(a) Experimental PDFs for δ-MnO2 synthesized as a function of pH, showing the reverse variation of the Mn⋯MnL and Mn⋯MnIL pairs as a result of the layer-to-interlayer migration of MnL at acidic pH. The closest approach of any two MnIL atoms is 7.2 Å. This occurs when the two Mn atoms are located on opposite sides of the layer and positioned on a diagonal across an intervening layer Mn (⋯ MnL⋯ configuration), as illustrated in Fig. 6(c). (b) Best-fit PDF profiles up to 8.5 Å calculated for a model containing 17% vacancies (Fig. 6c). This model reproduces the pH variation of the Mn⋯Mn pairs, except for the MnL⋯Mn3IL correlation, which is overestimated. (c)–(e) Best-fit PDF profiles up to 7 Å calculated for a chalcophanite model (Fig. 6d). This model reproduces the short-range relaxation of the Mn⋯Mn and Mn—O distances around vacancies.