Integral and differential cross sections for pure rotational and simultaneous rotational-vibrational excitation of H2 by Li + impact have been computed following the coupled-channel formalism using two different SCF potential energy hypersurfaces and a CI hypersurface at 0.6 and 1.2 eV. Sensitivity of integral cross sections to (a) choice of ab initio potential energy surface and (b) expansion length of a Legendre polynomial representation of one of the energy surfaces is examined. It is seen that preparation of H2 in the υ=0, j=2 state leads to four- and fivefold increases in excitation cross sections to the υ′=1, j′=i, i=0,2,4 states relative to excitation of ground state (υ=0, j=0) H2. Differential cross sections are reported at 1.2 eV for up to five quantum rotational and for vibrational transitions on one of the energy hypersurfaces. All angular distributions required for determining ratios (inelastic: elastic) of differential cross sections needed for comparison with recent time-of-flight experiments at 0.6 eV are computed using both SCF and CI potential energy surfaces and compared. Further comparisons are made with experiment, beyond those that have appeared to date, which indicate that a significant discrepancy at one of the three angles for which measurements are available is due to experiment. Copyright © 1975 American Institute of Physics.