Diamagnetic Diatomic Molecules. Part 1
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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 Figure 8. Just as we write electron configurations for atoms, we can write the molecular electronic configuration by listing the orbitals with superscripts indicating the number of electrons present. For clarity, we place parentheses around molecular orbitals with the same energy.
In this case, each orbital is at a different energy, so parentheses separate each orbital. It is common to omit the core electrons from molecular orbital diagrams and configurations and include only the valence electrons. 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 that results from the filling of the molecular orbitals by electrons.
When using Lewis structures to describe the distribution of electrons in molecules, we define bond order as the number of bonding pairs of electrons between two atoms. Thus a single bond has a bond order of 1, a double bond has a bond order of 2, and a triple bond has a bond order of 3. We define bond order differently when we use the molecular orbital description of the distribution of electrons, but the resulting bond order is usually the same. The MO technique is more accurate and can handle cases when the Lewis structure method fails, but both methods describe the same phenomenon.
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. We can determine bond order with the following equation:. The order of a covalent bond is a guide to its strength; a bond between two given atoms becomes stronger as the bond order increases Table 1 in Chapter 8. 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.
We next look at some specific examples of MO diagrams and bond orders.
8.4 Molecular Orbital Theory
A dihydrogen molecule H 2 forms from two hydrogen atoms. A dihydrogen molecule, H 2 , readily forms because the energy of a H 2 molecule is lower than that of two H atoms. We represent this configuration by a molecular orbital energy diagram Figure 9 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 we have. Because the bond order for the H—H bond is equal to 1, the bond is a single bond.
A helium atom has two electrons, both of which are in its 1 s orbital.
Two helium atoms do not combine to form a dihelium molecule, He 2 , 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.
We would write the hypothetical electron configuration of He 2 as as in Figure The net energy change would be zero, so there is no driving force for helium atoms to form the diatomic molecule. In fact, helium exists as discrete atoms rather than as diatomic molecules.
Paramagnetism and diamagnetism (video) | Khan Academy
The bond order in a hypothetical dihelium molecule would be zero. Eight possible homonuclear diatomic molecules might be formed by the atoms of the second period of the periodic table: Li 2 , Be 2 , B 2 , C 2 , N 2 , O 2 , F 2 , and Ne 2. However, we can predict that the Be 2 molecule and the Ne 2 molecule would not be stable. We can see this by a consideration of the molecular electron configurations Table 3.
SET 1: Species with (1-3), (3-5), (5-7), (7-10), or (13-16) Electrons
We predict valence molecular orbital electron configurations just as we predict electron configurations of atoms. Valence electrons are assigned to valence molecular orbitals with the lowest possible energies. However, this is not always the case. The MOs for the valence orbitals of the second period are shown in Figure Looking at Ne 2 molecular orbitals, we see that the order is consistent with the generic diagram shown in the previous section. Obtain the molecular orbital diagram for a homonuclear diatomic ion by adding or subtracting electrons from the diagram for the neutral molecule.
You can practice labeling and filling molecular orbitals with this interactive tutorial from the University of Sydney. This switch in orbital ordering occurs because of a phenomenon called s-p mixing.
Diamagnetic Diatomic Molecules Part 1
When a single p orbital contains a pair of electrons, the act of pairing the electrons raises the energy of the orbital. Because of this, O 2 , F 2 , and N 2 only have negligible s-p mixing not sufficient to change the energy ordering , and their MO diagrams follow the normal pattern, as shown in Figure Using the MO diagrams shown in Figure 11 , we can add in the electrons and determine the molecular electron configuration and bond order for each of the diatomic molecules.
As shown in Table 3 , Be 2 and Ne 2 molecules would have a bond order of 0, and these molecules do not exist. The combination of two lithium atoms to form a lithium molecule, Li 2 , is analogous to the formation of H 2 , but the atomic orbitals involved are the valence 2 s orbitals. Each of the two lithium atoms has one valence electron. Because both valence electrons would be in a bonding orbital, we would predict the Li 2 molecule to be stable. The molecule is, in fact, present in appreciable concentration in lithium vapor at temperatures near the boiling point of the element. All of the other molecules in Table 3 with a bond order greater than zero are also known.
