Draw the molecular orbital diagram of CS.

Draw the molecular orbital diagram of CS. Determine bond order, magnetism, spin multiplicity, and HOMO/LUMO.

The Correct Answer and Explanation is:

To draw the molecular orbital diagram of carbon monosulfide (CS), we need to consider the bonding between carbon (C) and sulfur (S). CS is a diatomic molecule and its molecular orbital diagram involves the combination of atomic orbitals of carbon and sulfur atoms.

Steps for constructing the molecular orbital diagram:

1. Determine the electron configuration of atoms:
   • Carbon (C): 1s² 2s² 2p²
   • Sulfur (S): 1s² 2s² 2p⁶ 3s² 3p⁴
   Since sulfur is in the third period, its 3s and 3p orbitals will interact with carbon’s 2s and 2p orbitals, respectively.
2. Orbital interactions:
   • The lowest-energy molecular orbitals are formed from the combination of the atomic 2s and 3s orbitals, followed by the 2p and 3p orbitals.
3. Fill the molecular orbitals:
   The molecular orbitals are arranged in increasing energy order (for a heteronuclear molecule like CS):
   • σ(2s), σ*(2s)
   • σ(3s), σ*(3s)
   • π(2p), π*(2p) (degenerate, higher energy)
   • σ(2p), σ*(2p)
   Based on this, the total number of electrons in CS is 10 (from carbon) + 6 (from sulfur) = 16 electrons.
4. Filling the molecular orbitals:
   • 2 electrons in σ(2s) (bonding)
   • 2 electrons in σ*(2s) (antibonding)
   • 2 electrons in σ(3s) (bonding)
   • 2 electrons in σ*(3s) (antibonding)
   • 4 electrons in π(2p) (bonding)
   • 2 electrons in π*(2p) (antibonding)
5. Determine bond order:
   • Bond order = (number of bonding electrons – number of antibonding electrons) / 2
   • Bond order = (2 + 2 + 4) – (2 + 2) / 2 = 4 / 2 = 2
6. Magnetism:
   CS has no unpaired electrons in its molecular orbitals, meaning it is diamagnetic.
7. Spin multiplicity:
   The spin multiplicity is calculated as 2S + 1, where S is the total spin quantum number. Since all electrons are paired, S = 0, and the spin multiplicity is 1 (singlet).
8. HOMO and LUMO:
   • The Highest Occupied Molecular Orbital (HOMO) is the π*(2p) orbital.
   • The Lowest Unoccupied Molecular Orbital (LUMO) is the σ*(2p) orbital.

Summary:

• Bond order: 2
• Magnetism: Diamagnetic
• Spin multiplicity: 1 (singlet)
• HOMO: π*(2p)
• LUMO: σ*(2p)