Showing papers by "Alexandre Tkatchenko published in 2020"

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

Abstract: 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.

Machine Learning for Molecular Simulation.

Abstract: Machine learning (ML) is transforming all areas of science. The complex and time-consuming calculations in molecular simulations are particularly suitable for an ML revolution and have already been profoundly affected by the application of existing ML methods. Here we review recent ML methods for molecular simulation, with particular focus on (deep) neural networks for the prediction of quantum-mechanical energies and forces, on coarse-grained molecular dynamics, on the extraction of free energy surfaces and kinetics, and on generative network approaches to sample molecular equilibrium structures and compute thermodynamics. To explain these methods and illustrate open methodological problems, we review some important principles of molecular physics and describe how they can be incorporated into ML structures. Finally, we identify and describe a list of open challenges for the interface between ML and molecular simulation.

Machine Learning Force Fields

Abstract: In recent years, the use of Machine Learning (ML) in computational chemistry has enabled numerous advances previously out of reach due to the computational complexity of traditional electronic-structure methods. One of the most promising applications is the construction of ML-based force fields (FFs), with the aim to narrow the gap between the accuracy of ab initio methods and the efficiency of classical FFs. The key idea is to learn the statistical relation between chemical structure and potential energy without relying on a preconceived notion of fixed chemical bonds or knowledge about the relevant interactions. Such universal ML approximations are in principle only limited by the quality and quantity of the reference data used to train them. This review gives an overview of applications of ML-FFs and the chemical insights that can be obtained from them. The core concepts underlying ML-FFs are described in detail and a step-by-step guide for constructing and testing them from scratch is given. The text concludes with a discussion of the challenges that remain to be overcome by the next generation of ML-FFs.

Exploring chemical compound space with quantum-based machine learning

Abstract: Rational design of compounds with specific properties requires understanding and fast evaluation of molecular properties throughout chemical compound space — the huge set of all potentially stable molecules. Recent advances in combining quantum-mechanical calculations with machine learning provide powerful tools for exploring wide swathes of chemical compound space. We present our perspective on this exciting and quickly developing field by discussing key advances in the development and applications of quantum-mechanics-based machine-learning methods to diverse compounds and properties, and outlining the challenges ahead. We argue that significant progress in the exploration and understanding of chemical compound space can be made through a systematic combination of rigorous physical theories, comprehensive synthetic data sets of microscopic and macroscopic properties, and modern machine-learning methods that account for physical and chemical knowledge. Machine-learning techniques have enabled, among many other applications, the exploration of molecular properties throughout chemical space. The specific development of quantum-based approaches in machine learning can now help us unravel new chemical insights.

Machine learning for chemical discovery.

Abstract: Discovering chemicals with desired attributes is a long and painstaking process. Curated datasets containing reliable quantum-mechanical properties for millions of molecules are becoming increasingly available. The development of novel machine learning tools to obtain chemical knowledge from these datasets has the potential to revolutionize the process of chemical discovery. Here, I comment on recent breakthroughs in this emerging field and discuss the challenges for the years to come.

Machine Learning Force Fields and Coarse-Grained Variables in Molecular Dynamics: Application to Materials and Biological Systems.

Abstract: Machine learning encompasses a set of tools and algorithms which are now becoming popular in almost all scientific and technological fields This is true for molecular dynamics as well, where machine learning offers promises of extracting valuable information from the enormous amounts of data generated by simulation of complex systems We provide here a review of our current understanding of goals, benefits, and limitations of machine learning techniques for computational studies on atomistic systems, focusing on the construction of empirical force fields from ab-initio databases and the determination of reaction coordinates for free energy computation and enhanced sampling

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

Abstract: 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.

Density Functional Model for van der Waals Interactions: Unifying Many-Body Atomic Approaches with Nonlocal Functionals

Abstract: Noncovalent van der Waals (vdW) interactions are responsible for a wide range of phenomena in matter. Popular density-functional methods that treat vdW interactions use disparate physical models for these intricate forces, and as a result the applicability of these methods is often restricted to a subset of relevant molecules and materials. Aiming towards a general-purpose density functional model of vdW interactions, here we unify two complementary approaches: nonlocal vdW functionals for polarization and interatomic methods for many-body interactions. The developed nonlocal many-body dispersion method (MBD-NL) increases the accuracy and efficiency of existing vdW functionals and is shown to be broadly applicable to molecules, soft and hard materials including ionic and metallic compounds, as well as interfaces between organic molecules and inorganic materials.

