experimental measurements were carried out using 
 the cambridge 
 hese spectrometer , which measures the 
 isf i(k , t ) , 
 related to the dynamic structure factor s(k, ) and the pair correlation function g(r , t ) by temporal and spatial 
 fourier transforms , respectively . as 
 such , hese is a uniquely noninvasive technique that can be used to 
 study the detailed mechanism of individual atomic jumps on well - defined 
 surfaces . , 
 the netherlands ) was cleaned by repeated cycles of argon sputtering , 
 flash annealing , oxidation , and reduction , and the surface quality was monitored using helium reflectivity 
 measurements . molecular h ( air liquide , 99.999% purity ) was dosed 
 by backfilling the scattering chamber , and surface uptake of atomic 
 h was followed using the specularly scattered helium beam to achieve 
 a coverage of 0.2 monolayer ( ml ) , determined from the known dose of 
 h and sticking probability . all 
 dft calculations were performed within a periodic plane - wave 
 framework using projector - augmented wave potentials in the vasp code modified for pimd simulations . the 
 pimd simulations were performed with 16 replicas ( i.e. , beads of the 
 ring - polymers ) . tests with 32 and 64 beads showed very good agreement 
 with the 16 bead simulations . pimd - based qtst gives the jump rate 
 over the 
 reaction coordinate  ( the fcc - hcp diffusion path ) as1where v is 
 the thermal 
 velocity : v = ( 2kbt/m ) . p(,t ) and p(0,t ) are the centroid 
 ( center of mass of the ring polymer ) probability densities at the 
 transition state  and initial ( fcc ) state 
 0 , respectively , and f is 
 the corresponding free - energy difference obtained from a series of 
 constrained - centroid pimd simulations . although representing the reaction coordinate in terms of centroid 
 positions becomes inaccurate for highly asymmetric potentials at temperatures 
 far below the crossover to quantum tunneling , it should provide 
 an accurate description for the moderately asymmetric potential just 
 below the crossover temperature as studied here .
an 
 understanding of hydrogen diffusion on metal surfaces is important 
 not only for its role in heterogeneous catalysis and hydrogen fuel 
 cell technology but also because it provides model systems where tunneling 
 can be studied under well - defined conditions . 
 here we report helium 
 spin  echo measurements of the atomic - scale motion of hydrogen 
 on the ru(0001 ) surface between 75 and 250 k. quantum effects are 
 evident at temperatures as high as 200 k , while below 120 k we observe 
 a tunneling - dominated temperature - independent jump rate of 1.9  
 109 s1 , many orders of magnitude faster 
 than previously seen . 
 quantum transition - state theory calculations 
 based on ab initio path - integral simulations reproduce the temperature 
 dependence of the rate at higher temperatures and predict a crossover 
 to tunneling - dominated diffusion at low temperatures . 
 however , the 
 tunneling rate is underestimated , highlighting the need for future 
 experimental and theoretical studies of hydrogen diffusion on this 
 and other well - defined surfaces .