Cyclic identity

Alternatively, we could use the Jacobi cyclic identity (1.14b) to write directly... 

The measured Joule-Thomson coefficient /jljt provides valuable information about how the enthalpy of real gases depends on variables other than temperature. To obtain information about the P dependence of H, we can employ the Jacobi cyclic identity (1.14b) to rewrite the Joule-Thomson coefficient as... 

For a binary fluid with c = 2, p = 2, the phase rule gives / = 2 degrees of freedom. Under these conditions, we know from the Jacobi cyclic identity (1.14b) that... 

When a cyclic component carries more than one identical side chain, the name of the cyclic component is followed by di-, tri-, etc., and then by the name of the acyclic component, and it is preceded by the locants for the side chains. Examples are... 

When side chains of two or more different kinds are attached to a cyclic component, only the senior side chain is named by the conjunctive method. The remaining side chains are named as prefixes. Likewise, when there is a choice of cyclic component, the senior is chosen. Benzene derivatives may be named by the conjunctive method only when two or more identical side chains are present. Trivial names for oxo carboxylic acids may be used for the acyclic component. If the cyclic and acyclic components are joined by a double bond, the locants of this bond are placed as superscripts to a Greek capital delta that is inserted between the two names. The locant for the cyclic component precedes that for the acyclic component, e.g., indene-A - -acetic acid. 

Many biochemical and biophysical studies of CAP-DNA complexes in solution have demonstrated that CAP induces a sharp bend in DNA upon binding. This was confirmed when the group of Thomas Steitz at Yale University determined the crystal structure of cyclic AMP-DNA complex to 3 A resolution. The CAP molecule comprises two identical polypeptide chains of 209 amino acid residues (Figure 8.24). Each chain is folded into two domains that have separate functions (Figure 8.24b). The larger N-terminal domain binds the allosteric effector molecule, cyclic AMP, and provides all the subunit interactions that form the dimer. The C-terminal domain contains the helix-tum-helix motif that binds DNA. 

Like the un-ionized hydroxyl group, an alkoxy group is a weak nucleophile. Nevertheless, it can operate as a neighboring nucleophile. For example, solvolysis of the isomeric p-bromobenzenesulfonate esters 6 and 7 leads to identical prxKluct nuxtures, suggesting the involvement of a common intermediate. This can be explained by involvement of the cyclic oxonium icai which would result from intramolecular participation. ... 

Applying the above symmetry formulation to armchair (n = m) and zigzag (m = 0) nanotubes, we find that such nanotubes have a symmetry group given by the product of the cyclic group and Cj , where 2n consists of only two symmetry operations the identity, and a rotation by 2ir/2n about the tube axis followed by a translation by T/2. Armchair and zig-... 

FIGURE 6.44 Several possible symmetric arrays of identical protein snbnnits, inclnding (a) cyclic symmetry, (b) dihedral symmetry, and (c) cubic symmetry, inclnding examples of tetrahedral (T), octahedral (O), and icosahedral (I) symmetry. (Irving GAs)... 

Emission spectra have been recorded for four aryl-substituted isoindoles rmder conditions of electrochemical stimulation. Electrochemiluminescence, which was easily visible in daylight, was measured at a concentration of 2-10 mM of emitter in V jV-dimethylformamide with platinum electrodes. Emission spectra due to electrochemi-luminescence and to fluorescence were found to be identical, and quantum yields for fluorescence were obtained by irradiation with a calibrated Hght source. Values are given in Table X. As with peak potentials determined by cyclic voltammetry, the results of luminescence studies are interpreted in terms of radical ion intermediates. ... 

Quinoxalin-2-ones are in tautomeric equilibrium with 2-hydroxy-quinoxalines, but physical measurements indicate that both in solution and in the solid state they exist as cyclic amides rather than as hydroxy compounds. Thus quinoxalin-2-one and its A -methyl derivative show practically identical ultraviolet absorption and are bases of similar strength. In contrast, the ultraviolet spectra of quinoxalin-2-one and its 0-methyl derivative (2-methoxyquinoxaIine) are dissimilar. The methoxy compound is also a significantly stronger base (Table II). Similar relationships also exist between the ultraviolet absorption and ionization properties of 3-methylquinoxalin-2-one and its N- and 0-methyl derivatives. The infrared spectrum of 3- (p-methoxy-benzyl)quinoxalin-2-one (77) in methylene chloride shows bands at 3375 and 1565 cm" which are absent in the spectrum of the deuterated... 

They have also carried out the oxidation of selinene by means of ozone and potassium permanganate and have thus been able to establish that the regenerated selinene is not absolutely identical with the natural selinene. They are the first to record the existence of a hemi-cyclic-sesquiterpene this compound is termed pseudo-()3)-selinene. By passing a current of ozone into a solution of natural selinene (pseudo-( 8)-selinene). in acetic acid, there is obtained a diketone, CjjHogOj, which is purified by treatment with permanganate in acetone solution. Its properties are as. follows —... 

