Action spectroscopy of single molecules reactions with STM – My personal view back from 2001-

Having obtained an invitation to submit this personal view back to 2001 when I started to work with Prof. Maki Kawai for developing a theory of lateral hopping of a single CO molecule on Pd (1 1 0) with Bo Persson, I briefly describe how I got an idea for elementary processes of vibrationally mediated reactions of single molecules on metal surfaces. During the work with Prof. S.G. Thihodeev on a theory of inelastic electron tunneling spectroscopy (IETS) with scanning tunneling spectrum (STM-IETS), I found that IET current is expressed in terms of a vibrational density of states of a single molecule. This enabled me to propose a formula for a reaction rate $R\left(V\right)$ or yield per electron $Y\left(V\right)=R\left(V\right)/I$, here I is a tunneling current, i.e., action spectrum (STM-AS) of a single molecule reaction. I applied this formula to reproduce the experimental result of a CO molecule hopping on Pd (1 1 0) surface and more insights into the elementary process were revealed. Thomas Frederiksen and Magus Paulsson jointed me to develop a general formula of $Y\left(V\right)$ and successfully applied it to analyse the experimental results of H-atom relay reaction of a linear chain, H(D)₂O-OH(D)-O(D) H → H(D)-H(D)₂-OH(D)  → H(D)-H(D)-OH(D)₂ that was observed by Takashi Kumagai and Hiroshi Okuyama. Actually a hydrogen atom excited at one end of a linear chain composed of H₂O and several OH generates another one at the other end. We employed our formula of to reproduce the experimental result of $Y\left(V\right)$. It was found that excitation of the three characteristic vibrational modes (free OH/OD stretch, OH^∗ = OD^∗ stretch, and H₂O scissors, where H^∗ = D^∗ denotes the shared H/D^∗ atom in the H bond) were involved in the relay reaction. It was remarked that the OH(D^∗) = OD(D^∗ stretch modes are significantly redshifted from free OH/OD stretch and also characterized by very large broadening. The significant mode softening with respect to the free stretch modes and spectacular enhancement of the width are known to originate in the strong anharmonic character of a single H bond. Thomas investigated the reaction pathway from total energy calculations for the H-atom transfer reaction by the nudged elastic band method. The initial step is translation of the shared H-atom to the center hydroxyl, which is almost barrierless. The subsequent H-bond cleavage between OH and the center water molecule constitutes the highest barrier in which the displacement of the center water molecule along the [0 0 1] direction is mainly involved. The OH, OH^∗ stretch and H₂O scissors modes are therefore postulated to couple to the reaction coordinate for the H-bond cleavage. We have demonstrated a vibrationally induced H-atom-bond relay reaction within H-bonded chains assembled on Cu(1 1 0). In this reaction H-atom transfer results in the ‘structural’ transfer of a water molecule from one end of the chain to the other end without changing the platform of the chain, or actually transferring the molecule.

I have been thinking the unresolved issue of C₂H(D)₂ rotation on Cu (1 0 0) since it was published in 1998 by the W. Ho group. This experimental methods and the results obtained as the first demonstration of a single molecule switch are widely recognized as a milestone report of a single molecule manipulation by tunneling current and applied bias voltage which excites the vibrational modes of a molecule. They observed the STM images rotated at 90 degrees before and after applying appropriate bias voltage. They further compared the IETS spectrum and the $Y\left(V\right)$ for the rotation. The observed peak beautifully agreed with the threshold bias voltage, which clearly evidenced that a rotation is induced by excitation of a particular vibrational mode of C₂H(D)₂. In particular a crossover from a single electron process to a two electron process with increase in a tunneling current are of great interest. Sergei and his PhD student Yulia E. Shchadilova at that time and Magnus helped me much to reproduce all the experimental results by employing the Keldysh Green’s function theory combined with ab initio density functional theory (DFT) calculation of the optimized adsorption geometry and sophisticated vibrational analysis done by Magus. The experimental result of $Y\left(V\right)$ was reproduced by assuming a single electron process to excite the C-H stretch mode, and two electron process (ladder climbing of the C-H vibrational levels) and a excitation of the combination band. I also describe a brief theory of STM-AS I developed with Bo, Sergei, Magnus and Thomas.