The O 2 molecule has enough electrons to half fill the , level. We expect the two electrons that occupy these two degenerate orbitals to be unpaired, and this molecular electronic configuration for O 2 is in accord with the fact that the oxygen molecule has two unpaired electrons Figure The presence of two unpaired electrons has proved to be difficult to explain using Lewis structures, but the molecular orbital theory explains it quite well.
In fact, the unpaired electrons of the oxygen molecule provide a strong piece of support for the molecular orbital theory. When two identical atomic orbitals on different atoms combine, two molecular orbitals result see Figure 3. The bonding orbital is lower in energy than the original atomic orbitals because the atomic orbitals are in-phase in the molecular orbital. The antibonding orbital is higher in energy than the original atomic orbitals because the atomic orbitals are out-of-phase.
In a solid, similar things happen, but on a much larger scale. Each bonding orbital will show an energy lowering as the atomic orbitals are mostly in-phase, but each of the bonding orbitals will be a little different and have slightly different energies. The antibonding orbitals will show an increase in energy as the atomic orbitals are mostly out-of-phase, but each of the antibonding orbitals will also be a little different and have slightly different energies.
The allowed energy levels for all the bonding orbitals are so close together that they form a band, called the valence band. Likewise, all the antibonding orbitals are very close together and form a band, called the conduction band. Figure 13 shows the bands for three important classes of materials: insulators, semiconductors, and conductors.
In order to conduct electricity, electrons must move from the filled valence band to the empty conduction band where they can move throughout the solid. The size of the band gap, or the energy difference between the top of the valence band and the bottom of the conduction band, determines how easy it is to move electrons between the bands. Only a small amount of energy is required in a conductor because the band gap is very small. Semiconductors, such as silicon, are found in many electronics. Semiconductors are used in devices such as computers, smartphones, and solar cells.
Solar cells produce electricity when light provides the energy to move electrons out of the valence band.
The electricity that is generated may then be used to power a light or tool, or it can be stored for later use by charging a battery. From this diagram, calculate the bond order for O 2. How does this diagram account for the paramagnetism of O 2? We draw a molecular orbital energy diagram similar to that shown in Figure Each oxygen atom contributes six electrons, so the diagram appears as shown in Figure The main component of air is N 2. From the molecular orbital diagram of N 2 , predict its bond order and whether it is diamagnetic or paramagnetic.
Will this ion be stable? The valence electron configuration for C 2 is. Since this has six more bonding electrons than antibonding, the bond order will be 3, and the ion should be stable.
Would it be paramagnetic or diamagnetic? Creating molecular orbital diagrams for molecules with more than two atoms relies on the same basic ideas as the diatomic examples presented here. However, with more atoms, computers are required to calculate how the atomic orbitals combine.
See three-dimensional drawings of the molecular orbitals for C 6 H 6. Molecular orbital MO theory describes the behavior of electrons in a molecule in terms of combinations of the atomic wave functions. The resulting molecular orbitals may extend over all the atoms in the molecule. Bonding molecular orbitals are formed by in-phase combinations of atomic wave functions, and electrons in these orbitals stabilize a molecule. Antibonding molecular orbitals result from out-of-phase combinations of atomic wave functions and electrons in these orbitals make a molecule less stable.
They can be formed from s orbitals or from p orbitals oriented in an end-to-end fashion. We can describe the electronic structure of diatomic molecules by applying molecular orbital theory to the valence electrons of the atoms. Materials with unpaired electrons are paramagnetic and attracted to a magnetic field, while those with all-paired electrons are diamagnetic and repelled by a magnetic field. Correctly predicting the magnetic properties of molecules is in advantage of molecular orbital theory over Lewis structures and valence bond theory.
Differences: Bonding orbitals result in holding two or more atoms together. Antibonding orbitals have the effect of destabilizing any bonding that has occurred. An odd number of electrons can never be paired, regardless of the arrangement of the molecular orbitals. It will always be paramagnetic. Bonding orbitals have electron density in close proximity to more than one nucleus. The interaction between the bonding positively charged nuclei and negatively charged electrons stabilizes the system.
The pairing of the two bonding electrons lowers the energy of the system relative to the energy of the nonbonded electrons. Yes, fluorine is a smaller atom than Li, so atoms in the 2 s orbital are closer to the nucleus and more stable. Skip to content Increase Font Size. Chapter 8.