  A surface-adsorbed molecule is contacted with the tip of a scanning tunneling
microscope (STM) at a pre-defined atom. On tip retraction, the molecule is
peeled off the surface. During this experiment, a two-dimensional differential
conductance map is measured on the plane spanned by the bias voltage and the
tip-surface distance. The conductance map demonstrates that tip retraction
leads to mechanical gating of the molecular wire in the STM junction. The
experiments are compared with a detailed ab initio simulation. We find that
density functional theory (DFT) in the local density approximation (LDA)
describes the tip-molecule contact formation and the geometry of the molecular
junction throughout the peeling process with predictive power. However, a
DFT-LDA-based transport simulation following the non-equilibrium Green's
functions (NEGF) formalism fails to describe the behavior of the differential
conductance as found in experiment. Further analysis reveals that this failure
is due to the mean-field description of electron correlation in the local
density approximation. The results presented here are expected to be of general
validity and show that, for a wide range of common wire configurations,
simulations which go beyond the mean-field level are required to accurately
describe current conduction through molecules. Finally, the results of the
present study illustrate that well-controlled experiments and concurrent ab
initio transport simulations that systematically sample a large configuration
space of molecule-electrode couplings allow the unambiguous identification of
correlation signatures in experiment.
