Force fields must accurately account for torsion-induced structural relaxations in order to produce accurate free energy profiles, thus the standard practice of generating QM data for MM force field parameterization involves minimizing the QM potential energy with the torsion angle of interest constrained to various values, e.g. on a regularly spaced grid. The result of this calculation is a set of QM constrained optimized structures and energies that includes relaxation effects from orthogonal degrees of freedom, which can be used to develop more accurate torsion parameters in the context of other energy contributions in the force field. In addition, two or more dihedral angles can be varied independently on a multi-dimensional grid to sample the conformational space more broadly, and/or to generate data for parameterizing torsion-torsion coupling or CMAP energy terms used in some force fields. For relevant molecular systems, the feasible geometry optimization methods involve local energy minimization starting from an initial guess structure. The optimized structure and energy, as well as the probability of the optimization algorithm successfully converging to a minimum, both depend strongly on the initial guess. The straightforward approach to this problem involves carrying out a series of constrained minimizations where the con-straint value is scanned along the grid, and each minimization is initiated from the optimized structure of the previous one. This calculation, which we term a "serial relaxed scan", is a standard feature in several widely used quantum chemistry and geometry optimization codes. The serial relaxed scanning approach has some major drawbacks. For one, the resulting optimized structures are dependent on the chosen sequence of calculations, such as the direction of the one-dimensional scan. This is because a series of constrained minimizations often stays in the same qualitative local minimum as determined by the orthogonal degrees of freedom, even if another local minimum with lower energy is reachable by scanning in the opposite direction; the other local minimum is found only if the energy barrier vanishes, which is not guaranteed. The result thus has a risk of including structures with unnecessarily high potential energies, which are not appropriate for fitting force field parameters because they introduce a bias toward thermodynamically unlikely conformations. This problem becomes more serious for multi-dimensional scanning as a greater number of choices need to be made for the scanning direction, and the results may depend on the ordering of dimensions. Another drawback is the lack of an efficient way to use multiple initial guesses, such as those resulting from a conformer generation method; 30,31 intuitively it should be possible to perform one scan using several initial guesses and keep the lowest energy structure from each, but at a lower total cost compared to running each scan independently.