Quantum-mechanical force balance between multipolar dispersion and Pauli repulsion in atomic van der Waals dimers

in Physical Review Research (2021)

van der Waals Dispersion Interactions in Biomolecular Systems: Quantum-Mechanical Insights and Methodological Advances

Doctoral thesis (2020)

Intermolecular interactions are paramount for the stability, dynamics and response of systems across chemistry, biology and materials science. In biomolecules they govern secondary structure formation ... [more ▼]

Intermolecular interactions are paramount for the stability, dynamics and response of systems across chemistry, biology and materials science. In biomolecules they govern secondary structure formation, assembly, docking, regulation and functionality. van der Waals (vdW) dispersion contributes a crucial part to those interactions. As part of the long-range electron correlation, vdW interactions arise from Coulomb-coupled quantum-mechanical fluctuations in the instan- taneous electronic charge distribution and are thus inherently many-body in nature. Common approaches to describe biomolecular systems (i.e., classical molecular mechanics) fail to capture the full complexity of vdW dispersion by adapting a phenomenological, atom-pairwise formalism. This thesis explores beyond-pairwise vdW forces and the collectivity of intrinsic electronic behav- iors in biomolecular systems and discusses their role in the context of biomolecular processes and function. To this end, the many-body dispersion (MBD) formalism parameterized from density-functional tight-binding (DFTB) calculations is used. The investigation of simple molecular solvents with particular focus on water gives insights into the vdW energetics and electronic response properties in liquids and solvation as well as emergent behavior for coarse-grained models. A detailed study of intra-protein and protein–water vdW interactions highlights the role of many-body forces during protein folding and provides a funda- mental explanation for the previously observed “unbalanced” description and over-compaction of disordered protein states. Further analysis of the intrinsic electronic behaviors in explicitly solvated proteins indicates a long-range persistence of electron correlation through the aque- ous environment, which is discussed in the context of protein–protein interactions, long-range coordination and biomolecular regulation and allostery. Based on the example of a restriction enzyme, the potential role of many-body vdW forces and collective electronic behavior for the long-range coordination of enzymatic activity is discussed. Introducing electrodynamic quantum fluctuations into the classical picture of allostery opens up the path to a more holistic view on biomolecular regulation beyond the traditional focus on merely local structural modifications. Building on top of the MBD framework, which describes vdW dispersion within the interatomic dipole-limit, a practical extension to higher-order terms is presented. The resulting Dipole- Correlated Coulomb Singles account for multipolar as well as dispersion-polarization-like contri- butions beyond the random phase approximation by means of first-order perturbation theory over the dipole-coupled MBD state. It is shown that Dipole-Correlated Coulomb Singles become particularly relevant for relatively larger systems and can alter qualitative trends in the long-range interaction under (nano-)confinement. Bearing in mind the frequent presence of confinement in biomolecular systems due to cellular crowding, in ion channels or for interfacial water, this so-far neglected contribution is expected to have broad implications for systems of biological relevance. Ultimately, this thesis introduces a hybrid approach of DFTB and machine learning for the accu- rate description of large-scale systems on a robust, albeit approximate, quantum-mechanical level. The developed DFTB-NN rep approach combines the semi-empirical DFTB Hamiltonian with a deep tensor neural network model for localized many-body repulsive potentials. DFTB- NN rep provides an accurate description of energetic, structural and vibrational properties of a wide range of small organic molecules much superior to standard DFTB or machine learning. Overall, this thesis aims to extend the current view of complex (bio)molecular systems being governed by local, (semi-)classical interactions and develops methodological steps towards an advanced description and understanding including non-local interaction mechanisms enabled by quantum-mechanical phenomena such as long-range correlation forces arising from collective electronic fluctuations. [less ▲]

DFTB+, a software package for efficient approximate density functional theory based atomistic simulations

in Journal of Chemical Physics (2020), 152(12), 124101

DFTB+ is a versatile community developed open source software package offering fast and efficient methods for carrying out atomistic quantum mechanical simulations. By implementing various methods ... [more ▼]

DFTB+ is a versatile community developed open source software package offering fast and efficient methods for carrying out atomistic quantum mechanical simulations. By implementing various methods approximating density functional theory (DFT), such as the density functional based tight binding (DFTB) and the extended tight binding method, it enables simulations of large systems and long timescales with reasonable accuracy while being considerably faster for typical simulations than the respective ab initio methods. Based on the DFTB framework, it additionally offers approximated versions of various DFT extensions including hybrid functionals, time dependent formalism for treating excited systems, electron transport using non-equilibrium Green’s functions, and many more. DFTB+ can be used as a user-friendly standalone application in addition to being embedded into other software packages as a library or acting as a calculation-server accessed by socket communication. We give an overview of the recently developed capabilities of the DFTB+ code, demonstrating with a few use case examples, discuss the strengths and weaknesses of the various features, and also discuss on-going developments and possible future perspectives. [less ▲]

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

in Chemical Society Reviews (2019), 48

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 ... [more ▼]

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. [less ▲]