Atomic-scale structural control over matter is the ultimate challenge for engineering. A particularly promising version of this idea considers the use of organic molecules as pre-fabricated functional building blocks which can be tailored chemically with millions of options and billions of identical copies. The research that has been triggered by this vision is typically restricted to molecules in their naturally found adsorption structures, since our means of precise molecular manipulation are as yet very limited, not to mention the absence of a clear idea how individual molecules could be assembled into functional devices.
I will introduce the possibilities offered by the controlled mechanical manipulation of molecules (CM3) with a scanning probe microscope (SPM) [1,2]. In the CM3 approach, molecules are almost handled like macroscopic work-pieces, “grabbed” at a specific atom by an actuator (SPM tip) and mechanically guided into a certain conformation. Once fully implemented, CM3 could enable access to many molecular degrees of freedom (bending, stretching, tilting, rotating, flipping, displacing, detaching), sub-Angstrom precise conformational changes along all these degrees of freedom, and a manipulation that is deterministic and not stochastic.
The formidable many-particle problem that is inherent to CM3 and that is not yet solved is the inference of the complex molecular conformation (i.e. of the N spatial coordinates of all atoms) during manipulation on the basis of only a single SPM measurement channel.
In CM3 only the tip-contacted atom can be moved at will, while all other atoms in the molecule respond to that according to the intramolecular mechanics and external constraints like the surface. Hence, only three-dimensional subspaces within the N-dimensional configuration space can be reached by CM3. The 3D subspaces are not connected because the molecular conformation can change abruptly and irreversibly during manipulation, much like a ratchet. Since there is a finite number of subspaces (i.e. possible molecular conformations) at a given SPM tip position, the inference of conformations reduces primarily to a problem of multinomial classification.
I will discuss the molecular mechanics model [3–5] that could be used to generate the labels for such a classification and the possibility of experimentally mapping out the mechanical stiffness dFz/dz of the tip-molecule-surface junction within individual subspaces. These subspace “fingerprints” could then serve as input for a machine learning algorithm that has been trained beforehand either on the molecular mechanics model of the respective molecule or primarily on experimental data.
 N. Fournier, C. Wagner, C. Weiss, R. Temirov, and F. S. Tautz, Phys. Rev. B 84, 035435 (2011).
 M. F. B. Green, T. Esat, C. Wagner, P. Leinen, A. Grötsch, F. S. Tautz, and R. Temirov, Beilstein J. Nanotechnol. 5, 1926 (2014).
 C. Wagner, N. Fournier, F. S. Tautz, and R. Temirov, Phys. Rev. Lett. 109, 076102 (2012).
 C. Wagner, N. Fournier, V. G. Ruiz, C. Li, K. Müllen, M. Rohlfing, A. Tkatchenko, R. Temirov, and F. S. Tautz, Nat. Commun. 5, 5568 (2014).
 C. Wagner, N. Fournier, F. S. Tautz, and R. Temirov, Beilstein J. Nanotechnol. 5, 202 (2014).
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