Isotope effect in acetylene C2H2 and C2D2 rotations on Cu(001)

A comprehensive analysis of the elementary processes behind the scanning tunneling microscope controlled rotation of C2H2 and C2D2, isotopologues of a single acetylene molecule adsorbed on the Cu(001) surface, is given, with a focus on the isotope effects. With the help of density-functional theory we calculate the vibrational modes of C2H2 and C2D2 on Cu(001) and estimate the anharmonic couplings between them, using a simple strings-on-rods model. The probability of the elementary processes, nonlinear and combination band, is estimated using the Keldysh diagram technique. This allows us to clarify the main peculiarities and the isotope effects of the C2H2 and C2D2 on Cu(001) rotation, discovered in the pioneering work [B. C. Stipe et al., Phys. Rev. Lett. 81, 1263 (1998)], which have not been previously understood.