Scanning tunneling microscopy has repeatedly resolved individual atoms on a number of metal surfaces with atomic distances 2.5–3 Å. This is in sharp contradiction to the resolution limits previously predicted, 6–9 Å. We present a theory of such atomic resolution in terms of actual tip states, for example, ${\mathit{d}}_{\mathit{z}}^2$ tip states on tungsten tips. Quantitative interpretation of the observed images is obtained with no adjustable parameters. We predict that to achieve atomic resolution, the tip material should be either a d-band metal or certain semiconductor.

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