QM7-X: A comprehensive dataset of quantum-mechanical properties spanning the chemical space of small organic molecules

Abstract: We introduce QM7-X, a comprehensive dataset of 42 physicochemical properties for $\approx$ 4.2 M equilibrium and non-equilibrium structures of small organic molecules with up to seven non-hydrogen (C, N, O, S, Cl) atoms. To span this fundamentally important region of chemical compound space (CCS), QM7-X includes an exhaustive sampling of (meta-)stable equilibrium structures - comprised of constitutional/structural isomers and stereoisomers, e.g., enantiomers and diastereomers (including cis-/trans- and conformational isomers) - as well as 100 non-equilibrium structural variations thereof to reach a total of $\approx$ 4.2 M molecular structures. Computed at the tightly converged quantum-mechanical PBE0+MBD level of theory, QM7-X contains global (molecular) and local (atom-in-a-molecule) properties ranging from ground state quantities (such as atomization energies and dipole moments) to response quantities (such as polarizability tensors and dispersion coefficients). By providing a systematic, extensive, and tightly-converged dataset of quantum-mechanically computed physicochemical properties, we expect that QM7-X will play a critical role in the development of next-generation machine-learning based models for exploring greater swaths of CCS and performing in silico design of molecules with targeted properties.

Mechanical and Tribological Properties of Layered Materials under High Pressure: Assessing the Importance of Many-Body Dispersion Effects.

Abstract: The importance of many-body dispersion effects in layered materials subjected to high external loads is evaluated. State-of-the-art many-body dispersion density functional theory calculations performed for graphite, hexagonal boron nitride, and their heterostructures were used to fit the parameters of a classical registry-dependent interlayer potential. Using the latter, we performed extensive equilibrium molecular dynamics simulations and studied the mechanical response of homogeneous and heterogeneous bulk models under hydrostatic pressures up to 30 GPa. Comparison with experimental data demonstrates that the reliability of the many-body dispersion model extends deep into the subequilibrium regime. Friction simulations demonstrate the importance of many-body dispersion effects for the accurate description of the tribological properties of layered material interfaces under high pressure.

Interactions between Large Molecules: Puzzle for Reference Quantum-Mechanical Methods

Abstract: Quantum-mechanical methods are widely used for understanding molecular interactions throughout biology, chemistry, and materials science. Quantum diffusion Monte Carlo (DMC) and coupled cluster with single, double, and perturbative triple excitations [CCSD(T)] are two state-of-the-art and trusted wavefunction methods that have been categorically shown to yield accurate interaction energies for small organic molecules. These methods provide valuable reference information for widely-used semi-empirical and machine learning potentials, especially where experimental information is scarce. However, agreement for systems beyond small molecules is a crucial remaining milestone for cementing the benchmark accuracy of these methods. Approaching such well-converged predictive power in larger molecules has motivated major developments in CCSD(T) as well as DMC algorithms in the past years, resulting in orders of magnitude time-to-solution reductions. Here, we show that CCSD(T) and DMC interaction energies are not in consistent agreement for a set of polarizable supramolecules. Whilst agreement is found for some of the complexes, in a few key systems disagreements of up to 8 kcal/mol remained. This leads to differences of up to 6 orders of magnitude in the corresponding binding association constant at room temperature for systems which are well within the accustomed domain of applicability for both methods. These findings thus indicate that more caution is required when aiming at reproducible non-covalent interactions between extended molecules. Our data contradicts the expectation that the most comprehensive and robust wavefunction methods predict identical non-covalent interactions and indicate an unsolved challenge for benchmark approaches.

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

Abstract: 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 learn a non-linear 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-NN$_{\sf{rep}}$ 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 high potential of combining semi-empirical electronic-structure methods with physically-motivated machine learning approaches for predicting localized many-body interactions. We conclude by discussing future advancements of the DFTB-NN$_{\sf{rep}}$ approach that could enable chemically accurate electronic-structure calculations for systems with tens of thousands of atoms.

From quantum to continuum mechanics in the delamination of atomically-thin layers from substrates.

