Similarity Carbo

Carbo-Dorca, R., Amat, LL, Besalu, E., Girones, X., Robert, D. In Fundamentals of Molecular Similarity, Carbo-Dorca, R., Girones, X., Mezey, P.G. (Eds.), Kluwer Acade-mic/Plenum Press, New York, 2001, pp. 187-320. 

Carbo-Dorca R. Quantum Similarity. Carbo-Dorca R, Mezey PG, eds. Advances in Molecular Similarity. Vol. 2. London JAI Press, 1998 1-42. 

The resulting similarity measures are overlap-like Sa b = J Pxi ) / B(r) Coulomblike, etc. The Carbo similarity coefficient is obtained after geometric-mean normalization Sa,b/ /Sa,a Sb,b (cosine), while the Hodgkin-Richards similarity coefficient uses arithmetic-mean normalization Sa,b/0-5 (Saa+ b b) (Dice). The Cioslowski [18] similarity measure NOEL - Number of Overlapping Electrons (Eq. (10)) - uses reduced first-order density matrices (one-matrices) rather than density functions to characterize A and B. No normalization is necessary, since NOEL has a direct interpretation, at the Hartree-Fodt level of theory. 

Cosine similarity coefficient Also known as the Carbo index c. EllWiB s... 

Carbo R, L Leyda and M Arnau 1980. An Electron Density Measure of the Similarity Between Tw Compounds. International Journal of Quantum Chemistry 17 1185-1189. 

V. -(l-Carbobemoxy-4 -piperidyl)propionyl chloride. /3-(iV-carbo-benzyloxy-4-piporidyl)ethyl 3-indolyl ketone (208) was obtained similarly by the condensation of ]3-(A -carbobenzoxy-4-piperidyl)-propionyl chloride with indole magnesium bromide in ether. ... 

Alkylation results in a bathochromic shift of 10 mp in the and 8-carbohne spectra, and ind-N- and p /r-A -alkylation causes a similar shift in the spectrum of the quaternary j3-carbo-linium ion. ... 

The ultraviolet absorption spectra of 3,4-dihydro-jS-carboline derivatives exhibit a dependence on pH similar to that shown by the speetra of the fully aromatie compounds. 3,4-Dihydro-/S-carboline and 1-methyl- and 7-methoxy-l-methyl-3,4-dihydro-jS-carbo-line serve as examples. The quaternary 3,4-dihydro-jS-earbolin-ium salts obtained on p /r-A-alkylation of these dihydro-j3-earbo-lines show a bathoehromic shift of 5 mp, eompared to the... 

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 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. 

When the Pd bears chiral ligands, these reactions can be enantioselective. TT-Allylmolybdenum compounds behave similarly.Because palladium compounds are expensive, a catalytic synthesis, which uses much smaller amounts of the complex, was developed. That is, a substrate such as an allylic acetate, carbo-... 

Hence, the rate depends only on the ratio of the partial pressures of hydrogen and n-pentane. Support for the mechanism is provided by the fact that the rate of n-pentene isomerization on a platinum-free catalyst is very similar to that of the above reaction. The essence of the bifunctional mechanism is that the metal converts alkanes into alkenes and vice versa, enabling isomerization via the carbenium ion mechanism which allows a lower temperature than reactions involving a carbo-nium-ion formation step from an alkane. 

Although Ce(IV) oxidation of carboxylic acids is slow and incomplete under similar reaction conditions , the rate is greatly enhanced on addition of perchloric acid. No kinetics were obtained but product analysis of the oxidations of -butyric, isobutyric, pivalic and acetic acids indicates an identical oxidative decarboxylation to take place. Photochemical decomposition of Ce(IV) carbo-xylates is highly efficient unity) and Cu(ll) diverts the course of reaction in the same way as in the thermal oxidation by Co(IIl). Direct spectroscopic evidence for the intermediate formation of alkyl radicals was obtained by Greatorex and Kemp ° who photoirradiated several Ce(IV) carboxylates in a degassed perchloric acid glass at 77 °K in the cavity of an electron spin resonance spectro-... 

