Session Y22: Van der Waals Bonding in Advanced Materials: Methods

Quasi-local approximation of non-local exchange-correlation kernels in the adiabatic-connection fluctuation-dissipation theorem

The adiabatic-connection fluctuation-dissipation theorem (ACFDT) is a formal theoretical framework to treat van der Waals (vdW) dispersion interactions. Under the random phase approximation (RPA), it yields the correct asymptotic behavior at large distances, but the short-range correlation is overestimated. It has been demonstrated that non-local exchange-correlation kernels can systematically correct the errors of RPA for homogenous electron gas. However, direct extension of non-local kernels derived from the electron gas model to inhomogeneous systems raises several issues. In addition to the high computational expense, the non-local kernels worsen the rare gas dimer binding curve as compared to RPA. In this study, we propose a quasi-local approximation of the non-local kernel in order to address these issues.   

The Connection between Diagrams and Electrodynamics in the Long-Range Dispersion Energy

In this talk, we will discuss the different avenues that lead to the complete treatment of the long-range dispersion interaction energy between isolated fragments that are located outside the area of orbital (or electron density) overlap. By analyzing the higher-order terms in the perturbative expansion of the dispersion energy \textit{via} a dipole response function formalism, we show that each of these terms can be expressed as physically meaningful quantities in classical electrodynamics. Based on this approach, we generalize the connection between the higher-order perturbative contributions to the dispersion energy, the different classes of diagrams (e.g. rings, ladders, etc.), and the aforementioned electrodynamical response functions.   

A fully consistent spin formalism for the nonempirical van der Waals density functional vdW-DF

We present a proper nonempirical spin-density formalism for the van der Waals density functional (vdW-DF) method. We show that this generalization, termed svdW-DF, is firmly rooted in the single-particle nature of exchange and we test it on a range of spin systems. We investigate in detail the role of spin in the van der Waals driven adsorption of H$_2$ and CO$_2$ in the linear magnets Mn-MOF74, Fe-MOF74, Co-MOF74, and Ni-MOF74. In all cases, we find that spin plays a significant role during the adsorption process despite the general weakness of the molecular-magnetic responses. The case of CO$_2$ adsorption in Ni-MOF74 is particularly interesting, as the inclusion of spin effects results in an increased attraction, opposite to what the diamagnetic nature of CO$_2$ would suggest. We explain this counter-intuitive result, tracking the behavior to a coincidental hybridization of the O $p$ states with the Ni $d$ states in the down-spin channel. More generally, by providing insight on van der Waals interactions in concert with spin effects, our nonempirical svdW-DF method opens the door for a deeper understanding of weak nonlocal magnetic interactions.   

Dispersion Interactions in High-Density Molecular Crystals

Dispersion interactions are ubiquitous quantum mechanical phenomena arising from correlated electron density fluctuations in molecules and materials. As a key component of non-bonded interactions, dispersion forces play a critical role in determining the structure and stability of molecular crystals. Due to the relative intermolecular separation in high-density molecular crystals, an accurate description of these non-bonded interactions requires the inclusion of terms beyond the asymptotic induced-dipole--induced-dipole ($C_6/R^6$) contribution. In this work, we have developed a first principles based approach within the framework of Density Functional Theory (i.e., that only depends on the charge density $n(\mathbf{r})$) for capturing the higher-order induced multipolar contributions to the correlation energy. As a first application of this method, we have investigated the structure and stability of the high-density ice molecular crystal polymorphs at the ice VI---ice VII---ice VIII triple point (278K, 2.1GPa) using \textit{ab-initio} molecular dynamics in the isobaric-isothermal ($NpT$) ensemble.   

