PAGE 01
Pauli, spin and occupancy
Why orbital superposition is allowed, why identical spin-orbitals cannot be occupied twice, and why a spatial orbital can still hold two opposite-spin electrons.
Open page →Visual quantum chemistry · roadmap
From one-electron orbitals to molecules, solids and magnetic order.
A sequence of visual models, each adding one physical idea at a time. The goal is to keep track of what mathematical object is being visualized: a one-electron orbital, a many-electron occupation pattern, a localized bonding model, or a collective solid-state model.
PAGE 02
Orbital superposition studio
Construct normalized combinations of hydrogenic s, p and d functions and inspect the signed wavefunction in three dimensions and in section.
Open studio →PAGE 03
From atoms to simple molecules
Enter recipes such as H*2 + O → H2O and see a localized orbital-overlap picture: central-atom hybridization, σ bonds and lone-pair directions.
Open page →OFF-TOPIC A
Aufbau → Pascal → Fibonacci
Keep the orbital energy ordering, add a toy nearest-neighbour exclusion rule, and count the legal occupation strings. The shallow diagonals of Pascal’s triangle sum to Fibonacci numbers.
Open side quest →PAGE π
π density, interference and acidity
Separate total π density into atomic and interference terms, inspect molecular-orbital phase, Coulson charges and electrostatic potential, then compare simple descriptors with measured pKa.
Open π-density lab →PAGE 04
Crystal fields and d-level splitting
Move from isolated d orbitals to symmetry-adapted energy levels in octahedral, tetrahedral and lower-symmetry environments.
PAGE 05
Local moments and exchange
Separate local d-electron moments from magnetic order, then compare FM, AFM and frustrated trial states using a nearest-neighbour exchange model.
PAGE 06
From orbitals to bands
See how repeated atomic states become Bloch states and bands, and why metallic magnetism cannot generally be inferred from isolated-atom filling alone.
Conceptual progression
one-electron
wavefunction
wavefunction
→
many-electron
occupancy
occupancy
→
localized
bonding model
bonding model
→
collective
solid-state model
solid-state model
→
band and correlation
refinements
refinements
Design principle. Each page should say explicitly what is being assumed. A localized hybrid-orbital cartoon is useful for understanding bonding,
but it is not the same object as a delocalized molecular orbital, and neither is the same object as a solid-state band or a magnetic ground state.