We calculate numerically the collapse of slowly rotating, non-magnetic, massive molecular clumps, which conceivably could lead to the formation of massive stars. Because radiative acceleration on dust grains plays a critical role in the clump's dynamical evolution, we utilize a wavelength-dependent radiation transfer and a three component dust model: amorphous carbon particles, silicates and "dirty ice"-coated silicates. We do not spatially resolve the innermost regions of the molecular clump and assume that all material in the innermost grid cell accretes onto a single object. We introduce a semi-analytical scheme for augmenting existing evolution tracks of pre-main sequence protostars by including the effects of accretion. By considering an open outermost boundary, an arbitrary amount of material could, in principal, be accreted onto this central star. However, for the three cases considered (30, 60, and 120 solar masses originally within the computation grid), radiation acceleration limited the final masses to 31.6, 33.6, and 42.9 solar masses, respectively, for wavelength-dependent radiation transfer and to 19.1, 20.1, and 22.9 solar masses for comparison simulations with grey radiation transfer. We demonstrate that massive stars can in principle be formed via accretion through a disk. We conclude with the warning that a careful treatment of radiation transfer is a mandatory requirement for realistic simulations of the formation of massive stars.

39 pages, 13 figures, 4 tables, AASTEX v5.0, accepted by ApJ