The subjects of this section are two reactions that do not actually involve carbo-cation intermediates. They do, however, result in carbon to carbon rearrangements that are structurally similar to the pinacol rearrangement. In both reactions cyclic intermediates are formed, at least under some circumstances. In the Favorskii rearrangement, an a-halo ketone rearranges to a carboxylic acid or ester. In the Ramberg-Backlund reaction, an a-halo sulfone gives an alkene. 

R. Carbo (ed.) Molecular Similarity and Reactivity From Quantum... 

Besalu, E., Carbo, R., Meslres, J. and Sola, M. Foundations and Recent Developments on Molecular Quantum Similarity. 173, 31-62 (1995). 

Rearrangements that involve radicals are found to be much less common than otherwise similar rearrangements that involve carbo-cations. In this they resemble carbanions (cf. p. 292), and the reason for the resemblance becomes apparent when we compare the T.S.s for a 1,2-alkyl shift in the three series ... 

Dicyanopyridazine 4-145 has been used for the synthesis of carbo- and het-ero-cage systems employing nonconjugated dienes such as cyclooctadiene 4-146, or 4-148 or 4-150 to give 4-147, 4-149 and 4-151, respectively (Scheme 4.31) [50]. In a similar way, dihydrofurans, dihydropyrans, pyrrolines, and enol ethers have also been used [51],... 

Sola, M., J. Mestres, R. Carbo, and M. Duran. 1996. A Comparative Analysis by Means of Quantum Molecular Similarity Measures of Density Distributions Derived from Conventional ab initio and Density Functional Methods. J. Chem. Phys. 104, 636. 

Carbo, R., B. Calabuig, L. Vera, andE. Basalu. 1994. Molecular Quantum Similarity Theoretical Framework, Ordering principles, and Visualization Techniques. 25, 253. 

Mestres, J., M. Sola, M. Duran, and R. Carbo. 1996. On the Calculation of Ab Initio Quantum Molecular Similarities for Large Systems Fitting the Electron Density. J. Comp. Chem. 15, 1113. 

In summary, transifion-metal-catalyzed alkene-polymerization reactions highlight the metal-induced electrophilic activation of C—C n bonds to form carbo-cation-like alkene complexes. Considerations involving substituent pi-donor or pi-acceptor strength (i.e., tendency toward carbocation formation) will be useful in similarly rationalizing polymerization reactions (4.105) for more general alkenes. 

Two objects are similar and have similar properties to the extent that they have similar distributions of charge in real space. Thus chemical similarity should be defined and determined using the atoms of QTAIM whose properties are directly determined by their spatial charge distributions [32]. Current measures of molecular similarity are couched in terms of Carbo s molecular quantum similarity measure (MQSM) [33-35], a procedure that requires maximization of the spatial integration of the overlap of the density distributions of two molecules the similarity of which is to be determined, and where the product of the density distributions can be weighted by some operator [36]. The MQSM method has several difficulties associated with its implementation [31] ... 

The presence of one or more heteroatoms in either the 4jt or In component allows the synthesis of six-memebered heterocycles via the Diels-Alder process. These strategies have been successfully developed (218) leading to a diverse array of natural products. Similar to the carbo-Diels-Alder reaction, many of these processes are amenable to Lewis acid acceleration, and several have been developed using chiral catalysts. 

In 1980, Carbo et al. were the first to express molecular similarity using the electron density [17]. They introduced a distance measure between two molecules A and B in the sense of a Euclidean distance in the following way ... 

Many applications of QSM use not the MQSM values as such but similarity indices. There exist many such indices and for a review, the reader is referred to Willett et al. [54]. One example that was touched upon above is the Carbo index. The Carbo index is one of the so-called C-class descriptors giving a value between 0 and 1 where a higher value indicates higher similarity. Although originally defined for overlap MQSM, it can be generalized to different operators f so that the Carbo index becomes... 

According to some authors, the similarity between shape functions might give more interesting information than using the electron density [63]. In this context, it should be mentioned that the Carbo index retains the same value. Moreover, it has... 

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