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CH221 CLASS 2 CHAPTER 1: STRUCTURE AND BONDING, CONTINUED Synopsis. This class takes a more detailed look at the covalent bonding of organic molecules (and some important inorganic molecules), especially from the viewpoint of atomic orbital hybridization. Finally, the molecular orbital model is used to describe and bonds, the two most important kinds of covalent bonds found in organic molecules. Ground State and Bonding State Electronic Configurations A glance at carbon, whose ground state electronic configuration is 1s2s22p2, would suggest initially that this element might be bivalent. However, carbon is well known to be tetravalent in the vast majority of its organic compounds, hence it must use the 2s orbital, as well as the three 2p orbitals in its bonding electronic configuration. This means that some sort of energy promotion is required from the ground state: The stability gained by forming 4 bonds, instead of 2, more than compensates for the promotional energy. Hybridization: sp3 Orbitals and Methane From the above picture, it is expected that methane (CH 4) has two kinds of C-H bonds – one type from the carbon 2s orbital and the other kind from the 2p orbitals – but this is not the case. Linus Pauling, in 1931, showed how an s orbital and three p orbitals can combine or hybridize to form four equivalent sp3 hybrid atomic orbitals, that are arranged tetrahedrally about the carbon nucleus. This is illustrated in the diagram overleaf. 2s + 3 x 2p atomic orbitals 4 x sp3 hybrid orbitals A set of 4 sp3 hybrid orbitals Linus Pauling Each sp3 hybrid has asymmetric directionality, and like p orbitals there is one angular node: When the four identical orbitals of an sp3 hybridized carbon atom overlap with the 1s orbitals of four hydrogen atoms, four identical C-H bonds are produced and methane results: Each angle HCH is 109.5o, the so-called tetrahedral angle. Whenever carbon forms four single bonds (“saturated carbon”), the hybridization mode is always sp3, as shown for the saturated hydrocarbon ethane (C2H6), below Ethane is the simplest molecule containing a carbon-carbon bond: it can be represented by several formula types, the most important of which are shown below. H H H H .. .. H:C:C:H CH3CH3 H C C H .. .. H H H H Purely 2-dimensional formulas HH H H C H H C H H H HH H Formulas depicting 3 dimensions (for the eclipsed conformer) The same kind of hybridization is used by carbon in millions of other compounds, including more complex alkanes, the family of hydrocarbons to which methane and ethane belong. More complex alkanes or other organic compounds can be written conveniently as line formulas. These formulas omit the symbols for carbon and hydrogen and show only the carbon-carbon bonds and bonds to heteroatoms (O, N, S, Cl, etc) or to functional groups (OH, NH2, COOCH3, etc). Carbon is assumed to be at line intersections or at the end of lines. Some examples are shown overleaf. Line formula CH3 CH3 CH3CHCH2CHCH3 2,4-Dimethylpentane CH3CH2OCH2CH3 Diethyl ether O O O C CH CH CH.CH 2,4-Cyclopentadienone Hybridization: sp2 Orbitals and the Structure of Ethylene (Ethene) Although sp3 hybridization is the most common electronic bonding state of carbon (saturated carbon), there are many other situations (unsaturated carbon) where carbon uses a different kind of hybridization in its bonding. Such an example is ethylene (ethene), the simplest member of the alkene family of hydrocarbons. Here, the two carbon atoms are linked by a double bond, the molecule is planar and the bond angles are approximately 120 o, giving a trigonal planar structure. In this molecule, each carbon atom forms three equivalent sp 2 hybrids from the 2s orbital and two of the 2p orbitals, leaving a p orbital unperturbed. This is illustrated overleaf. 2s + 2 x 2p atomic orbitals 3 x sp 2 hybrid orbitals A set of 3 sp2 hybrid orbitals A set of 3 sp2 hybrids and a p orbital for each carbon atom of ethylene. The orbital lobes are elongated for clarity. The three sp2 hybrids form the skeleton of ethene, by head-on overlap with another sp2 hybrid (carbon) or 1s orbitals (hydrogen), whilst the p orbitals overlap sideways to form a bond, as shown on the next page. Again, the orbital lobes are deliberately elongated, for clarity. The double bond of ethylene is both shorter and stronger than the C-C single bond of ethane, because it is formed by sharing four electrons, instead of just two. See the table at the end of class1 and Table 1.3 on p. 17 of the textbook. The structure of ethylene is summarized below. Hybridization: sp Orbitals and the Structure of Acetylene (Ethyne) Using similar arguments as for ethane and ethylene, the bonding in the molecule acetylene is illustrated on the next page. Note the presence of a triple bond, formed by the sideways overlap of four p orbitals (two on each carbon atom). The sp skeleton is shown in A, whereas the two bonds are emphasized in B. 2s + 2p atomic orbitals 2 x sp hybrid orbitals A set of 2 sp hybrid orbitals Acetylene is thus a linear molecule with an even shorter and stronger carboncarbon bond than ethylene (see table at the end of class 1 and Table 1.3 on p. 17 of the textbook). Its structure is summarized below. Hybridization and Other Atoms Nitrogen, oxygen and other elements commonly found in organic molecules, also use sp3, sp2 and sp hybrid atomic orbitals to form covalent bonds. Electron pairs in hybrid orbitals that are not used in bonding are called lone pairs or non-bonded pairs, as illustrated for ammonia (NH3) and water (H2O), overleaf. Note that hybridization leads to weaker lone pair-bond pair repulsions, which endows additional stability. The organic derivatives of ammonia (e.g. amines) and of water (e.g. alcohols and ethers) have similar bonding arrangements. Oxygen and nitrogen that are doubly or triply bonded in organic molecules use, like carbon, sp 2 and sp hybrid orbitals, respectively. Class Question What is the hybridization of carbon and, where appropriate, nitrogen and oxygen in the following molecules? Molecular Orbital Theory of Bonding Like valence-bond (VB) theory, molecular orbital (MO) theory recognizes that electrons cannot be localized on a single atom when that atom is part of a molecule. One major difference between the two methods is that MO theory calculates the molecular orbitals that may be produced from the available atomic orbitals. Only after this determination are electrons allocated to molecular energy levels, according to the Aufbau principle and the Pauli exclusion principle. The VB method concentrates on electron pairs from the beginning and determines the energy of various canonical (or resonance) structures, which collectively have all the electrons in the molecule paired in all possible ways. MO theory in essence describes covalent bond formation as arising from a mathematical combination of the wave functions of the atomic orbitals. If the atomic orbital wave functions are in phase, the combination is constructive and results in a bonding molecular orbital (m.o.). On the other hand, if the a.o. wave functions are out of phase, the combination is destructive and leads to an antibonding (*) m.o. Both molecular orbitals are derived by combination of the atomic orbitals, as illustrated for one of the simplest cases, H2, below. For more complex (polyatomic) molecules the picture is much more involved, as shown for methane, overleaf. Thus, any MO description in this course will be largely confined to individual bonds. For example, the bonding and * antibonding m.o. of ethylene, resulting from combination of p atomic orbitals can be represented simply as follows.