1 Lin Lin Joint work with Roberto Car (Princeton), Joseph Morrone (Columbia) and Michele Parrinello (ETHZ) Computational Research Division, Lawrence Berkeley National Lab Displaced Path Integral Method for Computing the Momentum Distribution of Quantum Nuclei
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Lin Lin
Joint work with Roberto Car (Princeton), Joseph Morrone (Columbia) and Michele Parrinello (ETHZ)
Computational Research Division, Lawrence Berkeley National Lab
Displaced Path Integral Method for Computing the Momentum Distribution of Quantum Nuclei
Most molecular dynamics simulation treats nuclei as classical particles: Is this always a good approximation?
Momentum distribution of protons in water at room temperature. Data from [Reiter et al, Braz. J. Phys. 2004]
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Classical statistical mechanics β’ Kinetic energy (equi-partition theorem)
πΎ = β« ππ ππ
2π π π = 3ππ΅π
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β’ Prediction from classical statistical mechanics at
273K: K=35.3 meV 270K: K=34.9 meV
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Experimental evidence of nuclear quantum effects
Temperature dependence of kinetic energy of protons in water Prediction from classical statistical mechnics at 273K: 35meV Data from [Pietropolo et al, Phys. Rev. Lett., 2008]
Melting point (273K)
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Hydrogen atoms (and other light atoms) should be treated as quantum particles. How to compute the momentum distribution of quantum nuclei?
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Quantum statistical mechanics β’ Single body Hamiltonian for simplicity, extendable to the many
body case
π» = π π + π π = ββ2
2ππ»2 + π π
β’ π(π): Only for nuclei; obtained from force-field model, or density functional theory [Hohenberg-Kohn, 1964; Kohn-Sham 1965]
Environmental part of the end-to-end distribution β’ π π = πβ
ππ₯2
2π½β2 π π₯π(0)
β‘ πβππ₯2
2π½β2ποΏ½π(π)
β’ ποΏ½π contains all the environmental information of the quantum system.
β’ Superposition of ποΏ½π for all protons in hexagonal ice (log scale), reflecting the symmetry of the underlying oxygen sublattice (experimental verification under process)
β’ Classical dynamics: ποΏ½π β‘ 1
β’ [LL-Morrone-Car-Parrinello, Phys. Rev. B. 2011]
Conclusion β’ Displaced path integral method: efficient and accurate
method for estimating the momentum distribution
β’ Directional character: useful for crystal system.
β’ Factorized free particle and environmental contribution
β’ Improve the applicability of the free energy perturbation method using enhanced sampling technique for displaced path method [LL-Quah-Car-Parrinello, in preparation]
Acknowledgment Luis Alvarez fellowship supported by LBNL and DOE.