Molecular Geometry & Bonding
what the shape decides
Concept

Spin-orbit — where it appears

The coupling between an electron's spin and its orbital motion. It returns some of the orbital angular momentum a ligand field quenched, which is what moves a g value away from the free-electron value.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

The spin-only count against nine measured moments. Each ion's magnetic moment computed from the number of unpaired electrons alone, √(n(n+2)) Bohr magnetons, beside the measured value. The two agree to a hundredth for the first five and the measurement exceeds the count by up to 0.93 for Co²⁺ — always in the same direction, which is what an omission looks like rather than noise.

A moment counts electrons, not orbitals

A magnetic moment is one of the few chemical measurements that returns an integer. Feed the count of unpaired electrons into √(n(n+2)) and nine first-row ions come back within a hundredth for five of them — and the five that miss all miss the same way, which is what a missing term looks like.

applied · Magnetism Which way the line moves counts the electrons. Three ions, their computed g-values and their measured ones. The shift is −2λ times a sum of squared matrix elements over energy denominators; the matrix elements are exactly two for Lz between dx²−y² and dxy and exactly one for Lx between dx²−y² and dyz, which is why the shift along the axis is four times the shift across it. The last column is what is left over — the orbital reduction factor, which is below one when the electron spends part of its time on the ligands and is a covalency measured with a magnet.

The g-value is the orbital coming back

A ligand field quenches the orbital angular momentum of a d electron, and spin-orbit coupling gives some of it back — upward for a shell more than half full and downward for one less than half full. Which way a resonance line moves counts the electrons, and the size of the move comes from two matrix elements and one optical splitting.

applied · Magnetism

Named alongside it

The objects these essays reach for when they reach for this one.

d orbitalsDegeneracyLigand fieldMagnetic momentSplittingAngular momentumCovalent bondingHund's ruleMagnetismMatrix elementSpin-onlyUnpaired electrons

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