Session F9: Focus Session: van der Waals Bonding in Advanced Materials: Advances in Theory

Short-range Cut-Off of the Summed-Up van der Waals Series

van der Waals interactions are important in typical van der Waals-bound systems such as noble-gas, hydrocarbon, alkali and alkaline-earth dimers. The summed-up van der Waals series [1,2] works well and gives an accurate result at large separation between two atoms. But it has a strong singularity at short non-zero separation, where the two atoms touch. In this work we remove that singularity with a reasonable and physical choice of the cut-off distance. Only one fitting parameter has been introduced for the short-range cut off. The parameter in our model has been optimized for each system, and a system-averaged value has been used to get the final binding energy curves. When this correction is added to the binding energy curve from the semilocal density functional meta-GGA-MS2, we get vdW- corrected binding energy curve. These curves are compared with the results of other vdW-corrected methods such as PBE-D2 and vdW-DF2 .Binding energy curves are in reasonable agreement with those from experiment. These curves also predict reasonably good equilibrium bond length. [1] J.P. Perdew, A. Ruzsinszky, J. Sun and S. Glindmeyer, Physical Review A 86, 062714 (2012). [2] A. Ruzsinszky, J.P. Perdew, J. Tao, and G.I. Csonka Physical Review Letters 109, 233203 (2012).   

A van der Waals density functional built upon the electron-gas foundation

The vdW-DF method is designed to be a systematic extension of the constraint-based generalized-gradient approximation (GGA) and can therefore serve as general purpose density functional [PRB 90, 075148 (2014)]. Yet the early versions can have issues both with bulk systems and with weak chemisorption. We present a recent nonempirical version, vdW-DF-cx [J. Chem. Phys. 140, 18A539 (2014), PRB 89, 035412 (2014)], that resolves these issues. The version is designed to have a consistent combination of exchange and correlation. We show that it performs well for inter-molecular binding and that it can even be better than PBE for describing cohesion and structure of molecules and solids. These results validate the robustness of the vdW-DF plasmon-pole model, which we show is closed linked to the exchange correlation hole of constraint-based GGA.   

A Local Representation Of The Dielectric Response Function

The screened dielectric response function ($\chi$) is a fundamental physical quantity that captures the many-electron correlation effects, key to the accurate description of van der Waals dispersion interaction in the ground state and a range of excited state properties. Although $\chi$ is non-local by definition, a real space partition of $\chi$ onto local structural motifs can help us gain further physical insight into, e.g., effective local screening properties. Because the construction of bare response function, $\chi_0$, is associated with the product of electron - hole orbitals, standard localization procedures for electron wave functions can not be directly applied. In this work, we propose a new method to decompose $\chi_0$ into contributions from local response functions. Exemplary results of finite and bulk systems are discussed.   

An Efficient Coupled Dipole Method: TCDM

An overview of a memory-efficient and cost-effective method, called Trace-Coupled Dipole Method (TCDM), which can accurately predict the van der Waals (VDW) forces between dielectric materials will be presented. CDM is an intrinsically atomistic method which includes all the many-body interaction terms self-consistently. TCDM, an alternative way to execute CDM, is to obtain VDW interaction energy by calculating the trace of a 3NX3N matrix, rather than its eigenvalues. It will be demonstrated that the power series expansion in TCDM is equivalent to that of the perturbation theory. The advantage of adopting TCDM over the conventional perturbation theory or CDM will also be discussed. The use of TCDM will make it practical for any interested future users to calculate the accurate VDW interaction in large systems like those found in computer simulation studies without serious increase in computational burden.   

