Conductance in monatomic metal contacts is quantized; it increases in discrete steps of one conductance quantum 2e 2 =h. By contrast, in a vacuum barrier between two metal surfaces we find that conductance increases linearly and continuously with the interaction energy between individual atoms. This behavior shows unambiguously that current flow between single atoms is a measure for their chemical interaction. In the controlled environment of a scanning tunneling microscope it should allow us to study the formation of covalent bonds up to the point where these atoms finally jump into contact. DOI: 10.1103/PhysRevLett.91.036803 PACS numbers: 73.40.Gk, 71.15.Mb, 73.23.Hk Because of their importance for technical applications the conductance properties of metals have been widely researched. In metal break junctions at close to zero temperature the conductance of single atomic contacts has been measured with great accuracy, and it was generally found that conductance increases in discrete steps of one conductance quantum 2e 2 =h [1][2][3][4][5]. The rupture of a bond probes into material properties from the starting point of material stability. Quite the opposite is true for the operation of scanning probe microscopes. There, the interaction between two separate surfaces is generally kept at such a low level that the small changes in the forces between the surfaces or in the number of electrons tunneling through the vacuum barrier can be used as an indication of the surface topographic and electronic properties. The intermediate range between these two methods continues to be problematic. In particular, the role of chemical interactions in scanning probes, even though widely researched [6 -13], is still not well understood. Part of the problem is the theoretical representation of the situation in different frameworks: perturbation methods are generally limited to high distances, they can incorporate chemical interactions only from the outset [13][14][15]. Scattering methods, while electronically accurate, cannot treat atomic interactions and their shift of position at low distances [16]. Nonequilibrium methods are in principle reliable, but they cannot simulate actual probe scans due to their innate restrictions of the symmetry of the combined system [17,18].Here, we propose a new method, which incorporates chemical interactions in a natural way. The method is based on extensive ab initio calculations of coupled systems. These calculations, including chemical interactions from the outset, establish that the suggested perturbation method is in general sufficient to reach the highest level of experimental accuracy.A system, composed of a conducting surface and an equally conducting probe, will be completely decoupled if the distance between the surface atoms and the foremost atom of the probe (apex atom) is substantially greater than 1 nm. Then the electron states of surface and probe are orthogonal: every productwill be zero. If the two systems are brought into closer contact, with a distance of about 0.5-0.6 nm,...