Abstract: Anomalous proximity effects have been observed in adhesive systems ranging from proteins, bacteria, and gecko feet suspended over semiconductor surfaces to interfaces between graphene and different substrate materials. In the latter case, long-range forces are evidenced by measurements of non-vanishing stress that extends up to micrometer separations between graphene and the substrate. State-of-the-art models to describe adhesive properties are unable to explain these experimental observations, instead underestimating the measured stress distance range by 2–3 orders of magnitude. Here, we develop an analytical and numerical variational approach that combines continuum mechanics and elasticity with quantum many-body treatment of van der Waals dispersion interactions. A full relaxation of the coupled adsorbate/substrate geometry leads us to conclude that wavelike atomic deformation is largely responsible for the observed long-range proximity effect. The correct description of this seemingly general phenomenon for thin deformable membranes requires a direct coupling between quantum and continuum mechanics. The unexpectedly long-ranged interface stress observed in recent delamination experiments is yet to be clarified. Here, the authors develop an analytical approach to show the wavelike atomic deformation as the origin for the observed ultra long-range stress in delamination of graphene from various substrates.

Molecular force fields with gradient-domain machine learning (GDML): Comparison and synergies with classical force fields.

Abstract: Modern machine learning force fields (ML-FF) are able to yield energy and force predictions at the accuracy of high-level ab initio methods, but at a much lower computational cost. On the other hand, classical molecular mechanics force fields (MM-FF) employ fixed functional forms and tend to be less accurate, but considerably faster and transferable between molecules of the same class. In this work, we investigate how both approaches can complement each other. We contrast the ability of ML-FF for reconstructing dynamic and thermodynamic observables to MM-FFs in order to gain a qualitative understanding of the differences between the two approaches. This analysis enables us to modify the generalized AMBER force field by reparametrizing short-range and bonded interactions with more expressive terms to make them more accurate, without sacrificing the key properties that make MM-FFs so successful.

Four-Dimensional Scaling of Dipole Polarizability in Quantum Systems

Abstract: Polarizability is a key response property of physical and chemical systems, which has an impact on intermolecular interactions, spectroscopic observables, and vacuum polarization. The calculation of polarizability for quantum systems involves an infinite sum over all excited (bound and continuum) states, concealing the physical interpretation of polarization mechanisms and complicating the derivation of efficient response models. Approximate expressions for the dipole polarizability, $\alpha$, rely on different scaling laws $\alpha \propto$ $R^3$, $R^4$, or $R^7$, for various definitions of the system radius $R$. Here, we consider a range of atom-like quantum systems of varying spatial dimensionality and having qualitatively different spectra, demonstrating that their polarizability follows a universal four-dimensional scaling law $\alpha = C (4 \mu q^2/\hbar^2)L^4$, where $\mu$ and $q$ are the (effective) particle mass and charge, $C$ is a dimensionless ratio between effective excitation energies, and the characteristic length $L$ is defined via the $\mathcal{L}^2$-norm of the position operator. The applicability of this unified formula is demonstrated by accurately predicting the dipole polarizability of 36 atoms and 1641 small organic~molecules.

Dynamical Strengthening of Covalent and Non-Covalent Molecular Interactions by Nuclear Quantum Effects at Finite Temperature

Abstract: Nuclear quantum effects (NQE) tend to generate delocalized molecular dynamics due to the inclusion of the zero point energy and its coupling with the anharmonicities in interatomic interactions Here, we present evidence that NQE often enhance electronic interactions and, in turn, can result in dynamical molecular stabilization at finite temperature The underlying physical mechanism promoted by NQE depends on the particular interaction under consideration First, the effective reduction of interatomic distances between functional groups within a molecule can enhance the $n\to\pi^*$ interaction by increasing the overlap between molecular orbitals or by strengthening electrostatic interactions between neighboring charge densities Second, NQE can localize methyl rotors by temporarily changing molecular bond orders and leading to the emergence of localized transient rotor states Third, for noncovalent van der Waals interactions the strengthening comes from the increase of the polarizability given the expanded average interatomic distances induced by NQE The implications of these boosted interactions include counterintuitive hydroxyl--hydroxyl bonding, hindered methyl rotor dynamics, and molecular stiffening which generates smoother free-energy surfaces Our findings yield new insights into the versatile role of nuclear quantum fluctuations in molecules and materials

Construction of Machine Learned Force Fields with Quantum Chemical Accuracy: Applications and Chemical Insights

