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How to use
Pick a molecule or a preset. Drag to rotate, click atoms (up to four) to measure a distance, angle or dihedral; the selected centre also drives the VSEPR readout. Choose a vibration mode to animate it (slow motion; amplitude is the real thermal amplitude times the exaggeration slider), switch the model (ball and stick, space-filling, sticks, wireframe), add a van der Waals or electron-density surface, or open the orbital views. Space pauses, R resets.
What to try. 1) Compare H2O, NH3 and CH4: one, two lone pairs squeeze the angle below 109.5°. 2) Open XeF4 and SF4 to see why AX4E2 is square planar and AX4E is a seesaw. 3) Compare the CO2 symmetric stretch (no dipole change, IR inactive) with the asymmetric one. 4) Raise the temperature to enlarge the vibration amplitude. 5) Drag the density isovalue and watch the surface grow from a bonded skeleton to a vdW envelope. 6) Open the 3d z² orbital and count the lobes and nodes. 7) In the H2 view slide R: the overlap S(R) falls and the antibonding node plane stays at the midpoint.
Atom sprites and the bench backdrop are rendered in Blender 5.2 (Cycles); all chemistry is computed in the page.
The science
Geometry data. Each of the 41 molecules is built from experimental internal coordinates (bond lengths r and angles, NIST CCCBDB / Herzberg / WebBook style tables, re or r0 depending on source) converted to Cartesian coordinates in Angstrom, centred on the centre of mass and rotated to the principal axes. Every tabulated length and angle is re-measured from those coordinates by the in-page checks. Methyl and CH2 hydrogens of methanol and cyclohexane use idealised tetrahedral placement and are labelled as such.
VSEPR. Steric number SN = X + E. Lone pairs on an atom are counted from valence electrons, E = (V - sum of bond orders) / 2 so that, for example, XeF4 gives AX4E2 and square planar. Lone pairs repel more strongly than bonding pairs, which is why H-O-H is 104.5° and H-N-H 106.7° instead of 109.5°. Simplifications: a double or triple bond counts as one electron domain; ligand electronegativity and size (which also change angles) are ignored; hypervalent centres use the formal valence-shell count. The predicted ideal angle is the idealised polyhedron value and is shown next to the measured one.
Normal modes. The potential is a valence force field,
V = ∑ ½ kr (Δr)² + ∑ ½ kθ (Δθ)² + ∑ ½ koop h²
with stretch constants kr in N/m by bond type, bend constants kθ in aJ/rad², and an out-of-plane term only for planar three-coordinate centres (angle terms alone give zero harmonic stiffness there). The Hessian is formed by central differences, mass-weighted D = M-1/2 H M-1/2, D L = L Λ, ν̃ = √λ / (2πc)
and diagonalised with a Jacobi solver; zero eigenvalues (translations and rotations) are dropped, leaving 3N-6 modes (3N-5 for linear molecules). For a diatomic the result must equal ν̃ = (1/2πc) √(k/μ) and for the CO2 symmetric stretch (carbon stays at rest) ν̃ = (1/2πc) √(k/mO); both are checked. Honest limits: a plain valence force field has no stretch-stretch or stretch-bend coupling, so the model is within about 5-15 % of the observed fundamentals (the observed values are listed beside it); a handful of force constants (CO2, SO2, O3, HCN, N2O, NH3, H2O, H2S, H2CO) are tuned to land close, and diatomic constants are taken from the observed ωe. Torsions are not modelled, so ethane, H2O2 and methanol show one mode fewer than 3N-6 and benzene lacks its soft out-of-plane ring modes. Relative IR intensity is proportional to |∂μ/∂Q|² computed from the bond-polarity charges below, so it is exactly zero for the CO2 symmetric stretch and for homonuclear molecules (a qualitative model, not a quantum calculation).
Amplitude and speed. The quantum thermal rms normal coordinate is ⟨Q²⟩ = (ℏ / 2ω) coth(ℏω / 2kBT) and the peak is √2 times the rms; the Cartesian displacement of an atom is Q li/√mi. The slider multiplies this physical amplitude (a real zero-point amplitude is only about 0.05-0.1 Å for hydrogen). Motion is shown in slow motion: 1600 cm-1 plays at 1.2 Hz, other modes scale in proportion to their wavenumber. Zero-point energy is ZPE = ½ h c ∑ ν̃.
Polarity and dipole. Bond ionic character follows Hannay and Smyth, i = 0.16 |Δχ| + 0.035 (Δχ)² with Pauling electronegativities, giving a charge shift on each bond. The model dipole μ = ∑ qi ri is compared with the observed value. It reproduces HF and HCl to within about 5 % and gives exactly zero for symmetric molecules, but it has no lone-pair or polarisation contribution, so H2O and NH3 come out 25-40 % too small. Surface colours (red negative, blue positive) are a qualitative point-charge potential, not a computed electrostatic potential.
Electron density. The isosurface uses a promolecular density: a sum of atomic densities, each a sum of Slater-type shells,
ρA(r) = ∑shells Ns (2ζ)2n+1 / [(2n)! 4π] · r2n-2 e-2ζr, ζ = (Z - S)/n*
with the screening constant S from Slater's rules. Atoms are spherical and not allowed to relax, so there is no build-up of density between bonded atoms; real SCF densities differ by up to a few hundredths of an e/bohr³ in the valence region. The default isovalue 0.002 e/bohr³ is the usual convention for a van der Waals-like envelope. The hydrogen atom shell reproduces the exact value ρ(0) = 1/π. The van der Waals surface is the union of spheres with Bondi radii.
Orbitals. Hydrogenic functions ψ = Rnl(r) Ylm are normalised in atomic units (for example R10 = 2Z3/2e-Zr, R32 = (4/81√30) Z3/2(Zr)² e-Zr/3) with real spherical harmonics; energy is -13.606 Z²/n² eV and the number of radial nodes is n-l-1. The two coloured lobes (blue +, red -) are the isosurfaces |ψ| = const chosen so that the enclosed probability equals the slider (default 90 %). The H2 view is an LCAO of two Slater 1s functions, ψ± = (φA ± φB) / √(2(1 ± S)), S = e-ζR(1 + ζR + ζ²R²/3)
with ζ = 1.24, the variational optimum for H2. It shows the node of the antibonding orbital and the density build-up of the bonding one; it does not compute energies or correlation.
Rotation. The moments of inertia come from the coordinates and isotopic masses; the rotational constant is B = h / (8π² c I) = 16.8576 / I(amuŲ) cm-1 and is checked against the observed Be of CO and HCl.