2009/05/11 by Tomáš Zimmermann, Tomas Zimmermann, Jiří Vaníček +1
Chemistry · Physics and Astronomy · #Ab initio #Advanced Chemical Physics Studies #Anharmonicity #Chemistry #Computational chemistry #Deuterium #Feynman diagram #Harmonic oscillator #Kinetic isotope effect #Molecular Spectroscopy and Structure #Partition function (quantum field theory) #Path integral formulation #Physics #Quantum #Quantum mechanics #Quantum, superfluid, helium dynamics #Statistical physics #physics.chem-ph #physics.comp-ph
paper · pdf · doi:10.1063/1.3167353
published as J. Chem. Phys. 131, 024111 (2009) · 14 pages, 8 figures, 6 tables
arxiv created 2009/05/11 · openalex publication_date 2009/07/13 · arxiv updated 2015/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A general and rigorous methodology to compute the quantum equilibrium isotope effect is described. Unlike standard approaches, ours does not assume separability of rotational and vibrational motions and does not make the harmonic approximation for vibrations or rigid rotor approximation for the rotations. In particular, zero point energy and anharmonicity effects are described correctly quantum mechanically. The approach is based on the thermodynamic integration with respect to the mass of isotopes and on the Feynman path integral representation of the partition function. An efficient estimator for the derivative of free energy is used whose statistical error is independent of the number of imaginary time slices in the path integral, speeding up calculations by a factor of approximately 60 at 500 K and more at room temperature. We describe the implementation of the methodology in the molecular dynamics package AMBER 10. The method is tested on three [1,5] sigmatropic hydrogen shift reactions. Because of the computational expense, we use ab initio potentials to evaluate the equilibrium isotope effects within the harmonic approximation and then the path integral method together with semiempirical potentials to evaluate the anharmonicity corrections. Our calculations show that the anharmonicity effects amount up to 30% of the symmetry reduced reaction free energy. The numerical results are compared with recent experiments of Doering et al., [J. Am. Chem. Soc. 128, 9080 (2006); J. Am. Chem. Soc.129, 2488 (2007)] confirming the accuracy of the most recent measurement on 2,4,6,7,9-pentamethyl-5-(5,5-(2)H(2))methylene-11,11a-dihydro-12H-naphthacene as well as concerns about compromised accuracy, due to side reactions, of another measurement on 2-methyl-10-(10,10-(2)H(2))methylenebicyclo[4.4.0]dec-1-ene.