Abstract: Highly accurate force fields are a mandatory requirement to generate predictive simulations. Here we present the path for the construction of machine learned molecular force fields by discussing the hierarchical pathway from generating the dataset of reference calculations to the construction of the machine learning model, and the validation of the physics generated by the model. We will use the symmetrized gradient-domain machine learning (sGDML) framework due to its ability to reconstruct complex high-dimensional potential energy surfaces (PES) with high precision even when using just a few hundreds of molecular conformations for training. The data efficiency of the sGDML model allows using reference atomic forces computed with high-level wave-function-based approaches, such as the gold standard coupled-cluster method with single, double, and perturbative triple excitations (CCSD(T)). We demonstrate that the flexible nature of the sGDML framework captures local and non-local electronic interactions (e.g., H-bonding, lone pairs, steric repulsion, changes in hybridization states (e.g., \(sp^2 \rightleftharpoons sp^3\)), n → π∗ interactions, and proton transfer) without imposing any restriction on the nature of interatomic potentials. The analysis of sGDML models trained for different molecular structures at different levels of theory (e.g., density functional theory and CCSD(T)) provides empirical evidence that a higher level of theory generates a smoother PES. Additionally, a careful analysis of molecular dynamics simulations yields new qualitative insights into dynamics and vibrational spectroscopy of small molecules close to spectroscopic accuracy.

Molecular Force Fields with Gradient-Domain Machine Learning (GDML): Comparison and Synergies with Classical Force Fields

Abstract: Modern machine learning force fields (ML-FF) are able to yield energy and force predictions at the accuracy of high-level $ab~initio$ methods, but at a much lower computational cost. On the other hand, classical molecular mechanics force fields (MM-FF) employ fixed functional forms and tend to be less accurate, but considerably faster and transferable between molecules of the same class. In this work, we investigate how both approaches can complement each other. We contrast the ability of ML-FF for reconstructing dynamic and thermodynamic observables to MM-FFs in order to gain a qualitative understanding of the differences between the two approaches. This analysis enables us to modify the generalized AMBER force field (GAFF) by reparametrizing short-range and bonded interactions with more expressive terms to make them more accurate, without sacrificing the key properties that make MM-FFs so successful.

Coulomb Interactions between Dipolar Quantum Fluctuations in van der Waals Bound Molecules and Materials

Abstract: 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 vdW interaction. Taking into account these broad implications, we advocate for the systematic assessment of so-called Coulomb singles in large molecular systems and discuss their relevance for explaining several recent puzzling experimental observations of collective behavior in nanostructured materials.

Improved description of ligand polarization enhances transferability of ion-ligand interactions.

Abstract: The reliability of molecular mechanics (MM) simulations in describing biomolecular ion-driven processes depends on their ability to accurately model interactions of ions simultaneously with water and other biochemical groups. In these models, ion descriptors are calibrated against reference data on ion-water interactions, and it is then assumed that these descriptors will also satisfactorily describe interactions of ions with other biochemical ligands. The comparison against the experiment and high-level quantum mechanical data show that this transferability assumption can break down severely. One approach to improve transferability is to assign cross terms or separate sets of non-bonded descriptors for every distinct pair of ion type and its coordinating ligand. Here, we propose an alternative solution that targets an error-source directly and corrects misrepresented physics. In standard model development, ligand descriptors are never calibrated or benchmarked in the high electric fields present near ions. We demonstrate for a representative MM model that when the polarization descriptors of its ligands are improved to respond to both low and high fields, ligand interactions with ions also improve, and transferability errors reduce substantially. In our case, the overall transferability error reduces from 3.3 kcal/mol to 1.8 kcal/mol. These improvements are observed without compromising on the accuracy of low-field interactions of ligands in gas and condensed phases. Reference data for calibration and performance evaluation are taken from the experiment and also obtained systematically from "gold-standard" CCSD(T) in the complete basis set limit, followed by benchmarked vdW-inclusive density functional theory.

Accurate Molecular Dynamics Enabled by Efficient Physically Constrained Machine Learning Approaches

Abstract: We develop a combined machine learning (ML) and quantum mechanics approach that enables data-efficient reconstruction of flexible molecular force fields from high-level ab initio calculations, through the consideration of fundamental physical constraints. We discuss how such constraints are recovered and incorporated into ML models. Specifically, we use conservation of energy—a fundamental property of closed classical and quantum mechanical systems—to derive an efficient gradient-domain machine learning (GDML) model. The challenge of constructing conservative force fields is accomplished by learning in a Hilbert space of vector-valued functions that obey the law of energy conservation. We proceed with the development of a multi-partite matching algorithm that enables a fully automated recovery of physically relevant point group and fluxional symmetries from the training dataset into a symmetric variant of our model. The symmetric GDML (sGDML) approach is able to faithfully reproduce global force fields at the accuracy high-level ab initio methods, thus enabling sample intensive tasks like molecular dynamics simulations at that level of accuracy. (This chapter is adapted with permission from Chmiela (Towards exact molecular dynamics simulations with invariant machine-learned models, PhD thesis. Technische Universitat, Berlin, 2019).)

