>> Key Terms (indicated in blue within the text below):

axial bond dipole dsp3 d2sp3 electron spin resonance spectroscopy equatorial heteronuclear infrared spectroscopy

linear molecular geometry nonpolar octahedral permanent dipole moment pi () bond planar triangle polar sigma () bond

sp sp2 sp3 tetrahedral trigonal bipyramid valence shell electron pair  repulsion (VSEPR) theory

Not every molecule fits nicely into a Lewis structure. Oxoacids, for example, have skeletal structures in which the hydrogen is bonded to oxygen rather than to the central atom. Many central atoms expand their octets to 10 or 12 electrons. Only atoms with d orbitals (all atoms with Z > 12 have d orbitals available although not all use them) can expand their octets. These atoms expand their octets to lower their formal charge. Other atoms may have deficient octets. For example, boron may have only six electrons. The other atoms that may have a deficient octet are beryllium (four electrons) and aluminum (six electrons). Although these two atoms normally form ionic bonds, both are metalloids, so the division between ionic and covalent bonds is not distinct. Therefore the character of these bonds may be considered covalent.

Another type of molecule that does not lend itself to a traditional Lewis structure is a molecule with an odd number of electrons. If the total number of electrons is an odd number, it is impossible for every atom to have an octet; one atom will only have seven electrons. The least electronegative atom is the atom most likely to have only seven electrons. The bonding theory that deals best with molecules with an odd number of electrons is molecular orbital theory.

Molecular orbital theory of heteronuclear (two types of atoms) diatomic molecules skews the diagram. The more electronegative atom is lower is energy, so its atomic orbitals are closer to the bonding molecular orbitals. The atomic orbitals of the less electronegative atom are closer in energy to the antibonding molecular orbitals. Molecular orbitals close to an atomic orbital are said to have more of that atom's character. Since electrons fill from lowest (bonding) energy level to highest, the odd and unpaired electron will be in an orbital that has the character of the less electronegative atom. Thus, regardless of whether Lewis theory or molecular orbital theory is used, the odd electron is associated with the less electronegative atom.

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The presence of the unpaired electron can be detected with electron spin resonance spectroscopy. An experienced spectroscopist can even tell which atom the unpaired electron is associated with. This technique supports the prediction from molecular orbital theory.

Another technique used to test bonding theory is infrared spectroscopy. This technique measures the energy of bond vibrations. Double bonds require more energy to vibrate than single bonds (and less than triple bonds). This technique can then experimentally verify the predictions of Lewis and molecular orbital theory.

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Lewis structures only show which atoms are bonded to which. They do not determine how these atoms are arranged in space (molecular geometry). One theory that does predict molecular geometry is the valence shell electron pair repulsion (VSEPR) theory. In VSEPR theory each group of electrons tries to be as far from the other groups as possible. A group of electrons is a lone pair, a single bond, double bond, or triple bond. If there are two groups of electrons, the groups will be 180° from each other, and the shape is linear (Figure 7.19). The shape of three groups is a planar triangle with bond angles of 120° (Figure 7.18). Four groups of electrons form a tetrahedral geometry with an angle between the bonds of 109.5° (Figure 7.17). If there are five groups of electrons, the shape is a trigonal bipyramid. A trigonal bipyramid has two positions, axial positions are 90° from the equatorial positions, which are 120° from each other (Figure 7.21). Six groups of electrons form an octahedral, where each group is 90° from the others (Figure 7.20).

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These basic shapes are the orientation of the groups of electrons. However, molecular geometry describes the orientation of the atoms. Since lone pairs do not have another atom at the end, they are not part of the molecular geometry. They do, however, influence it, since they are one of the repelling groups. In fact, the repulsion generated by a lone pair is greater than that of a bond, making the angles between bonds even smaller than that described previously.

The greater repulsion of electrons affects the position of lone pairs. In a trigonal bipyramid there are two types of positions. Lone pairs position themselves in the equatorial positions because they are further from the other groups than the axial positions. In an octahedral orientation, although all positions are initially the same, if there is an even number of lone pairs, those pairs will be opposite (180°) from each other.

Molecular geometries, with and without lone pairs, are summarized in Table 7.2.

Another theory that predicts molecular geometry is valence bond theory. Valence bond theory predicts that atomic orbitals hybridize (mix to become all the same) when part of a molecule. When orbitals overlap, they form a bond. The more they overlap, the stronger the bond. When orbitals overlap end on, they form a sigma () bond. When orbitals overlap sideways, they form a pi () bond. (This is similar to the and bonding of molecular orbital theory.) A single bond in a Lewis structure is a bond. A double bond is a and a bond and a triple bond is a and two bonds.

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The molecular geometry is predicted from the hybridization of the central atom. (All atoms in a molecule hybridize, but the shape of the molecule as a whole is determined by the central atom.) One atomic orbital for each lone pair and each bond (regardless of whether it is a single, double, or triple bond) will hybridize. If two atomic orbitals hybridize, both orbitals become sp orbitals and exist 180° from each other (Figures 7.26 and 7.27). Thus, sp hybridization produces a linear shape. (Just like two groups of electrons in VSEPR theory!) The hybridization of three atomic orbitals is sp² with planar triangle shape (Figures 7.24 and 7.25) and 120° separation between orbitals and sp³ hybridization and tetrahedral geometry results from the hybridization of four orbitals (Figure 7.23A). If five atomic orbitals hybridize, the hybridization is dsp³. There are no more p orbitals to hybridize. Also, if there are five hybrid orbitals, the atom must have expanded its octet. Therefore valence bond theory explains why only atoms with available d orbitals expand their octet. Therefore dsp³ hybridizes in a trigonal bipyramid orientation and d²sp³ hybridizes as an octahedral orientation (Figure 7.29).

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Atoms of greater electronegativity have a greater attraction on the electrons of the bond, forming a bond dipole. Within a molecule the sum of these bond dipoles might cancel when the dipoles are equal and opposite, creating a molecule that is nonpolar overall. If the bond dipoles do not cancel, there will be a net dipole on the overall molecules, creating a permanent dipole moment. The polar (or nonpolar) nature of a molecule determines many of its chemical and physical properties.

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