LOCALIZED ELECTRON (LE) THEORY I. LEWIS STRUCTURES A. Background. Lewis structures (named for G.N. Lewis) provide a two-dimensional picture of bonding in covalent compounds. They are based on the theory (commonly known as the octet rule) that stable atoms have eight electrons in their outmost shell. While there are notable exceptions to this rule, it is a useful starting point when considering bonding in covalent compounds. An abbreviated approach for drawing Lewis structures for covalent molecules is given below. For a more comprehensive overview of Lewis structures see Zumdahl, pg. 375 – 388. B. Drawing Lewis Structures 1. Identify the “central” atom. If the identity of the central atom is not obvious, place the least electronegative atom in the center. Organic molecules (those that contain carbon) do not always have a single central atom. In such cases, there will usually be two or more “centers” to the molecule, arranged in a chain. 2. Find the total number of valence electrons given by all atoms in the molecule (the number of valence electrons is equal to the group number of the element). For polyatomic cations (i.e. NH4+), decrease the number of electrons by the charge on the ion. For polyatomic anions (i.e. SO42-), increase the number of electrons by the charge on the ion. 3. Draw a single bond from the central atom to each of the surrounding atoms. Each single bond uses two of the available valence electrons. 4. Arrange the remaining valence electrons in pairs to achieve an octet around each atom in the structure. Represent each electron pair, also known as a lone pair, as a pair of dots (:). Do this for the surrounding atoms first; then place any leftover electron pairs around the central atom. Check to make sure that each atom is surrounded by 8 electrons. (See below for exceptions to this rule). 5. If the central atom has fewer than 8 electrons after step 4, make multiple bonds by changing a lone pair from a surrounding atom into a bonding pair. Indicate a double bond by using two dashes between atoms. Indicate a triple bond by using three dashes. C. Exceptions to the octet rule: 1. Hydrogen: Because hydrogen only utilizes a 1s orbital, it can be surrounded by at most 2 electrons (duet rule). As such, hydrogen will never act as a central atom or be surrounded by lone pairs. 2. Boron and Beryllium: When acting as a central atom in a molecule, these atoms are often electron deficient. As such, they typically have fewer than 8 electrons surrounding them.
3. Atoms in period 3 or higher: These atoms may exceed the octet rule, as it is possible for them to expand the valence shell to include empty d orbitals. Since elements in periods 1 and 2 do not have available d orbitals, only those from period 3 or higher may have more than an octet. D. Resonance. Resonance occurs when more than one valid Lewis structure is possible for a given molecule. It is necessary to incorporate resonance due to the limitation of Lewis structures to correctly represent bonding in a molecule. 1. Same atomic arrangement (i.e. same central atom) 2. Differ in arrangement of electrons 3. Actual bonding = average of all possible resonance structures 4. Molecules that exhibit resonance often: a. Contain multiple bonds b. Can utilize an expanded octet (period 3 or higher) 5. Types of resonsance: a. Equivalent (having the same number of single and multiple bonds) b. Non-equivalent (having different numbers of single and multiple bonds). .
II. VSEPR A. VSEPR. VSEPR stands for Valence Shell Electron Pair Repulsion. The idea is that the most probable 3-D arrangement of atoms in a molecule is one that minimizes electron repulsion. This is accomplished by arranging electron pairs (bonding and non-bonding) as far apart as possible from each other. See Zumdahl, pg. 389 – 400 for a complete discussion of VSEPR. B. Determining Molecular Shape 1. Draw the correct Lewis structure. 2. Identify the correct geometric family (Table 1) by counting the total number of electron pairs surrounding the central atom. For VSEPR, double and triple bonds count as a single electron pair.
Table 1. Geometric Families and Hybrid Orbitals TOTAL ELECTRON PAIRS
120° and 90°
3. Identify the correct molecular geometry by counting the number of non-bonding electron pairs around the central atom (Table 2). Table 2. Molecular Geometry TRIGONAL PLANAR Trigonal Planar
GEOMETRIC FAMILY TRIGONAL TETRAHEDRAL BIPYRAMIDAL Trigonal Tetrahedral Bipyramidal Trigonal See-Saw Pyramidal
# NON-BONDING ELECTRON PAIRS
OCTAHEDRAL Octahedral Square Pyramidal
III. HYBRID ORBITALS A. Definition:. orbitals that result from cross breeding of valence shell atomic orbitals (s, p, d, f) of a given energy level (n = 2, n = 3, etc). Since conventional atomic orbitals (s, p, d, f) do not allow for the bond angles observed when VSEPR is applied, hybrid orbitals are used instead. B. Covalent bonding occurs when orbitals (hybrid or otherwise) overlap 1.
C. Types of Hybrid Orbitals: the type of hybrid orbital needed depends on # of electron pairs surrounding the atom in question (see Table 2). 1.
sp hybrids: 1 s orbital + 1 p orbital = 2 sp hybrid orbitals
sp2 hybrids: 1 s orbital + 2 p orbitals = 3 sp2 hybrid orbitals
sp3 hybrids: 1 s orbital + 3 p orbitals = 4 sp3 hybrid orbitals
dsp3 hybrids: 1 s orbital + 3 p orbitals + 1 d orbital = 5 dsp3 hybrid orbitals
d2sp3 hybrids: 1 s orbital + 3 p orbitals + 2 d orbitals = 6 d2sp3 hybrid orbitals
Practice Exercises Fill in the table below as appropriate. When specifying the molecular geometry, do so around each “central” atom. Circle those molecules which may exhibit resonance. MOLECULE
H-C ≡ C-H
# SIGMA BONDS IN MOLECULE
# PI BONDS IN MOLECULE
# SIGMA BONDS IN MOLECULE
# PI BONDS IN MOLECULE