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# If x is the internuclear axis, then which type of overlapping is/are responsible for the formation of N.B.M.O?(This type of question has multiple correct options)                 (A) ${d_{xy}} + {p_x}$                  (B) ${d_{xy}} + s$                  (C) $s + {p_y}$                  (D) $s + {p_z}$

Hint: If two atomic orbitals have orientations such that they are not suitable for overlapping, non-bonding molecular orbitals will be formed.

-First of all let us see what non-bonding molecular orbitals are.
According to the molecular orbital theory when two atomic orbitals overlap, they lose their identity and form new orbitals known as molecular orbitals. In molecules electrons are filled in these molecular orbitals.
There exist 3 types of molecular orbitals: (1) Bonding molecular orbitals
(2) Anti-bonding molecular orbitals
(3) Non-bonding molecular orbitals
-Any molecular orbital for which the addition or removal of an electron does not cause change in the energy of the molecule is known as non-bonding molecular orbital (N.B.M.O.). The linear combination of atomic orbitals causes formation of molecular orbitals.
-For such orbitals there is complete lack of symmetry in the compatibility of any two bonding atomic orbitals and thus these newly formed molecular orbitals will have neither positive nor negative interactions with each other. The bond between two atoms is not affected by such orbitals.
-For example: In HF the ${p_x}$ and ${p_y}$ orbitals are present, they do not have orientations favourable to undergo overlapping. Hence they form non-bonding molecular orbital.
-We can thus conclude that if two atomic orbitals are in orientations where they cannot overlap, they will form non-bonding molecular orbitals.
-In the given options the orbitals which cannot undergo overlapping due to their orientations are: (${d_{xy}} + {p_x}$), (${d_{xy}} + s$), ($s + {p_y}$) and ($s + {p_z}$).
So, all of these orbitals will form non-bonding molecular orbitals.

Hence the correct options are: (A) ${d_{xy}} + {p_x}$
(B) ${d_{xy}} + s$
(C) $s + {p_y}$
(D) $s + {p_z}$

Note: Do not confuse non-bonding molecular orbitals (N.B.M.O.) with anti-bonding molecular orbitals (A.B.M.O.). Anti-bonding molecular orbitals are those in which the electron density is concentrated or collected behind the nucleus of the two bonding atoms and so these two nuclei are pulled away from each other. The bond between atoms is weakened due to such orbitals while N.B.M.O do not affect bond between two atoms.