Deep-Dive Guides · Atomic & Molecular Structure

Atomic & Molecular Structure — the complete deep dive

Quantum numbers and orbital shapes, screening and Slater's rules, Russell–Saunders coupling and term symbols, spin–orbit splitting and the selection rules that govern atomic spectra — then the same logic carried into molecules through LCAO-MO diagrams and molecular term symbols.

Free extract — the opening section of the guide, in full.

0. How to use this guide — the two recipes

Almost every question in this unit is one of two chains, run forwards or backwards. Learn the chains and the individual facts stop being a list to memorise.

ATOM: configuration → L, S (couple) → term 2S+1L → J (spin–orbit) → level 2S+1LJ → spectrum recipe 1
MOLECULE: atomic orbitals → symmetry match → MO diagram → configuration → Λ, S, g/u, ± → term recipe 2
The three questions to ask of any structure problem: (1) How many electrons are outside closed shells? Closed shells contribute L = 0, S = 0 and are invisible to the term symbol. (2) Are the open-shell electrons equivalent or inequivalent? Equivalent electrons (same n and l) are restricted by the Pauli principle, so only some terms survive; inequivalent ones are not. (3) Is the coupling Russell–Saunders or j–j? Light atoms (Z ≲ 30) couple L and S first; heavy atoms couple l and s on each electron first.

Three more habits worth building now. Count microstates before you write terms — the count is a free check on your answer. Treat a filled subshell as a spherical, L = 0, S = 0 core — and a half-filled one as L = 0 but maximalS (p³ is S = 3/2, d⁵ is S = 5/2, f⁷ is S = 7/2). Spherical symmetry kills the orbital angular momentum, not the spin — which is exactly why Mn²⁺ and Fe³⁺ are ⁶S₅/₂ with 5.92 μ_B, not diamagnetic. And when a question mentions magnetism, remember that the spin-only formula ignores the orbital contribution that the term symbol is telling you about; for first-row ions with A or E ground terms the agreement is good, for Co(II) and the lanthanides it is not.

Read the rest of this guide

The remaining 10 sections — Quantum numbers & hydrogenic orbitals, Many-electron atoms — screening, Slater, configurations, Term symbols & Hund's rules, Spin–orbit coupling & atomic spectra and more — are part of ChemVidya Full Access, along with the other guides, the books, the study notes and 6,000+ practice questions with worked solutions.

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