Session H6: Focus Session: van der Waals Bonding in Advanced Material - Methods and Application to Water and Ice

van der Waals interactions in water and ice from density functional theory simulations: improvements and challenges

Accounting for long range van der Waals (vdW) type correlations in the description of water and ice has proven to be one of the most important improvements in density functional theory (DFT)-based simulations of water. I will show how our understanding of the network structure in liquid water has changed with the newly available vdW density functionals, derived from the original version of Dion et al. [Phys. Rev. Lett. 92, 246401 (2004)]. In particular I will focus on the links between the density of water and the interplay between the hydrogen bonds and the so called vdW-bonds, easily identifiable in the liquid. These new vdW-DFs have also proven to be very important in the description of ice. In particular I will show how they are capable of accurately describing the anomalous nuclear quantum effects in ice, bringing DFT simulations and experimental results very close together. Our results show that current vdW-DFs are capable of correctly describing the subtle interplay between inter-molecular libration modes and intra-molecular stretching modes in ice, thus reproducing the experimental results once the zero point of these modes is accounted for in the simulations.   

The Effect of van der Waals Interactions on the Structure of Liquid Water.

In this work, we demonstrate the importance of including van der Waals (vdW) interactions in the theoretical prediction of the structure of liquid water. These effects are investigated by computing and analyzing the oxygen-oxygen, oxygen-hydrogen, and hydrogen-hydrogen radial distribution functions (RDFs) obtained from highly accurate \textit{ab initio}molecular dynamic simulations that explicitly account for vdW interactions. In particular, we utilize an efficient order(N) algorithmic implementation of the self-consistent energy and analytical forces of the density functional based vdW correction proposed by Tkatchenko and Scheffler (PRL 102, 073005 (2009)) to demonstrate the importance of vdW interactions in obtaining RDFs that are in close agreement with experiment. In addition, we also provide an analysis of finite size effects in vdW-based liquid water simulations as well as a comparison to several other competitive theoretical methods for treating vdW interactions.   

Van der Waals interactions and vibrational effects in ice from first principles

We present a comparative study of the equation of state and of the electronic and vibrational properties of ice XI and VIII, as obtained with ab-initio calculations using semi-local (PBE) and nonlocal, van der Waals functionals. The two functionals yield similar electronic properties for both phases, however they perform very differently in describing their vibrational properties, and the transition pressure from the low to the high pressure phase. The latter is overestimated by a factor of about 6 when using PBE and in agreement with experiment when dispersion forces are taken into account. The inclusion of zero point energy contributions does not affect the computed transition pressure, while it substantially affects structural properties, including equilibrium volumes and bulk moduli, especially for the high pressure phase.   

Hydrogen Bonds and van der Waals Forces in Ice at Ambient and High Pressures

The balance between van der Waals (vdW) forces and hydrogen bonding in ambient and high pressure phases of ice has been examined with the first principles approaches, density-functional theory (DFT) and quantum Monte Carlo. At higher pressure, the contribution to the lattice energy from vdW increases and that from hydrogen bonding decreases, leading vdW to have a substantial effect on the transition pressures between the crystalline ice phases. An important consequence, likely to be of relevance to molecular crystals in general, is that the transition pressures obtained from DFT functionals which neglect vdW forces are greatly overestimated [Phys. Rev. Lett. \textbf{107}, 185701 (2011)].   

Higher-order van der Waals coefficients from static multipole polarizability

van der Waals interaction is a long-range nonlocal correlation arising from instantaneous charge fluctuations on each fragment. Though very weak, it considerably affects the properties of molecules and solids. Evaluation of van der Waals coefficients is of strong current interest. In this work, we have derived a general expression for these coefficients in terms of static multipole polarizability only. Applications of the present theory to atom as well as molecular pair interactions have been made.   

Quantum Monte Carlo Simulation of condensed van der Waals Systems

Van der Waals forces are as ubiquitous as infamous. While post-Hartree-Fock methods enable accurate estimates of these forces in molecules and clusters, they remain elusive for dealing with many-electron condensed phase systems. We present Quantum Monte Carlo [1,2] results for condensed van der Waals systems. Interatomic many-body contributions to cohesive energies and bulk modulus will be discussed. Numerical evidence is presented for crystals of rare gas atoms, and compared to experiments and methods [3]. Sandia National Laboratories is a multiprogram laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. DoE's National Nuclear Security Administration under Contract No. DE-AC04-94AL85000.\\[4pt] [1] J. Kim, K. Esler, J. McMinis and D. Ceperley, SciDAC 2010, J. of Physics: Conference series, Chattanooga, Tennessee, July 11 2011 \\[0pt] [2] QMCPACK simulation suite, http://qmcpack.cmscc.org (unpublished)\\[0pt] [3] O. A. von Lillienfeld and A. Tkatchenko, J. Chem. Phys. 132 234109 (2010)   

Van der Waals interactions based on maximally localized Wannier functions in ABINIT

We review the recent implementation\footnote{C. Espejo et al. Computer Phys. Comm. In press (2011), doi:10.1016/j.cpc.2011.11.003} of the method to evaluate van der Waals (vdW) interactions based on maximally localized Wannier functions\footnote{P. L. Silvestrelli. Phys. Rev. B., \textbf{100}, 053002 (2008)}$^,$\footnote{P. L. Silvestrelli. J. Phys. Chem. A., \textbf{113}, 5224 (2009)} in the DFT software ABINIT\footnote{X. Gonze et al. Computer Phys. Comm. \textbf{180}, 2582 (2009)}. The implementation allows for the evaluation of vdW interaction energies for molecular and periodic systems on the same grounds and at a low additional computational cost as compared with a normal DFT calculation. Some results on test systems such as Ar$_2$, benzene dimer and graphene bilayer show both its reliabilty and performance. Discussion of new defined variables controlling the calculation and guide lines for the user will be presented along with an application to MoS$_2$ structure.   

