Delocalized LUMO

PPDs donate hydrogen atoms while QDI reacts generally by addition to the radical. Examining the LUMO orbitals of PPD and QDI rationalizes one source of the large difference in reactivity. The reaction site of the PPD will be the LUMO of the H atom attached to the N atoms. While for QDI the delocalized LUMO in the conjugated diimine ring is the reaction site. These are shown in Figure 16.1. 

Figure 4.23 shows one example of the interaction of LUMOs (T/ and W ) to form new supermolecular orbitals that are delocalized over the complex. If the HOMOs are too far apart in energy to interact, as in this example, then they will of course remain localized on the partner molecules excitation of an electron from a localized HOMO to a delocalized LUMO results in partial... 

In contrast with the substitution inert character of the M-NO bond, the assignment of bound NO + as an electrophilic moiety predicts that the delocalized LUMO in MNO may be the site of attack for a variety of nucleophiles, as described by Equation 7.4 ... 

The most important classes of functionalized [60]fullerene derivatives, e.g. methanofullerenes [341, pyrrolidinofullerenes [35], Diels-Alder adducts [34i] and aziridinofullerene [36], all give rise to a cancellation of the fivefold degeneration of their HOMO and tlireefold degeneration of their LUMO levels (figure Cl.2.5). This stems in a first order approximation from a perturbation of the fullerene s 7i-electron system in combination with a partial loss of the delocalization. 

Molecular orbitals are useful tools for identifying reactive sites m a molecule For exam pie the positive charge m allyl cation is delocalized over the two terminal carbon atoms and both atoms can act as electron acceptors This is normally shown using two reso nance structures but a more compact way to see this is to look at the shape of the ion s LUMO (the LUMO is a molecule s electron acceptor orbital) Allyl cation s LUMO appears as four surfaces Two surfaces are positioned near each of the terminal carbon atoms and they identify allyl cation s electron acceptor sites... 

In order for a substitution to occur, a n-complex must be formed. The term a-complex is used to describe an intermediate in which the carbon at the site of substitution is bonded to both the electrophile and the hydrogen that is displaced. As the term implies, a a bond is formed at the site of substitution. The intermediate is a cyclohexadienyl cation. Its fundamental structural characteristics can be described in simple MO terms. The a-complex is a four-7t-electron delocalized system that is electronically equivalent to a pentadienyl cation (Fig. 10.1). There is no longer cyclic conjugation. The LUMO has nodes at C-2 and C-4 of the pentadienyl structure, and these positions correspond to the positions meta to the site of substitution on the aromatic ring. As a result, the positive chargex)f the cation is located at the positions ortho and para to the site of substitution. 

Compare atomic charges and electrostatic potential maps for the three cations. For each, is the charge localized or delocalized Is it associated with an empty a-type or Tt-type orbital Examine the lowest-unoccupied molecular orbital (LUMO) of each cation. Draw all of the resonance contributors needed for a complete description of each cation. Assign the hybridization of the C" atom, and describe how each orbital on this atom is utilized (o bond, n bond, empty). How do you explain the benzene ring effects that you observe ... 

Another useful way to think about carbon electrophilicity is to compare the properties of the carbonyls lowest-unoccupied molecular orbital (LUMO). This is the orbital into which the nucleophile s pair of electrons will go. Examine each compound s LUMO. Which is most localized on the carbonyl group Most delocalized Next, examine the LUMOs while displaying the compounds as space-filling models. This allows you to judge the extent to which the LUMO is actually accessible to an approaching nucleophile. Which LUMO is most available Least available ... 

Consider now the rr-system in benzene. The MO approach will generate linear combinations of the atomic p-orbitals, producing six rr-orbitals delocalized over the whole molecule with four different orbital energies (two sets of degenerate orbitals). Figure 7.3. The stability of benzene can be attributed to the large gap between the HOMO and LUMO orbitals. 

The frontier orbital theory [7-9] assumes that the stabihzation by the electron delocalization could control chemical reactions. The stabilization comes from the interactions between the occupied molecular orbitals of one molecule and the unoccupied molecular orbitals of another (Sect. 1.4). The strong interaction occurs when the energy gap is small (Sect. 1.3). The HOMO and the LUMO are the closest in energy to each other. The HOMO-LUMO interaction, especially the interaction between the HOMO of electron donors and the LUMO of electron acceptors, controls the chemical reactions (Scheme 20). The HOMO and the LUMO are termed the frontier orbitals. ... 

