libMBD: A general-purpose package for scalable quantum many-body dispersion calculations.

Many-body dispersion (MBD) is a powerful framework to treat van der Waals (vdW) dispersion interactions in density-functional theory and related atomistic modeling methods. Several independent implementations of MBD with varying degree of functionality exist across a number of electronic structure codes, which both limits the current users of those codes and complicates dissemination of new variants of MBD. Here, we develop and document libMBD, a library implementation of MBD that is functionally complete, efficient, easy to integrate with any electronic structure code, and already integrated in FHI-aims, DFTB+, VASP, Q-Chem, CASTEP, and Quantum ESPRESSO. libMBD is written in modern Fortran with bindings to C and Python, uses MPI/ScaLAPACK for parallelization, and implements MBD for both finite and periodic systems, with analytical gradients with respect to all input parameters. The computational cost has asymptotic cubic scaling with system size, and evaluation of gradients only changes the prefactor of the scaling law, with libMBD exhibiting strong scaling up to 256 processor cores. Other MBD properties beyond energy and gradients can be calculated with libMBD, such as the charge-density polarization, first-order Coulomb correction, the dielectric function, or the order-by-order expansion of the energy in the dipole interaction. Calculations on supramolecular complexes with MBD-corrected electronic structure methods and a meta-review of previous applications of MBD demonstrate the broad applicability of the libMBD package to treat vdW interactions.

Theory and practice of modeling van der Waals interactions in electronic-structure calculations.

The accurate description of long-range electron correlation, most prominently including van der Waals (vdW) dispersion interactions, represents a particularly challenging task in the modeling of molecules and materials. vdW forces arise from the interaction of quantum-mechanical fluctuations in the electronic charge density. Within (semi-)local density functional approximations or Hartree-Fock theory such interactions are neglected altogether. Non-covalent vdW interactions, however, are ubiquitous in nature and play a key role for the understanding and accurate description of the stability, dynamics, structure, and response properties in a plethora of systems. During the last decade, many promising methods have been developed for modeling vdW interactions in electronic-structure calculations. These methods include vdW-inclusive Density Functional Theory and correlated post-Hartree-Fock approaches. Here, we focus on the methods within the framework of Density Functional Theory, including non-local van der Waals density functionals, interatomic dispersion models within many-body and pairwise formulation, and random phase approximation-based approaches. This review aims to guide the reader through the theoretical foundations of these methods in a tutorial-style manner and, in particular, highlight practical aspects such as the applicability and the advantages and shortcomings of current vdW-inclusive approaches. In addition, we give an overview of complementary experimental approaches, and discuss tools for the qualitative understanding of non-covalent interactions as well as energy decomposition techniques. Besides representing a reference for the current state-of-the-art, this work is thus also designed as a concise and detailed introduction to vdW-inclusive electronic structure calculations for a general and broad audience.

Quantum-Mechanical Relation between Atomic Dipole Polarizability and the van der Waals Radius.

The atomic dipole polarizability α and the van der Waals (vdW) radius R_{vdW} are two key quantities to describe vdW interactions between atoms in molecules and materials. Until now, they have been determined independently and separately from each other. Here, we derive the quantum-mechanical relation R_{vdW}=const×α^{1/7}, which is markedly different from the common assumption R_{vdW}∝α^{1/3} based on a classical picture of hard-sphere atoms. As shown for 72 chemical elements between hydrogen and uranium, the obtained formula can be used as a unified definition of the vdW radius solely in terms of the atomic polarizability. For vdW-bonded heteronuclear dimers consisting of atoms A and B, the combination rule α=(α_{A}+α_{B})/2 provides a remarkably accurate way to calculate their equilibrium interatomic distance. The revealed scaling law allows us to reduce the empiricism and improve the accuracy of interatomic vdW potentials, at the same time suggesting the existence of a nontrivial relation between length and volume in quantum systems.

Dynamics of Spatially Confined Bisphenol A Trimers in a Unimolecular Network on Ag(111).

