The visualization of molecular orbitals (MOs) is important for analyzing the results of quantum chemistry simulations. The functions describing the MOs are computed on a three- dimensional lattice, and the resulting data can then be used for plotting isocontours or isosurfaces for visualization as well as for other types of analyses. Existing software pack- ages that render MOs perform calculations on the CPU and require runtimes of tens to hundreds of seconds depending on the complexity of the molecular system. We present novel data-parallel algorithms for computing lattices of MOs on modern graphics processing units (GPUs) and multi-core CPUs. The fastest GPU algorithm achieves up to a 125-fold speedup over an optimized CPU implemen- tation running on one CPU core. We also demonstrate pos- sible benets of dynamic GPU kernel generation and just-in- time compilation for MO calculation. We have implemented these algorithms within the popular molecular visualization program VMD, which can now produce high quality MO ren- derings for large systems in less than a second, and achieves the rst-ever interactive animations of quantum chemistry simulation trajectories using only on-the-y calculation.