For perturbation, we alchemically modify the potential energy function (described in detail below) to slowly annihilate and then restore ligand interactions with the environment, resulting in a sequence of reduced potentials u t that incorporate the timedependent interactions of the ligand with its environment. In the middle of the protocol, when the ligand is no longer interacting with the environment, we rotate the ligand into a new orientation in an operation that does not change the potential energy of the system. This is done by translating the center of mass of the ligand to the origin, applying a rotation matrix to its coordinates, and reversing the translation to restore the ligand's original center of mass. The rotation matrix is drawn uniformly over the space of all rotations using a quaternion approach, in which a random quaternion is generated uniformly over a 4D hypersphere and converted to a rotation matrix. This ensures the probabilities of generating a particular rotation matrix and its inverse are equal so that the overall proposals are time-symmetric.