Name: mo diagrams, bond order, and mixing
Uploaded: 2020-09-03T13:38:29.000Z
Duration: 3 min 51 s
Channel: JoVE

K12 Standards

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Ohio’s Learning Standards and Model Curriculum

9-12

Chemistry

Structure And Properties Of Matter

Chemical bonding

Molecular Orbital Theory II

A molecular orbital diagram represents the relative energies of the constituent atomic orbitals, shown on the left and right, and the resultant molecular orbitals, shown in the middle.

As with atomic orbitals, each molecular orbital can accommodate a maximum of two electrons with opposite spins.The electrons from the overlapping atomic orbitals are placed in the molecular orbitals from lowest to highest energy, following Hund&#8217;s rule as needed.

For example, the two electrons of molecular hydrogen are both in the lower-energy &#963;1s bonding molecular orbital.

Molecular orbital theory predicts the stability of covalent bonds from the bond order of the molecule, which is the number of electrons in bonding orbitals minus the number of electrons in antibonding orbitals divided by two.

A bond order of greater than zero indicates that one or more covalent bonds can exist, whereas a bond order of zero means that bonds should not exist. Molecular hydrogen has a bond order of one and a single bond between the hydrogens. However, covalently bound dihelium does not exist as it would have a bond order of zero.

Molecular orbital diagrams typically only include valence orbitals because the contributi

molecular orbital theory ii

<h4>Molecular Orbital Energy Diagrams</h4>

The relative energy levels of atomic and molecular orbitals are typically shown in a molecular orbital diagram. For a diatomic molecule, the atomic orbitals of one atom are shown on the left, and those of the other atom are shown on the right. Each horizontal line represents one orbital that can hold two electrons. The molecular orbitals formed by the combination of the atomic orbitals are shown in the center. Dashed lines show which of the atomic orbitals combine to form the molecular orbitals. For each pair of atomic orbitals that combine, one lower-energy (bonding) molecular orbital and one higher-energy (antibonding) orbital result. 

The distribution of electrons in these molecular orbitals is done as per the aufbau principle. Lower-energy orbitals fill first; electrons spread out among degenerate orbitals before pairing, and each orbital can hold a maximum of two electrons with opposite spins.

<h4>Bond Order</h4>

The filled molecular orbital diagram shows the number of electrons in both bonding and antibonding molecular orbitals. The net contribution of the electrons to the bond strength of a molecule is identified by determining the bond order. In the molecular orbital model, an electron contributes to a bonding interaction if it occupies a bonding orbital, and it contributes to an antibonding interaction if it occupies an antibonding orbital. The bond order is calculated by subtracting the destabilizing (antibonding) electrons from the stabilizing (bonding) electrons. Since a bond consists of two electrons, we divide by two to get the bond order. The equation for determining the bond order is as follows:

<img alt="Bond order equation, chemistry formula; (# e&#8315; in bonding MOs - # e&#8315; in antibonding MOs)/2." src="/files/core/CDNSource/lessons/1077/1077_Equations-01.png" style="height: 40px;" data-altupdatedat="1761830439000" data-alt="Eq1" />

The bond order is a guide to the strength of a covalent bond; a bond between two given atoms becomes stronger as the bond order increases. If the distribution of electrons in the molecular orbitals between two atoms is such that the resulting bond would have a bond order of zero, a stable bond does not form. 

<h4>Bonding in Homonuclear Diatomic Molecules</h4>

A hydrogen molecule (H2) forms from two hydrogen atoms. When the atomic orbitals of the two atoms combine, the electrons occupy the molecular orbital of lowest energy, the &#963;1s bonding orbital. A dihydrogen molecule, H2, readily forms because the energy of a H2 molecule is lower than that of two H atoms. Both electrons in the H2 molecule are in the &#963;1s bonding orbital; the electron configuration is (&#963;1s)2. This configuration is represented by a molecular orbital energy diagram in which a single upward arrow indicates one electron in an orbital, and two (upward and downward) arrows indicate two electrons of opposite spin. A dihydrogen molecule contains two bonding electrons and no antibonding electrons, so the bond order is equal to 1. Thus, the H&#8211;H bond is a single bond.

A helium atom has two electrons, both of which are in its 1s orbital. Two helium atoms do not combine to form a dihelium molecule, He2, with four electrons, because the stabilizing effect of the two electrons in the lower-energy bonding orbital would be offset by the destabilizing effect of the two electrons in the higher-energy antibonding molecular orbital. The hypothetical electron configuration of He2 is (&#963;1s)2(&#963;*1s)2. The bond order in a hypothetical dihelium molecule would be zero. This indicates that no bond is formed between the two helium atoms.

<h4>Bonding in Homonuclear Diatomic Molecules of the Second Period</h4>

Eight possible homonuclear diatomic molecules might be formed by the atoms of the second period of the periodic table: Li2, Be2, B2, C2, N2, O2, F2, and Ne2. The Be2 molecule and the Ne2 molecule would not be stable due to zero bond order. 

For the valence molecular orbital electron configurations, the valence electrons are assigned to valence molecular orbitals with the lowest possible energies. Consistent with Hund&#8217;s rule, whenever there are two or more degenerate molecular orbitals, electrons fill each orbital of that type singly before any pairing of electrons takes place. 

&#963; orbitals are usually more stable than &#960; orbitals. However, this is not always the case. For atoms with three or fewer electrons in the p orbitals (Li through N), a different pattern is observed, in which the &#963;p orbital is higher in energy than the &#960;p set. 

