A strategy to obtain quantum corrections to the cumulative reaction probability from a subspace of active coordinates is analyzed. The kinetic energy operator exactly takes into account the constraints due to inactive coordinates. The geometry of the inactive skeleton is adiabatically adjusted to the dynamical variables or simply frozen according to the coupling to the active space. Dynamics is carried out using the curvilinear coordinates of the Z-matrix so that computation of the potential energy surface and dynamics are coupled. The cumulative reaction probability N(E) is obtained directly in a large range of energy by a time independent formulation of the Zhang and Light transition state wave packet method. N-nD(E) is first computed in the active n-dimensional space and then convoluted with a bath. The efficiency of the Chebyshev expansion of the microcanonical projection operator delta(E-(H) over cap (nD)) appearing in the quantum expression of N-nD(E) is checked. The method is implemented for the study of tunneling effect in H transfer. The coordinates are three spherical coordinates referred to the frozen or adiabatic skeleton. We compare the quantum corrections brought about by different 2D groups of internal coordinates.