Electronic Properties of Polarizable Systems with Self-Consistent Interatomic van der Waals Density Functional

Ubiquitous long-range van der Waals (vdW) interactions play a fundamental role in the structure and stability of a wide range of systems. Within the DFT framework, the vdW energy represents a crucial, but tiny part of the total energy, hence its influence on the electronic density, $n({\bf r})$, and electronic properties is typically assumed to be rather small. Here, we address this question \textit{via} a fully self-consistent (SC) implementation of the interatomic Tkatchenko-Scheffler vdW functional [1] and its extension to surfaces [2]. Self-consistency leads to large changes in the binding energies and electrostatic moments of highly polarizable alkali metal dimers. For some metal surfaces, vdW interactions increase dipole moments and induce non-trivial charge rearrangements, leading to visible changes in the metal workfunctions. Similar behavior is observed for molecules adsorbed on metals. Our study reveals a non-trivial connection between electrostatics and long-range electron correlation effects. [1] A. Tkatchenko and M. Scheffler PRL (2009). [2] V. G. Ruiz, W. Liu, E. Zojer, M. Scheffler, and A. Tkatchenko PRL (2012).   

Many-body dispersion meets non-local density functionals: A unified approach for van der Waals correlations

It is an ongoing challenge to develop an efficient method for van der Waals (vdW) non-local correlation within DFT which would be both accurate and broadly applicable. Current approaches can be loosely divided into the fragment-based ones, two-point density functionals and methods based on the density-density response function. The fragment-based models utilize parameters not derivable from the electron density. Two-point approaches are explicit density functionals, but difficult to generalize to include many-body correlations. Here, we show that these seemingly contrasting approaches can be unified within a single framework based on the adiabatic-connection formalism in the random-phase approximation. We use a local response-function model from the VV09 functional\footnote{O. A. Vydrov, T. Van Voorhis, Phys. Rev. Lett. 103, 063004} together with the many-body dispersion approach to create an atom-based model with no external parameters. We introduce a consistent correlation-functional-based coupling of the short- and long-range correlation energy. We show that this unification provides new insights into the different approaches, naturally deals with the partitioning of ionic and delocalized states and paves path towards self-consistent description of many-body vdW correlations.   

Farsightedness of the Correlation Energy in Polarizable Non-Metallic Nanostructures

The success of semi-local approaches to the electron correlation energy is commonly attributed to the relative \textit{nearsightedness} of the electronic matter--a powerful concept introduced by Walter Kohn. However, recent theoretical and experimental evidence indicates that electron correlation can be characterized by strong ``action at a distance'', especially in low-dimensional polarizable nanomaterials. Here we systematically analyze the influence of relevant properties, namely dimensionality, topology and polarizability, on the convergence and power laws governing the correlation energy. Using an accurate model system of coupled quantum harmonic oscillators we find that many-body effects can induce collective and strongly delocalized charge-fluctuation modes. These modes are ultimately responsible for a marked non-locality of the response, and an unconventional power-law decay of the dispersion interaction, which significantly deviates from the asymptotic predictions of finite-order perturbative theories. Notably, the degree of \textit{farsightedness} of the correlation energy could possibly be tuned, opening the way to an appropriate control of the interaction in complex polarizable nanostructures.   

Van der Waals Interactions Between Subsystems with Overlapping Electron Density

The subsystem formulation of DFT known as Frozen Density Embedding (FDE) provides a divide-and-conquer approach to Kohn--Sham DFT for weakly bound systems. We claim that a subsystem formulation of DFT can simplify both the theoretical framework and the computational effort for calculating the electronic structure of condensed phase systems. In addition, the naturally subsystem-like form of molecular aggregates makes subsystem DFT a better descriptor of the underlying physics than regular DFT of the supersystem. As an example, we present a novel van der Waals theory based on subsystem DFT which can treat seamlessly non-overlapping as well as overlapping subsystem electron densities. The theory is amenable to sensible approximations, such as RPA, and offers natural algorithms to fold in post-RPA corrections. Application of the theory to the computation of binding energies of dimers in the S22 set, as well as computation of selected potential energy surfaces is presented.   

