Session H35: Focus Session: DFT III: Weak Bonding and Liquid Phase Systems

Weakly Interacting Subsystems in DFT

In chemistry, one is frequently interested in systems that are composed of weakly interacting fragments: a solute dissolved in a solvent phase, the base pairs in DNA, molecules in a crystal. In all these cases, our physical picture is that electronic states of the assembly emerge from small perturbations of states localized on the fragments. In frustrating fashion, standard functionals completely fail to reproduce this qualitative picture: the excited states of molecular assemblies are dominated not by local, valence excitations, but by spurious charge transfer states; weak van der Waals forces that hold molecules together are typically absent; excess spin and charge tend to be strongly delocalized even when the physical coupling between centers is extremely weak. In this talk we will discuss how truly nonlocal density functionals can mollify these trends. In particular, we will highlight the recent derivation and implementation of nonlocal van der Waals density functionals that account for long-range correlation in terms of two-point density interactions.   

Towards Efficient and General Method for Many-Body van-der-Waals Interactions

Van der Waals interactions are intrinsically many-body phenomena, arising from collective electron fluctuations in a given material. Adiabatic connection fluctuation-dissipation theorem (ACFDT) allows to compute the many-body vdW interactions accurately. However, the ACFDT computational cost is prohibitive for real materials, even when the random-phase approximation is employed for the response function. We show how the problem of computing the long-range many-body vdW energy for real systems can be solved efficiently by mapping the system (molecule or condensed matter) onto a collection of quantum harmonic oscillators. Currently, our method, which couples density-functional theory with the many-body dispersion energy (DFT+MBD), is developed for non-metallic system [A. Tkatchenko, R. A. DiStasio Jr., R. Car, M. Scheffler, submitted]. The DFT+MBD method includes the hybridization effects by using the Tkatchenko-Scheffler approach [PRL 102, 073005 (2009)], the long-range Coulomb screening through classical electrodynamics [B. U. Felderhof, Physica 29, 1569 (1974)], and the many-body vdW energy from the coupled-fluctuating dipole model [M. W. Cole et al., Mol. Simul. 35, 849 (2009)]. The successes of the DFT+MBD approach and the many challenges that lie ahead will be discussed.   

Dispersion Interactions with Density-Functional Theory: Benchmarking Semiempirical and Interatomic Pairwise Corrected Density Functionals

We present a comparative assessment of the accuracy of two approaches for evaluating dispersion interactions: inter-atomic pair-wise corrections and semi-empirical meta-generalized-gradient-approximation (meta-GGA) based functionals. This is achieved by employing conventional (semi-)local and (screened-)hybrid functionals, as well as semi-empirical hybrid and non-hybrid meta-GGA functionals of the M06 family, with and without pair-wise Tkatchenko-Scheffler corrections. All those are tested against the benchmark S22 set of weakly bound systems, a representative larger molecular complex, and a representative dispersively bound solid. We also compare our results with those obtained from Grimme's pair-wise correction (DFT-D3) and Langreth-Lundqvist functionals (vdW-DF1/2). We find that the semi-empirical kinetic-energy-density dependence of the M06 functionals mimics some of the non-local correlation needed to describe dispersion. However, long-range contributions are still missing. Pair-wise corrections provide for a satisfactory level of accuracy irrespectively of the underlying functional.   

{\it Ab-inito} liquid water with hybrid functionals and dispersion interactions

We report {\it ab-initio} molecular dynamics simulations of liquid water using the hybrid PBE0 functional plus self-consistent dispersion forces based on the scheme of Ref.\footnote{A. Tkatchenko and M. Scheffler, Phys. Rev. Lett. {\bf 102}, 073005 (2009).} Simulations were performed at T=300K and at T=330K to approximately account for nuclear quantum effect on the oxygen-oxygen(O-O) RDF, as suggested by previous path integral simulations. Focusing on O-O RDF, we find that the combined effect of the hybrid functional and of the dispersion interactions significantly improves the agreement of the simulated structure with experiment.   

Understanding the role of London dispersion forces in molecular surface processes

The interactions and dynamics of molecules at surfaces and within pores are essential to many chemical processes, ranging from molecular storage to catalysis and self-assembly. A molecular level understanding of molecule-surface interactions is crucial for tuning surface/pore selectivity and reactivity. While it is clear that strong chemisorption bonds facilitate these interactions, the role of weaker van der Waals (vdW) forces, which include London dispersion and $\pi$-$\pi$ stacking interactions, are often unknown or overlooked. Recent advances in density functional theory (DFT) have now made it possible to reliably account for London dispersion interactions. In this paper, I will discuss the use of one such technique, the Rutgers-Chalmers vdW non-local correlation functional,\footnote{M. Dion, H. Rydberg, E. Schr\"{o}der, B. I. Lundqvist and D. C. Langreth, Phys. Rev. Lett., {\bf 92}, 246401 (2004)}$^,$\footnote{T. Thonhauser, V. R. Cooper, S. Li, A. Puzder, P. Hyldgaard, and David C. Langreth, Phys. Rev. B, {\bf 76}, 125112 (2007)} to demonstrate how the inclusion of London dispersion forces is critical for a truly first principles understanding of processes sensitive to molecule-surface interactions, such as the loading of H$_2$ within porous materials and the chemisorption of organic molecules at surfaces. These works highlight the fundamental importance of London dispersion interactions in the broader context of chemical physics. This work was supported by the Department of Energy, BES, Materials Sciences and Engineering Division.\footnote{Collaborators: Guo Li, Isaac Tamblyn, Yungok Ihm, Jun-Hyung Cho, Shixuan Du, Jeffrey B. Neaton, Hong-Jun Gao, Zhenyu Zhang, James R. Morris}   

