molecular orbitals

Definition: Molecular orbital (MO) theory explains the behavior of electrons in molecules. It is crucial for understanding chemical bonding and molecular stability.

Basic Concept: Hydrogen (H) atoms combine to form a hydrogen molecule (H2).
- Each hydrogen atom has 1 valence electron located in the 1s orbital.
- The two hydrogen atoms can be designated as Hydrogen A and Hydrogen B, referred to as 1s_a and 1s_b respectively.

Conservation of Orbitals: When atomic orbitals mix, the total number of molecular orbitals created equals the number of atomic orbitals combined.
- E.g., Mixing two 1s orbitals results in two molecular orbitals (bonding and antibonding).

Electrons as Waves: Treating electrons as waves helps understand their behavior during bonding:
- Constructive Interference: When two waves are in phase, they amplify each other, resulting in a higher probability of finding an electron in that area.
- Bonding Molecular Orbital (MO): Formed by the addition of in-phase atomic orbitals (1s_a + 1s_b).
- Represents a region of high electron probability between the two nuclei (where atomic nuclei are positive charges).
- This configuration promotes molecule formation.
- Graphical Representation:
- Higher electron probability region located between Hydrogen atoms' nuclei.

Attractive Forces:
- Each nucleus has protons that attract surrounding electrons (from the other atom) leading to overall attractive forces favoring bond formation.
Net Force Analysis:
- Consider the forces acting on the protons in the bonds:
- Four attractive forces (two protons attracting their respective electrons) versus two repulsive forces (the protons repelling each other).
- Conclusion: Bond formation is energetically favorable when electrons are situated between nuclei.

Destructive Interference: When atomic orbitals are out of phase, they result in the cancellation of probabilities, hence forming an antibonding molecular orbital (1s_a - 1s_b).
- Characteristics of Antibonding MO:
- Probability of finding electrons in between the nuclei becomes very low (node is created in this region).
- Electrons are more likely found away from the region between the nuclei.
Visual Representation:
- Electrons are more distributed towards outer sides of the hydrogen atoms.

Energy Diagram:
- Combining two H atoms’ orbitals leads to:
- Bonding MO (lower energy): Denoted as σ1s
- Antibonding MO (higher energy): Denoted as σ1s^*
Energy and Stability:
- Electrons naturally seek lower energy states; thus, they tend to fall into bonding MOs.
- Bond formation is exothermic, releasing energy.
Bond Order Calculation:
- Bond Order (BO) is calculated using:
  ext{BO} = \frac{( ext{Number of Bonding Electrons}) - ( ext{Number of Antibonding Electrons})}{2}
- For H2: BO = 1 (indicating a stable single bond).

Paramagnetic vs Diamagnetic:
- Paramagnetic: Molecules with unpaired electrons (attracted by magnetic fields).
- Diamagnetic: Molecules with all paired electrons (repelled by magnetic fields).
- H2 is diamagnetic due to paired electrons.

Bond Order Values and Stability:
- Single Bond (BO = 1) → stable, as in H2.
- Double Bond (BO = 2) → as in O2.
- Triple Bond (BO = 3) → as in N2, highly stable.

Configuration and Stability of H2^-:
- Calculate bond order:
- Electrons: 2 bonding (σ1s) - 1 antibonding (σ1s^*) → BO = 1/2.
- Electron Configuration: σ1s (2 electrons), σ1s^* (1 electron).
Diamagnetic vs Paramagnetic:
- H2^- has unpaired electrons (one), so it is paramagnetic.

Dihelium (He2):
- Helium has 2 electrons in the 1s orbital.
- Bond Order Calculation: 2 bonding - 2 antibonding = 0 (no bond exists).
- Conclusion: Dihelium does not exist as a molecule. Helium exists as individual atoms.
Electron Configuration:
- He2: σ1s (2 electrons) and σ1s^* (2 electrons).