An orbital is a standing wave. A plucked string's lowest note has no nodes — that is 1s. Every higher note has nodes, points that never move, with the string displaced the opposite way either side. 2p's two lobes are exactly that: one wave, opposite sign across a node — not two things sitting side by side.
Drag the slider up — as the electron orbits faster, the trail fills in and starts to look like a fuzzy cloud. That cloud is the "electron cloud" you see around atoms in the other modes.
Every dot is one position drawn at random from |ψ|², the actual probability density. The electron is not travelling between them — there is no path. Turn the speed up to collect samples faster and watch the shape emerge. Compare 2s, which has a hollow shell where the electron is simply never found, against the planetary orbit, which can never produce a gap like that.
Bonding electron density
near O
--
near H
--
0 samples
Core 1s² (tight around O, don't bond)
O valence (bonding O-side + lone pairs)
H valence (bonding, started near H)
Four bonding electrons orbit between O and the H atoms. H electrons spend most of their time near O; it pulls them harder (that's electronegativity), which is why the red-and-blue cloud at high speed matches Mode 1: red where electrons pile up near O, blue where they're sparse near the Hs. That asymmetry is a polar covalent bond.
Toggle the lone-pair electrons above: oxygen holds two extra pairs of electrons not used in bonds. Oxygen's nucleus has 8 protons pulling on its electrons; that strong nuclear pull is why oxygen both draws the shared bonding electrons toward itself (electronegativity) and holds two lone pairs. The lone pairs and the polarity are consequences of that pull, not its cause.
Teaching simplification: real electrons aren't tiny balls following orbits. The cloud itself is the fundamental description (probability of finding the electron somewhere) — it isn't built by averaging a fast classical motion. You'll meet the real story in a quantum chemistry course.
This one is not a simplification. These are the exact hydrogen wavefunctions, and the dots are genuinely drawn from |ψ|² — the cloud is the orbital. The only liberty taken is showing the electron marker at the most recent sample, which is where it was found, not where it is "going". Colour is the sign of ψ; that sign is what decides whether two orbitals bond or cancel.
—mV live
equation predicts — mV
K⁺EK = — mV
outsidemM
insidemM
P
Na⁺ENa = — mV
outsidemM
insidemM
P
Cl⁻ECl = — mV
outsidemM
insidemM
P
T°C
Na⁺/K⁺ pump
ATP%
Membrane potential, last 30 s
Concentration and permeability sliders are logarithmic because the voltage depends on the log
of the ratio: equal slider travel is equal millivolts. Dragging [K⁺] outside from 5 to 50 mM
changes EK by the same 61 mV as 50 to 500.
The dots are a sample of each side, one dot per 2 mM: with ∞ bath (the default) each side
is a vast reservoir, so a crossing never changes the density. The top and bottom wrap around:
this is a slice of a much taller membrane. Ions cross only through their own channels (coloured
gaps; more channels, higher permeability). Every net crossing leaves a + on one face and a − on
the other, and the live voltage is just that count times 4 mV. That is the whole model: no
forces between ions, and the rates are chosen so the balance point is exactly the Goldman
equation, which the dashed line shows.
With a cell, the inside is finite: every crossing changes it by 0.5 mM. A real cell is
vastly larger, so a minute here stands for hours. At rest K⁺ leaks out and Na⁺ leaks in at
equal rates, and the pump undoes exactly that, 3 Na⁺ out and 2 K⁺ in per ATP, faster when Na⁺
has built up inside. Turn the ATP down and watch the battery drain; the pump is the charger.
Concentrations follow Marieb, Human Anatomy & Physiology 12e, Ch. 11. The five cell
presets follow the University of Arizona Nernst/Goldman Equation Simulator (Branch & Wright,
UA College of Medicine, 2007), which may be freely copied and displayed; this is a new
implementation of the same equations.
Molecular orbitals — click a level
■ ψ positive
■ ψ negative
This is what resonance means. The two structures with a double-headed arrow between them are a notation problem, not a physical one — the molecule is not flipping between them, and it is not a mixture of them. There is one orbital, spread over every carbon at once, and it is on screen.
Line the p orbitals up and they interfere just like any other waves. The lowest orbital has every lobe in phase — bonding all the way along. Each orbital above it adds a node, and nodes cost energy, exactly as they do on a string.
Where aromaticity comes from. A ring's levels come as one lowest orbital plus degenerate pairs. Filling every bonding level exactly therefore takes 2 + 4n electrons — that is Hückel's 4n+2, and it is arithmetic about the level pattern rather than a rule to memorise. Bring 4n electrons instead and the top level is a degenerate pair holding one electron each: an open shell, which is worse than not conjugating at all.
