Thermal rate constants are calculated for the H CH4 f CH3 H2 reaction employing the potential energy surface of Espinosa-Garci a (Espinosa-Garci a, J. J. Chem. Phys. 2002, 116, 10664). Two theoretical approache are used. First, we employ the multicon?gurational time-dependent Hartree method combined with ?ux correlation functions. In this way rate constants in the range 225 400 K are obtained and compared with previous results using the same theoretical method but the potential energy surface of Wu et al. (Wu, T. Werner, H.-J.; Manthe, U. Science 2004, 306, 2227). It is found that the Espinosa-Garci a surface results in larger rate constants. Second, a harmonic quantum transition state theory (HQTST) implementation of instanto theory is used to obtain rate constants in a temperature interval from 20 K up to the crossover temperatur at 296 K. The HQTST estimates are larger than MCTDH ones by a factor of about three in the common temperature range. Comparison is also made with various tunneling correctins to transition state theory and quantum instanton theory.