First principles Monte Carlo simulations of vapor--liquid equilibria: Density functionals, basis sets, and dispersion corrections

Gibbs ensemble Monte Carlo simulations are used to compute the vapor--liquid equilibria for water, methanol, and methane using Kohn-Sham density functional theory. Results for BLYP and PBE functionals, BLYP with Grimme D2 and D3 dispersion corrections, and various basis sets are compared. Although none of the combinations of functional, dispersive correction, and basis set is found to yield highly accurate predictions for liquid densities, vapor pressures, and heats of vaporization for all three compounds, the results for dispersion corrected BLYP with large basis set are promising.   

Incorporation of an Improved Radial Distribution Function into Classical DFT

An expression for the radial distribution function $g(\vec{r})$ for a fluid can be found using classical density functional theory. We use this expression in place of the mean-field value ({\it e.g.}, $g=1$ for Lennard Jones fluids) in the excess Helmholtz free energy functional for the pair interactions to achieve self-consistent density profiles. We will discuss the differences found with this improved choice for $g(\vec{r})$ compared to other, simpler approximations. We will show results for liquid-vapor systems containing hard-sphere fluids with Lennard-Jones and dipolar interactions.   

Solvation of the chloride anion in water: ab initio simulations

We studied the structural, vibrational and electronic properties of the chloride anion in water using ab initio molecular dynamics. Our investigation has three main objectives: understand the range of perturbation exerted by the anion on the water hydrogen bonded network; identify signatures of the anion perturbation in infrared spectra of the solution and study the extent of charge localization on the anion, as predicted by semi-local (PBE) and hybrid functionals (PBE0). In agreement with recent experiments, we find that the presence of the anion substantially affects only the hydrogen bonding in the first solvation shell, due to a decrease of the dipole moment of the first shell water molecules and thus a weakening of the hydrogen bonds. Such a weakening leads to a slightly blue shifted band in the computed IR spectra. While structural and vibrational properties of the solution are similar within PBE and PBE0, the electronic properties exhibit marked differences.   

Entropy of Liquid Water from Ab Initio Molecular Dynamics

The debate on the structural properties of water has been mostly based on the calculation of pair correlation functions. However, the simulation of thermodynamic and spectroscopic quantities may be of great relevance for the characterization of liquid water properties. We have computed the entropy of liquid water using a two-phase thermodynamic model and trajectories generated by ab initio molecular dynamics simulations [1]. In an attempt to better understand the performance of several density functionals in simulating liquid water, we have performed ab initio molecular dynamics using semilocal, hybrid [2] and van der Waals density functionals [3]. We show that in all cases, at the experimental equilibrium density and at temperatures in the vicinity of 300 K, the computed entropies are underestimated, with respect to experiment, and the liquid exhibits a degree of tetrahedral order higher than in experiments. We also discuss computational strategies to simulate spectroscopic properties of water, including infrared and Raman spectra.\\[4pt] [1] C.Zhang, L.Spanu and G.Galli, {\it J.Phys.Chem. B} 2011 (in press)\\[0pt] [2] C.Zhang, D.Donadio, F.Gygi and G.Galli, {\it J. Chem. Theory Comput.} 7, 1443 (2011)\\[0pt] [3] C.Zhang, J.Wu, G.Galli and F.Gygi, {\it J. Chem. Theory Comput.} 7, 3061 (2011)   

Mean-field Density Functional Theory of Triple Junction

A triple junction in a three-phase fluid system is modeled by a mean-field density functional theory. We use a variational approach to find the Euler-Lagrange equations. Analytic solutions are obtained in the two-phase regions at large distances from the triple junction. We employ a triangular grid and use a successive over-relaxation method to find numerical solutions in the entire domain for the special case of equal interfacial tensions for the two-phase interfaces. We use the Kerins-Boiteux formula to obtain a line tension associated with the triple junction. This line tension turns out to be negative. We associate line adsorption with the change of line tension as the governing potentials change.   

Structural and vibrational properties of sulphate-water clusters from ab-initio calculations

Hydrated clusters of sulfuric acid derivatives play an important role in many processes of interest, e.g. environmental sciences and electrochemistry. Determining their structural and electronic properties is a challenging task: they exhibit a complex free energy landscape and there is no direct experimental measurement of their geometry, which is usually inferred from spectral signatures obtained, e.g. by infrared (IR) measurements [1]. We have used \textit{ab initio} molecular dynamics simulations to investigate the stability, electronic properties and IR of sulphate-water clusters containing $12$ and $13$ water molecules. We discuss how the entire hydrogen bonded network of the cluster may be affected by the presence of a single, additional water molecule, leading to geometrical arrangements not yet identified in experiments. We also show that clusters with different structures may have similar IR spectra, thus making it difficult to use spectral signatures to unequivocally determine the cluster geometry. Finally we discuss the electronic properties of the clusters and in particular differences obtained in the computed ionization potentials when using semi-local and hybrid functionals.\\[4pt] [1] Zhou \textit{et al.} J. Chem. Phys. \textbf{11,} 111102 (2006)).