## Abstract

A dualQMandMMapproach for computing equilibrium isotope effects has been described. In the first partition, the potential energy surface is represented by a combined quantum mechanical and molecular mechanical (QM/MM) method, in which a solute molecule is treated quantum mechanically, and the remaining solvent molecules are approximated classically by molecular mechanics. In the second QM/MM partition, differential nuclear quantum effects responsible for the isotope effect are determined by a statistical mechanical double-Averaging formalism, in which the nuclear centroid distribution is sampled classically by Newtonian molecular dynamics and the quantum mechanical spread of quantized particles about the centroid positions is treated using the path integral (PI) method. These partitions allow the potential energy surface to be properly represented such that the solute part is free of nuclear quantum effects for nuclear quantum mechanical simulations, and the double-Averaging approach has the advantage of sampling efficiency for solvent configuration and for path integral convergence. Importantly, computational precision is achieved through free energy perturbation (FEP) theory to alchemically mutate one isotope into another. The PI-FEP approach is applied to model systems for the ^{18}O enrichment found in cellulose of trees to determine the isotope enrichment factor of carbonyl compounds in water. The present method may be useful as a general tool for studying isotope fractionation in biological and geochemical systems.

Original language | English (US) |
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Article number | 2644 |

Journal | Molecules |

Volume | 23 |

Issue number | 10 |

DOIs | |

State | Published - Oct 15 2018 |

### Bibliographical note

Funding Information:Funding: This research was funded by the National Institutes of Health, grant number GM46736. M.L. acknowledges financial support for graduate studies by Jilin University. Article Processing Charge was sponsored by MDPI.

Publisher Copyright:

© 2018 by the authors. Licensee MDPI, Basel, Switzerland.

## Keywords

- Combined QM/MM
- Equilibrium isotope effects
- Nuclear quantum effects
- PI-FEP
- Path integral simulation