Theoretical study Empirical calculation

In agreement with the previously reported theoretical study, the results of semi-empirical calculations showed that the formation of the Dewar isomer is favored [99H(50)1115]. Probably, the observed formation of the azirine derives from a thermal isomerization of the first photoproduct, in line with that described in the case of furan and thiophene derivatives (Fig. 11). 

Very recently there has been an experimental and theoretical study of electronic substituent effects in 4-aminoaryl (4-substituted aryl) sulfones146. PMR, 13C NMR and infrared measurements were involved and semi-empirical all-valence CNDO/2 calculations, with and without sulfur d orbitals, were carried out. Various correlations between spectral results and substituent constants are presented. There is good agreement between experimental and theoretical data, which does not depend on the inclusion or exclusion of the sulfur d orbitals from the calculations. 

Although the first mechanism is intuitively, and for reasons of simplicity, preferred to the second one, there is no experimental evidence for excluding the latter. Theoretical evidence for preferring the former mechanism stems from a study by Jansen and Ros (1969), who performed non-empirical calculations on several configurations of a model system, viz. protonated carbon monoxide. They found that the linear +... 

Previous theoretical studies of isolated and doped PA have mostly dealt with geometrical structures and charge and spin wavess. A few have dealt with the vibrational spectrumS2i = using force fields derived from fits to experimental infrared and Raman spectra of smaller polyenes or from scaled force constants obtained from semi-empirical SCF calculations on these systems. Very little the-... 

Theoretical studies aimed at rationalizing the interaction between the chiral modifier and the pyruvate have been undertaken using quantum chemistry techniques, at both ab initio and semi-empirical levels, and molecular mechanics. The studies were based on the experimental observation that the quinuclidine nitrogen is the main interaction center between cinchonidine and the reactant pyruvate. This center can either act as a nucleophile or after protonation (protic solvent) as an electrophile. In a first step, NH3 and NH4 have been used as models of this reaction center, and the optimal structures and complexation energies of the pyruvate with NH3 and NHa, respectively, were calculated [40]. The pyruvate—NHa complex was found to be much more stable (by 25 kcal/mol) due to favorable electrostatic interaction, indicating that in acidic solvents the protonated cinchonidine will interact with the pyruvate. 

The main difficulty in the theoretical study of clusters of heavy atoms is that the number of electrons is large and grows rapidly with cluster size. Consequently, ab initio "brute force" calculations soon meet insuperable computational problems. To simplify the approach, conserving atomic concept as far as possible, it is useful to exploit the classical separation of the electrons into "core" and "valence" electrons and to treat explicitly only the wavefunction of the latter. A convenient way of doing so, without introducing empirical parameters, is provided by the use of generalyzed product function, in which the total electronic wave function is built up as antisymmetrized product of many group functions [2-6]. 

Although continuum solvation models do appear to reproduce the structural and spectroscopic properties of many molecules in solution, parameterization remains an issue in studies involving solvents other than water. In addition, the extension of these approaches to study proteins embedded in anisotropic environments, such as cell membranes, is clearly a difficult undertaking96. As a result, several theoretical studies have been undertaken to develop semi-empirical methods that can calculate the electronic properties of very large systems, such as proteins28,97 98. The principal problem in describing systems comprised of many basis functions is the method for solving the semi-empirical SCF equations ... 

More recently, infrared data have found further application in conformational studies of complex quinolizine derivatives, such as the previously mentioned alkaloid cytisine 9. Comparison of experimental values for the and t co) frequencies with the theoretical values obtained from semi-empirical calculations for... 

Mechanistic and theoretical studies of the Diels-Alder reaction have resulted in the characterization of this reaction as a concerted, although not necessarily synchronous, single-step process28-31 45. The parent reaction, the addition of 1,3-butadiene to ethylene yielding cyclohexene, has been the subject of an ongoing mechanistic debate. Experimental results supported a concerted mechanism, whereas results from calculations seemed to be dependent on the method used. Semi-empirical calculations predicted a stepwise mechanism, whereas ab initio calculations were in favor of a concerted pathway. At the end of the 80s experimental and theoretical evidence converged on the synchronous mechanism29-31. 

