Introduction

The molecular orbital (MO) theory is a way of looking at the structure of a molecule via using molecular orbitals that belong to the molecule as a whole rather than to the individual atoms. When simple bonding happens between 2 atoms, the pair of electrons shaping the bond occupies an MO that is a mathematical grouping of the wave functions of the atomic orbitals of the 2 atoms involved. The MO technique originated in the work of Friedrich Hund and Robert S. Mulliken (Advameg, 2008).

Definition of Bonding

When atoms combine to form a molecule, the number of orbitals in the molecule equivalents the numeral of orbitals in the combining atoms. When two extremely easy atoms, each through one atomic orbital, are combined, two molecular orbitals are formed. One is a bonding orbital, shorter in power than the atomic orbitals, and derived from their sum. It is termed sigma. The other is an antibonding orbital, higher in energy than the atomic orbitals, and consequential from their dissimilarity (Advameg, 2008).  It is termed sigma-starred (σ*). (See the diagram in Figure).

Fig: Combination of Two 1s Atomic Orbitals to Form a Sigma Bonding Orbital or a Sigma-starred Antibonding Orbital

The basic idea might best be illustrated via believing on diatomic molecules of hydrogen and helium. The energy diagrams are revealed in Figure. Each hydrogen atom has one 1s electron. In the H₂ molecule the two hydrogen electrons go into the shortest energy MO available, the sigma orbital. In the case of helium, each helium atom has 2 electrons, so the He₂ molecule would have four. Two would go into the lower energy bonding orbital, but the other two would have to go into the higher energy sigma-starred orbital.

Fig: Molecular Orbital Energy Diagrams for (a) H₂ illustrating both Electrons in the Bonding Sigma MO; and (b) He₂ in that two of the Electrons are in the Antibonding sigma-starred MO.

Bond order

The numeral of bonds between a pair of atoms is said the bond order. Bond orders can be calculated from Lewis structures that are the heart of the valence-bond model. Oxygen, for example, has a bond order of two.

                                           ::O=O::

When there is more than one Lewis structure for a molecule, the bond order is an average of these structures (Advameg, 2008). The bond order in sulfur dioxide, for instance, is 1.5 the average of an S-O single bond in one Lewis structure and an S=O double bond in the other (Purdue, 2009).

Fig: molecular orbital theory,

In molecular orbital theory, we compute bond orders via assuming that 2 electrons in a bonding molecular orbital donate one net bond and that 2 electrons in an antibonding molecular orbital cancel the consequence of one bond. We can compute the bond order in the O₂ molecule via noting that there are 8 valence electrons in bonding molecular orbitals and 4 valence electrons in antibonding molecular orbitals in the electron configuration of this molecule. Therefore, the bond order is two.

Bond order = (bonding electrons - antibonding electrons)/2 = (6-4)/2=1

Even though the Lewis structure and molecular orbital forms of oxygen yield the similar bond order, there is a significant dissimilarity between such models. The electrons in the Lewis structure are all paired, but there are 2 unpaired electrons in the molecular orbital explanation of the molecule. As a result, we can examination the forecasts of such theories via studying the consequence of a magnetic field on oxygen. Atoms or molecules in that the electrons are paired are diamagnetic repelled by both poles of a magnetic. Those that have one or more unpaired electrons are paramagnetic magnetized to a magnetic field. Liquid oxygen is magnetized to a magnetic field and can in fact bridge the gap between the poles of a horseshoe magnet. The molecular orbital model of O₂ is consequently superior to the valence-bond model, which can't clarify this property of oxygen.

