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# Adaptive quantum/molecular mechanics: what have we learned, where are we, and where do we go from here?

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Adaptive quantum‐mechanics/molecular‐mechanics (QM/MM) methods feature on‐the‐fly reclassification of atoms as QM or MM during a molecular dynamics (MD) simulation, allowing the location and contents of the QM subsystem to be dynamically updated as needed. Such flexibility is a distinct advantage over conventional QM/MM, where a ‘static’ boundary is retained between the QM and MM subsystems. The ‘dynamic’ boundary in adaptive QM/MM allows a finite‐size QM to sustain simulations with an arbitrary length of time. To ensure smooth transitions between QM and MM, the energy or forces are interpolated. Special treatments are applied so that artifacts are eliminated or minimized. Recent developments have shed light on the relationship between the adaptive algorithms that describe Hamiltonian and non‐Hamiltonian systems. Originally developed to model an ion solvated in bulk solvent, adaptive QM/MM has been enhanced in many aspects, including the treatment of molecular fragments in macromolecules, monitoring molecules entering/leaving binding sites, and tracking proton transfer via the Grotthuss mechanism. Because the size of the QM region can be set as small as possible in adaptive QM/MM, the computational costs can be kept low. Small QM subsystems also facilitate the utilization of high‐level QM theory and long simulation time, which can potentially lead to new insights. WIREs Comput Mol Sci 2017, 7:e1310. doi: 10.1002/wcms.1310

(a) Proton indicator I (green) as the QM‐zone center. The position of I depends on the coordinates of the donor D and acceptor A. It superimposes with the shared H in the Zundel‐structure limit and the hydronium O in the Eigen‐structure limit, and varies smoothly in between. (b) Potentials of mean force for H+ relay in bulk water by PAP simulations using two different sizes of the QM region. In both cases, the buffer zone is 0.5 Å thick. The reaction coordinate is defined as dr = |r AH − r DH|. ‘Adaptive’ denotes modified‐PAP calculations, while ‘Large QM’ denotes the reference conventional QM/MM with sufficiently large QM subsystem (r = 12 Å) such that boundary effects are negligible during the 10‐ps simulations. Convergence of the barrier at dr = 0 for H+ transfer toward the reference (~0.1 kcal/mol) is observed when r min increases from 4 Å to 6 Å. (Adapted from Ref with permission. Copyright 2015 American Chemical Society)
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Pseudo‐atom X (orange) as the center of a binding site on a surface, which is described by QM in adaptive QM/MM simulations. QM groups are in red, buffer group in green, and MM groups in blue.
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Transport of an ion (purple sphere) through a channel in the direction indicated by the red arrows. The pore residues are colored by their residue ID numbers. The mobile solvation shell (dashed circle) is treated by QM along the translocation path.
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Example of partitioning configurations for N = 2 in the PAP scheme. In this snapshot, the QM group is red, the two buffer groups green, and the MM group blue. In total 4 partitioning configurations V A, $V 1 A$, $V 2 A$, and $V 1,2 A$ are computed, where the buffer groups are shown in red if treated by QM or blue if by MM, respectively.
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Interpolation of energy between two sets of potentials. The QM/MM potential energy of the system is V A (blue curve) when the buffer group is treated at the MM level and $V 1 A$ (red curve) when treated at the QM level. The green curve represents the smooth transition between V A and $V 1 A$ in the buffer‐zone range (r min ≤ ri  ≤ r max).
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QM/MM modeling of a hydrated ion (purple sphere) in bulk water. The QM subsystem (highlighted in yellow) consists of the ion and its solvation shell. The two blue arrows indicate possible exchange of water molecules between the solvation shell and bulk solvent. Color code: red, O; gray, H.
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Example of buffer zone inserted between the QM and MM zones in adaptive QM/MM. The QM zone (light yellow) consists of a solute A (purple) and its solvation‐shell molecules (red). Centered at the solute, the buffer zone (light blue) is a spherical shell of radius between r min and r max. A solvent molecule becomes a buffer group (green) if the distance ri between it and the solute satisfies r min ≤ ri  ≤ r max. Solvent molecules in the MM zone are shown as in blue color.
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