The formation of molecular orbital is explained by wave mechanics. The Schrodinger wave equation and the linear combination of atomic orbitals provide the solution for the calculation of bonding and antibonding molecular orbitals. This molecular orbital study material explains the formation of the bonding and antibonding molecular orbitals and the necessary conditions required for their formation. It depends on the energy level combination and stability of these orbitals after combination. The main thing to consider is the stability of an orbital that leads to the formation of a molecule and defines its properties. It even explains the magnetic properties of compounds as they depend on their electronic configuration.

Molecular orbital theory overview

R.S. Mulliken and F. Hund provided this theory with some basic features that explain how atomic orbitals combine to form molecules. This led to the base of molecule formation and provided deep insights into molecular properties and behaviour. These features include

• For the formation of a molecular orbital, two or more atomic orbitals of comparable energies and suitable geometry can participate.
• In an atomic orbital, the electrons are influenced by one nucleus, whereas in molecular orbitals, electrons are influenced by the nucleus of all combining atoms.
• In molecular orbitals, the electrons of all combining atoms exert repulsive forces on each other.
• Molecular orbitals can be represented similarly as atomic orbital.
• The number of combining atoms equals the number of molecular orbitals formed. These molecular orbitals are equally split into bonding and antibonding orbitals.
• The bonding molecular orbitals are highly stable due to less repulsion among their electrons. 

Schrodinger’s equation and linear combination of atomic orbitals

The combination of more than one electron to form a molecule could not be explained by the Schrodinger wave equation alone because it can express only a single electron function. To overcome this, the linear combination of the atomic orbital (LCAO) model was proposed. It takes into consideration the electronic wave function provided by the Schrodinger wave equation for all combining atomic orbitals.

• The basic atom is Hydrogen with 1 electron in its ground state. The base of LCAO considers the combination of two hydrogen atoms.
• Let the wave function associated with one atom be Ψ(A) and that with other be Ψ(B).
• Applying the LCAO provides an equation based on the wave functions of two atomic orbitals.
• Ψ(final) = Ψ(A) ± Ψ(B)
• With this, we get two values that represent the combination and bonding of electrons.
  • σ = Ψ(A) + Ψ(B) represents bonding molecular orbitals.
  • σ = Ψ(A) – Ψ(B) represents anti-bonding molecular orbitals.

The bonding molecular orbitals provide a stable energy state in a molecule due to less repulsion as compared to the antibonding molecular orbitals.

Conditions for the formation of molecular orbital

The formation of a molecular orbital involves the combination of atomic orbitals. This is provided by the linear combination of atomic orbitals, but combining atomic orbitals should maintain some criteria. This is required for the formation of bonding molecular orbitals and antibonding molecular orbitals. The required conditions are

• The combining atomic orbitals should have comparable energy levels so that stable molecular orbital can be formed. It means that 3s orbital can combine with comparable energy levels like that of 3s of another atom and not with higher energy levels like 4s, 5s, etc.
• The other important criteria are symmetry; molecular orbital should be symmetrical. For example, 2pz can combine with 2pz and not with 2py or 2px, even if it has the same energy.
• After these two criteria are satisfied, the atomic orbitals need to do maximum overlapping to ensure the formation of a strong molecular orbital bond.

Filling of energy levels in molecular orbital

The energy levels in molecular orbitals are found using various experiments that involve spectroscopy. It has been observed that there are two different ways in which energy levels are filled in a molecule. It involves bonding molecular orbitals and antibonding molecular orbitals.

The ascending order of energy in molecular orbitals is

• For molecules like F and O is σ1s<σ∗1s<σ2s<σ∗2s<σ2pz<(π2px=π2py)<(π∗2px=π∗2py)<σ∗2pz
• For other molecules including C, Be, etc. is σ1s<σ∗1s<σ2s<σ∗2s<(π2px=π2py)<σ2pz<(π∗2px=π∗2py)<σ∗2pz

This energy equation helps to fill in the electrons in respective molecular orbitals as each orbital can take a maximum of two electrons. This can be found in the molecular orbital study material.

Factors determined by molecular orbital theory

The bonding and antibonding molecular orbitals are very informative as they determine the electronic configuration of a molecule. They provide details about the stability, magnetic nature, etc., of a molecule.

• Stability: If more electrons occupy bonding orbitals than antibonding orbitals, then the molecule is stable.
• Bond Order: It is equal to half of the difference between electrons in bonding and antibonding orbitals.
• Nature of Bond: It determines the strength of the molecular bond. It is inversely proportional to the bond order.
• Magnetic Nature: If all the molecular orbitals have 2 electrons, then the molecule is diamagnetic, or else it is paramagnetic.

Conclusion

The molecular orbital study material provides a brief explanation about the formation of molecules, the conditions required for their formation, their nature, filling of energy levels, and the factors determined by the molecular orbitals. Hence, it is necessary to consider all the criteria before filling the energy levels because they determine the behaviour of a molecule in specific conditions, e.g., in the magnetic field or electric field. The bonding orbitals and antibonding orbitals determine the final properties of a molecule. They are responsible for the interaction of molecules during chemical reactions.