The bond order for a molecule can be found out as follows: bond order = ½ (bonding electrons - antibonding electrons). As a result, the H₂ molecule has a bond order of ½ (2 - 0) = 1. In other words, there is a single bond connecting the two H atoms in the H₂ molecule. In the case of He₂, on the other hand, the bond order is ½ (2 - 2) = 0. This means that He₂ isn't a stable molecule (Advameg, 2008). We utilize bond orders to expect the stability of molecules. If the bond order for a molecule is equivalent to zero, the molecule is unstable. A bond order of greater than zero proposes a stable molecule. The higher the bond order is, the more stable the bond. We can utilize the molecular orbital diagram to expect whether the molecule is paramagnetic or diamagnetic. If all the electrons are paired, the molecule is diamagnetic. If one or more electrons are unpaired, the molecule is paramagnetic (Purdue, 2009).

Instances:

1. The molecular orbital diagram for a diatomic hydrogen particle, H₂, is

                 - σ*_1S

                  ↑↓ σ_1S

The bond order is 1. Bond Order = 1/2(2 - 0) = 1

The bond order above zero suggests that H₂ is stable.

Since there are no unpaired electrons, H₂ is diamagnetic.

2. The molecular orbital diagram for a diatomic helium particle, He₂, illustrates the subsequent.

                        ↑↓ σ*_1S

                         ↑↓ σ_1S  

The bond order is 0 for He₂. Bond Order = 1/2(2 - 2) = 0

The zero bond order for He₂ suggests that He₂ is unstable.

If He₂ did form, it would be diamagnetic.

3. The molecular orbital diagram for a diatomic oxygen molecule, O₂,

                                 - σ*_2S

                         ↑ π*_2P                ↑ π*_2P                 

                    ↑↓ π_2P                 ↑↓ π_2P  

                                    ↑↓ σ_2P

                                       ↑↓ σ*_2S

                                      ↑↓ σ_2S

                                       ↑↓ σ*_1S

                                        ↑↓ σ_1S

is O₂ has a bond order of 2.   Bond Order = 1/2(10 - 6) = 2

The bond order of 2 suggests that the oxygen molecule is s table.

The two unpaired electrons show that O₂ is paramagnetic.

3. The molecular orbital diagram for a diatomic fluorine molecule, F₂, is

                                  - σ*_2P

                          ↑↓ π*_2P           ↑↓ π*_2P

                         ↑↓ π_2P             ↑↓ π_2P

                                        ↑↓ σ_2P

                                        ↑↓ σ*_2P

                                         ↑↓ σ_2S

                                         ↑↓ σ*_1S

F₂ has a bond order of 1. Bond Order = 1/2(10 - 8) = 1

The bond order of one suggests that the fluorine molecule is stable. Because all of the electrons are paired, F₂ is diamagnetic.

4.  The molecular orbital diagram for a diatomic neon molecule, Ne2, is

                                                          ↑↓ σ*_2P

                                  ↑↓ π*_2P                                   ↑↓ π*_2P          

                                    ↑↓ π_2P                                   ↑↓ π_2P          

                                                          ↑↓ σ_2P

                                                          ↑↓ σ*_2S

                                                          ↑↓ σ_2S

                                                           ↑↓ σ*_1S

                                                            ↑↓ σ_1S

Ne₂ has a bond order of 0. Bond Order = 1/2(10 - 10) = 0

The zero bond order for Ne2   suggests that Ne2   is unstable.  If Ne₂ did form, it would be diamagnetic (Mark, 2009).

We can explain diatomic molecules composed of atoms of different elements in a similar way. The bond between the carbon and oxygen in carbon monoxide is very strong despite what looks like a strange and perhaps unstable Lewis structure.

:CΞO:

The plus formal charge on the more electronegative oxygen and the minus formal charge on the less electronegative carbon would suggest instability. The molecular orbital diagram predicts CO to be very stable with a bond order of three.

                                              - σ*_2P

                                     -π*_2P              -π*_2P                                                       

                                   ↑↓ π_2P            ↑↓ π_2P          

                                            ↑↓ σ_2P

                                           ↑↓ σ*_2S

                                           ↑↓ σ_2S

                                           ↑↓ σ*_1S

                                           ↑↓ σ_1S

We predict the nitrogen monoxide molecule to be unstable according to the Lewis approach to bonding.