Density-Functional Theory with Screened van der Waals Interactions for the Modeling of Hybrid Inorganic/Organic Systems

The electronic properties and the function of hybrid inorganic/organic systems (HIOS) are intimately linked to their geometry, with van der Waals (vdW) interactions playing an essential role for the latter. Here we show that the inclusion of the many--body collective response of the substrate electrons inside the inorganic bulk enables us to reliably predict the HIOS geometries and energies. Specifically, dispersion-corrected density-functional theory (the DFT+vdW approach) [\textit{PRL} {\bf 102}, 073005 (2009)], is combined with the Lifshitz-Zaremba-Kohn theory [\textit{PRB} {\bf 13}, 2270 (1976)] for the non--local Coulomb screening within the bulk. Our method (DFT+vdW$^{\rm surf} $) includes both image-plane and interface polarization effects. We show that DFT+vdW$^{\rm surf}$ yields geometries in remarkable agreement ($ \approx $~0.1 \AA) with normal incidence x--ray standing wave measurements for the 3,4,9,10--perylene--tetracarboxylic acid dianhydride (C$_{24}$H$_{8}$O$_{6}$, PTCDA) molecule on Cu(111), Ag(111), and Au(111). Similarly accurate results are obtained for xenon and benzene adsorbed on metal surfaces.   

Stress and Vibrational Properties of non-local van der Waals exchange-correlation functionals

Van der Waals interaction is an essential component in the description of soft matter and plays an important role in many other systems, from adsorbates to water interaction. Within the framework of Density Functional Theory in the last years a great effort has been made to overcome the limitations of LDA or GGA functionals, and a new class of non-local functionals is now filling the gap giving interesting results. We present here several new improvements in this field, and some selected applications. In particular, i) we worked out the theoretical formalism needed to define both the stress tensor and the phonon vibrations associated to the non-local functional form proposed by Dion[1], and ii) we developed and implemented in the Quantum ESPRESSO simulation package a new functional inspired by the work of Vydrov and Van Voorhis[2], simple to compute efficiently in plane wave approach and with great performances on the S22 set. Finally we present some results obtained on aminoacid crystal and other simple molecules where these new tools are benchmarked and compared with experimental results and other theoretical approaches. \\[4pt] [1] M. Dion, B. I. Lundqvist et al., Phys. Rev. Lett. 92, 246401 (2004); \\[0pt] [2] Oleg A. Vydrov and Troy Van Voorhis , Phys. Rev. Lett. 103, 06300   

Dispersion interactions in Density Functional Theory

Semilocal functionals in Density Functional Theory (DFT) achieve high accuracy simulating a wide range of systems, but miss the effect of dispersion (vdW) interactions, important in weakly bound systems. We study two different methods to include vdW in DFT: First, we investigate a recent approach [1] to evaluate the vdW contribution to the total energy using maximally-localized Wannier functions. Using a set of simple dimers, we show that it has a number of shortcomings that hamper its predictive power; we then develop and implement a series of improvements [2] and obtain binding energies and equilibrium geometries in closer agreement to quantum-chemical coupled-cluster calculations. Second, we implement the vdW-DF functional [3], using Soler's method [4], within ONETEP [5], a linear-scaling DFT code, and apply it to a range of systems. This method within a linear-scaling DFT code allows the simulation of weakly bound systems of larger scale, such as organic/inorganic interfaces, biological systems and implicit solvation models. [1] P. Silvestrelli, JPC A 113, 5224 (2009). [2] L. Andrinopoulos et al, JCP 135, 154105 (2011). [3] M. Dion et al, PRL 92, 246401 (2004). [4] G. Rom{\'a}n-P{\'e}rez, J.M. Soler, PRL 103, 096102 (2009). [5] C. Skylaris et al, JCP 122, 084119 (2005).   

A Qbox Implementation of van der Waals Density Functionals with Applications

We present an implementation of the non-local van der Waals correlation functional proposed by Dion et al. [1] in the Qbox code [2]. We develop a simple approach to remove the logarithmic singularity in the kernel function, and derive the non-local potential needed for self-consistent calculations of energies, ionic forces and stress for simulations in arbitrary-shaped unit cells. We compare the performance of five different van der Waals functionals in applications to the benzene-water dimer, the benzene crystal and other organic molecular crystals. \\[4pt] [1] M. Dion et al. Phys. Rev. Lett. 92, 246401 (2004)\\[0pt] [2] http://eslab.ucdavis.edu/software/qbox