The role of quantum tunneling in hydrogen shift in linear heptyl radicals is explored using multidimensional, small-curvature tunneling Method for the transmission coefficients and a potential energy surface Computed at the CBS-QB3 level Of theory. Several one-dimensional approximations (Wigner, Skodje and Truhlar, and Eckart methods) were compared to the multidimensional results. The Eckart method was found to be sufficiently accurate in comparison to the small-curvature tunneling results for a wide range of temperature, but this agreement is in fact fortuitous and caused by error cancellations. High-pressure limit rate constants were calculated using the transition state theory with treatment of hindered rotations and Eckart transmission coefficients for all hydrogen transfer isomerizations in n-pentyl to n-octyl radicals Rate constants,are found in good agreement with experimental kinetic data available for n-pentyl and n-hexyl radicals. In the case of n-heptyl and n-octyl, our calculated rates agree well with limited experimentally derived data. Several conclusions made in the experimental studies of Tsang et al (Tsang, W.; McGivern, W. S.; Manion, J. A. Proc. Combust. Inst. 2009, 32, 131-138) are confirmed theoretically: older low-temperature experimental data, characterized by small pre- exponential factors and activation energies, can be reconciled with high temperature data by taking into account tunneling; at low temperatures, transmission coefficients are substantially larger for H-atom transfers through a five-membered ring transition state than those with six-membered rings; channels with transition ring structures involving greater than 8 atoms can be neglected because of entropic I effects that inhibit such transitions. The set of computational kinetic rates were used to derive a general rate rule that explicitly accounts for tunneling The rate rule is shown to reproduce closely the theoretical rate constants