Ethene natural bond orbitals

Similarly, the orbitals determined in both semiempirical and Hartree-Fock calculations may be transformed into natural bond orbitals (NBOs), which provide pictures of localized bonds and lone pairs that correspond closely with Lewis structure bonding models. " For example. Figure 4.53 shows the NBOs for ethene cch/ o ccr ai d ncc bonds. 

FIGURE 4. Basis orbitals for (planar) cycloalkanes with ring size n. Basis orbitals comprise the radially oriented spi and spo hybrid orbitals at C, the tangentially oriented Pip (in plane) and Pop (out of plane) orbitals at C as well as in-phase and out-ofphase combinations of the two 1 s(H) orbitals, which combine with spo t and pop orbitals, respectively. Note that ethene is included as a two-membered ring where the ring is symbolized by two bent bonds and the CH bonds are shown to define the orientation of the ring plane (parallel to the drawing plane). The nature of each orbital set (c or n,... 

The presence of the k bond confers properties on an alkene that mark it out as different from an alkane. In particular, the n bond, by the nature of its sideways overlap of the constituent p orbitals, is weaker than a a bond. Moreover, the electrons of the n bond are relatively exposed, above and below the plane of the alkene. These electrons are the source of reactivity of the alkene toward electrophiles, as in, say, electrophilic addition of bromine (Chapter 4). The n bond in ethene (and other alkenes) is, however, sufficiently strong that it prevents rotation around the carbon-carbon a bond, which is a well-documented property of the carbon-carbon bond in ethane (Section 1.6). The bonding between sp2... 

The hybridization concept indicates some additional aspects of molecular stmcture. The tetrahedral, trigonal, and digonal natures of sp, sp, and sp carbon atoms provide an approximation of bond angles. The idea that tt bonds are formed by the overlap of p orbitals puts some geometrical constraints on structure. Ethene, for example, is planar to maximize p-orbital overlap. Allene, on the other hand, must have the terminal CH2 groups rotated by 90° to accommodate two tt bonds at the central sp carbon. 

The two sides of alkenes are due to the nature of the four-electron double bond. In the simplest picotre, we assign two of its electrons to a basic, garden-variety CT bond between the atoms. The other two electrons are then placed in two parallel p orbitals, overlapping sideways to fomi the ir bond. This tr-type overlap prevents the carbons at each end of the double bond from rotating with respect to one another. Ethene, therefore, is a perfectly flat molecule, and, in general, the carbons of the alkene functional group and all the atoms attached to them will lie in a plane, with the n electrons above and below. 

In order to illustrate the nature and some of the limitations of the HMO procedure, we will begin with a very simple n molecular system, that of ethene. As shown in Figure 4.1, the HMO model uses the (r,n formulation for carbon-carbon double bonds. We assume that two carbon atoms are close enough to each other that a carbon-carbon cr bond can be formed through overlap of an sp hybrid orbital on each. The other two sp orbitals on each carbon atom are used to form C-H bonds. Each carbon atom has a remaining p orbital that is perpendicular to the plane defined by the sp orbitals. It is the interaction of the two p orbitals that will produce the n molecular orbitals. Note that in HMO theory we assume that the a and n systems may be treated separately and that the specific case of two p orbitals produces equation 4.2. 

Description of the electronic stmcture of molecules by using this molecular orbital model provides important information about the nature of molecules. One of the most important pieces of information is the electron density distribution. While in a -bonds the electron density is largest between the atoms i.e. along the line of the chemical bond in % bonds the electron density is concentrated not between the atoms but above and below the plane which contains the bond line . This is represented in the next figure, hi an ethane molecule, which possess only a -bonds, the electron cloud is situated between the C-atoms. However, in the ethene molecule, with a x-bond, the electron density is highest above and below the plane in which all the atoms are located. Electron clouds in ethene are not blocked by the atoms and are situated on the open side of the molecule where other particles can attack it. Consequently an ethene molecule is much more chemically reactive then ethane. 

Problem 7.13 In the example of ethene, the two pj orbitals perpendicular to the molecular plane form orbitals of a r-bonding nature. For more complex alkenes we can treat the <7-orbital system and r-orbitals separately, as they will not mix by symmetry. The 3T-orbitals usually also contain the chemically important frontier (HOMO and LUMO) orbitals. In this problem we will treat just the p -orbitals of hexatriene and derive the relavant MOs. 

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