Several older theoretical studies are included in the review by Knowles <1996CHEC-II(7)489>, and little has been reported since. Nagy et al. carried out quantum calculations on several [l,2,3]triazolo[4,5-t/ pyridazines to reveal electron distributions in the ground and the excited state using the semi-empirical Hiickel molecular orbital (MO) method to explain the fluorescence of such compounds (see Section 10.13.3.2) <2002JPH83>. 

In view of the remarkably swift development of the chemistry of sulfur heterocycles, an extension of quantum-chemical calculations to various additional physical properties as well as a more systematic approach in both experimental and theoretical studies can be expected in the near future. Even though it is not possible to put forward responsibly an optimum unique set of HMO empirical parameters, Model B (8S = 1, 3C(a) = 0.1, pcs = 0.7) may perhaps be recommended for the beginning of a systematic treatment. As for other parameters, the set given by Streitwieser4 can be recommended the value 0.5 has proved suitable for p8S. It is quite obvious, however, that such studies should develop simultaneously with application of more sophisticated methods, above all the configuration interaction method.42... 

Hope et al. (116) presented a combined volumetric sorption and theoretical study of the sorption of Kr in silicalite. The theoretical calculation was based on a potential model related to that of Sanders et al. (117), which includes electrostatic terms and a simple bond-bending formalism for the portion of the framework (120 atoms) that is allowed to relax during the simulations. In contrast to the potential developed by Sanders et al., these calculations employed hard, unpolarizable oxygen ions. Polarizability was, however, included in the description of the Kr atoms. Intermolecular potential terms accounting for the interaction of Kr atoms with the zeolite oxygen atoms were derived from fitting experimental results characterizing the interatomic potentials of rare gas mixtures. In contrast to the situation for hydrocarbons, there are few direct empirical data to aid parameterization, but the use of Ne-Kr potentials is reasonable, because Ne is isoelectronic with O2-. 

There is no change in the chemical composition of the reacting species in reactions (a) and (b) nevertheless, it is possible to measure the rate of these reactions by studying the process of the change in the spin state of the nuclei (ortho-para conversion). Theoretically, reactions (a)-(d) are of special interest because for them rather accurate non-empirical calculations of the potential energy surface, as well as detailed, up to quantum mechanical, calculations of the nuclear dynamics during an elementary reaction act can be carried out. 

However, again, as in the case of calculations of energy spectra, it is much more efficient to use universal computer programs to perform accurate theoretical or semi-empirical calculations of electron transition and other properties and quantities of atoms or ions, particularly if they may be combined with the relevant experimental studies [187-191]. 

Thus, making use of modern methods of theoretical atomic spectroscopy and available computer programs, one is in a position to fulfill more or less accurate purely theoretical (ab initio) or semi-empirical calculations of the energy spectra, transition probabilities and of the other spectroscopic characteristics, in principle, of any atom or ion of the Periodical Table, their isoelectronic sequences, revealing in this way their structure and properties, to model the processes in low- and high-temperature plasma. Such calculations could be done prior to the corresponding experimental measurements, instead of them, or after them to help to interpret the interesting phenomena found in experimental studies. 

The design of large natural draft cooling towers and analysis of their performance are complicated by the effects of variations in ambient air humidity. Often the effluent air from the tower is assumed to be at 100% relative humidity, to simplify calculations for design parameters. This study avoids the simplification, and proposes a procedure for determining the major design parameters for a natural draft tower. The theoretical and empirical relationships applicable to heat balance, heat transfer and transport, and tower draft and air resistance are given. 13 refs, cited. 

The theoretical study of thicno[3,4-z/ thiepine 15 and furo[3,4-rf thiepine 16, as dienes in thiophene or furan moieties, respectively, in the Diels-Alder reaction was investigated with semi-empirical AMI calculations <1995JHC1499>. S-Methylation at the thiophene moiety of thieno[3,4-t/]thiepine 15 was predicted to lower the activation energy and facilitate reaction with less reactive dienophiles, such as ethylene. 

As early as in 1972, a theoretical study of the structure of unknown 1,2,3,4-thiatriazole was carried out using the semiempirical complete neglect of differential overlap (CNDO) method <1972JCD73>. Because of the known large discrepancy for the C-S length predicted by semi-empirical calculations compared with the experimental data for l,2,3,4-thiatriazole-5-thiolate <1986ICA71>, this study has only historical interest. 

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