the electrostatic valence principle

This is Pauling's second rule, and it is a simple bookkeeping idea: in a stable ionic crystal, the negative charge of each anion is paid off, locally, by the positive cations that bond to it, no more and no less. Picture each anion as owing a debt equal to its charge, and each neighbouring cation chipping in a share of its own charge to cover that debt. When the shares reaching an anion add up exactly to its charge, the books balance and the structure is happy.

Define a cation's electrostatic bond strength (its bond valence) as its charge divided by its coordination number, s = z / CN. Each anion should have the bond strengths reaching it sum to its own charge. Work it for rutile, TiO2: titanium is Ti4+ in six-fold coordination, so each Ti-O bond carries strength s = 4/6 = 2/3. Each oxygen is O2- and is surrounded by three titaniums, so the strengths reaching it total 3 times 2/3 = 2, exactly the oxygen's charge. The rule is satisfied, and it even told us oxygen must be three-coordinated here.

This local-neutrality rule is the quantitative workhorse of Pauling's set. It predicts how many cations must surround each anion, screens out compositions that cannot balance charge, and is the ancestor of the modern bond-valence method used to check and refine real crystal structures. It also explains a deep fact: charge balance is satisfied locally, anion by anion, not just globally for the whole formula, which is a strong constraint on which structures can exist at all.