Chemistry 2000 Lecture 8: Valence bond theory
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1 Chemistry 000 Lecture 8: Valence bond theory Marc R. Roussel January 9, 08 Marc R. Roussel Valence bond theory January 9, 08 / 5
2 MO theory: a recap A molecular orbital is a one-electron wavefunction which, in principle, extends over the whole molecule. Two electrons can occupy each MO. MOs have nice connections to a number of experiments, e.g. photoelectron spectroscopy, Lewis acid-base properties, etc. owever, correlating MO calculations to bond properties is less straightforward. Marc R. Roussel Valence bond theory January 9, 08 / 5
3 Valence-bond theory Valence-bond (VB) theory takes a different approach, designed to agree with the chemist s idea of a chemical bond as a shared pair of electrons between two particular atoms. Bonding is described in terms of overlap between orbitals from adjacent atoms. This overlap gives a two-electron bond wavefunction, not a one-electron molecular orbital. The description of bonding in VB theory is a direct counterpart to Lewis diagrams. Marc R. Roussel Valence bond theory January 9, 08 3 / 5
4 Example: For diatomic molecules, the VB and MO descriptions of bonding are superficially similar. In VB theory, we start with the Lewis diagram, which for is We need to make a single bond. We take one s orbital from each atom, and overlap them to make a valence bond: Two electrons occupy this valence bond. The overlap operation is not the same as the linear combinations of LCAO-MO theory. Marc R. Roussel Valence bond theory January 9, 08 4 / 5
5 Polyatomic molecules In traditional chemical theory (e.g. Lewis diagrams), a chemical bond consists of one or more pairs of electrons being shared between two atoms. Valence-bond theory builds two-electron bond wavefunctions. These wavefunctions should occupy the space between two atoms and not extend very far outside this region. (Again, think in terms of the lines in a Lewis diagram.) Problem: Atomic orbitals don t necessarily point in the right directions in space, nor are they necessarily confined to the region between two atoms. Solution: Use mixtures of atomic orbitals ( hybrid orbitals ) instead of the AOs themselves. Marc R. Roussel Valence bond theory January 9, 08 5 / 5
6 Be Suppose that we wanted to make VB wavefunctions for the two Be- bonds in Be. We can t use a Be s orbital to form the valence bonds because this orbital extends into the bonding regions for both atoms: Another way to think about this is that a valence bond made between one of the atoms and the Be atom using the s orbital would interfere with the valence bond to the other atom. Marc R. Roussel Valence bond theory January 9, 08 6 / 5
7 ybrid atomic orbitals To fix this problem, we add atomic orbitals on Be to get hybrid atomic orbitals that point towards each of the atoms, with little extension in the opposite direction. Specifically, for a linear molecule, we use sp hybrids made by adding (or subtracting) the s and p z atomic orbitals on the same atom:.5 + = = Marc R. Roussel Valence bond theory January 9, 08 7 / 5
8 ybrid atomic orbitals (continued) Once we have the hybrid orbitals, we can overlap them with the s AOs to form two valence bond wavefunctions. Notation: Each of these bonds would be described as Be(sp)-(s). Marc R. Roussel Valence bond theory January 9, 08 8 / 5
9 Linear combinations in MO and VB theory At this point, you may be a little confused about the difference between MO and VB theory since both involve linear combinations of atomic orbitals. In MO theory, we combine AOs from different atoms to make an MO. These MOs (in principle) extend over the whole molecule. In VB theory we combine AOs from one atom to make hybrid atomic orbitals. These hybrid orbitals are used to construct a wavefunction for a shared electron pair involved in a chemical bond. There are no MOs in VB theory. To avoid confusion, we only use the term LCAO in connection with MO theory. In VB theory, we say hybridization. Marc R. Roussel Valence bond theory January 9, 08 9 / 5
