Foundations — VBT applied to complexes — inner vs outer orbital, hybridization, magnetism

Before you can run the 6-step VBT recipe on the parent topic, you must own every symbol it throws at you. This page builds each one from nothing, in an order where every new idea rests only on earlier ones.

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1. An orbital — the empty box

The picture we will use everywhere: draw an orbital as a box ▢. An empty box is a room with no one in it; a box with one arrow ↑ has one electron; a box with ↑↓ is full.

Why the topic needs this: VBT is entirely a story about which boxes are empty (ligands need empty boxes to donate into) and which arrows are unpaired (that gives magnetism). If you cannot picture a box and its arrows, nothing later makes sense.

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2. Spin and the arrow ↑↓

Picture: an electron is a little bar magnet. Two electrons in the same box point opposite ways (↑↓) so their magnetisms cancel. A lone ↑ in a box does not cancel — it leaves a leftover magnetism.

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3. The $d$-orbitals, and inner vs outer

Orbitals come in families named $s,p,d$. Each family has a fixed number of boxes:

Family	Boxes	Holds up to
$s$	1	2 electrons
$p$	3	6 electrons
$d$	5	10 electrons

Why the topic needs this: the entire "inner vs outer orbital complex" distinction is just which $d$ boxes got used — the closer-in $3d$ (inner) or the further-out $4d$ (outer). Five boxes in the $d$ family is why octahedral complexes can borrow two of them.

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4. Electron configuration and $d^n$

How to fill the boxes — Hund's rule: spread electrons out singly (all ↑) before doubling up, because electrons repel and prefer separate rooms.

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5. Oxidation state — the charge symbol

Why the topic needs it: you cannot know $d^n$ until you know the ion. See Oxidation State Determination. The recipe is charge-balance:

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6. Ligand, lone pair, and coordinate bond

Why: this is the actual metal–ligand bond in VBT. The number of ligand hands = coordination number (next).

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7. Coordination number and geometry

Each C.N. forces a shape so the ligand hands sit as far apart as possible:

C.N.	Shape
2	linear
4	tetrahedral or square planar
6	octahedral

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8. Hybridization — reshaping the boxes

The key pair to distinguish:

• $d^{2}s{p}^3$ — uses inner $(n-1)d$ → inner orbital complex.
• $s{p}^3{d}^2$ — uses outer $nd$ → outer orbital complex.

Same octahedral shape, different $d$-boxes — that's the entire "$s{p}^3{d}^2$ vs $d^{2}s{p}^3$" subtlety.

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9. Strong vs weak field ligands

Why the topic needs it: pairing electrons empties inner $d$ boxes, which is the only way to get $d^{2}s{p}^3$ (inner) hybridization. Weak ligands don't pair, so no inner box opens → the metal must use outer $nd$. This single choice controls inner-vs-outer AND magnetism. (VBT can't explain the ordering — that needs Crystal Field Theory.)

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10. The magnetic moment symbol $\mu$

$\mu =0$ ⟹ diamagnetic (no lonely arrows); $\mu >0$ ⟹ paramagnetic. This ties directly to Magnetic Properties of Complexes. You met the symbol here; the parent derives why the formula looks like that.

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Prerequisite map

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Equipment checklist

Test yourself — say the answer aloud before revealing.