This chapter discusses the physics and properties of four types of atomic forces occurring in STM and AFM: the van der Waals force, the hard core repulsion, the ionic bond, and the covalent bond. The general mathematical form of the van der Waals force between a tip and a flat sample is derived. The focus of this chapter is the covalent-bond force, which is a key in the understanding of STM and AFM. The concept of covalent bond is illustrated by the hydrogen molecular ion, the prototypical molecule used by Pauling to illustrate Heisenberg's concept of resonance. The Herring-Landau perturbation theory of the covalent bond, an analytical incarnation of the concept of resonance, is presented in great detail. It is then applied to molecules built from many-electron atoms, to show that the perturbation theory can be applied to practical systems to produce simple analytic results for measurable physical quantities with decent accuracy.
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