Theory of Molecular Orbitals

Atoms are combined into molecules due to chemical bonds. And the electrons participating in the formation of these bonds are located in the outer layer of these atoms. There are several theories describing the binding process. One of them is the theory of valence bonds, according to which the bonds between atoms are formed when the atoms exchange electron pairs from overlapping orbitals. The other is the theory of molecular orbitals.

Such approximate theories are useful because we get a simple, intuitive way of representing physical processes. On the other hand, modern computers give us the opportunity to calculate the binding energies with high accuracy, but such calculations do not bring us nearer to an understanding of what happens when atoms join. The role of the theories is precise to give us this understanding.

The theory of molecular orbitals is based on the idea that the electron orbital in an atom is described by a wave function (see the Schrodinger equation). The theory explains how, during the course of a chemical reaction, atomic orbitals are converted into molecular orbitals. Like most of the types of waves known to us, the wave functions of electrons in orbitals undergo interference. It turns out that the orbitals in molecules can, with good approximation, be represented as the result of interference of atomic wave functions.

For example, consider what happens when two atomic orbitals of neighboring atoms interact. If in the region of overlapping of orbitals the wave functions undergo constructive interference, electrons spend most of the time between the nuclei, attracting the atoms to each other. On the other hand, if the interference in the overlapping region is destructive, the electron density between the nuclei is zero, and the resultant repulsive force arises between the atoms. Thus, two atomic orbitals are combined to form two molecular orbitals: one tends to bind atoms (the binding molecular orbital), and the other – to push them away (loosening molecular orbitals). And their interaction determines whether a stable molecule will be formed.

To understand how this model works, let’s try to understand why hydrogen forms a molecule of two atoms and helium – from one. In the formation of a bond between two hydrogen atoms, one electron from each atom participates, and on the lowest (binding) molecular orbital there is just a place for two electrons. The electrons are mostly between the nuclei, which means that the atoms are attracted and the hydrogen molecule can form. In helium, four electrons participate in the formation of the bond between two atoms, therefore both binding and loosening atomic orbitals are involved. Numerical calculations show that in this case, the repulsive effect will predominate, and even if helium molecules are formed, they will be extremely unstable. Therefore, the helium gas molecule consists of one atom.

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