21: Resonance and Molecular Orbital Methods

Last updated
Save as PDF

Page ID: 21985

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

Molecular orbital theory is a method for determining molecular structure in which electrons are not assigned to individual bonds between atoms, but are treated as moving under the influence of the nuclei in the whole molecule. The spatial and energetic properties of electrons within atoms are fixed by quantum mechanics to form orbitals that contain these electrons. While atomic orbitals contain electrons ascribed to a single atom, molecular orbitals, which surround a number of atoms in a molecule, contain valence electrons between atoms. There are two popular approaches to the formulation of the structures and properties of organic compounds based on quantum mechanics - resonance and molecular-orbital methods. In the past, there has been great controversy as to which of these methods actually is more useful for qualitative purposes and, indeed, the adherents to one or the other could hardly even countenance suggestions of imperfections in their choice. Actually, neither is unequivocally better and one should know and use both - they are in fact more complementary than competitive.

21.1: Prelude to Resonance and Molecular Orbital Methods
The structural theory of organic chemistry originated and developed from the concepts of valence and the tetrahedral carbon atom. It received powerful impetus from the electronic theory of bonding, as described in Chapter 6. We now express the structures of many organic compounds by simple bond diagrams which, when translated into three-dimensional models, are compatible with most observed molecular properties.
21.2: Characteristics of Simple Covalent Bonds
The simplest kind of bond is that between univalent atoms in diatomic molecules, such as H2 and F2, and so on. In the gas phase the molecules are in rapid motion, colliding with one another and the walls of the container. The atoms vibrate with respect to one another, and the molecules have rotational energy as well. Despite this activity, we can assign an average equilibrium bond distance and an average bond energy for normal, unexcited molecules.
21.3: Comparison of the Resonance and Molecular-Orbital Methods
In this section, we will sketch the similarities and differences in the resonance (or valence-bond, VB) and molecular-orbital (MO) approaches for electron-pair bonds. Both methods normally start with atomic orbitals, but where the methods differ is in how these orbitals are used.
21.4: The Benzene Problem
Our task here is to see what new insight the VB and MO treatments can give us about benzene, but first we will indicate those properties of benzene that are difficult to explain on the basis of simple structure theory.
21.5: Application of the MO Method to 1,3-Butadiene
To treat the ππ -electron system of 1,3-butadiene by simple MO theory, we combine the four pp carbon orbitals of an atomic-orbital model. We can estimate a stabilization energy for butadiene from heats of hydrogenation, and it is useful to compare the values obtained with the calculated delocalization energy.
21.6: Application of MO Theory to Other Systems
Many important molecules have alternating single and double bonds (are conjugated), but have atoms that are more (or less) electron-attracting than carbon. Analysis of the electronic configuration resulting from the MO calculations accords generally with the VB hybrids. We also consider how the MO approach can be used to understand these differences in excitation energy.
21.7: Which Is Better- MO or VB?
The calculated energy of the electron-pair bond of the hydrogen molecule as a function of H−H intermolecular distance r by the ab initio (exact), MO, and VB procedures show that neither the MO nor the VB calculations come close to the ab initio calculation in reproducing the experimental dissociation energy or the variation of the energy with the intermolecular distance. The VB method gives a little better energy value at the minimum and the MO method gives poor results at larger values of r .
21.8: More on Stabilization Energies
Benzene is 36 - 38 kcal more stable than the hypothetical molecule 1,3,5-cyclohexatriene on the basis of the differences between experimental heats of combustion, or hydrogenation, and heats calculated from bond energies. We call this energy difference the stabilization energy (SE) of benzene. We have associated most of this energy difference with ππ -electron delocalization, which is the delocalization energy (DE).
21.9: Bond Lengths and Double-Bond Character
Bond lengths frequently are cited as evidence for, or against, electron delocalization, although some caution should be exercised in this respect. For instance, if the hybrid structure of benzene is considered to be represented by the two possible Kekule structures, then each carbon-carbon bond should be halfway between a single bond and a double bond.
21.10: Hückel's 4n + 2 Rule
Because the bonding molecular orbitals for \(\pi\) systems will be just filled with 2, 6, or 10 electrons to give singlet states, a \(\left( 4n + 2 \right)\) \(\pi\)-electron rule was formulated for stable configurations and a \(4n\) \(\pi\)-electron rule for unstable configurations, where \(n\) is an integer. Thus 2, 6, 10, 14, ... \(\pi\) electrons will be favorable and 4, 8, 12 ... \(\pi\) electrons will be unfavorable. The rule is Huckel's \(4n + 2\) rule.
21.11: Pericyclic Reactions
There are numerous reactions in organic chemistry that proceed through cyclic transition states. They may be classified generally as pericyclic reactions. An important and familiar example is the Diels-Alder reaction, in which a conjugated diene cycloadds to an alkene or alkyne.
21.12: Evidence Bearing on the Mechanism of [2 + 2] Cycloadditions
We have not given you much evidence to decide why it is that some thermal [2 + 2] cycloadditions occur but not others. What is special about fluoroalkenes, allenes, and ketenes in these reactions? One possibility is that Mobius rather than the Huckel transition states are involved, but the Mobius transition states are expected to suffer from steric hindrance. It is also possible that [2 + 2] cycloadditions, unlike the Diels-Alder additions, proceed by stepwise mechanisms.
21.E: Resonance and Molecular Orbital Methods (Exercises)
These are the homework exercises to accompany Chapter 21 of the Textmap for Basic Principles of Organic Chemistry (Roberts and Caserio).

Contributors and Attributions

John D. Robert and Marjorie C. Caserio (1977) Basic Principles of Organic Chemistry, second edition. W. A. Benjamin, Inc. , Menlo Park, CA. ISBN 0-8053-8329-8. This content is copyrighted under the following conditions, "You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format."