Download Nuclear quantum effects in molecular dynamics simulations

Nuclear quantum effects in molecular dynamics simulations
Fabien Brieuc 1 , Marc Hayoun2 , Hichem Dammak 1
1
Laboratoire Structures, Propriétés et Modélisation des Solides, CNRS UMR 8580, École Centrale
Paris, F-92295 Châtenay-Malabry, France
2
Laboratoire des Solides Irradiés, École Polytechnique, CEA -DSM, CNRS, F-91128 Palaiseau,
France
[email protected]
Molecular dynamics (MD) is a powerful numerical method to investigate properties of
condensed matter systems. Interatomic forces are calculated using either force fields or ab initio
schemes, such as density functional theory (DFT), while the dynamics of the nuclei is based on
classical mechanics. These calculations are thus only valid in the classical limit and so for large
temperatures. The quantum effects associated with the dynamics of the nuclei are completely
neglected. However, nuclear quantum effects (NQE), such as zero point energy or tunneling effect,
are important in some cases and a quantum treatment of the dynamics of the nuclei is needed. For
example, it is necessary to include NQE to study the low temperature regime, the dynamics of light
atoms (such as hydrogen) or the isotope effects.
The method commonly used to simulate quantum dynamics is path integral molecular dynamics
(PIMD) [1]. PIMD can provide exact results for any type of cohesive energy, however it is
particularly time consuming and therefore the range of its applicability is reduced. A new approach
based on modified Langevin dynamics has been recently proposed by Dammak et al. [2] and
Ceriotti et al. [3]. In these semiclassical methods the system is in contact with a quantum thermal
bath (QTB) allowing the inclusion of NQE into MD simulations. QTB-MD saves at least two orders
of magnitude of computation time compared to PIMD and yields accurate results. Although this
new approach is based on the harmonic approximation, it is able to reproduce experimental results,
for instance the behavior of the heat capacity of a MgO crystal [2] (figure 1), the isotope effects in
LiH/LiD [4] (figure 2) and vibrational spectra of molecules [5]. However, the method can become
approximate when dealing with strongly anharmonic potentials.
Figure 1 : Heat capacity of a MgO crystal calculated by QTB-MD simulation [2]. The QTB values agree with the
experimental data. The standard MD simulation gives reliable values only at temperatures higher than the Debye one
(940 K).
We show that it is possible to combine QTB with PIMD [6] in order to extend the scope of QTBMD. By applying the QTB thermostat, with the correct power spectral density, to PIMD
simulations, the computation time is reduced by at least a factor of 4 compared to usual PIMD. The
QTB-PIMD combination is able to provide satisfactory results even for strongly anharmonic
systems in reasonable computation times.
Figure 2 : Isotopic shift in lattice parameter, for both 7LiH and 7LiD, versus T [4]. (a) Experimental results; QTB-MD
simulations by using (b) DFT within the GGA or (c) the shell model. In order to point out quantum effects, results of
standard MD are included in the case of the shell model potential.
[1] D. M. Ceperley, “Path integrals in the theory of condensed helium”, Rev. Mod. Phys. 67, pp. 279-355 (1995).
[2] H. Dammak, Y. Chalopin, M.Laroche, M.Hayoun, J.J. Greffet, “Quantum thermal bath for molecular dynamics
simulation”, Phys. Rev. Lett. 103, p. 190601 (2009).
[3] M. Ceriotti, G. Bussi, M. Parrinello, “Nuclear quantum effects in solids using colored-noise thermostat”, Phys. Rev.
Lett. 103, p. 030603 (2009).
[4] H. Dammak, E. Antoshchenkova, M. Hayoun, F. Finocchi, “Isotope effects in lithium hydride and lithium deuteride
crystals by molecular dynamics simulations”, J. Phys : Condens. Matter 24, pp. 435402-435407 (2012).
[5] F. Calvo, N.T. Van-Oanh, P. Parneix, C. Falvo, “Vibrational spectra of polyatomic molecules assisted by quantum
thermal baths”, Phys. Chem. Chem. Phys. 14, pp. 10503-10506 (2012).
[6] M. Ceriotti, D. E. Manolopoulos, M. Parrinello, “Accelerating the convergence of path integral dynamics with a
generalized Langevin equation”, J. Chem. Phys. 134, p. 084104 (2011).