Molecular Orbital Theory

The molecular orbital theory is one of the most productive models of chemical bonding. It is the basis of quantitative calculations, including those regarding the computer-generated images. Molecular orbital theory in general involves a lot of complicated mathematics. However, the fundamental ideas behind the theory are very easy to understand.

The simple Lewis and VSEPR models are based on the one-center orbitals of individual atoms. The molecular orbital theory involves sophisticated hybridization models, according to which the orbital can be modified by the interaction with other atoms.

However, the valence bond models, explained by the molecular orbital theory, are normally very limited in their applicability and predictive power. This is because the valence electrons are governed by positive centers.

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Molecular Orbital Theory Notes

When the force of attraction between an electron and two nuclei exceeds the electrostatic repulsion between the two nuclei, chemical bonding occurs. The electron must be in the binding region in order to do so. If the electron is located on another side in an anti-binding region, it in fact, enhances the repulsion between two nuclei and pushes them away.

If you want to visualize a molecular orbital, you can do it easily by picturing two separate isolated atoms having their own electron orbitals. These are just orbitals of those atoms. The next thing is to predict the manner in which these atomic orbitals interact with each other and bring the atoms close to each other. When the internuclear distance complies with the molecule under study, the corresponding orbitals will be the molecular orbitals of the new molecule.

To see the working nature of this, let us consider a simple molecule, i.e. a hydrogen molecule. The molecule consists of two nuclei having charge +1 and shares a single electron between them.

When two hydrogen nuclei move towards each other, the 1s orbitals of the isolated atoms merge to form a new molecular orbital. The greatest electron density of the new molecular orbital falls between the two nuclei. At this position, the force exerted by electrons on the nuclei is maximum. Thus this arrangement gives rise to a bonding molecular orbital.

Since the phenomena occur in a three-dimensional region of space, it is symmetrical about the imaginary line that connects the centers of the two nuclei. Based on the usual nomenclature, this is called σ (sigma) orbital.

Types of Molecular Orbitals

According to the molecular orbital theory, there are two types of primary molecular orbitals which are formed due to the linear combination of atomic orbitals. These orbitals are mentioned below.

1. Bonding Molecular Orbital 

This is the type of molecular orbital that is formed by the addition of overlapping an atomic orbital. Bonding Molecular Orbital is indicated by the addition of wave function indicating any molecular orbital. This type of molecular orbital shows the least relative  energy which implies that the orbital energy of the resultant orbital is always lower than that of the bonding species. The reason behind this is that the nuclei of both the sharing electrons show more attraction. 

2. Anti Bonding Molecular Orbitals

In antibonding molecular orbital, the electron density of the two bonding atoms is concentrated behind the nuclei. As a result, the distance between the nuclei of the two atoms increases. The anti-bonding molecular orbital weakens the bonds between two atoms.

The type of molecular orbital is opposite to that of bonding molecular orbital as it is formed when the overlapping atomic orbital is subtracted. It is formed by subtraction of wave function. So, the energy of the orbital that is formed after bonding is always higher than that of the parent orbital. This also implies that the relative energy of the anti-bonding orbital is always greater. The reason behind this is that the nuclei of the sharing electrons repulse each other. 

3. Non-Bonding Molecular Orbitals

This is the third type of molecular orbital and is formed when the atomic orbitals are not unsymmetrical. These two atomic orbitals may have slightly different energies or in other words, they may be less compatible. There is no symmetry between two bonding atomic orbitals in the case of the non-bonding molecular orbital. The molecular orbital thus formed doesn’t have any positive or negative interaction between each other. The bond between the atoms is not affected by these types of orbitals.

Molecular Orbital Theory Diagram

The bonding and antibonding orbitals are usually depicted by the molecular orbital diagram. Below mentioned is the molecular orbital diagram of the hydrogen ion H₂⁺. The atomic valence electrons (which are represented by the left and right boxes) at first fills the lower-energy molecular orbitals, and then it fills the higher ones. This is the same as that of the atomic orbitals. Therefore, the single electron of the molecule goes into the bonding orbital and leaves the anti-bonding orbital empty.

Orbitals have space for a maximum of two electrons, and therefore the bonding orbital in H₂⁺ is half-filled. This single electron doesn't have the required energy; the lower the potential energy of one mole of hydrogen nuclei pairs by 270 kJ, thereby making them stick together and behave like distinct molecular species.

H₂⁺ is highly stable in an energetic sense and is an extremely reactive molecule. It even reacts with itself, and hence these ions are not commonly found.

Salient Features of the Molecular Orbital Theory

• The molecular orbitals are created because of the overlapping of the atomic orbitals. The atomic orbitals merge with each other to form the molecular orbital.

• The electrons of the molecules fill the new energy states of the molecular orbitals, similar to filling up of the energy states of the atomic orbitals.

• The probability of finding the distribution of electrons around the nuclei of a molecule is given by the molecular orbital.

• The two atomic orbitals which combine to form the molecular orbital should possess energy values of similar orientation. For example, 1s can combine with only 1s and both with 2s or 2p.

• The number of molecular orbitals is equal to the number of combinations of the atomic orbitals.

• The shape of the molecular orbitals depends on the shape of the atomic orbitals.

What is Molecular Orbital Theory? 

The valence-bond theory couldn't explain the presence of two or more equivalent bonds with bond orders between that of a single bond and a double bond in some molecules like in those molecules that are resonance-stabilized. Then F. Hund and R. S. Mulliken came up with the Molecular Orbital Theory (MOT). This theory was based on chemical bonding and explained the properties of different molecules and their structure. With the help of this theory, we can understand the geometries of different molecules. Now, let's talk about some features of the Molecular Orbital Theory.

There are different types of molecular orbitals such as bonding, anti-bonding, non-bonding, etc. Anti-bonding orbitals have energy higher than that of parent orbitals while bonding orbitals have energy lower than that of parent orbitals. Also, the number of molecular orbitals are always equal to the number of atomic orbitals that are responsible for forming them. In molecular orbitals, the electrons with the lowest energy are always filled first which means that electrons are always filled in the increasing order of the orbital energy. Molecular orbitals are usually formed when the energy of the atomic orbitals of bonding species are similar. Molecular orbitals can also be formed from the atomic orbitals with slightly different energies but these combinations are not that effective. So, the overall idea of the molecular orbital theory is that molecular orbitals can be formed by each atom which may combine to form it. This means that the possibility of finding an electron is uncertain as the electron can be in various atomic orbitals. In other words, an electron can be found anywhere inside a molecule.

The Molecular Orbital Theory changed the whole scenario of understanding the chemical bonding of all the atomic orbitals. With the help of this theory, we are now able to understand the process of bonding. The molecular orbital theory considers that the atomic orbitals combine linearly to form molecular orbitals. 

Postulates of Molecular Orbital Theory:

• The number of molecular orbitals which are formed by different bonding species is always equal to the atomic orbitals of those species. 

• The electrons in the molecular orbital are filled in the increasing order of orbital energy (from orbital having lower energy to orbital having higher energy).

• Electrons are filled in the increasing order of the orbital energies which means the orbital with lower energy will be filled first and the orbital with higher orbital energy will be filled last. 

• As per the Molecular Orbital Theory, three types of orbital are based on the electron bonding pattern. The three molecular orbitals are Bonding molecular orbital, Non-bonding molecular orbital, Anti-bonding molecular orbital.

• In many atomic orbitals, electrons can be found bonded to different nuclei and every atom may combine to form a molecular orbital. 

• If the parent orbitals have the same energies then the combinations of atomic orbitals that would occur, would be the most effective. 

• An electron can be found anywhere in a molecule.