                        :.N=O::

The unpaired electron  and  the  lack  of  an  octet  of  electrons around nitrogen  would  suggest  an unstable molecule (Mark, 2009). NO is actually quite stable. The molecular orbital diagram predicts this via showing the molecule to have a bond order of 2.5.

Bond length

In molecular geometry, bond length or bond distance is the average distance between nuclei of two bonded atoms in a molecule. The qualitative relationship between bond order and bond length is that bond order is inversely proportional to bond length.

Bond energy

Bond energy is a measure of the strength of a chemical bond. The larger the bond energy the stronger the bond. The bond energy is essentially the average enthalpy change for a gas reaction to break all the similar bonds. For the methane molecule, C(-H)4, 435 kJ  is required to break a single C-H bond for a mole of methane, but breaking all four C-H bonds for a mole requires 1662 kJ. Thus the average bond energy is (1662/4) 416 (not 436) kJ/mol.

Bond dissociation energy

The O-H bond of a water molecule (H-O-H) has 493.4 kJ mol-1 of bond dissociation   energy, and 424.4 kJ mol^-1 is needed to cleave the remaining O-H bond. The bond energy of the O-H bonds in water is 458.9 kJ mol^-1, which is the average of the values. The qualitative relationship between bond order and bond dissociation energy is that bond order is directly proportional to bond dissociation energy.

Force constant

The qualitative relationship between bond order and force constant is that bond order is directly proportional to force constant.

Multiple bonds

A good deal of insight may be obtained from a very simple model of a Double or triple bonds involve two or three pairs of bonding electrons. Single bonds are always sigma bonds, but in multiple bonds the first bond is sigma, while any second or third bonds are pi bonds. The overlap of p orbitals can yield either pi or sigma MOs, as shown in Figure. When they overlap end to end, they form sigma orbitals, but when they overlap side to side, they form pi orbitals.

Consider now the oxygen molecule. The Lewis structure for oxygen is: Ö::Ö: The double bond is necessary in order to satisfy the octet rule for both oxygen atoms. The measured bond length for oxygen supports the presence of a double bond. Yet we know that this Lewis formula cannot be the correct structure for oxygen because oxygen is paramagnetic, which means that the oxygen molecule must have unpaired electrons.

Look now at the MO diagram for oxygen, which is shown in Figure. It still indicates a bond order of 2 [½(10 - 6) = 2], but it as well illustrates 2 unpaired electrons. The MO theory as well works well for larger molecules such as N₂O, CO₂, and BF₃ and for ions such as NO₃^- and CO₃^2-, in which the bonding MOs are delocalized, involving three or more atoms. It is especially helpful for aromatic matic molecules these as benzene. In this case all six C atoms in the ring are uniformly included in a delocalized pi electron cloud that envelops the complete molecule. The MO theory can even be expanded to complex ions and to solids, as well as substances these as superconductors and semiconductors (Advameg, 2008).

Fig: MO Energy Diagram for O₂. Eight Electrons from each Oxygen atom add up to 16 Electrons in the O₂ molecule. They combine to form the Molecular Orbitals indicated above.

Tutorsglobe: A way to secure high grade in your curriculum (Online Tutoring)

Expand your confidence, grow study skills and improve your grades.

Since 2009, Tutorsglobe has proactively helped millions of students to get better grades in school, college or university and score well in competitive tests with live, one-on-one online tutoring.

Using an advanced developed tutoring system providing little or no wait time, the students are connected on-demand with an expert at https://www.tutorsglobe.com. Students work one-on-one, in real-time with a tutor, communicating and studying using a virtual whiteboard technology.  Scientific and mathematical notation, symbols, geometric figures, graphing and freehand drawing can be rendered quickly and easily in the advanced whiteboard.

Free to know our price and packages for online chemistry tutoring. Chat with us or submit request at [email protected]