Calculations cyclizations

Despite the contribution of the above factors, it is clear that bending of the two alkyne moieties toward each other increases the energy of the system as illustrated by the three plots in Fig. 7.24 These plots illustrate the relation between the ring size and calculated cyclization parameters in more detail and dependence of the total energy of the system from the c-d distance. Interestingly, simple bending of alkyne moiety reproduced the effect of cyclic restraints reasonably well. A similar conclusion has been reached even earlier by Kraka and Cremer.40... 

Conrotatory and disrotatory eoncerted reaetions ean often be distinguished by chemical means. For example, using the results of the previous calculation, predict whether the cyclizations of hexa-2,4-diene will lead to cii or traa.i dimethyl cyclo-butene... 

When this stereoelectronic requirement is combined with a calculation of the steric and angle strain imposed on the transition state, as determined by MM-type calculations, preferences for the exo versus endo modes of cyclization are predicted to be as summarized in Table 12.3. The observed results show the expected qualitative trend. The observed preferences for ring formation are 5 > 6, 6 > 7, and 8 > 7, in agreement with the calculated preferences. The relationship only holds for terminal double bonds. An additional alkyl substituent at either end of the double bond reduces the relative reactivity as a result of a steric effect. 

The free energy of activation at the QCISD(T)/6-31 H-- -G(d,p) level amounts to 21.1 kcal/mol. According to the authors, the large electron density redistribution arising upon cyclization makes it necessary to use extended basis sets and high-order electron correlation methods to describe the gas-phase thermodynamics, which indicates clearly the gas-phase preference of the azido species. However, the equilibrium is shifted toward the tetrazole as the polarity of a solvent is increased. For instance, SCRF calculations (e = 78.4) yield a relative free energy of solvation with respect to the cw-azido isomer of —2.4 kcal/mol for the tmns-zziAo compound and of —6.8 kcal/mol for the tetrazole isomer. At a much lower level, the... 

The asymmetric synthesis of (4i ,9S, 9ai )-4-phenyl-l-trimethylsilyloxy-9-vinylperhydropyrido[2,l-c][l,4]oxazine by a high level of stereoselectivity in the cyclization of (3i ,5i )-5-phenyl-3-phenylsulfanyl-4-(6-trimethylsila-nylhex-4-enyl)-2-trimethylsilyloxymorpholine was rationalized via AMI calculations (98T10309). 

Activation parameters. Calculate AW and AS for the cyclization of the 5-hexenyl radical, whose rate is given in Eq. (5-39). 

The previously outlined mechanistic scheme, postulating reversible propagation and cyclization, was simplified by neglecting the de-cyclization because in the very short time of the studied reaction the extent of de-cyclization is negligible. The rate constants appearing in the appropriate differential equations were computer adjusted until the calculated conversion curves, shown in Fig. 7, fit the experimental points. The results seem to be reliable inspite of the stiffness of the differential equations. 

In this case, the crosslinking density is the sum of the effective crosslinking density and the secondary cyclization, since both crosslinkages are elastically effective. The calculation conditions are the same as Figure 1 except that the number of secondary cycles formed per effective crosslinkage T) is 20. 

For this low mole fraction of divinyl monomer (f2o 1-52 xlO ) the effect of cyclization should not be significant, and the calculated results for weight fraction of gel agree with experimental data satisfactorily. But to accurately calculate the structural properties of the gel such as crosslinking density, it will be necessary to consider the effect of cyclization. 

The above methodology has been extremely useful for the synthesis of a variety of INOC precursors. For instance, treatment of 0-trimethylsilyl a-bro-moaldoximes 52b, e, f with F ion in presence of unsaturated alcohols 57 produces oximino ethers 58 which can be readily oxidized using NaOCl (Scheme 8) [29]. The transient nitrile oxide intermediates formed undergo spontaneous cyclization to fused isoxazolines 59. The preferred stereoisomer in the formation of the five-membered ring ethers is trans whereas in the six-membered ring ethers the cis isomer predominates (see Table 5). MM2 calculations helped rationalize the experimentally observed stereoselectivites (see Table 5). 

