Molecular Orbital TheoryTable of contentsThe Molecular Orbital Theory, initially developed by Robert S. Mullikan, incorporates the wave like characteristics of electrons in describing bonding behavior. In Molecular Orbital Theory, the bonding between atoms is described as a combination of their atomic orbitals. While the Valence Bond Theory and Lewis Structures sufficiently explain simple models, the Molecular Orbital Theory provides answers to more complex questions. In the Molecular Orbital Theory, the electrons are delocalized. Electrons are considered delocalized when they are not assigned to a particular atom or bond (as in the case with Lewis Structures). Instead, the electrons are “smeared out” across the molecule. The Molecular Orbital Theory allows one to predict the distribution of electrons in a molecule which in turn can help predict molecular properties such as shape, magnetism, and Bond Order. IntroductionAtoms form bonds by sharing electrons. Atoms can share two, four, or six electrons, forming single, double, and triple bonds respectively. Although it is impossible to determine the exact position of an electron, it is possible to calculate the probability that one will find the electron at any point around the nucleus using the Schrödinger Equation . This equation can help predict and determine the energy and spatial distribution of the electron, as well as the shape of each orbital. The figure below shows the first five solutions to the equation in a three dimensional space. The colors show the phase of the function. In this diagram, blue stands for negative and red stands for positive. Note, however, that the 2s orbital has 2 phases, one of which is not visible because it is inside the other. Principles of Molecular Orbital TheoryIn molecules, atomic orbitals combine to form molecular orbitals which surround the molecule. Similar to atomic orbitals, molecular orbitals are wave functions giving the probability of finding an electron in certain regions of a molecule. Each molecular orbital can only have 2 electrons, each with an opposite spin. Take a hydrogen molecule (H2) for example. It has two molecular orbitals, an antibonding orbital and a bonding orbital. Compared to the original atomic orbitals, a bonding molecular orbital has lower energy and is therefore more stable. Where the atomic orbitals overlap, there is an increase in electron density and therefore an increase in the intensity of the negative charge. This increase in negative charge causes the nuclei to be drawn closer together. Due to the lower potential energy in molecular bonds than in separate atomic orbitals, it is more energy efficient for the electrons to stay in a molecular bond rather than be pushed back into the 1s orbitals of separate atoms. This is what keeps bonds from breaking apart. A bonding orbital can only be formed if the orbitals of the constituent atoms have the same phase (here represented by colors). The wave functions of electrons of the same phase interfere constructively which leads to bonding.
If the atomic orbitals have the different phases, they interfere destructively and an antibonding molecular orbital is formed (see the top part of the figure below). Antibonding molecular orbitals have a higher energy than the atomic orbitals of their constituent atoms. When antibonds are formed, the interaction creates a decrease in the intensity of the negative charge, which causes a decrease in the plus minus attraction in the molecular bond. This smaller attraction leads to the higher potential energy. This type of bond destabilizes the attraction between atoms, so the number of antibonding orbitals in a molecule must be less than the number of bonding orbitals.
Sigma BondsMolecular orbitals that are symmetrical about the axis of the bond are called sigma molecular orbitals, often abbreviated by the Greek letter σ. The diagram to the left shows the 1s orbitals of 2 Hydrogen atoms forming a sigma orbital. There are two types of sigma orbitals formed, antibonding sigma orbitals (abbreviated σ*), and bonding sigma orbitals (abbreviated σ). In sigma bonding orbitals, the in phase atomic orbitals overlap end to end causing an increase in electron density along the bond axis. Where the atomic orbitals overlap, there is an increase in electron density and therefore an increase in the intensity of the negative charge. This increase in negative charge causes the nuclei to be drawn closer together. In sigma antibonding orbitals (σ*), the out of phase 1s orbitals interfere destructively which results in a low electron density between the nuclei as seen on the top of the diagram. The diagram below is a representation of the energy levels of the bonding and antibonding orbitals formed in the hydrogen molecule. Two molecular orbitals were formed, one antibonding (σ*) and one bonding (σ).The two electrons in the hydrogen molecule have antiparallel spins. Notice that the σ* orbital is empty and has a higher energy than the σ orbital. Sigma bonding orbitals and antibonding orbitals can also be formed between p orbitals (shown below). Notice that the orbitals have to be in phase in order to form bonding orbitals. Sigma molecular orbitals formed by p orbitals are often differentiated from other types of sigma orbitals by adding the subscript p below it. So the antibonding orbital shown in the diagram below would be σ*p.
Pi BondsThe pi bonding bonds as a side to side overlap, which then causes there to be no electron density along the axis, but there is density above and belong the axis. The diagram below shows a pi antibonding molecular orbital and a pi bonding molecular orbital.
2py Orbitals
The two 2py atomic orbitals overlap parallely to form two pi molecular orbitals which are asymmetrical about the axis of the bond. 2pz orbitals
The two 2pz orbitals overlap to create another pair of pi 2p and pi *2p molecular orbitals. The 2pz-2pz overlap is similar to the 2py-2py overlap because it is just the orbitals of the 2pz rotated 90 degrees about the axis. The new molecular orbitals have the same potential energies as those from the 2py-2py overlap. Drawing Molecular Orbital Diagrams
Determining Bond OrderBond Order indicates the strength of the bond. The higher the Bond Order, the stronger the bond. Bond Order= 1/2(a-b) where a is the number of e- in bonding Molecular Orbitals and b is the number of e- in antibondng Molecular Orbitals. Determining the Stability of the MoleculeIf the Bond Order is Zero, then no bonds are produced and the molecule is not stable (for example He2). If the Bond Order is 1, then it is a single covalent bond. The higher the Bond Order, the more stable the molecule is. An advantage of Molecular Orbital Theory when it comes to Bond Order is that it can more accurately describe partial bonds (for example in H2+, where the Bond Order=1/2), than Lewis Structures. Outside linksReferences
Problems
Solutions1. The molecular orbital diagram for a diatomic hydrogen molecule, H2, is
2. The molecular orbital diagram for a diatomic helium molecule, He2, shows the following.
3. The molecular orbital diagram for a diatomic oxygen molecule, O2, is
4.The molecular orbital diagram for a diatomic Neon molecule, Ne2, is
5. The molecular orbital diagram for the diatomic fluorine molecule, F2 is
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