Molecules have some occupied and some unoccupied orbitals. There occur diverse interactions (Scheme 1) when molecules undergo reactions. According to the frontier orbital theory (Sect 3 in Chapter Elements of a Chemical Orbital Theory by Inagaki in this volume), the HOMO d) of an electron donor (D) and the LUMO (fl ) of an electron acceptor (A) play a predominant role in the chemical reactions (delocalization band in Scheme 2). The electron configuration D A where one electron transfers from dio a significantly mixes into the ground configuration DA where... 

Thermal dimerization of ethylene to cyclobutane is forbidden by orbital symmetry (Sect 3.5 in Chapter Elements of a Chemical Orbital Theory by Inagaki in this volume). The activation barrier is high E =44 kcal mof ) [9]. Cyclobutane cannot be prepared on a preparative scale by the dimerization of ethylenes despite a favorable reaction enthalpy (AH = -19 kcal mol" ). Thermal reactions between alkenes usually proceed via diradical intermediates [10-12]. The process of the diradical formation is the most favored by the HOMO-LUMO interaction (Scheme 25b in chapter Elements of a Chemical Orbital Theory ). The intervention of the diradical intermediates impfies loss of stereochemical integrity. This is a characteric feature of the thermal reactions between alkenes in the delocalization band of the mechanistic spectrum. 

The primary delocalization occurs from tz of alkenes to of ketenes (Scheme 25). The pseudoexcitations occur through the HOMO-HOMO and LUMO-LUMO interactions (Scheme 4). The HOMO of the donors is n as usual, whereas the HOMO of the acceptors is not but The HOMO-HOMO interaction occurs between the C=C bonds of alkenes and ketenes and promotes the reaction accross the C=C bond of ketenes. The important DA configuration is the intramolecular... 

As is outlined for ene reactions of singlet oxygen in Scheme 15, the prototypical ene reaction starts with the electron delocalization from the HOMO of propene to the LUMO of X=Y. The delocalization from the HOMO, a combined n and orbital with larger amplitude on n, leads to a bond formation between the C=C and X=Y bonds. Concurrent elongation of the bond enables a six-membered ring transition stracture, where partial electron density is back-donated from the LUMO of X=Y having accepted the density, to an unoccupied orbital of propene localized on the bond. As a result, the partial electron density is promoted (pseudoex-cited) from the HOMO (it) to an unoccupied orbital (ct n ) of alkenes. This is a reaction in the pseudoexcitation band. 

Strong donor-acceptor interaction shifts the reaction from the pseudoexcitation band to the transfer band. Electrons delocalize from the HOMO of propene to the LUMO of X=Y too much to form a bond between the double bonds. One electron transfers and a radical ion pair forms. The negatively charged X=Y... 

The orientation of the reactions of EDG-substituted benzenes is determined by delocalization from EDG to E via B. The delocalization contains the cyclic interactions of the electron-donating orbital (edg) of EDG, electron-accepting orbital (e ) of the electrophile, and the HOMO (b) and the LUMO (b ) of the benzene ring (Scheme 17). For the ortho and para orientations, the delocalization is favored by the orbital phase... 

Fukui applied the orbital mixing rule [1,2, 59] to the orbital hybridization or the deformation of the LUMO of cyclohexanone to explain the origin of the Jt-facial selectivity in the reduction of cyclohexanone. Cieplak [60] proposed that electron delocalization occurs from the bonds into the o orbital of the incipient bonds at the transition state. 

As described before, the rr-electrons of porphyrin are delocalized over the molecule and the energy levels of the HOMO and the LUMO are high and low, respectively. The resultant narrow intramolecular HOMO-LUMO gap causes absorption of the entire region of visible light. Usually, porphyrins are red to purple and phthalocyanines are blue to green. Furthermore, the long lifetime of their excited states is appHcable to the construction of photo-induced electron and/or energy transfer systems. 

Conjugation of the 7t-electrons of the carbon-carbon double bond with the LUMO sulfur 3d-orbitals would be expected to stabilize the Hiickel 4n -I- 2 (n = 0) array of n-electrons in the thiirene dioxide system. No wonder, therefore, that the successful synthesis of the first member in this series (e.g. 19b) has initiated and stimulated several studies , the main objective of which was to determine whether or not thiirene dioxides should be considered to be aromatic (or pseudo-aromatic ) and/or to what extent conjugation effects, which require some sort of n-d bonding in the conjugatively unsaturated sulfones, are operative within these systems. The fact that the sulfur-oxygen bond lengths in thiirene dioxides were found to be similar to those of other 802-containing compounds, does not corroborate a Hiickel-type jr-delocalization... 

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