Several simple quantum correction factors for classical line shapes, connecting dipole autocorrelation functions to infrared spectra, are compared to exact quantum data in both the frequency and time domain. In addition, the performance of the centroid molecular dynamics approach to line shapes and time-correlation functions is compared to that of these a posteriori correction schemes. The focus is on a tunable model that is able to describe typical hydrogen bonding scenarios covering continuously phenomena from tunneling via low-barrier hydrogen bonds to centered hydrogen bonds with an emphasis on floppy modes and anharmonicities. For these classes of problems, the so-called "harmonic approximation" is found to perform best in most cases, being, however, outperformed by explicit centroid molecular dynamics calculations. In addition, a theoretical analysis of quantum correction factors is carried out within the framework of the fluctuation-dissipation theorem. It can be shown that the harmonic approximation not only restores the detailed balance condition like all other correction factors, but that it is the only one that also satisfies the fluctuation-dissipation theorem. Based on this analysis, it is proposed that quantum corrections of response functions in general should be based on the underlying Kubo-transformed correlation functions.

One striking anomaly of water ice has been largely neglected and never explained. Replacing hydrogen ( 1 H) by deuterium ( 2 H) causes ice to expand, whereas the "normal" isotope effect is volume contraction with increased mass. Furthermore, the anomaly increases with temperature T , even though a normal isotope shift should decrease with T and vanish when T is high enough to use classical nuclear motions. In this study, we show that these effects are very well described by ab initio density functional theory. Our theoretical modeling explains these anomalies, and allows us to predict and to experimentally confirm a counter effect, namely that replacement of 16 =0 [15]. This "normal" isotope effect corresponds to a ∼12% zero-point expansion of 20 Ne relative to a hypothetical "classical" or "frozen" lattice [16,17]. Since H 2 O and Ne have similar molecular masses, one might expect similar effects. However, the volume of H 2 O at T = 0 is ∼0.1% smaller than that of D 2 O [12,13]. It has rarely been mentioned in the literature that this is opposite to the usual behavior, and no explanation has been offered.In this paper, we explain this effect as an interesting coupling between quantum nuclear motion and hydrogen bonding, that may be relevant also to the structure of liquid water. Our analysis shows that, despite the anomalous isotope effect, quantum ice actually has a volume 1% larger than it would have with classical nuclei. The effects are smaller than in Ne mostly because of delicate cancellations. We exploit these cancellations to make critical comparisons of: (i) quasiharmonic theory versus fully anharmonic path-integral molecular dynamics (PIMD); (ii) ab initio forces versus flexible and polarizable empirical force fields (EFF); and (iii) various flavors of ab initio density-functional theory (DFT) exchange and correlation (XC) density functionals (DF) with and without inclusion of van der Waals (vdW) interactions. We find: (i) quasiharmonic theory is satisfactory for this problem; (ii) present state of the art EFFs are not good enough to describe nuclear quantum effects in water; and (iii) all the DFs considered describe qualitatively the anomalous effects, although some versions perform better than others.Within the volume-dependent quasiharmonic approximation (QHA), the equilibrium volume V (T ) is obtained by minimizing at each T the Helmholtz free energy F (V, T ) [18,19]:where E 0 (V ) is the energy for classical (T = 0 or frozen) nuclei, at the relaxed atomic coordinates for each volume. ω k are the phonon frequencies, with k combining the branch index and the phonon wave vector within the Brillouin zone. Their volume dependence is linearized as:whereis the Grüneisen parameter of the mode, and V 0 is the equilibrium volume of E 0 (V ). ω k (V 0 ) and γ k (V 0 ) are obtained by diagonalizing the dynamical matrix, computed by finite differences from the atomic forces in a (3 × 3 × 3) supercell, at two volumes slightly below and above V 0 . As shown in the supplementary information [20] (SI), this li...

Based on the results of density functional theory calculations, a novel mechanism for the diffusion of water dimers on metal surfaces is proposed, which relies on the ability of H bonds to rearrange through quantum tunneling. The mechanism involves quasifree rotation of the dimer and exchange of H-bond donor and acceptor molecules. At appropriate temperatures, water dimers diffuse more rapidly than water monomers, thus providing a physical explanation for the experimentally measured high diffusivity of water dimers on Pd[111] [Science 297, 1850 (2002)]].

