the coordination of the substrate to the Lewis acid giving a more favorable reaction with a lower transition-state energy. Furthermore, a more asynchronous transition-structure for the cycloaddition step, compared to the uncatalyzed reaction, has also been found for this class of reactions. 

Generally, the number of the shell chains in a microsphere ranges from a few hundred to a few thousand. The range of the diameter of the core is from 10-100 nm. Such a core-shell structure is very similar to the (AB)n type star block copolymers, which have many arms and spherical polymer micelles of the block or graft copolymers formed in selective solvents that are good for the corona sequence and bad for the core sequence. In fact, many theoretical investigations of the chain con-... 

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