Frontier carbon atom

The formulae given above can be illustrated by numerical estimates of the magnitude of the renormalization of the QM parameters and changes in the DMM forces and torques appearing in the vicinity of an sjA carbon atom located on the intersubsystem frontier. The changes in the QM one-center Hamiltonian parameters due to elongation of one of the MM bonds incident to the frontier carbon atom are ... 

On the other hand the changes in the one- and two-electron densities on the HO centered on the frontier atom lead to the following forces and torques acting on the MM atoms immediately bound to the frontier carbon atom ... 

An alternative approach is in terms of frontier electron densities. In electrophilic substitution, the frontier electron density is taken as the electron density in the highest filled MO. In nucleophilic substitution the frontier orbital is taken as the lowest vacant MO the frontier electron density at a carbon atom is then the electron density that would be present in this MO if it were occupied by two electrons. Both electrophilic and nucleophilic substitution thus occur at the carbon atom with the greatest appropriate frontier electron density. 

The LUMO, which is the frontier orbital in reactions with nucleophiles, has a larger coefficient on the /3-carbon atom, whereas the two occupied orbitals are distorted in such a way as to have larger coefficients on oxygen. The overall effect is that the LUMO is relatively low-lying and has a high coefficient on the /3-carbon atom. The frontier orbital theory therefore predicts that nucleophiles will react preferentially at the /3-carbon atom. 

When enantiomerically pure allyl p-tolyl sulfoxide is deprotonated and then treated with electrophilic 2-cyclopentenone, a conjugate addition occurs forming a new carbon-carbon bond with very high control of absolute stereochemistry (equation 25)65. See also Reference 48. Similarly, using more substituted enantiomerically pure allylic sulfoxides leads to virtually complete diastereocontrol, as exemplified by equations 26 and 27 the double bond geometry in the initial allylic sulfoxide governs the stereochemistry at the newly allylic carbon atom (compare equations 26 vs. 27)66. Haynes and associates67 rationalize this stereochemical result in terms of frontier molecular orbital considerations... 

The first paper of the frontier-electron theory pointed out that the electrophilic aromatic substitution in aromatic hydrocarbons should take place at the position of the greatest density of electrons in the highest occupied (HO) molecular orbital (MO). The second paper disclosed that the nucleophilic replacement should occur at the carbon atom where the lowest unoccupied (LU) MO exhibited the maximum density of extension. These particular MO s were called "frontier MO s . In homolytic replacements, both HO and LU.were shown to serve as the frontier MO s. In these papers the "partial" density of 2 pn electron, in the HO (or LU) MO, at a certain carbon atom was simply interpreted by the square of the atomic orbital (AO) coefficient in these particular MO s which were represented by a linear combination (LC) of 2 pn AO s in the frame of the Huckel approximation. These partial densities were named frontier-electron densities . 

The behaviour of the frontier electrons was also attributed to a certain type of electron delocalization between the reactant and the reagent 40). A concept of pseudo-n-orbital was introduced by setting up a simplified model, and the electron delocalization between the 71-electron system of aromatic nuclei and the pseudo-orbital was considered to be essential to aromatic substitutions. The pseudo-orbital was assumed to be built up out of the hydrogen atom AO attached to the carbon atom at the reaction center and the AO of the reagent species, and to be occupied by zero, one, and two electrons in electrophilic, radical, and nucleophilic reactions. A theoretical quantity called "superdelocalizability was derived from this model. This quantity will be discussed in detail later in Chap. 6. 

The reactivity of hydrogens in norbomane towards abstraction is of interest since the difference between two hydrogen atoms attached to the same carbon atom of position 2 can well be explained. The frontier electron density values 105> are in accord with the reactive exo hydrogen (Fig. 7.20). 

In a completely different interpretation Zefirov (242) proposed a new concept of frontier-orbital mixing (243) to explain how conformational and electronic effects in monosubstituted cyclohexanes are transmitted to remote 8-carbon atoms (Scheme 36). The orbitals at C(l) and C(4) in 112 are considered to be equatorial (242). A perturbation at C(l) (H is replaced by X) produces an electron-density shift from H(4) toward C(4) (242), which is associated with an upheld shift of the latter s signal. Although this approach appears to be quite crude and does not account for axial substituents, it deserves fiirther attention. 

An enormous amount of work has been done in this wide field and a number of excellent reviews on different aspects of sulfur electrochemistry has been published [1-7], so here we confine our attention to some principal reactions and interesting apphcations of both anodic and cathodic activation of sulfur-containing molecules. Compared to other chalco-genides, sulfur has frontier orbitals that have volume, symmetry, and energy more suitable for efficient interaction with adjacent carbon atoms. The ionization of molecular sulfur requires about 10 eV. Conjugation of the pz orbitals of sulfur with a 7T-system lowers the ionization potential by ca. 2 eV. For this reason, compounds of divalent sulfur undergo oxidation rather easily often giving rise to cation radicals or dications. The stability of this species is in line with the... 

The diastereoselectivities in the nucleophilic addition reactions of l,3-dioxane-5-ones 37 and l,3-dithiane-5-ones 38 were studied by employing two newly available theoretical tools, the exterior frontier orbital electron (EFOE) density of the 7tc=o -orbitals and the 7t-plane-divided accessible space (PDAS) as quantitative measures of the 7t-facial steric effects <1999CRV1243, 1999CC621, 1999CL1161, 2000H(52)1435, 2001HAC358>. The two parameters predict correctly the experimentally observed stereochemical reversal of 37 and 38 (R = Ph see Table 1) in particular, the PDAS values for both substrates clearly show the opposite steric environment about the carbonyl carbon atom of these heterocyclic ketones and prove sizeable ground-state conformational differences to be responsible for the observed reversed facial stereoselection. 

Note that, upon examination of the AMI linear combination of atomic orbitals (LCAO) coefficients for the two aluminum on poly(/>-phenylenevinylene) systems, the highest occupied molecular orbitals are localized in character. The HOMO and HOMO-1 levels are almost totally localized to the aluminum atoms and to the carbon atoms within the moieties to which the aluminum atoms are attached. The conjugation within the frontier orbitals is thus totally lost... 

In the HMO if> of styrene, the coefficients at the a and / carbon atoms are ca. 0-4 and 0-6 respectively. In the HMO ifi7 of acenaphthylene, the coefficients at carbon atoms 1 and 2 are ca. — 032 and 0-32. Therefore, the directive effect for addition is syn in styrene and anti in acenaphthylene Second, MO calculations may be helpful in new or different systems. With respect to eliminations, Fukui and Fujimoto (1965) used frontier electron theory to provide reactivity indices for two model... 

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