10 B 3 B 3 is trigonal planar. The s and p orbitals of boron do not point toward the corners of an equilateral triangle. We will create a set of hybrid orbitals that do point toward the corners of an equilateral triangle and can thus be used in the VB treatment of B 3. The p orbitals point along the Cartesian axes. We will need two p orbitals to create orbitals that point toward different directions in a plane. We will therefore construct sp hybrids from the s, p x and p y atomic orbitals. Marc R. Roussel Valence bond theory January 9, 08 0 / 5
11 In general, combining two p wavefunctions gives another p wavefunction, but rotated: (p x) + 3 (p y ) = Note: (, 0, 0) + 3 (0,, 0) is a vector that points 0 counter-clockwise from the x axis. Adding in an appropriate amount of s character then cancels off most of the wave in one of the lobes: = Marc R. Roussel Valence bond theory January 9, 08 / 5
12 sp hybrids (s) + (p x ) = 3 6 (s) (p x ) + (p y ) = (s) 6 (p x ) (p y ) = Marc R. Roussel Valence bond theory January 9, 08 / 5
13 C 4 We now need to make hybrid orbitals that point to the corners of a tetrahedron. The idea is exactly as with the trigonal planar geometry, except that we now need our hybrid orbitals to point to directions in the full three-dimensional space. We therefore need all three p orbitals, resulting in sp 3 hybrids. Marc R. Roussel Valence bond theory January 9, 08 3 / 5
14 sp 3 hybrids (s + p x + p y + p z ) = z 0 0 x 0 y (s p x p y + p z ) = z 0 0 x 0 y Marc R. Roussel Valence bond theory January 9, 08 4 / 5
15 (s p x + p y p z ) = z 0 0 x 0 y (s + p x p y p z ) = z 0 0 x 0 y Marc R. Roussel Valence bond theory January 9, 08 5 / 5
16 All four sp 3 hybrids together: z 0 x 0 0 y Marc R. Roussel Valence bond theory January 9, 08 6 / 5
17 ybridization and VSEPR The VSEPR electronic geometries are each uniquely associated with a hybridization state: Electronic geometry ybridization Linear sp Trigonal planar sp Tetrahedral sp 3 In a lot of cases, this table is all you need to know about VB theory... Example: N 3 has a tetrahedral electronic geometry, therefore sp 3 hybridization at N. Marc R. Roussel Valence bond theory January 9, 08 7 / 5
18 Ethene C C Trigonal planar carbons = sp hybridization sp hybrids used to make σ bonds to atoms (with their s orbitals) and between the C atoms: C C (s) C(sp ) valence bond C(sp ) C(sp ) valence bond Marc R. Roussel Valence bond theory January 9, 08 8 / 5
19 Ethene (continued) This leaves one unused p orbital on each carbon atom: C C The overlap of these p orbitals forms a π valence bond. Marc R. Roussel Valence bond theory January 9, 08 9 / 5
20 Ethyne C C Linear geometry around each carbon = sp hybridization Each carbon atom has two p orbitals left over: C C These p orbitals combine into two π bonds. Marc R. Roussel Valence bond theory January 9, 08 0 / 5
21 Formaldehyde :O: C Trigonal planar geometry at the carbon atom = sp hybridization The O atom can form a σ bond using a p orbital. :O: C O(p) C(sp) valence bond (s) C(sp ) valence bonds Why use the O(p) rather than the O(s) for bonding? The general assumption in VB theory is that lone pairs go into the lowest-energy AO. Marc R. Roussel Valence bond theory January 9, 08 / 5
22 Formaldehyde The carbon atom has one p orbital left over which can combine with the corresponding orbital on O to form the π bond. Marc R. Roussel Valence bond theory January 9, 08 / 5
23 Ozone O.... O.. :O.. O.. O.. O:.. The sigma framework of ozone is easy: The central O is sp hybridized. One of the sp hybrids contains a lone pair. The other two form σ bonds with one p orbital on each of the terminal O atoms. What about the double bond? Resonance! Marc R. Roussel Valence bond theory January 9, 08 3 / 5
24 Construct VB wavefunctions corresponding to both of these structures and average these wavefunctions together: one sp hybrid as lone pair, extra p used for pi bonding O.... O.. :O.. O.. O.. O:.. s and one p as lone pairs, extra p used for pi bonding s and two p s as lone pairs Marc R. Roussel Valence bond theory January 9, 08 4 / 5
25 Shortcomings of VB theory A lot of things that fall out naturally in MO theory are hard in VB theory: Explanation of photoelectron spectra Explanation of paramagnetism of O Delocalized orbitals In its simplest form, VB theory only tells us what we already know based on Lewis diagrams and VSEPR. It only becomes a predictive theory in its most advanced forms. Marc R. Roussel Valence bond theory January 9, 08 5 / 5
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