Which of the following linear combination of atomic orbitals will lead to formation of molecular orbitals in homonuclear diatomic molecules [internuclear axis in $$z$$-direction] ? A. $$2p_z$$ and $$2p_x$$ B. 2 s and $$2p_x$$ C. 3 $$d_{xy}$$ and 3 $$d_{x^{2} - y^{2}}$$ D. 2 s and $$2p_z$$ E. $$2p_z$$ and $$3d_{x}^{2}- y^{2}$$ Choose the correct answer from the options given below:

For the formation of molecular orbitals in homonuclear diatomic molecules (with the internuclear axis along the $$z$$-direction), the combining atomic orbitals must have the same symmetry with respect to the internuclear axis.

The rule is: Orbitals combine only if they have the same symmetry about the molecular axis. Specifically, they must have the same value of $$m_l$$ along the z-axis ($$\sigma$$ for $$m_l = 0$$, $$\pi$$ for $$|m_l| = 1$$, $$\delta$$ for $$|m_l| = 2$$).

A. $$2p_z$$ and $$2p_x$$: $$2p_z$$ has $$m_l = 0$$, $$2p_x$$ has $$|m_l| = 1$$. Different symmetry. Cannot combine. No.

B. $$2s$$ and $$2p_x$$: $$2s$$ has $$m_l = 0$$ ($$\sigma$$), $$2p_x$$ has $$|m_l| = 1$$ ($$\pi$$). Different symmetry. Cannot combine. No.

C. $$3d_{xy}$$ and $$3d_{x^2-y^2}$$: $$3d_{xy}$$ has $$|m_l| = 2$$ ($$\delta$$), $$3d_{x^2-y^2}$$ also has $$|m_l| = 2$$ ($$\delta$$). Same symmetry, but these are on the same atom. For a homonuclear diatomic, the $$3d_{xy}$$ on one atom combines with $$3d_{xy}$$ on the other. The statement says combining $$3d_{xy}$$ with $$3d_{x^2-y^2}$$, which are different orbitals on different atoms with the same $$|m_l|$$ but different orientations. They do not form bonding/antibonding pairs with each other. No.

D. $$2s$$ and $$2p_z$$: Both have $$m_l = 0$$ ($$\sigma$$ symmetry). They can combine to form molecular orbitals. Yes.

E. $$2p_z$$ and $$3d_{x^2-y^2}$$: $$2p_z$$ has $$m_l = 0$$, $$3d_{x^2-y^2}$$ has $$|m_l| = 2$$. Different symmetry. Cannot combine. No.

Only D leads to formation of molecular orbitals.

The correct answer is Option B: D Only.