Since if is therefore an isomorphism, we have proven that any tree rooted on a cyclic state is identical to the tree rooted on the null configuration. I... 

Contained within intermediate 25 is an acid-labile mixed acetal group and it was found that treatment of 25 with camphorsulfonic acid (CSA) results in the formation of dioxabicyclo[3.3.0]octane 26 in 77 % yield. Acid-induced cleavage of the mixed cyclic acetal function in 25, with loss of acetone, followed by intramolecular interception of the resultant oxonium ion by the secondary hydroxyl group appended to C leads to the observed product. Intermediate 26 clearly has much in common with the ultimate target molecule. Indeed, the constitution and relative stereochemistry of the dioxabicyclo[3.3.0]octane framework in 26 are identical to the corresponding portion of asteltoxin. 

The addition of the anions of racemic cyclic allylic sulfoxides to various substituted 2-cyclopentenones gives y-l,4-adducts as single diastereomeric products22. The modest yields were due to competing proton-transfer reactions between the anion and enone. The stereochemical sense of these reactions is identical to that for the 1,4-addition reaction of (Z)-l-(/erf-butylsulfinyl)-2-methyl-2-butene to 2-cyclopentenone described earlier. 

Kinetic studies using 1,9-decadiene and 1,5-hexadiene in comparison widi catalyst 14 and catalyst 12 demonstrate an order-of-magnitude difference in their rates of polymerization, widi 14 being the faster of the two.12 Furdier, this study shows diat different products are produced when die two catalysts are reacted widi 1,5-hexadiene. Catalyst 14 generates principally lineal" polymer with the small amount of cyclics normally observed in step condensation chemistry, while 12 produces only small amounts of linear oligomers widi die major product being cyclics such as 1,5-cyclooctadiene.12 Catalyst 12, a late transition metal benzylidene (carbene), has vastly different steric and electronic factors compared to catalyst 14, an early transition metal alkylidene. Since die results were observed after extended reaction time periods and no catalyst quenching or kinetic product isolation was performed, this anomaly is attributed to mechanistic differences between diese two catalysts under identical reaction conditions. 

Figure 7. Cyclic voltammograms of poly(3-methylthiophene) in acetonitrile + 0.1 M E NCICV The solid line represents three identical voltammograms to +1.0 V. while the dashed line is for two subsequent scans to +2.0 V.1 (Reprinted with permission from Anal Chem. 65,696-703.1993. Copyright 1993, American Chemical Society.)...

Note. These recommendations may give rise to very different names for cyclic and acyclic forms of the same basic structures, resulting from different priorities. Thus, in Chart V, structures 1 and 2 are virtually identical, differing only by cyclization. The same holds for structures 3 and 4. 

Substituents replacing the hydrogen atom of an alcoholic hydroxy group of a saccharide or saccharide derivative are denoted as O-substituents. The 0- locant is not repeated for multiple replacements by the same atom or group. Number locants are used as necessary to specify the positions of substituents they are not required for compounds fully substituted by identical groups. Alternative periphrase names for esters, ethers, etc. may be useful for indexing purposes. For cyclic acetals see 2-Carb-28. 

Such effects are observed inter alia when a metal is electrochemically deposited on a foreign substrate (e.g. Pb on graphite), a process which requires an additional nucleation overpotential. Thus, in cyclic voltammetry metal is deposited during the reverse scan on an identical metallic surface at thermodynamically favourable potentials, i.e. at positive values relative to the nucleation overpotential. This generates the typical trace-crossing in the current-voltage curve. Hence, Pletcher et al. also view the trace-crossing as proof of the start of the nucleation process of the polymer film, especially as it appears only in experiments with freshly polished electrodes. But this is about as far as we can go with cyclic voltammetry alone. It must be complemented by other techniques the potential step methods and optical spectroscopy have proved suitable. 

In the ideal case, reversible cyclic voltammograms of redoxactive films should show completely symmetrical and mirror-image cathodic and anodic waves with identical peak potentials and current levels 34-i37) pjg... 

Solvolyses of these cyclic vinyl triflates at 100 in 50% aqueous ethanol, buffered with triethylamine, lead exclusively to the corresponding cyclo-alkanones. Treatment of 176 with buffered CH3COOD gave a mixture of cyclohexanone (85%) and 1-cyclohexenyl acetate (15%). Mass spectral analysis of this cyclohexanone product showed that the amount of deuterium incorporation was identical to that amount observed when cyclohexanone was treated with CH3COOD under the same conditions. This result rules out an addition-elimination mechanism, at least in the case of 174, and since concerted elimination is highly unlikely in small ring systems, it suggests a unimolecular ionization and formation of a vinyl cation intermediate in the solvolysis of cyclic triflates (170). The observed solvent m values, 174 m =. 64 175 m =. 66 and 16 m =. 16, are in accord with a unimolecular solvolysis. 

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