Orbitals of Ethene

A MO can contain 0, 1, or 2 electrons. The bonding MO, tc, in ethene has two paired electrons the antibonding orbital of ethene, ti, is empty. 

The side-by-side overlap of two 2p orbitals in ethene leads to two molecular orbitals. Constructive overlap gives the bonding n, molecular orbital. The destructive overlap of the two orbitals gives a higher energy, antibonding molecular orbital, ti.  

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Formation of a <7-bond by donation from the 7r-orbital of ethene into a vacant metal dsp2 hybrid orbital... 

The n orbital of ethene mixes a bonding orbital lying below out of phase, and the high-lying n orbital in phase with (7 (Scheme 5, cf. Scheme 3d). The in-phase and out-of-phase relations are placed where the strongest interactions occur, or between and the p orbital on the closer carbon (C ) in n and n. The phase relation between rand tv is uniquely determined. The signs of p orbitals in trand tr are the same on Cj and opposite on C. The r amplitude increases on C, and decreases on C. It follows that the HOMO of propene has large amplitude on C,. 

Figure 7.8 Thedouble bond of ethene (C2H4). The vertical p orbitals of ethene form a pi bond, while the horizontal sp orbitals form a sigma bond.

The simplest model of this kind—and admittedly a rather naive one—is to choose two-centre 7r-orbitals 7r(t as basis functions. The prototype for the jc is the -orbital of ethene. Because ejection of an electron from this orbital yields the low-energy band, at /[ = 10.5 eV, in the ethene PE spectrum shown in Figure 4, A = —I = —10.5 eV is... 

As can be seen from Table 2, the amount of s-character of the CH hybrid orbital of 1 is indeed increased relative to that of the CH hybrid orbitals of ethene, ethane and methane while at the same time the s-character of the CC hybrid orbitals is decreased. This seems to confirm predictions based on model calculations with orthogonal hybrid orbitals. However, closer inspection of the data in Table 2 reveals that s-character of the CH hybrid... 

The 32-electron dinuclear species MRh(/t-CO)2Cpf [114, M = Co (166) 115, M = Rh (166,167) and 116, M = Ir (110,168) ] contain short M-Rh separations, consistent with the presence of a formal double bond. Theoretical studies on Rh2( -CO)2Cp2 (112) reveal that it possesses an acceptor 2b2 and a donor 3a similar in character to the n and n orbitals of ethene. Complexes 114-116 react readily with a variety of ML fragments that are iso-labal with CH2, to afford trinuclear clusters (27,110,166), and several Rh-Pt... 

These three views of the ethylene molecule emphasize different aspects of the disposition of shared electron pairs in the various bonding orbitals of ethene (ethylene), (a) The backbone structure consisting of sigma (a) bonds formed from the three sp2-hybridized orbitals on each carbon, (b) The % (pi) bonding system formed by overlap of the unhybridized pz orbital on each carbon. The pi orbital has two regions of electron density extending above and below the plane of the molecule, (c) A cutaway view of the combined sigma and pi system. 

The comparison of the energies of a-, a -, 77- and 77 -orbitals of ethene is shown in Fig. 8.6. The bonding electrons are placed in the two orbitals with lowest energies, ct and 77, in the ground state of ethene. The 77-orbital is the highest occupied molecular orbital (HOMO) and 77 -orbital is the lowest unoccupied molecular orbital (LUMO). Both HOMO and LUMO are referred to as frontier orbitals (see FMO theory ) and are used in analyzing pericyclic reactions. 

The stabilization of benzene can be placed on a semiquantitative scale. If we define the stabilization of one electron in the pi orbital of ethene as P, then the stabilization of two electrons in a double bond is just 2p. The stabilization of six pi electrons in three double bonds is 6p. Benzene s MO energy levels are at 2p, ip, ip, and -Ip,-ip, -2P the first three are filled with two electrons each for a stabilization of 8p total (2 x 2p + 4 X ip). The six electrons of benzene pi loop are then 2p more stabilized than the six electrons in three isolated double bonds. 

Figure 7.5 Molecular orbitals of ethene and buta-1,3-diene...

A major factor is the absence of an electrophilic component, that is, a species with a low-lying LUMO. The energy of for of allyl anion lies well above the tt orbital of ethene. ... 

Let s review how the tt molecular orbitals of ethene are constructed. An MO description of ethene is shown in Figure 7.8. The twop orbitals can be either in-phase or out-of-phase. (The different phases are indicated by different colors.) Notice that the number of orbitals is conserved—the number of molecular orbitals equals the number of atomic orbitals that produced them. Thus, the two atomic p orbitals of ethene overlap to produce two molecular orbitals. Side-to-side overlap of in-phase p orbitals (lobes of the same color) produces a bonding molecular orbital designated i/ i (the Greek letter psi). The bonding molecular orbital is lower in energy than the p atomic orbitals, and it encompasses both carbons. In other words, each electron in the bonding molecular orbital spreads over both carbon atoms. 

A comparison of the energy levels of the IT molecular orbitals of ethene, 1,3-butadiene, 1,3,5-hexatriene, and benzene. 

Q Derive expressions for the wavefunctions and energies of the Huckel molecular orbitals of ethene. 

Figure 8.29 The bonding and antibonding HQckel moiecuiar orbitals of ethene...

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