Rules for Linear Combination of Atomic Orbitals | Conditions for LCAO

Rules for Linear Combination of Atomic Orbitals (LCAO)

Conditions for Linear Combination of Atomic Orbitals

Followings are the rules for the LCAO method- 1. The same energy of combining orbitals
The combining atomic orbitals must be of equal energy or approximately same energy. 2p orbital of an atom can combine with the other 2p orbital of another atom but 1s can not combine with 2p as they have appreciable energy difference.
2. Same symmetry along the atomic orbital
The combining atoms should have the same symmetry along the molecular axis for proper combination. All the 2p orbitals have same energy but the 2pz orbital of an atom can combine with only 2pz orbital of another atom. Do not think that 2px and 2py orbitals can combine because they have a different axis of symmetry. Generally, the z-axis is considered as the molecular axis of symmetry. 3. Proper overlap between the atomic orbitals
The two atomic orbitals will combione to form molecular orbital if and only if the overlapping is proper manner. Greater is the extend of overlap of atomic orbital, greater will be the nuclear density.

Which of the following combination is not allowed in the LCAO method for the formation of molecular orbital (consider Z-axis as the molecular axis) ?
a. s + p_x
b. s + p_z
c. p_x + p_x
d. p_z + p_z

Hints:

s and p_x orbitals do not have proper orientation to overlap and hence Molecular Orbital is not formed.

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Principle of Linear Combination

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