Hückel theory keeps only the π system, gives every carbon the same energy and every adjacent pair the same interaction, and ignores overlap and electron repulsion. It is crude, and it is not how the energies would be computed today. What survives the stripping is the part that depends only on which atoms are connected to which — and that is precisely what decides aromaticity, which is why a theory this rough still gets 4n+2 right.
■ ψ positive
■ ψ negative
This is why SN2 attacks from the back.
A nucleophile has to put its electron pair into the lowest empty orbital of the substrate, and for a C–X bond that is this σ*. Its density is pushed out of the bond by the node, onto the far side of the carbon — anti to the leaving group. There is nowhere else to donate. The carbon then turns inside out like an umbrella, which is the inversion of configuration.
E2's anti-periplanar requirement is the same statement: the C–H σ orbital has to line up with this σ* to hand its electrons over.
A bond is interference. Two atomic orbitals overlap, and like any two waves they can add in phase or out of phase — you always get both combinations, never just one.
In phase, the waves reinforce between the nuclei. That build-up of negative charge between two positive nuclei is what a bond physically is.
Out of phase, they cancel there instead, leaving a node exactly where the bond should be. That orbital is antibonding, marked with a star. It is normally empty — but it is where electrons go when something attacks.
Try the separation slider and watch S, the overlap. Note that end-on (σ) overlap beats side-on (π) at the same distance: that is why σ bonds are stronger, and why a π bond resists twisting — twisting misaligns the sideways overlap that holds it.
Built by adding the exact hydrogenic functions (LCAO), with an effective nuclear charge so orbital size matches real bond lengths — a bare Z = 1 2p orbital is several times longer than any bond, and at that size σ and π overlap come out the wrong way round. Drawn here is the densest 70% of the probability.
■ ψ positive
■ ψ negative
Drag to rotate — the tetrahedron only reads properly in motion. Drawn here is the densest 60% of the probability; orbitals have no edge, so any lobe you have ever seen drawn is a contour someone chose.
Adding the waves — ψ along the hybrid's axis
These are the real wavefunctions, not a sketch. Watch the bottom trace as you drag: s and p reinforce on the right and cancel on the left. What is left over is a lobe that points.
Why lobes at all?
An orbital is a standing wave, like a plucked string. The fundamental has no nodes — that is 1s, and it is just a sphere. Higher notes have nodes: places the wave passes through zero, with opposite sign either side.
A p orbital is the first one with an angular node — a flat plane through the nucleus, positive on one side and negative on the other. Two lobes is simply what one nodal plane looks like. (d orbitals have two nodal planes, which is why they have four lobes.)
The node is forced, not chosen: p has to be orthogonal to s, and s never changes sign, so p must be + in some places and − in others for the overlap to cancel exactly.
The lobes bulge at a distance instead of reaching the nucleus because an electron with angular momentum cannot sit on top of it. The wave is pushed outward, then pulled back by the nuclear charge; the balance sets where it swells.
A hybrid is those waves added together. s is positive everywhere, p is + one side and − the other, so they reinforce on one side and cancel on the other: one big lobe pointing out, a small stub behind. That is why a hybrid points, and it is why the drag slider changes the shape and the angle at the same time.
The balloon picture gets the arrangement right and the reason wrong. The two lobes of one p orbital are not two objects pushing each other apart — they are one wave, above and below zero, like the two halves of a vibrating string. And 109.5° is not the result of a shoving match: if you want four equivalent orbitals out of one s and three p, orthogonality forces cos θ = −1/3. VSEPR's repulsion story reaches the same number by different reasoning; both are models, neither is the literal mechanism.
Hybrid orbitals are a description, not an observable. Methane's photoelectron spectrum shows two ionisation energies, not four equal ones, because the true molecular orbitals are delocalised. The localised picture here is a valid transformation of those and is the right tool for predicting geometry and reactivity.
Click one atom for its hybrids, two for a bond length, three for an angle (the atom bonded to the other two is the vertex, in any click order). Drag to rotate.
Predict first
°
Click an atom for its electronegativity, two bonded atoms for the bond. Drag to rotate.
Predict first
Point charges, not quantum mechanics: μ = Σ qᵢrᵢ over the atoms and, for water, the TIP4P
M site. Bond arrows follow the book's convention, from δ+ to δ− with a cross at the
positive end, with lengths from electronegativity differences scaled together so they add
up to the molecular dipole: a bookkeeping picture, not separate measurements. The charge
map colours the electron cloud by the same charges' potential, red δ− to blue δ+; it uses
the force-field charges and does not change with the charge-set switch. 1 D = 3.336 ×
10⁻³⁰ C·m (OpenStax Organic Chemistry §2.2, ch02 line 148).
