Conjugated hydrocarbons, electronic

The Hiickel description of aromaticity was based in part on benzene, a cyclic fully conjugated hydrocarbon having (4n -l- 2) -electrons (ff = I) in the closed shell (ring). 

The Huckel method and is one of the earliest and simplest semiempirical methods. A Huckel calculation models only the 7t valence electrons in a planar conjugated hydrocarbon. A parameter is used to describe the interaction between bonded atoms. There are no second atom affects. Huckel calculations do reflect orbital symmetry and qualitatively predict orbital coefficients. Huckel calculations can give crude quantitative information or qualitative insight into conjugated compounds, but are seldom used today. The primary use of Huckel calculations now is as a class exercise because it is a calculation that can be done by hand. 

Aromaticity is usually described in MO terminology. Cyclic structures that have a particularly stable arrangement of occupied 7t molecular orbitals are called aromatic. A simple expression of the relationship between an MO description of stmcture and aromaticity is known as the Hiickel rule. It is derived from Huckel molecular orbital (HMO) theory and states that planar monocyclic completely conjugated hydrocarbons will be aromatic when the ring contains 4n + 2 n electrons. HMO calculations assign the n-orbital energies of the cyclic unsaturated systems of ring size 3-9 as shown in Fig. 9.1. (See Chapter 1, Section 1.4, p. 31, to review HMO theory.)... 

Moffitt, W., Proc. Roy. Soc. [London) A218, 486, The electronic spectra of conjugated hydrocarbons." Allyl radical treated as an example. 

Recently, a nonempirical rr-electron SCF approach was reported and applied to interpretations of spectra of various conjugated hydrocarbon radicals (147). The greatest attention, however, has been paid to radical ions derived from even alternant hydrocarbons (10, 58-60, 63, 125, 135, 148-153). Here, numerous experimental material suitable for systematic testing of the MO methods has been accumulated. In particular, the following sources of experimental data should be mentioned Hamill and collaborators (24) prepared... 

Gygax R, Wirz J, Sprague JT, Allinger NL. Electronic structure and photophysical properties of planar conjugated hydrocarbons with a 4n-membered ring. Part III. Conjugative stabilization in an antiaromatic system The conformational mobility of l,5-bisdehydro[12]annulene. Helv Chim Acta 1977 60 2522-9. 

In order to understand qualitatively how the frontier-electron density, (cconjugated hydrocarbons, it is convenient to take account of Stage III. In this stage it is easily proved that... 

Our interest in carbenes is closely related to our work on conjugated hydrocarbons containing four electrons. The parent molecules of three completely different families within this category are 1,3-cyclobutadiene (1), cyclo-propenylidene (2), and trimethylenemethane (3). 

A new class of conjugated hydrocarbons is that of the fullerenes [11], which represent an allotropic modification of graphite. Their electrochemistry has been studied in great detail during the last decade [126]. The basic entity within this series is the Ceo molecule (23). Because of its high electron affinity, it can be reduced up to its hexaanion (Fig. 4) [14,127]. Solid-state measurements indicate that the radical anion of Ceo reversibly dimerizes. NMR measurements confirm a u-bond formation between two radical anion moieties [128,129]. 

The above discussion was based on the results of molecular dynamics simulations on unsaturated or conjugated hydrocarbons. Although the general features can be extended to molecular structures of more general types, in practice it is appropriate to consider the specific form of the electron orbitals involved. For instance, d d transitions in transition metal ion complexes involve orbitals mainly localized on the metal ion that, in the crystal field... 

In order to perform calculations on larger molecules in a reasonable amount of time, approximations are made, which may involve the neglect of certain terms, or the inclusion of experimentally determined parameters. The best known and simplest example of this level of approximation are Hiickel Molecular Orbital (HMO) calculations, which treat only pi-electrons, in conjugated hydrocarbons, with neglect of overlap (1). While obviously limited in use, HMO methods are still used in certain research applications. 

Since gm is related to the orbital angular momentum vector L the second term is often written in terms of this operator. The first term is the Langevin term it is the expectation value of a one-electron operator 2 (xt2 + jV), and can therefore be obtained directly from the ground-state wavefunction. It has formed the basis for a quite successful additivity scheme, Pascal s rules, which work well except for the conjugated hydrocarbons where non-additivity is ascribed to ring currents. Nevertheless, as it depends on the square of the electron co-ordinates, xL will be sensitive to the basis set used in variational calculations. 

The success of such a description, however, rests upon the assumption that the chemical behavior of conjugated hydrocarbons is solely determined by its n electrons. Its advantage is that only one orbital per carbon atom is involved in the L.C.A.O. calculation, and the hydrogen Is orbitals can be neglected altogether. 

Quite apart from their singular topology, the fullerenes are distinguished from other conjugated hydrocarbons by their non-planarity. The geometrical aspects of fullerene formation as it relates to pyramidalization of the constituent carbon atoms has been recognized for some time (Haddon et al. 1986 Haddon 1988). Here we consider the effect of non-planarity on the electronic structure of the carbon atoms as it arises in the fullerenes (Haddon et al. 1986 Haddon 1992). 

Photochemistry of conjugated hydrocarbons can be rationalized by the common electronic and molecular structure of the surface crossing between a covalent excited state and the ground state. 

Three-Electron Conical Intersections of Conjugated Hydrocarbons... 

Polycyclic aromatic hydrocarbons contain extended conjugated rc-electron systems and are electroactive within the cathodic potential window of many organic sol-vent/tetraalkylammonium electrolyte combinations. For many of them reduction potentials were measured and reported. It is important to note that the reduction of polycyclic aromatics involves consecutive electron-transfers and protonations. The nature of the product depends on the number of electrons and protons consumed and higher numbers result in more hydrogenated, less conjugated and thus less electroactive products. A simplified reduction scheme for polycyclic aromatics is shown below. The products are divided into three groups (A) are reduced within the potential window and (B) require drastic reduction conditions as those described for the substrates in Chapt. 3. 

In a conjugated hydrocarbon, each carbon atom provides one it electron. Thus, for neutral systems, the number of atoms and the number of it electrons are identical. 

SAD Spin-alternant determinant. The VB determinant with one electron per site and with alternating spins. Other terms describing the same determinant are the quasiclassical (QC) state, and the antiferromagnetic (AF) state. In nonalternant hydrocarbons, where compete spin alternation is impossible, the determinant is called MS AD, namely, the maximum spin-alternating determinant. The SAD MSAD are the leading terms in the wave function of molecules with one electron per site, for example, conjugated hydrocarbons. In radicals (e.g., allyl radical) the SAD is the root cause of spin polarization (i.e., negative spin densities flanked by positive ones). See Chapters 7 and 8. 

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