Path-integral molecular dynamics (PIMD) simulations have been carried out to study the influence of quantum dynamics of carbon atoms on the properties of a single graphene layer. Finitetemperature properties were analyzed in the range from 12 to 2000 K, by using the LCBOPII effective potential. To assess the magnitude of quantum effects in structural and thermodynamic properties of graphene, classical molecular dynamics simulations have been also performed. Particular emphasis has been laid on the atomic vibrations along the out-of-plane direction. Even though quantum effects are present in these vibrational modes, we show that at any finite temperature classical-like motion dominates over quantum delocalization, provided that the system size is large enough. Vibrational modes display an appreciable anharmonicity, as derived from a comparison between kinetic and potential energy of the carbon atoms. Nuclear quantum effects are found to be appreciable in the interatomic distance and layer area at finite temperatures. The thermal expansion coefficient resulting from PIMD simulations vanishes in the zero-temperature limit, in agreement with the third law of thermodynamics.

We show that two graphene layers stacked directly on top of each other (AA stacking) form strong chemical bonds when the distance between planes is 0.156 nm. Simultaneously, C-C in-plane bonds are considerably weakened from partial double-bond (0.141 nm) to single bond (0.154 nm). This polymorphic form of graphene bilayer is meta-stable w.r.t. the one bound by van der Waals forces at a larger separation (0.335 nm) with an activation energy of 0.16 eV/cell. Similarly to the structure found in hexaprismane, C forms four single bonds in a geometry mixing 90^{0} and 120^{0} angles. Intermediate separations between layers can be stabilized under external anisotropic stresses showing a rich electronic structure changing from semimetal at van der Waals distance, to metal when compressed, to wide gap semiconductor at the meta-stable minimum.Comment: tar gzip latex 4 pages 4 figure

Ice Ih has been studied by path-integral molecular dynamics simulations, using the effective q-TIP4P/F potential model for flexible water. This has allowed us to analyze finite-temperature quantum effects in this solid phase from 25 to 300 K at ambient pressure. Among these effects we find a negative thermal expansion of ice at low temperatures, which does not appear in classical molecular dynamics simulations. The compressibility derived from volume fluctuations gives results in line with experimental data. We have analyzed isotope effects in ice Ih by considering normal, heavy, and tritiated water. In particular, we studied the effect of changing the isotopic mass of hydrogen on the kinetic energy and atomic delocalization in the crystal as well as on structural properties such as interatomic distances and molar volume. For D(2)O ice Ih at 100 K we obtained a decrease in molar volume and intramolecular O-H distance of 0.6% and 0.4%, respectively, as compared to H(2)O ice.

The out-of-plane fluctuations of carbon atoms in a graphene sheet have been studied by means of classical molecular dynamic simulations with an empirical force-field as a function of temperature. The Fourier analysis of the out-of-plane fluctuations often applied to characterize the acoustic bending mode of graphene is extended to the optical branch, whose polarization vector is perpendicular to the graphene layer. This observable is inaccessible in a continuous elastic model of graphene but it is readily obtained by the atomistic treatment. Our results suggest that the long-wavelength limit of the acoustic out-of-plane fluctuations of a free layer without stress is qualitatively similar to that predicted by a harmonic model under a tensile stress. This conclusion is a consequence of the anharmonicity of both in-plane and out-of-plane vibrational modes of the lattice. The most striking anharmonic effect is the presence of a linear term, ωA = vAk, in the dispersion relation of the acoustic bending band of graphene at long wavelengths (k → 0). This term implies a strong reduction of the amplitude of out-of-plane oscillations in comparison to a flexural mode with a k 2 -dependence in the long-wavelength limit. Our simulations show an increase of the sound velocity associated to the bending mode, as well as an increase of its bending constant, κ, as the temperature increases. Moreover, the frequency of the optical bending mode, ωO(Γ), also increases with the temperature. Our results are in agreement with recent analytical studies of the bending modes of graphene using either perturbation theory or an adiabatic approximation in the framework of continuous layer models.

With a view to a better understanding of the influence of atomic quantum delocalisation effects on the phase behaviour of water, path integral simulations have been undertaken for almost all of the known ice phases using the TIP4P/2005 model, in conjunction with the rigid rotor propagator proposed by Müser and Berne [Phys. Rev. Lett. 77, 2638]. The quantum contributions then being known, a new empirical model of water is developed (TIP4PQ/2005) which reproduces, to a good degree, a number of the physical properties of the ice phases, for example densities, structure and relative stabilities.