● donor H (N–H, O–H) ● acceptor O ┄ hydrogen bond. Drag to rotate.
two copies in Mode 1: drag one until a donor H meets the other's C=O and watch the energy drop
%
mm
2–3 mm is right
fast°C/min
slow°C/min
H-bonds intact — / —
A cartoon driven by the bench's melting range, not a simulation: heat in → vibrations grow →
H···O contacts stretch past 2.3 Å → the stack falls apart.
25.0 °C
0:00 on screen ≈ 0.0 min at the bench
onset — °C · clear — °C
Predict first (mixed-melting-point test)
A lookup, not physics: literature melting points, a melting-range rule for impurity,
packing and ramp rate, and a thermal-lag term, all stated in src/melt/model.ts. Time runs
12× faster than a real bench. The picture in the capillary is a cartoon of a packed solid
loosening; it is not a simulation of the crystal.
Newman projection (looking down the highlighted bond)
Energy profile
Energies come from an OPLS-AA molecular-mechanics force field. It reproduces the ethane barrier (12.6 vs 12.5 kJ/mol) and the methyl A-value (8.0 vs 7.3 kJ/mol) closely. The ring-flip barrier reads high (~60 vs ~45 kJ/mol) because the flip is driven along a single ring dihedral, while a real flip moves several at once — the shape and the ordering are right, the absolute height is not.
Add 2 H and 1 O, then drag atoms together. Without "Shed energy (stabilize)" turned on, a colliding pair can't shed its energy; watch it bounce apart. Turn it on and the capture sticks, releasing the bond energy as light and motion.
Teaching simplification: this is a classical cartoon of bonding, not quantum chemistry. There are no electrons or orbitals here, real reactions usually have an energy barrier this sandbox skips, and only radical-recombination reactions (like O + H) are shown. The flash of 'light' is a stand-in for the energy a new bond releases; real bond formation usually does not emit visible light (and H + H cannot emit light at all). You will meet the real story in a chemistry course.
300 K · 27 °C · 80 °F
coldvery hot
Add to Box (salt, ice, molecules)
Simulation Precision
Water O-H bonds are already constrained by the rigid-body rotation integrator — no SHAKE pass needed. Cutoff is the biggest perf lever; timestep the second; thread count matters at N > 200.
press V to center the view
What am I looking at?
You're watching a box of real molecules — not a cartoon. Each colored sphere is one atom, and atoms are bonded into molecules (e.g. H₂O: one red oxygen, two white hydrogens). The soft glow around each molecule is its electron cloud: red where electrons pile up (negative regions), blue where they're sparse (positive). Red-to-blue contrast is what drives polarity and hydrogen bonding.
The cluster sits in a roomy simulation box with empty space around it — that's intentional. You can drop more molecules in via "Add to Simulation" (under "Show box controls") and watch them join, repel, or mix with what's already there.
About the box edges: by default the box uses periodic boundaries — when a molecule drifts off one face, an identical copy enters from the opposite face. That's how we get bulk-fluid physics out of a tiny cell instead of a drop in vacuum. To see that infinity, turn on "Infinite box view" at the bottom of the main panel — it draws faded ghost copies in all 26 neighboring cells. It's off by default so the cluster reads cleanly on first load.
What the panel on the right shows: energy level (average molecular kinetic energy, displayed as 0–100% with a qualitative band), pressure (an approximate, uncalibrated virial readout), box side length, and nearest-neighbor distance. The energy level is regulated by a thermostat; it does what your slider tells it. The pressure value is qualitative only (small system, cutoff electrostatics), so read its trend rather than the number; the barostat (pressure regulator) is off by default and lives in "Show box controls".
Things to try:
Drag the energy slider — watch motion slow down toward "cold," speed up toward "hot."
Switch molecules: compare water (strongly polar, sticky) with methane (nonpolar, lonely).
Turn on Network to see lines connecting molecules that are currently attracting each other (mostly hydrogen bonds for water, but any attraction); they blink in and out as molecules move.
Pick an experiment from the dropdown for a guided demo.
Ask a Chemistry Tutor
The tutor sees your current simulation state plus your question.
Ctrl+Enter to send
Sim state sent with your question
(opens when you click Ask)
Backend & API key
Local setup: run ollama serve, then set backend = OpenAI-compatible,
endpoint = http://localhost:11434/v1/chat/completions, model = llama3.1:8b
(or qwen2.5:7b, etc.).