Bisphenol A (BPA) aggregates on Ag(111) shows a polymorphism between two supramolecular motifs leading to formation of distinct networks depending on thermal energy. With rising temperature a dimeric pairing scheme reversibly converts into a trimeric motif, which forms a hexagonal superstructure with complex dynamic characteristics. The trimeric arrangements notably organize spontaneously into a self-assembled one-component array with supramolecular BPA rotors embedded in a two-dimensional stator sublattice. By varying the temperature, the speed of the rotors can be controlled as monitored by direct visualization. A combination of scanning tunneling microscopy and dispersion-corrected density-functional tight-binding (DFTB-vdW(surf)) based molecular modeling reveals the exact atomistic position of each molecule within the assembly as well as the driving force for the formation of the supramolecular rotors.

Communication: Charge-population based dispersion interactions for molecules and materials.

We introduce a system-independent method to derive effective atomic C6 coefficients and polarizabilities in molecules and materials purely from charge population analysis. This enables the use of dispersion-correction schemes in electronic structure calculations without recourse to electron-density partitioning schemes and expands their applicability to semi-empirical methods and tight-binding Hamiltonians. We show that the accuracy of our method is en par with established electron-density partitioning based approaches in describing intermolecular C6 coefficients as well as dispersion energies of weakly bound molecular dimers, organic crystals, and supramolecular complexes. We showcase the utility of our approach by incorporation of the recently developed many-body dispersion method [Tkatchenko et al., Phys. Rev. Lett. 108, 236402 (2012)] into the semi-empirical density functional tight-binding method and propose the latter as a viable technique to study hybridorganic-inorganic interfaces.

Biomolecular dynamics with machine-learned quantum-mechanical force fields trained on diverse chemical fragments.

The GEMS method enables molecular dynamics simulations of large heterogeneous systems at ab initio quality.

Coulomb interactions between dipolar quantum fluctuations in van der Waals bound molecules and materials.

Mutual Coulomb interactions between electrons lead to a plethora of interesting physical and chemical effects, especially if those interactions involve many fluctuating electrons over large spatial scales. Here, we identify and study in detail the Coulomb interaction between dipolar quantum fluctuations in the context of van der Waals complexes and materials. Up to now, the interaction arising from the modification of the electron density due to quantum van der Waals interactions was considered to be vanishingly small. We demonstrate that in supramolecular systems and for molecules embedded in nanostructures, such contributions can amount to up to 6 kJ/mol and can even lead to qualitative changes in the long-range van der Waals interaction. Taking into account these broad implications, we advocate for the systematic assessment of so-called Dipole-Correlated Coulomb Singles in large molecular systems and discuss their relevance for explaining several recent puzzling experimental observations of collective behavior in nanostructured materials.

Accurate Many-Body Repulsive Potentials for Density-Functional Tight Binding from Deep Tensor Neural Networks.

We combine density-functional tight binding (DFTB) with deep tensor neural networks (DTNN) to maximize the strengths of both approaches in predicting structural, energetic, and vibrational molecular properties. The DTNN is used to construct a nonlinear model for the localized many-body interatomic repulsive energy, which so far has been treated in an atom-pairwise manner in DFTB. Substantially improving upon standard DFTB and DTNN, the resulting DFTB-NNrep model yields accurate predictions of atomization and isomerization energies, equilibrium geometries, vibrational frequencies, and dihedral rotation profiles for a large variety of organic molecules compared to the hybrid DFT-PBE0 functional. Our results highlight the potential of combining semiempirical electronic-structure methods with physically motivated machine learning approaches for predicting localized many-body interactions. We conclude by discussing future advancements of the DFTB-NNrep approach that could enable chemically accurate electronic-structure calculations for systems with tens of thousands of atoms.

Quantum mechanics of proteins in explicit water: The role of plasmon-like solute-solvent interactions.

Quantum-mechanical van der Waals dispersion interactions play an essential role in intraprotein and protein-water interactions-the two main factors affecting the structure and dynamics of proteins in water. Typically, these interactions are only treated phenomenologically, via pairwise potential terms in classical force fields. Here, we use an explicit quantum-mechanical approach of density-functional tight-binding combined with the many-body dispersion formalism and demonstrate the relevance of many-body van der Waals forces both to protein energetics and to protein-water interactions. In contrast to commonly used pairwise approaches, many-body effects substantially decrease the relative stability of native states in the absence of water. Upon solvation, the protein-water dispersion interaction counteracts this effect and stabilizes native conformations and transition states. These observations arise from the highly delocalized and collective character of the interactions, suggesting a remarkable persistence of electron correlation through aqueous environments and providing the basis for long-range interaction mechanisms in biomolecular systems.