Polyene model, cyclic

Both thermochemical and MO approaches agree that benzene is an especially stable molecule and are reasonably consistent with one another in the stabilization energy which is assigned. It is very significant that MO calculations also show a destabilization of certain conjugated cyclic polyenes, cyclobutadiene in particular. The instability of cyclobutadiene has precluded any thermochemical evaluation of the extent of destabilization. Compounds that are destabilized relative to conjugated noncydic polyene models are called antiaro-maticf ... 

Paldus, J., Takahashi, M., Cho, R.W.H. Coupled-cluster approach to electron correlation in one dimension cyclic polyene model in delocalized basis. Phys. Rev. B 1984, 30, 4267. 

The idea of the ec methodology originated in our studies of semi-empirical cyclic polyene models Cn n with a nondegenerate ground state N —... 

P. Piecuch, J. Cizek, and J. Paldus, Int. ]. Quantum Chem., 42, 165 (1992). Behaviour of the Coupled Cluster Energy in the Strong Correlated Limit of the Cyclic Polyene Model. Comparison with the Exact Results. 

Theoretical calculations of the dependence of the probability of electron tunneling on mutual orientation of donor and acceptor fragments in bridge molecules were presented in Ref. [304], With the use of a cyclic polyene model to construct wave functions of porphyrin fragments, a number of analytical expressions were obtained for orientation dependence of probabilities of tunneling between these fragments. 

Antiaromatic molecules are cyclic systems containing alternating single and double bonds, where the Jt-electron energy of antiaromatic compounds is higher than that of its open-chain counterpart Therefore, antiaromatic compounds are unstable and highly reactive often, antiaromatic compounds distort themselves out of planarity to resolve this instabihty. Antiaromatic compounds fail Hiickel s rale of aromaticity, that is, of (4 -i-2) it-electrons. Compounds that are destabilized relative to conjugated noncychc polyene models are called antiaromatic. 

Since the polyene is cyclic, the zeroth ethylenic unit is the same as the nth while the (n + l)th is just the first. In this model, the exact resonance energy of benzene is 2)3, while asymptotically, the exact resonance energy is... 

Crotonaldehyde, hydrogenation of, 43-48 Cubane, isomerization of, 148 Cyclic dienes, metathesis of, 135 Cyclic polyenes, metathesis of, 135 Cycloalkenes, metathesis of, 134-136 kinetic model, 164 ring-opening polymerization, 143 stereoselectivity, 158-160 transalkylation, 142-144 transalkylidenation, 142-144 Cyclobutane configuration, 147 geometry of, 145, 146 Cyclobutene, metathesis of, 135 1,5,9-Cyclododecatriene, metathesis of, 135... 

The localized many-body perturbation theory (LMBPT) applies localized HF orbitals which are unitary transforms of the canonical ones in the diagrammatic many-body perturbation theory. The method was elaborated on models of cyclic polyenes in the Pariser-Parr-Pople (PPP) approximation. These systems are considered as not well localized so they are suitable to study the importance of non local effects. The description of LMBPT follows the main points as it was first published in 1984 (Kapuy etal, 1983). 

By contrast, the Dewar resonance energy represents solely the contribution coming from the cyclic electron (bond) delocalization since the model reference structure is represented not by a system of isolated 7r-bonds, but by a hypothetical cyclic polyene with the number of tr- and tr-bonds equal to that in a given molecule. Making use of the additivity of bond energies in acyclic polyenes (65JA692), one may calculate the total energy... 

Fano, G., Ortolani, F., Ziosi, L. The density matrix renormalization group method Application to the PPP model of a cyclic polyene chain. J. Chem. Phys. 1998, 108(22), 9246. 

Model the transition states of Reactions (4.1)-(4.4) by the conjugated molecules 8, 9, 10 and 11, and use the PMO method to calculate their resonance energies (defined as the difference between the energy of the cyclic structure and its open chain polyene counterpart). Hence, deduce the feasibility of Reaction (4.1). 

The orbital requirements for radical attack on any polyene are given in Table 6. If H3, HC2 and Cl8 (see Walsh diagram, Fig. 2) can be taken as models, then three-center transition states will be linear. If, however, cyclic transition states can be formed, HMO theory indicates a preference for them (Fig. 1). Unfortunately, attempted radical displacements have not been observed, simply because the radicals take other reaction paths (Pryor, 1966). The transition states may have been linear, but for abstraction from rather than displacement on carbon (Bujake et al., 1961). If the radical and molecule generated in these cases remain in... 

It is possible in principle to deduce from the position of the first absorption band the twisting angle between the double bonds in cyclic conjugated polyenes, e.g. on the basis of a simple LCBO model . This has been attempted for cycloocta-l,3,5-triene 184 and cyclooctatetraene 239. For the former it was deduced that the 7r-system becomes... 

Cicek J, Paldus J. Stability conditions for the solutions of the Hartree-Fock equations for atomic and molecular systems. Application to the pi-electron model of cyclic polyenes. J Chem Phys 1967 47 3976-3985. 

The assumption of an angle of 90° between the a bonds at the metal makes descriptions 44 and 45 equivalent. Model 44 has to be preferred if one constructs the 7T MO s from individual AO s. The (pd)n-overlap integral is not reduced and it leads to the prediction of no cyclic conjugation across the metal. The resulting six-membered linear polyene-type ir system is occupied by eight 7r electrons, i.e. two electrons enter antibonding MO s. 

B and Q bands, but did provide qualitative data on how skeletal variations affect porphyrin absorption spectra. The stage was now set for the strengths of all these theories to be unified. Martin Gouterman did this by using configuration interaction, a technique vital in free electron and cyclic polyene theories, to describe the porphyrin excited states generated by Hiickel theory. He called this new synthesis the four-orbital model. ... 

How can we develop a more quantitative model of these bands One strategy is to model the infinite linear polyene not as a linear combination of smaller polyenes, but rather as an infinite cyclic tt system, -(CH) -. If n really is infinity, there is no difference between a line and a circle (from the viewpoint of electronic structure, that is, but not from the viewpoint of topology ). Recall Eq. 14.56, here restated as Eq. 17.1. This gives the HMO energies for any cyclic polyene, where i is the orbital number and N is the number of vertices (atoms or p orbitals in the cycle [infinity in this case]). In this equation / runs from f = 0, 1, 2... up to N/2 for even Nor (N-l)/2forodd N. As such, this index directly corresponds to the number of nodal planes in the MO. 

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