Quantum effects in graphene monolayers: Path-integral simulations

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Graphene bilayers display peculiar electronic and mechanical characteristics associated to their two-dimensional character and relative disposition of the sheets. Here we study nuclear quantum effects in graphene bilayers by using path-integral molecular dynamics simulations, which allow us to consider quantization of vibrational modes and study the effect of anharmonicity on physical variables. Finite-temperature properties are analyzed in the range from 12 to 2000 K. Our results for graphene bilayers are compared with those found for graphene monolayers and graphite. Nuclear quantum effects turn out to be appreciable in the layer area and interlayer distance at finite temperatures. Differences in the behavior of in-plane and real areas of the graphene sheets are discussed. The interlayer spacing has a zero-point expansion of 1.5 × 10 −2Å with respect to the classical minimum. The compressibility of graphene bilayers in the out-of-plane direction is found to be similar to that of graphite at low temperature, and increases faster as temperature is raised. The low-temperature compressibility increases by a 6% due to zero-point motion. Especial emphasis is laid upon atomic vibrations in the out-of-plane direction. Quantum effects are present in these vibrational modes, but classical thermal motion becomes dominant over quantum delocalization for large system size. The significance of anharmonicities in this atomic motion is estimated by comparing with a harmonic approximation for the vibrational modes in graphene bilayers.

Section: B Layer Areamentioning

confidence: 83%

Nuclear quantum effects in graphene bilayers

Herrero

Ramı́rez

2019

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“…Further simulation conditions are identical to those already described in our previous PIMD graphene simulations. 38,50…”

Section: Computational Conditionsmentioning

confidence: 99%

Phonon dispersion in two-dimensional solids from atomic probability distributions

Ramı́rez

Herrero

2019

We propose a harmonic linear response (HLR) method to calculate the phonon dispersion relations of two-dimensional (2D) layers from equilibrium simulations at finite temperature. This HLR approach is based on the linear response of the system, as derived from the analysis of its centroid density in equilibrium path integral simulations. In the classical limit, this approach is closely related to those methods that study vibrational properties by the diagonalization of the covariance matrix of atomic fluctuations. The validity of the method is tested in the calculation of the phonon dispersion relations of a graphene monolayer, a graphene bilayer, and graphane. Anharmonic effects in the phonon dispersion relations of graphene are demonstrated by the calculation of the temperature dependence of the following observables: the kinetic energy of the carbon atoms, the vibrational frequency of the optical E2g mode, and the elastic moduli of the layer.

“…The systems considered here are of great practical interest and demonstrate pronounced NQE even at ambient conditions. 11,13,14 We note in passing that the system shown in Fig. 2 does not correspond to a stable state, although such a system plays an important role in the study of hydrogen isotope transport.…”

Section: Effective Temperatures For Nuclei or Collective Vibratimentioning

confidence: 99%

“…2,3 In liquid water, where the underlying tetrahedral network is primarily governed by the positions of the hydrogen atoms, it has been shown that accurate and reliable descriptions of the hydrogen bonding, [4][5][6] proton momentum distribution, 7 hydrated excess proton, 8,9 transport mechanism of aqueous hydroxide ions, 10 and numerous other phenomena 11 require a theoretical treatment of NQE beyond the harmonic approximation. In this regard, such non-classical nuclear behavior has also been observed in a number of systems throughout biology, chemistry, physics, and materials science, including DNA base pairs, 12 aromatic molecules, 13 graphene, 14,15 and equilibrium fractionation of stable aqueous Li isotopes, 16 to name a few.…”

Section: Introductionmentioning

confidence: 94%

“…For the second quasi-classical term in Eq. (14), one has to perform the summation over all of the force components in every bead, and the temperature becomes P times the equilibrium temperature, T, i.e., β is replaced by β P ≡ β/P. As a result, this term transforms into the free-energy correction entering Eq.…”

Section: Effective Temperatures For Nuclei or Collective Vibratimentioning

confidence: 99%

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Perturbed path integrals in imaginary time: Efficiently modeling nuclear quantum effects in molecules and materials

Poltavsky

DiStasio

Tkatchenko

2017

Nuclear quantum effects (NQE), which include both zero-point motion and tunneling, exhibit quite an impressive range of influence over the equilibrium and dynamical properties of molecules and materials. In this work, we extend our recently proposed perturbed path-integral (PPI) approach for modeling NQE in molecular systems A. Tkatchenko, Chem. Sci. 7, 1368 (2016)], which successfully combines the advantages of thermodynamic perturbation theory with path-integral molecular dynamics (PIMD), in a number of important directions. First, we demonstrate the accuracy, performance, and general applicability of the PPI approach to both molecules and extended (condensed-phase) materials. Second, we derive a series of estimators within the PPI approach to enable calculations of structural properties such as radial distribution functions (RDFs) that exhibit rapid convergence with respect to the number of beads in the PIMD simulation. Finally, we introduce an effective nuclear temperature formalism within the framework of the PPI approach and demonstrate that such effective temperatures can be an extremely useful tool in quantitatively estimating the "quantumness" associated with different degrees of freedom in the system as well as providing a reliable quantitative assessment of the convergence of PIMD simulations. Since the PPI approach only requires the use of standard second-order imaginary-time PIMD simulations, these developments enable one to include a treatment of NQE in equilibrium thermodynamic properties (such as energies, heat capacities, and RDFs) with the accuracy of higher-order methods but at a fraction of the computational cost, thereby enabling first-principles modeling that simultaneously accounts for the quantum mechanical nature of both electrons and nuclei in large-scale molecules and materials. Published by AIP Publishing. https://doi