Several ways to suppress the 2-oxonium-[3,3]-rearrangements might be envisioned. Apart from the introduction of a bulky substituent R at the aldehyde (Scheme 23) a similar steric repulsion between R and R might also be observed upon introduction of a bulky auxiliary at R. A proof-of-principle for this concept was observed upon by using of a trimethylsilyl group as substituent R in the alkyne moiety (Scheme 25, R = TMS). This improvement provided an efficient access to polysubstituted dihydropyrans via a silyl alkyne-Prins cyclization. Ab initio theoretical calculations support the proposed mechanism. Moreover, the use of enantiomerically enriched secondary homopropargylic alcohols yielded the corresponding oxa-cycles with similar enantiomeric purity [38]. 

A plausible mechanism for this new alkyne aza-Prins cyclization is outlined in Scheme 27. Thus, reaction of the homopropargyl tosyl amine with an aldehyde promoted by ferric halide generates the W-sulfonyl iminium ion. This intermediate evolves to the corresponding piperidine, via the vinyl carbocation. Ah initio theoretical calculations support the proposed mechanism. 

A series of theoretical studies of the SCV(C)P have been reported [38,40,70-74], which give valuable information on the kinetics, the molecular weights, the MWD, and the DB of the polymers obtained. Table 2 summarizes the calculated MWD and DB of hyperbranched polymers obtained by SCVP and SCVCP under various conditions. All calculations were conducted, assuming an ideal case, no cyclization (i.e., intramolecular reaction of the vinyl group with an active center), no excluded volume effects (i.e., rate constants are independent of the location of the active center or vinyl group in the macromolecule), and no side reactions (e.g., transfer or termination). 

There have been a few approaches to calculate the effect of cyclization on the MWD [75-77]. Since each cyclization event generates a new multifunctional initiator, it becomes clear that cyclization is expected to narrow the MWD. 

Another major influence on the direction of cyclization is the presence of substituents. Attack at a less hindered position is favored by both steric effects and the stabilizing effect that most substituents have on a radical center. These have been examined by DFT (UB3LYP/6-31+G ) calculations, and the results for 5-hexenyl radicals are shown in Figure 10.14. For the unsubstituted system, the 5-exo chair TS is favored over the 6-endo chair by 2.7kcal/mol. A 5-methyl substituent disfavors the 5-exo relative to the 6-endo mode by 0.7kcal/mol, whereas a 6-methyl substituent increases the preference for the 5-exo TS to 3.3 kcal/mol.322... 

Jug and co-workers investigated the mechanism of cycloaddition reactions of indolizines to give substituted cycl[3,2,2]azines <1998JPO201>. Intermediates in this reaction are not isolated, giving evidence for a concerted [8+2] cycloaddition, which was consistent with results of previous theoretical calculations <1984CHEC(4)443>. Calculations were performed for a number of substituted ethenes <1998JPO201>. For methyl acrylate, acrylonitrile, and ethene, the concerted [8+2] mechanism seems favored. However, from both ab initio and semi-empirical calculations of transition states they concluded that reaction with nitroethene proceeded via a two-step intermolecular electrophilic addition/cyclization route, and dimethylaminoethene via an unprecedented two-step nucleophilic addition/cyclization mechanism (Equation 1). 

Intramolecular inverse electron-demand Diels-Alder reaction of iV-propargyl-2-(pyrimidin-2-yl)pyrrolidine provides an alternative route to pyridopyrrolizines. For example, heating of 130 to 170 °C in nitrobenzene affords the cyclized product with the loss of HCN <1992JOC3000> (Equation 9). The above reference includes molecular orbital (MO) calculations on relative reactivities in this series. 

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