We present an efficient implementation of the van der Waals density functional of Dion et al. [Phys. Rev. Lett. 92, 246401 (2004)], which expresses the nonlocal correlation energy as a double spatial integral. We factorize the integration kernel and use fast Fourier transforms to evaluate the self-consistent potential, total energy, and atomic forces, in O(NlogN) operations. The resulting overhead, for medium and large systems, is a small fraction of the total computational cost, representing a dramatic speedup over the O(N(2)) evaluation of the double integral. This opens the realm of first-principles simulations to the large systems of interest in soft matter and biomolecular problems. We apply the method to calculate the binding energies and the barriers for relative translation and rotation in double-wall carbon nanotubes.

It is known that ab initio molecular dynamics (AIMD) simulations of liquid water at ambient conditions, based on the generalized gradient approximation (GGA) to density functional theory (DFT), with commonly used functionals fail to produce structural and diffusive properties in reasonable agreement with experiment. This is true for canonical, constant temperature simulations where the density of the liquid is fixed to the experimental density. The equilibrium density, at ambient conditions, of DFT water has recently been shown by Schmidt et al. [J. Phys. Chem. B, 113, 11959 (2009)] to be underestimated by different GGA functionals for exchange and correlation, and corrected by the addition of interatomic pair potentials to describe van der Waals (vdW) interactions. In this contribution we present a DFT-AIMD study of liquid water using several GGA functionals as well as the van der Waals density functional (vdW-DF) of Dion et al. [Phys. Rev. Lett. 92, 246401 (2004)]. As expected, we find that the density of water is grossly underestimated by GGA functionals. When a vdW-DF is used, the density improves drastically and the experimental diffusivity is reproduced without the need of thermal corrections. We analyze the origin of the density differences between all the functionals. We show that the vdW-DF increases the population of non-H-bonded interstitial sites, at distances between the first and second coordination shells. However, it excessively weakens the H-bond network, collapsing the second coordination shell. This structural problem is partially associated to the choice of GGA exchange in the vdW-DF. We show that a different choice for the exchange functional is enough to achieve an overall improvement both in structure and diffusivity.

Porous metal-organic frameworks (MOFs) display a tremendous range of crystal structures, [1] rich host-guest chemistry, and potential for major impact in adsorption and separation technologies [2] and catalysis. [3] A growing sub-class of "soft" MOFs behave in a remarkable guest-responsive fashion upon gas or solvent adsorption/desorption and have gained considerable attention, exhibiting a wide range of structural transitions [4,5] and the topic has been the subject of a recent review.[6] Here, we focus on the experimentally well-documented MIL-53(Al) material [6] known for its reversible switching between a large pore (lp) and a narrow pore (np) form upon gas or solvent adsorption. Interestingly, Liu et al. [7] have recently reported the occurrence of the lp to np transition without a guest molecule, establishing the intrinsic bistable behavior of the MIL-53(Al) host. While previous simulation studies [8] have examined the role of guest molecules in the lp to np transition, the driving force for the formation of the guest-free np structure has yet to be elucidated. More generally, the question of the origin of the intrinsic bistability of this topical MOF remains open. Here we show that dispersive interactions cause the np structure to stabilize at low temperature and entropy drives the structural transition to the lp phase. Figure 1 depicts the np and lp MIL-53(Al) structures: between 325 K and 375 K a marked transition occurs where the unit cell volume nearly doubles from 864 3 in the np structure to 1419 3 in the lp structure. It has been suggested that the driving force for this transition is provided by low energy phonon modes [7] and we speculate that dispersion interactions, potentially emanating from p-p stacking of the phenyl ligands may be important. Density functional theory (DFT) offers the possibility of probing the structure-energy relationship. However, previously reported DFT [7] and forcefield [8] studies have been unable to stabilize the np structure. The np structure opens up on relaxation to give the lp form. A suspicion is that dispersive interactions, which are absent from "standard" GGA functionals used for DFT (e.g. leading to the exfoliation of graphite into unconnected sheets), may be key to understanding the bistability of this material. Here, we examine two complementary approaches to explore the role of dispersive effects within the DFT regime: 1) An efficient non-local functional, [9] vdW-DF, where dispersion is calculated self-consistently and depends on the unique electron density on each atom. 2) Dispersive interactions that depend on empirical ÀC 6 r À6 terms, the DFT-D method [10] and its solid-specific reparameterization.[11] Further details of the methods and settings used in this work are presented in the Supporting Information.In Table 1, we present a summary of our results. In keeping with previous work, with a standard GGA functional the np structure yields no local minimum and the structure opens up to give the lp form. Furthermore, when the atomic

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Molecular hydrogen adsorption in a nanoporous metal organic framework structure (MOF-74) was studied via van der Waals density-functional calculations. The primary and secondary binding sites for H2 were confirmed. The low-lying rotational and translational energy levels were calculated, based on the orientation and position dependent potential energy surface at the two binding sites. A consistent picture is obtained between the calculated rotational-translational transitions for different H2 loadings and those measured by inelastic neutron scattering exciting the singlet to triplet (para to ortho) transition in H2. The H2 binding energy after zero point energy correction due to the rotational and translational motions is predicted to be ∼100 meV in good agreement with the experimental value of ∼90 meV.PACS numbers: 68.43. Bc, 68.43.Fg, 84.60.Ve The adsorption of molecules within the nanopores of a sparse material and their low-lying excitations provide rich phenomena of fundamental interest that are seldom explored by first principles methods, even for molecules as simple as H 2 . For example, one can ask how the wellknown para-ortho transition of H 2 survives in a recognizable form in the presence of the rotational barriers and hindrances provided by the adsorbing material, and how it changes for different concentrations of H 2 . The necessity of proper treatment of van der Waals interactions has foiled traditional density functional treatments. Here, by using the van der Waals density functional (vdW-DF) of Dion et al.[1], we are able to predict a picture of the low-lying excitations which provides a credible match for the results of inelastic neutron diffraction (INS) [2] for different hydrogen loadings in a nanoporous material of a type thought to provide a possible path toward future hydrogen storage technology.The material studied here is a metal-organic framework (MOF) compound, namely the material that has been called , chosen because of recent inelastic neutron scattering measurements [2] with varying amounts of H 2 adsorption. More generally MOFs are a relatively new class of materials which are composed of metal clusters connected by organic ligands [4]. The search for a MOF structure with high binding strength to H 2 has become very active recently [5,6]. The dynamical properties of the adsorbed dihydrogen such as vibrational and hindered rotational motion play a significant role in determining the H 2 binding energy, especially for caged structures with nanopores. This area is even less explored than the modeling of hydrogen uptake based only on the depth of the potential well. An attempt along this line studied the rotational transition of H 2 adsorbed over benzene molecule which is often a fraction of the organic linker in MOF materials [7]. However, the interaction between full MOF and H 2 usually differs significantly from that between a fraction of MOF and H 2 [8]. A very recent paper studied the rotational transition in another MOF (HKUST-1) with generalized gradient approximation (GGA) ca...