Diarylethene derivatives are photochromic molecular switches, undergoing a ring-opening/-closing reaction by illumination with light. The symmetry of the closed form is determined by the Woodward-Hoffmann rules according to which the reaction proceeds by conrotatory rotation in that case. Here, we show by a combined approach of scanning tunneling microscopy (STM) and density functional theory (DFT) calculations that the open isomer of 4,4'-(4,4'-(Per\-fluo\-ro\-cyclo\-pent-1-ene-1,2-diyl)\-bis(5-me\-thyl\-thio\-phene-4,2-diyl)di\-py\-ri\-dine) (PDTE) retains its open form upon adsorption on a Ag(111) surface. It can be switched into a closed form, which we identify as the disrotatory cyclization product, by controlled manipulation with the STM tip. Evidence of an electric-field dependent switching process is interpreted on the basis of a simple electrostatic model, which suggests that the reaction proceeds {\it via} an ``upright'' intermediate state. This pathway thus strongly differs from the switching reaction in solution.