On the pseudopotential approximation in the van der Waals density functional calculations

The van der Waals density functional (vdW-DF)[1,2] is a density functional that is able to describe van der Waals and covalent interactions in a seamless fashion, and has been applied to a variety of systems. In practical calculations, the pseudopotential (PP) approximation has been employed, for which the PPs should be generated consistently for the chosen exchange correlation XC functional. However, usually PPs generated with a generalized gradient approximation (GGA) XC functional are used and the effect of the approximation to the XC functional applied in the PP generation is scarcely discussed. In this work, we discuss the appropriate XC functionals in the PP generation for the vdW-DF calculations. Furthermore, we compare the vdW-DF results for several systems using the PP's generated with appropriate XC and those with GGA XC[3].\\[4pt][1] M.~Dion \textit{et al}. Phys. Rev. Lett. \textbf{92}, 246401 (2004).\\[0pt][2] K.~Berland, \textit{et al}., Rep. Prog. Phys. \textbf{78}, 066501 (2015).\\[0pt] [3] M.~Callsen and I.~Hamada, Phys. Rev. B \textbf{91}, 195103 (2015).   

Van der Waals Interactions Between Subsystems with Overlapping Electron Density

We claim that a subsystem formulation of Density-Functional Theory (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, and computation of selected potential energy surfaces is presented. [1] ``FDE-vdW: A van der Waals Inclusive Subsystem Density-Functional Theory'', J. Chem. Phys., 141, 044127 (2014) [2] ``Exact Kinetic Energy Enables Accurate Evaluation of Weak Interactions by the FDE-vdW Method'', J. Chem. Phys., 143, 084120 (2015) [3] ``Subsystem Density-Functional Theory as an Effective Tool for Modeling Ground and Excited States, their Dynamics, and Many-Body Interactions'', J. Phys.: Condens. Matter, 27, 183202 (2015)   

The Dipole Polarizability of a Water Molecule \textit{in} Liquid Water

The dipole polarizability, $\alpha$, provides a measure of the tendency of a molecule or material to deform (or polarize) in the presence of an electric field. Within the framework of density functional theory (DFT), we present a hierarchy of first principles based approaches for computing $\alpha$ of a molecule located in the condensed phase. This hierarchy includes a successive treatment of both short-range (hybridization, Pauli exchange-repulsion, etc.) and long-range (Coulomb) electrodynamical response screening in the computation of $\alpha$, while simultaneously accounting for the surrounding condensed-phase environment. Utilizing highly accurate liquid water configurations generated from van der Waals inclusive hybrid DFT based \textit{ab initio} molecular dynamics, we computed $\alpha$ for a given water molecule \textit{in} liquid water as a first application of this approach. Our findings will be compared and contrasted with $\alpha$ computed for an isolated gas-phase water molecule.   

Study of correlations from Ab-Initio Simulations of Liquid Water

An accurate understanding of the dynamics and the structure of H2O molecules in the liquid phase is of extreme importance both from a fundamental and from a practical standpoint. Despite the successes of Molecular Dynamics (MD) with Density Functional Theory (DFT), liquid water remains an extremely difficult material to simulate accurately and efficiently because of fine balance between the covalent O-H bond, the hydrogen bond and the attractive the van der Waals forces. Small errors in those produce dramatic changes in the macroscopic properties of the liquid or in its structural properties. Different density functionals produce answers that differ by as much as 35\% in ambient conditions, with none producing quantitative results in agreement with experiment at different mass densities [J. Chem Phys. 139, 194502(2013)]. In order to understand these differences we perform an exhaustive scanning of the geometrical coordinates of MD simulations and study their statistical correlations with the simulation output quantities using advanced correlation analyses and machine learning techniques.   

