1. Condition for LCAO to occur

For atomic orbitals to combine and form molecular orbitals effectively, the following standard conditions must be satisfied:

• Comparable / same energy of combining atomic orbitals
• Same symmetry about the molecular axis
• Appreciable (maximum) overlap, not minimum overlap

So let us check each statement.

2. Evaluate statement A: "have the same energy"

This is essentially correct in MO theory.

Atomic orbitals combine effectively when their energies are equal or nearly equal. Hence this is taken as a valid condition.

So, A is correct.

3. Evaluate statement B: "have the minimum overlap"

This is incorrect.

For molecular orbital formation, overlap must be appreciable / maximum, because greater overlap gives stronger interaction and better MO formation.

So, B is incorrect.

4. Evaluate statement C: "have same symmetry about the molecular axis"

This is correct.

Only orbitals with the same symmetry relative to the internuclear axis can combine.

Example: two $s$ orbitals can combine; an $s$ orbital and a properly oriented $p_z$ orbital can combine; but orbitals of incompatible symmetry cannot.

So, C is correct.

5. Evaluate statement D: "have different symmetry about the molecular axis"

This is the opposite of the required condition.

Orbitals with different symmetry do not combine effectively.

So, D is incorrect.

6. Select the correct option

Correct statements are:

$A \text{ and } C$

From the given options, this corresponds to Option D.

7. Comparison with stored answer

Stored correct answer = D

Derived answer = D

They match.