Start with the quantum rules that make orbital mixing meaningful, then build a linear combination such as 1s + 2p, 2px − 2py, or 2s + 0.5*3dz2. The app evaluates the signed wavefunction ψ and visualizes interference. Bare p means pz; bare d means dz².
Before mixing orbitals
Pauli constrains occupation, not superposition.
A single electron may occupy any normalized superposition of basis orbitals. The exclusion principle enters when several electrons are assigned spin-orbitals.
For the orbital-box diagrams, antisymmetry argument and filling examples, use the dedicated primer.
Interpretation. This is a linear combination of normalized hydrogenic atomic orbitals at one center. Calling the result a “hybrid orbital” is appropriate only when the chosen basis and coefficients represent a hybridization model. In particular, 1s + 2p is a superposition, not a conventional valence hybrid.
3D signed level surface
Drag to rotate · wheel to zoom · amber ψ > 0 · teal ψ < 0
x–z slice at y = 0
Brightness tracks |ψ|; phase is encoded by sign. The same extent and grid are used as the 3D field.
positive phasenegative phaseatomic units: Z = 1, a₀ = 1
Preset library
Save states built above, then add any saved state into the current expression. Presets are stored locally in this browser.
Local moments · exchange model
d¹ orbital lattice and magnetic order
This section separates orbital shape from magnetic order. Each rendered site carries one illustrative local
3d basis function and one spin-½ moment. The spin pattern is an input to a nearest-neighbour Heisenberg toy model,
not a prediction from the orbital picture alone.
A real d basis function is shown at each site. A real crystal-field eigenstate may instead be a linear combination of these functions.
J < 0 favours parallelJ > 0 favours antiparallel
This proxy only visualizes lobe orientation. It does not calculate a hopping integral or determine J.
Drag to rotate · wheel to zoom · amber/teal show the sign of ψ (red/blue are kept for charge) · arrows show the assumed local spin direction.
Nearest-neighbour bond thickness can encode a geometric orbital-direction proxy.
