Note that g is computed in Cartesian coordinates before being transformed to any other coordinate system that might be used for geometry optimization. When vibrational frequency calculations are performed on a geometry that has been optimized using fixed-atom constraints, the result is often numerous (up to 3N fix ) imaginary frequencies, due to an inconsistent treatment of the gradient and the Hessian, if no adjustments are made to the latter. In our previous work, fixed-atom vibrational frequency calculations were performed in that way. However, problems with imaginary frequencies can be mitigated somewhat by means of a makeshift approach based on a Hessian matrix (H) whose elements are