Adiabatic-connection fluctuation-dissipation DFT for the structural properties of solids - the renormalized ALDA and other electron gas kernels

The adiabatic-connection fluctuation-dissipation formulation of density-functional theory (ACFD-DFT) provides a natural pathway for the calculation of electron correlation energies going beyond the random-phase approximation (RPA). The key ingredient of ACFD-DFT is the exchange-correlation kernel $f_{xc}$ of time-dependent DFT. The last few decades have seen the development of a number of model kernels, often based on studies of the homogeneous electron gas (HEG). Here, we introduce a selection of these HEG kernels and use them to calculate the structural properties of a test set of solids within ACFD-DFT. Amongst our kernels we include the recently-introduced renormalized adiabatic local-density approximation (rALDA) [T. Olsen and K. S. Thygesen, Phys. Rev. B 88, 115131 (2013)], and also consider kernels which (a) satisfy known limits of the HEG, (b) carry a frequency dependence or (c) include a long-range component. By comparing the kernels to each other, to the RPA and to experiment we shall identify the essential properties of a kernel for ACFD-DFT applications. We shall also discuss the technical challenges of applying HEG kernels to inhomogenous systems, and identify key areas for future progress.   

The role of delocalization error in non-covalent interactions from dispersion-corrected density-functional theory

Extensive benchmarking of dispersion-corrected density functional theory (dcDFT) methods has shown that it is nowadays feasible to calculate, with great accuracy, binding energies of small dimers and lattice energies of molecular crystals. However, there are many outstanding questions that can only be answered by a proper understanding of the interplay between base functional and dispersion correction. In this talk, I explore how delocalization error from the exchange-correlation functional impacts the calculation of non-covalent donor-acceptor interactions. Delocalization error arises from the failure of most functionals to model the long-range behavior of the exchange-correlation hole. Its primary consequence for non-covalent interactions is that the stability of donor-acceptor interactions is overestimated. Errors caused by delocalization error are particularly harmful in systems with strong and extensive hydrogen-bonded networks (water clusters and ice) or strong donor-acceptor interactions (halogen bonding), and can not be corrected using a pairwise dispersion correction. In addition, I present how delocalization error affects real-life applications of dcDFT, such as molecular adsorption on iron-oxide nanoparticles and surfaces.   

Ultra-long-ranged dispersion interaction between degenerate molecules

It is known (see e.g. [1]) that extended nano-systems with zero electronic gaps can exhibit dispersion interactions that fall off with unexpected powers of distance $D$. We seek to find a similar phenomenon between finite molecules that have a strictly degenerate many-electron groundstate (zero gap). As a toy model we take H$_{\mathrm{3}}$ with the atoms constrained to lie on an equilateral triangle of side $a$, using a minimal (s) basis set, and with spin-orbit coupling omitted. Rotational symmetry at fixed spins guarantees a degenerate time-reversed pair of three-electron states. For sufficiently small atomic spacing $a$ where inter-atomic hopping kinetic energy dominates the electron-electron repulsion, these degenerate time-reversed pairs of states are many-electron groundstates. We confirm this groundstate degeneracy via limited-basis CI calculations. We show that the resulting dispersion energy between two such constrained H$_{\mathrm{3}}$ molecules falls off as $D$**(-3)instead of the usual \textit{D**(-6)}. Within the classification scheme proposed in ref [2], this effect can be interpreted as a ``type C non-additivity'' of the dispersion interaction. This model may be relevant to metal atom clusters. \\[4pt] [1] John F. Dobson, Angela White and Angel Rubio, Phys. Rev. Lett. \textbf{96} (2006) 073201.\\[0pt] [2] John F. Dobson, Int. J. Quantum Chem. 114, 1157 (2014).   

Optimization of a van der Waals Density Functional for water

In particularly delicate systems, like liquid water, ab initio exchange and correlation functionals are simply not accurate enough for many practical applications. In these cases, fitting the functional to reference data is a sensible alternative to empirical interatomic potentials. However, a global optimization requires functional forms that depend on many parameters and the usual trial and error strategy becomes cumbersome and suboptimal. We present a general and powerful optimization scheme called data projection onto parameter space (DPPS). In an arbitrarily large parameter space, DPPS expands the vector of unknown parameters in vectors of known data. Poorly sampled subspaces are determined by the physically-motivated functional shape of ab initio functionals, using Bayes' theory to combine this prior information with reference energies and electron densities of monomers, clusters, and condensed phases of water.