By contrast, the energy profile generated by TorsionDrive is more symmetrical, as expected from the twofold symmetry of the molecule. The improved result is due to the wavefront propagation procedure, which initiates constrained optimizations in both directions; although the central atoms still adopt pyramidal geometries, both "branches" of the potential energy surface are treated equally. Moreover, the final energy profile generated by TorsionDrive has significantly lower energy barriers compared to the serial scan, though the barrier is still quite high at around 30 kcal/mol. In terms of computational cost, the serial relaxed scan involved a total of 24 constrained optimizations (601 gradient evaluations), whereas the TorsionDrive calculation involved 19 wavefront propagation steps with a total of 91 constrained optimizations (2073 gradient evaluations). Although the total computational cost of TorsionDrive is higher, we note that the wall time to job completion may actually be faster if sufficient parallel resources are made available (for 1-D scans, 4 parallel jobs is mostly sufficient). Multi-dimensional torsion scans provide greater insight into the conformational degrees of freedom of many biologically relevant molecules. For example, the backbone torsion angles of proteins occur in (φ, ψ) pairs, and amino acid side chains and glycosidic bonds contain flexible chains with 2 or more connected torsions. When scanning the torsion angle in 2 or higher dimensions, the conventional serial scanning approach suffers from similar problems as in the 1-D case, but the problems may be more serious. In addition to the 2 choices of scan direction for each dimension, the ordering of dimensions may also affect the results because only one torsion angle may be varied between contiguous calculations while the others are held fixed. Molecular systems with 2 or more coupled torsions tend to exhibit a high degree of flexibility, which also increases the chances of multiple local minima that are easily missed by a sequential scan.