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Molecular Orbital Diagrams

UniversityChemistrySchematic homonuclear valence MO filling with Hund populations and signed hydrogenic LCAO isosurfaces

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About this experiment

Fill bonding and antibonding orbital boxes, predict bond order and unpaired electrons, and inspect the phase interference of atomic-orbital combinations in three dimensions.

Learning goals

  • Apply Pauli occupancy and Hund filling in degenerate orbitals.
  • Calculate model bond order from bonding and antibonding electron counts.
  • Relate unpaired electrons to a simple paramagnetic prediction.

How to use it

  1. 1Load oxygen and verify two unpaired electrons in its degenerate antibonding pi orbitals.
  2. 2Compare nitrogen and oxygen bond orders and their selected orbital surfaces.
  3. 3Clear the electrons, place them manually, and compare your populations with the ground-state fill.
  4. 4Inspect a bonding and antibonding combination and identify an inter-nuclear node where present.

The model

Bond order is the bonding-minus-antibonding population difference divided by two.
Relative AO phase determines constructive or destructive interference.
Opposite wavefunction signs are phase information, not opposite electric charges.

Assumptions

  • Energy rows are schematic. For B2, C2 and N2 the bonding pi levels lie below sigma-2p; for O2, F2 and Ne2 their order is reversed.
  • The second-period diagrams omit filled 1s core bonding and antibonding orbitals, whose bond-order contributions cancel. Hydrogen and helium use only 1s combinations.
  • Isosurfaces use unnormalised hydrogenic 1s, 2s or 2p combinations with a common effective length scale. They are not self-consistent molecular orbitals or measured energies.
  • Manual excited populations are allowed, and positive bond order alone is not a proof of real molecular stability. Magnetic classification is the elementary unpaired-electron rule.

Try this in class

  1. Q1Why does oxygen have unpaired electrons even though its total electron count is even?
  2. Q2Why does adding an electron to an antibonding orbital lower the bond order by one half?

Frequently asked questions

Why can the two colours meet at a node?

They denote opposite signs of the orbital amplitude. A node is a zero of the combined wavefunction; squaring it gives zero contribution from that orbital.

Why do the lower-period orbital rows change order?

The diagram includes the usual qualitative effect of s-p mixing for the lighter second-period diatomics. It does not calculate orbital energies from first principles.