The fundamental ideas for a non-local density functional theory -- capable of reliably capturing van der Waals interaction -- were already conceived in the 1990s. In 2004, a seminal paper introduced the first practical non-local exchange-correlation
functional called vdW-DF, which has become widely successful and laid the foundation for much further research. However, since then, the functional form of vdW-DF has remained unchanged. Several successful modifications paired the original functional with different (local) exchange functionals to improve performance and the successor vdW-DF2 also updated one internal parameter. Bringing together different insights from almost two decades of development and testing, we present the next-generation non-local correlation functional called vdW-DF3, in which we change the functional form while staying true to the original design philosophy. Although many popular functionals show good performance around the binding separation of van der Waals complexes, they often result in significant errors at larger separations. With vdW-DF3, we address this problem by taking advantage of a recently uncovered and largely unconstrained degree of freedom within the vdW-DF framework that can be constrained through empirical input, making our functional semi-empirical. For two different parameterizations, we benchmark vdW-DF3 against a large set of well-studied test cases and compare our results with the most popular functionals, finding good performance in general for a wide array of systems and a significant improvement in accuracy at larger separations. Finally, we discuss the achievable performance within the current vdW-DF framework, the flexibility in functional design offered by vdW-DF3, as well as possible future directions for non-local van der Waals density functional theory.
The non-local van der Waals density functional (vdW-DF) has had tremendous success since its inception in 2004 due to its constraint-based formalism that is rigorously derived from a many-body starting point. However, while vdW-DF can describe bindin
g energies and structures for van der Waals complexes and mixed systems with good accuracy, one long-standing criticism---also since its inception---has been that the $C_6$ coefficients that derive from the vdW-DF framework are largely inaccurate and can be wrong by more than a factor of two. It has long been thought that this failure to describe the $C_6$ coefficients is a conceptual flaw of the underlying plasmon framework used to derive vdW-DF. We prove here that this is not the case and that accurate $C_6$ coefficient can be obtained without sacrificing the accuracy at binding separations from a modified framework that is fully consistent with the constraints and design philosophy of the original vdW-DF formulation. Our design exploits a degree of freedom in the plasmon-dispersion model $omega_{mathbf{q}}$, modifying the strength of the long-range van der Waals interaction and the cross-over from long to short separations, with additional parameters tuned_ to reference systems. Testing the new formulation for a range of different systems, we not only confirm the greatly improved description of $C_6$ coefficients, but we also find excellent performance for molecular dimers and other systems. The importance of this development is not necessarily that particular aspects such as $C_6$ coefficients or binding energies are improved, but rather that our finding opens the door for further conceptual developments of an entirely unexplored direction within the exact same constrained-based non-local framework that made vdW-DF so successful in the first place.
Aluminum borohydride (Al(BH$_4$)$_3$) is an example of a promising hydrogen storage material with exceptional hydrogen densities by weight and volume and a low hydrogen desorption temperature. But, unfortunately, its production of diborane (B$_2$H$_6
$) gases upon heating to release the hydrogen restricts its practical use. To elucidate this issue, we investigate the properties of a number of metal borohydrides with the same problem and find that the electronegativity of the metal cation is not the best descriptor of diborane production. We show that, instead, the closely related formation enthalpy is a better descriptor and we find that diborane production is an exponential function thereof. We conclude that diborane production is sufficiently suppressed for formation enthalpies of $-$80 kJ/mol BH$_4$ or lower, providing specific design guidelines to tune existing metal borohydrides or synthesize new ones. We then use first-principles methods to study the effects of Sc alloying in Al(BH$_4$)$_3$. Our results for the thermodynamic properties of the Al$_{1-x}$Sc$_x$(BH$_4$)$_3$ alloy clearly show the stabilizing effect of Sc alloying and thus the suppression of diborane production. We conclude that stabilizing Al(BH$_4$)$_3$ and similar borohydrides via alloying or other means is a promising route to suppress diborane production and thus develop viable hydrogen storage materials.
We develop 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 o
f spin systems. We investigate in detail the role of spin in the nonlocal-correlation 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 nonlocal correlation in concert with spin effects, our nonempirical svdW-DF method opens the door for a deeper understanding of weak nonlocal magnetic interactions.
We study the effect of Zn alloying on the hydrogen desorption properties of Mg(BH$_4$)$_2$ using $it{ab initio}$ simulations. In particular, we investigate formation/reaction enthalpies/entropies for a number of compounds and reactions at a wide rang
e of temperatures and Zn concentrations in Mg$_{1-x}$Zn$_x$(BH$_4$)$_2$. Our results show that the thermodynamic stability of the resulting material can be significantly lowered through Zn alloying. We find that e.g. the solid solution Mg$_{2/3}$Zn$_{1/3}$(BH$_4$)$_2$ has a reaction enthalpy for the complete hydrogen desorption of only 25.3 kJ/mol H$_2$$-$a lowering of 15 kJ/mol H$_2$ compared to the pure phase and a corresponding lowering in critical temperature of 123 K. In addition, we find that the enthalpy of mixing is rather small and show that the decrease in reaction enthalpy with Zn concentration is approximately linear.
We present first-principles, density-functional theory calculations of the NMR chemical shifts for polycyclic aromatic hydrocarbons, starting with benzene and increasing sizes up to the one- and two-dimensional infinite limits of graphene ribbons and
sheets. Our calculations are performed using a combination of the recently developed theory of orbital magnetization in solids, and a novel approach to NMR calculations where chemical shifts are obtained from the derivative of the orbital magnetization with respect to a microscopic, localized magnetic dipole. Using these methods we study on equal footing the $^1$H and $^{13}$C shifts in benzene, pyrene, coronene, in naphthalene, anthracene, naphthacene, and pentacene, and finally in graphene, graphite, and an infinite graphene ribbon. Our results show very good agreement with experiments and allow us to characterize the trends for the chemical shifts as a function of system size.
We introduce an alternative approach to the first-principles calculation of NMR shielding tensors. These are obtained from the derivative of the orbital magnetization with respect to the application of a microscopic, localized magnetic dipole. The ap
proach is simple, general, and can be applied to either isolated or periodic systems. Calculated results for simple hydrocarbons, crystalline diamond, and liquid water show very good agreement with established methods and experimental results.
We examine the performance of a recently developed nonlocal density functional in predicting a model noncovalent interaction, the weak bond between an aromatic $pi$ system and an aliphatic C-H group. The new functional is a significant improvement ov
er traditional density functionals, providing results which compare favorably to high-level quantum-chemistry techniques but at considerably lower computational cost. Interaction energies in several model C-H/$pi$ systems are in generally good agreement with coupled-cluster calculations, though equilibrium distances are consistently overpredicted when using the revPBE functional for exchange. The new functional correctly predicts changes in energy upon addition of halogen substituents.
