Fill in the VSEPR chart

One row per steric number, one column per lone pair count. Each cell is a steric number / coordination number pair — name the molecular geometry it gives you. Rows you leave unchecked are filled in for you.

Shape flashcards

Single-association reps, drawn weighted toward the shapes you keep missing, within the steric numbers you picked on the chart drill.

From a formula

Type a formula and it counts the electrons the way you would on paper: valence electrons, charge, bonding pairs, lone pairs, steric number, then the shape, the angles and the polarity.

Isomers

How many different structures can a formula give? Ligands are placed on the vertices of the parent geometry and the arrangements are counted up to rotation — then each one gets its point group, polarity and bond angles.

Shape reference

Every geometry from steric number 2 through 6, down to a coordination number of SN−4. Wedges point toward you, hashes away; the shaded lobes are lone pairs.

Symmetry elements and point groups

You get a molecule, you tick every symmetry element it has and name its point group. Answers come with the full operation listing and the reasoning, so a miss tells you which element you overlooked rather than just "wrong".

Point groups from geometry

Perfect geometry, identical ligands, no distortion to argue about: you get a shape off the VSEPR chart and you name its point group. This is the step that turns a shape you already know into a symmetry answer, and it is where most of the marks in a point group question actually sit.

Vibrations, IR and Raman

Pick a molecule and it works the whole thing through: Γtotal from the atoms each operation leaves alone, minus translation and rotation to get Γvib, the stretches on their own, and then which of them you would actually see in an IR spectrum and which in a Raman spectrum.

Point group reference

How to classify a molecule

The groups

The operations column is the character-table listing, which counts operations; the elements column counts kinds of element. Methane is the classic case — 4 C₃ axes but 8 C₃ operations.

Chiral molecules

A molecule is chiral when it has no improper operation at all — no mirror plane, no inversion centre, no S_n. That leaves only the pure-rotation groups C₁, C_n and D_n. Asked for a chiral molecule that is not a tetrahedral carbon with four different groups, these are the ones to reach for.

Worked molecules

Electron configurations

Write out the configuration for the element you are shown. Any ordering is accepted — [Ar] 4s2 3d6 and 1s2 … 3d6 4s2 both pass — as are superscripts, carets and no spaces at all.

Slater's rules

Work out the shielding constant S and the effective nuclear charge Z_eff = Z − S for a named electron. Every answer is followed by the full working, grouped the way Slater prescribes.

Quantum numbers

Every electron is labelled by four numbers: n, ℓ, mℓ and mₛ. This asks you to list all of them for a given orbital, to count orbitals, electrons and nodes, and to spot sets that cannot exist.

Orbital contours

Shapes, phases and nodes for each subshell. Filled and open lobes are opposite phases; dashed straight lines are angular (planar) nodes seen edge-on, and dashed rings inside a lobe are radial nodes.

Periodic trends

Which atom is larger? Every pair is either in the same period or the same group, and the answer comes with the reasoning — including the Slater Z_eff values when the two share a period.

Z_eff calculator

Pick any element and orbital to see the Slater working in full — useful for checking your own homework rather than guessing at it.

Diatomic MO diagrams

Type a diatomic — homonuclear or not, neutral or charged — and it builds the diagram, fills it, and reads off the bond order, the magnetism and the frontier orbitals. Heteronuclear pairs get their atomic levels skewed by electronegativity, so you can see which atom owns the bonding orbitals.

Build the MO diagram

You get a molecule and a scrambled set of its molecular orbitals. Put them in energy order and fill in the electrons, one arrow at a time, the way you would on paper. Marking is per level and per orbital, so a miss tells you which one you put in the wrong place.

Click a level in the tray, then click the rung you want it on. Click a placed level to send it back. Click an orbital box to cycle it through empty → one electron → a pair.

Ligand group orbitals

Pick a shape and it counts how many ligand σ orbitals survive each symmetry operation, builds the reducible representation Γσ, and reduces it with n(Γᵢ) = (1/h) Σ g·χ(R)·χᵢ(R) — every term shown, so you can check your own arithmetic against it.

Polyatomic MO diagrams

The same molecule two ways: by inspection, counting bonds and lone pairs, and by symmetry, matching each central orbital against the SALCs of the same irreducible representation. Where the two disagree is usually where the interesting chemistry is.

Orbital shapes

The six molecular orbitals a diatomic diagram is built from, drawn with their phases and nodes. A filled lobe is one phase and an open lobe the other; dashed red lines are nodal planes.

Character tables

The eight groups used here, with the central-atom orbitals that span each irreducible representation — the column you need when matching SALCs.