9–15 However, achieving the first goal of efficiently optimizing these molecular geometries is still challenging this is because the potential energy surface is relatively flat along the intermolecular directions compared to intramolecular ones, and long sequences of energy and gradient evaluations are often required to reach a local minimum. In recent years, significant advances have been made toward the second goal, such as accurate approximations to high-level electronic structure theories 5–8 and energy decomposition analyses. 1–4 In theoretical chemistry, the fundamental tools for studying intermolecular interactions include optimizing the molecular geometry to locate the critical points on the many-dimensional potential energy surface, then calculating and characterizing the interactions at a given geometry. Intermolecular interactions are widely recognized for their central role in determining the structure, function, and properties of macromolecules, molecular complexes, and molecular materials. Our findings indicate that an explicit description of molecular translation and rotation is a natural way to traverse the many-dimensional potential energy surface. The method also introduces a new way to scan the molecular orientations while allowing orthogonal degrees of freedom to relax. When TRIC is incorporated into geometry optimization calculations, the performance is consistently superior to existing coordinate systems for a diverse set of systems including water clusters, organic semiconductor donor-acceptor complexes, and small proteins, all of which are characterized by nontrivial intermolecular interactions. The translations are described as the centroid position and the orientations are represented with the exponential map parameterization of quaternions. Here we introduce a new translation-rotation-internal coordinate (TRIC) system which explicitly includes the collective translations and rotations of molecules, or parts of molecules such as monomers or ligands, as degrees of freedom. The effective description of molecular geometry is important for theoretical studies of intermolecular interactions.
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