This switch in orbital ordering occurs because of a phenomenon called s-p mixing. s-p mixing does not create new orbitals; it merely influences the energies of the existing molecular orbitals. The &#963;s wavefunction mathematically combines with the &#963;p wavefunction, with the result that the &#963;s orbital becomes more stable, and the &#963;p orbital becomes less stable. Similarly, the antibonding orbitals also undergo s-p mixing, with the &#963;s* becoming more stable and the &#963;p* becoming less stable.

s-p mixing occurs when the s and p orbitals have similar energies. The energy difference between 2s and 2p orbitals in O, F, and Ne is greater than that in Li, Be, B, C, and N. Because of this, O2, F2, and Ne2 exhibit negligible s-p mixing (not sufficient to change the energy ordering), and their MO diagrams follow the normal pattern, as shown in the figure above. All of the other period 2 diatomic molecules do have s-p mixing, which leads to the pattern where the &#963;p orbital is raised above the &#960;p set.

This text is adapted from <a href="https://openstax.org/books/chemistry-2e/pages/8-4-molecular-orbital-theory">Openstax, Chemistry 2e, Section 8.4: Molecular Orbital Theory.</a>

Molecular Orbital Energy Diagrams

The relative energy levels of atomic and molecular orbitals are typically shown in a molecular orbital diagram. For a ...

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Chemical Bonding: Molecular Geometry and Bonding Theories

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KEY TERMS AND CONCEPTS

mo diagrams, bond order, and mixing

Molecular orbital diagrams show how atomic orbitals combine to make bonding and antibonding orbitals in diatomic molecules. In these diagrams, the atomic orbitals of one atom are placed on the left and the atomic orbitals of the other atom are placed on the right. The molecular orbitals appear in the center. Each horizontal line stands for one orbital, and each orbital can hold two electrons. Dashed lines show which atomic orbitals combine to form each molecular orbital.

When atomic orbitals combine, one lower-energy bonding orbital and one higher-energy antibonding orbital form. Electrons are placed into these molecular orbitals using the aufbau principle. Lower-energy orbitals fill first. Electrons also spread out among degenerate orbitals, which are orbitals with the same energy, before they pair up. Each orbital holds a maximum of two electrons with opposite spins.

A filled molecular orbital diagram shows how many electrons are in bonding and antibonding orbitals. This makes it possible to find the bond order, which describes the net bond strength between two atoms. In the molecular orbital model, electrons in bonding orbitals help the bond, while electrons in antibonding orbitals weaken it. Bond order is found by subtracting antibonding electrons from bonding electrons and dividing by two. A higher bond order means a stronger covalent bond. If the bond order is zero, a stable bond does not form.

Hydrogen is a simple example of molecular orbital bonding. Two hydrogen atoms combine to form H2, and the electrons go into the lowest-energy sigma 1s bonding orbital. The energy of H2 is lower than the energy of two separate H atoms. Its electron configuration is (sigma 1s)2. The molecular orbital diagram shows two bonding electrons and no antibonding electrons, so the bond order is 1. That means the H-H bond is a single bond.

Helium behaves differently. A helium atom has two electrons, both in its 1s orbital. Two helium atoms do not form a stable He2 molecule because the two electrons in the bonding orbital would be balanced by two electrons in the higher-energy antibonding orbital. The hypothetical configuration would be (sigma 1s)2(sigma* 1s)2. The bond order would be zero, so no bond would form between the two helium atoms.

The same ideas help explain the homonuclear diatomic molecules of the second period: Li2, Be2, B2, C2, N2, O2, F2, and Ne2. For valence electrons, the lowest-energy molecular orbitals fill first. Hund's rule also applies, so electrons enter degenerate orbitals one at a time before pairing. Sigma orbitals are usually more stable than pi orbitals, but that order can change in some molecules.

For atoms with three or fewer electrons in the p orbitals, from Li through N, sigma p is higher in energy than the pi p set. This shift comes from s-p mixing, a change in orbital energies when the s and p orbitals are close in energy. The s-p wavefunctions mix, which makes sigma s more stable and sigma p less stable. The same happens to the antibonding orbitals, with sigma s* becoming more stable and sigma p* becoming less stable. In O, F, and Ne, the 2s and 2p energy gap is larger, so s-p mixing is negligible and the normal orbital order stays in place. That is why O2, F2, and Ne2 follow the usual pattern, while the other period 2 diatomic molecules show the mixed-order pattern.

MO Diagrams, Bond Order, and Mixing

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Molecular orbital theory explains how electrons are arranged in molecules. It uses quantum mechanics and wave functions, written as Ψ, to describe electron behavior in a molecule. Like electrons in isolated atoms, electrons in molecules occupy discrete, quantized energy levels. A molecular orbital is the region where a valence electron is likely to be found. It is full when it contains two electrons with opposite spin. Molecular orbitals can be built by combining atomic orbitals through the...

Molecular orbital diagrams show how atomic orbitals combine to make bonding and antibonding orbitals in diatomic molecules. In these diagrams, the atomic orbitals of one atom are placed on the left and the atomic orbitals of the other atom are placed on the right. The molecular orbitals appear in the center. Each horizontal line stands for one orbital, and each orbital can hold two electrons. Dashed lines show which atomic orbitals combine to form each molecular orbital. When atomic orbitals...

key terms and concepts

Learn how molecular orbital diagrams fill electrons, how bond order predicts bond strength, and why s-p mixing changes the order for period 2 diatomic molecules.

MO Diagrams, Bond Order, and Mixing | JoVE K12

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MO Diagrams, Bond Order, and Mixing

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