Molecular orbitals phasing

The relative acidities in the gas phase can be detennined from ab initio or molecular orbital calculations while differences in the free energies of hydration of the acids and the cations are obtained from FEP sunulations in which FIA and A are mutated into FIB and B A respectively. 

Valence bond and molecular orbital theory both incorporate the wave description of an atom s electrons into this picture of H2 but m somewhat different ways Both assume that electron waves behave like more familiar waves such as sound and light waves One important property of waves is called interference m physics Constructive interference occurs when two waves combine so as to reinforce each other (m phase) destructive interference occurs when they oppose each other (out of phase) (Figure 2 2) Recall from Section 1 1 that electron waves m atoms are characterized by their wave function which is the same as an orbital For an electron m the most stable state of a hydrogen atom for example this state is defined by the Is wave function and is often called the Is orbital The valence bond model bases the connection between two atoms on the overlap between half filled orbifals of fhe fwo afoms The molecular orbital model assembles a sef of molecular orbifals by combining fhe afomic orbifals of all of fhe atoms m fhe molecule... 

Let us now examine the Diels-Alder cycloaddition from a molecular orbital perspective Chemical experience such as the observation that the substituents that increase the reac tivity of a dienophile tend to be those that attract electrons suggests that electrons flow from the diene to the dienophile during the reaction Thus the orbitals to be considered are the HOMO of the diene and the LUMO of the dienophile As shown m Figure 10 11 for the case of ethylene and 1 3 butadiene the symmetry properties of the HOMO of the diene and the LUMO of the dienophile permit bond formation between the ends of the diene system and the two carbons of the dienophile double bond because the necessary orbitals overlap m phase with each other Cycloaddition of a diene and an alkene is said to be a symmetry allowed reaction... 

The most extensive calculations of the electronic structure of fullerenes so far have been done for Ceo- Representative results for the energy levels of the free Ceo molecule are shown in Fig. 5(a) [60]. Because of the molecular nature of solid C o, the electronic structure for the solid phase is expected to be closely related to that of the free molecule [61]. An LDA calculation for the crystalline phase is shown in Fig. 5(b) for the energy bands derived from the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) for Cgo, and the band gap between the LUMO and HOMO-derived energy bands is shown on the figure. The LDA calculations are one-electron treatments which tend to underestimate the actual bandgap. Nevertheless, such calculations are widely used in the fullerene literature to provide physical insights about many of the physical properties. 

Unlike the stable molecule N2O, the sulfur analogue N2S decomposes above 160 K. In the vapour phase N2S has been detected by high-resolution mass spectrometry. The IR spectrum is dominated by a very strong band at 2040 cm [v(NN)]. The first ionization potential has been determined by photoelectron spectroscopy to be 10.6 eV. " These data indicate that N2S resembles diazomethane, CH2N2, rather than N2O. It decomposes to give N2 and diatomic sulfur, S2, and, hence, elemental sulfur, rather than monoatomic sulfur. Ab initio molecular orbital calculations of bond lengths and bond energies for linear N2S indicate that the resonance structure N =N -S is dominant. 

Among the diatomic molecules of the second period elements are three familiar ones, N2,02, and F2. The molecules Li2, B2, and C2 are less common but have been observed and studied in the gas phase. In contrast, the molecules Be2 and Ne2 are either highly unstable or nonexistent. Let us see what molecular orbital theory predicts about the structure and stability of these molecules. We start by considering how the atomic orbitals containing the valence electrons (2s and 2p) are used to form molecular orbitals. 

Figure 2.14. The molecular orbitals of gas phase carbon monoxide, (a) Energy diagram indicating how the molecular orbitals arise from the combination of atomic orbitals of carbon (C) and oxygen (O). Conventional arrows are used to indicate the spin orientations of electrons in the occupied orbitals. Asterisks denote antibonding molecular orbitals, (b) Spatial distributions of key orbitals involved in the chemisorption of carbon monoxide. Barring indicates empty orbitals.5 (c) Electronic configurations of CO and NO in vacuum as compared to the density of states of a Pt(lll) cluster.11 Reprinted from ref. 11 with permission from Elsevier Science.

According to frontier molecular orbital theory (FMO), the reactivity, regio-chemistry and stereochemistry of the Diels-Alder reaction are controlled by the suprafacial in phase interaction of the highest occupied molecular orbital (HOMO) of one component and the lowest unoccupied molecular orbital (LUMO) of the other. [17e, 41-43, 64] These orbitals are the closest in energy Scheme 1.14 illustrates the two dominant orbital interactions of a symmetry-allowed Diels-Alder cycloaddition. 

The bonding orbitals and of ethylenes are combined in phase to be the lowest TZ molecular orbitals (tTj) of butadiene (Scheme 18). The out-of-phase combined orbital (jtj) is the highest occupied molecular orbital (HOMO). The in-phase combination of... 

The energies, the phases and the amplitudes of the tz molecular orbitals of butadiene are shown in Scheme 19. The, n, and orbitals corresponds to half, one,... 

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