The Role of Anharmonicity and Nuclear Quantum Effects in the Pyridine Molecular Crystal: An \textit{ab initio} Molecular Dynamics Study

Molecular crystal structure prediction has posed a substantial challenge to first-principles methods and requires sophisticated electronic structure methods to determine the stabilities of nearly degenerate polymorphs [1,2,3]. In this work, we demonstrate that the anharmonicity from van der Waals interactions is relevant to the finite-temperature structures of pyridine and pyridine-like molecular crystals. Using such an approach, we find that the equilibrium structures are well captured with classical \textit{ab initio} molecular dynamics (AIMD), despite the presence of light atoms such as hydrogen. Employing path integral AIMD simulations, we demonstrate that the success of classical AIMD results from a separation of nuclear quantum effects between the intermolecular and intramolecular degrees of freedom. In this separation, the quasiclassical and anharmonic intermolecular degrees of freedom determine the equilibrium structure, while the quantum and harmonic intramolecular degrees of freedom are averaging to the correct intramolecular structure. [1] M A Neumann, F J J Leusen, and J Kendrick, Angew. Chem. Int. Ed. 47, 2427 (2008). [2] A Otero-de-la-Roza and E R Johnson, J. Chem. Phys. 137, 054103 (2012). [3] A M Reilly and A Tkatchenko, J. Phys. Chem. Lett. 4, 1028 (2013).   

Phonon dispersion in acene molecular crystals using van der Waals density functionals

Much progress has been made of late in understanding the fundamental processes in optoelectronic materials. An ongoing challenge is the accurate inclusion of nuclear motion and to go beyond the Born-Oppenheimer approximation. Especially in materials like molecular crystals, where van der Waals (vdW) forces dominate the cohesive energy and the electronic structure is very sensitive to intermolecular geometry, phonons can be an important facilitator and dissipation mechanism. Thus there is a need to assess and understand the efficacy of existing approaches for phonon dispersions in vdW-bound solids. In this work we use a vdW density functional to calculate the phonon dispersion of members of the acene family. We establish the accuracy of the method using naphthalene, obtaining excellent agreement with experimental results, and in a further step, we explore the strength of the electron-phonon coupling across the Brillouin zone. Taken all together, our calculations illustrate the potential for quantitative prediction of vibrational properties of weakly-bound organic crystals over the entire Brillouin zone from first principles.   

Ligand control of magnetic ordering temperature in copper-pyrazine square lattice antiferromagnets

Using a mixed-ligand synthetic scheme, we create a family of quasi-two-dimensional (Q2D) antiferromagnets: [Cu(HF$_2$)(pyz)$_2$]ClO$_4$ [pyz = pyrazine], [Cu$L_2$(pyz)$_2$](ClO$_4$)$_2$ [$L$ = pyO = pyridine-N-oxide and 4-phpyO = 4-phenylpyridine-N-oxide). These possess equivalent 2D [Cu(pyz)$_2$]$^{2+}$ nearly square layers, but show interlayer spacings from 6.57~\AA ~to 16.78~\AA, dictated by the axial ligands. Structural and magnetic properties are derived from x-ray diffraction, ESR, pulsed-field magnetometry and muon-spin rotation, and compared to those of the prototypical 2D magnetic polymer Cu(ClO$_4$)$_2$(pyz)$_2$. We find that the 2D exchange coupling remains largely unaffected by the axial ligand substitution, while the magnetic ordering temperature decreases slowly with increasing layer separation. Experimental data are compared to theory, including DFT.   

UNUSUALLY LARGE YOUNG'S MUDULI OF AMINO ACID MOLECULAR CRYSTALS*

Young's moduli of selected amino acid molecular crystals were studied both experimentally and computationally using nanoindentation and dispersion-corrected density functional theory. The Young modulus is found to be strongly facet-dependent, with some facets exhibiting exceptionally high values (as large as 44 GPa). The magnitude of Young's modulus is strongly correlated with the relative orientation between the underlying hydrogen-bonding network and the measured facet. Furthermore, we show computationally that the Young modulus can be as large as 70-90 GPa if facets perpendicular to the primary direction of the hydrogen-bonding network can be stabilized. This value is remarkably high for a molecular solid and suggests the design of hydrogen-bond networks as a route for rational design of ultra-stiff molecular solids. *Angew. Chem. Int. Ed.. doi: 10.1002/anie.201505813