Learning Representations of Molecules and Materials with Atomistic Neural Networks

Abstract: Deep learning has been shown to learn efficient representations for structured data such as images, text, or audio. In this chapter, we present neural network architectures that are able to learn efficient representations of molecules and materials. In particular, the continuous-filter convolutional network SchNet accurately predicts chemical properties across compositional and configurational space on a variety of datasets. Beyond that, we analyze the obtained representations to find evidence that their spatial and chemical properties agree with chemical intuition.

Fluctuational electrodynamics in atomic and macroscopic systems: van der Waals interactions and radiative heat transfer

Abstract: We present an approach to describing fluctuational electrodynamic interactions, particularly van der Waals (vdW) interactions as well as radiative heat transfer (RHT), between material bodies of potentially vastly different length scales, allowing for going between atomistic and continuum treatments of the response of each of these bodies as desired. Any local continuum description of electromagnetic response is compatible with our approach, while atomistic descriptions in our approach are based on effective electronic and nuclear oscillator degrees of freedom, encapsulating dissipation, short-range electronic correlations, and collective nuclear vibrations (phonons). While our previous works using this approach have focused on presenting novel results, this work focuses on the derivations underlying these methods. First, we show how the distinction between ``atomic'' and ``macroscopic'' bodies is ultimately somewhat arbitrary, as formulas for vdW free energies and radiative heat transfer look very similar regardless of how the distinction is drawn. Next, we demonstrate that the atomistic description of material response in our approach yields electromagnetic interaction matrix elements which are expressed in terms of analytical formulas for compact bodies or semianalytical formulas based on Ewald summation for periodic media; we use this to compute vdW interaction free energies as well as RHT powers among small biological molecules in the presence of a metallic plate as well as between parallel graphene sheets in vacuum, showing strong deviations from conventional macroscopic theories due to the confluence of geometry, phonons, and electromagnetic retardation effects. Finally, we propose formulas for efficient computation of fluctuational electrodynamic interactions among material bodies in which those that are treated atomistically as well as those treated through continuum methods may have arbitrary shapes, extending previous surface-integral techniques.

Accurate Description of Nuclear Quantum Effects with High-Order Perturbed Path Integrals (HOPPI).

Abstract: Imaginary time path-integral (PI) simulations that account for nuclear quantum effects (NQE) beyond the harmonic approximation are increasingly employed together with modern electronic-structure calculations. Existing PI methods are applicable to molecules, liquids, and solids; however, the computational cost of such simulations increases dramatically with decreasing temperature. To address this challenge, here, we propose to combine high-order PI factorization with perturbation theory (PT). Already for conventional second-order PI simulations, the PT ansatz increases the accuracy 2-fold compared to fourth-order schemes with the same settings. In turn, applying PT to high-order path integrals (HOPI) further improves the efficiency of simulations for molecular and condensed matter systems especially at low temperatures. We present results for bulk liquid water, the aspirin molecule, and the CH5+ molecule. Perturbed HOPI simulations remain both efficient and accurate down to 20 K and provide a convenient method to estimate the convergence of quantum-mechanical observables.

Nonlocal Electronic Correlations in the Cohesive Properties of High-Pressure Hydrogen Solids.

Abstract: High-pressure hydrogen exhibits remarkable phenomena including the insulator-to-metal (IM) transition; however, a complete resolution of its phase diagram is still an elusive goal despite many efforts and much controversy. Theoretical modeling is typically based on density functional theory (DFT) with a mean-field description of electronic correlations, which is known to be rather limited in describing IM transitions. Herein, we show that nonlocal electron correlations play a central role in the relative stability of solid hydrogen phases, and that DFT-correcting for these correlations by the many-body dispersion (MBD) model reaches the accuracy of quantum Monte Carlo (QMC) simulations and predicts the same C2/c-24 → Cmca-12 → Cs(IV) IM transition. In contrast with the conventional assumption that many-body electronic correlations become localized in metallic systems because of exponential screening with interelectronic distance, we find that the anisotropy of the electronic response of hydrogen solids un...

Fine-Structure Constant Connects the Polarizability of Atoms and Vacuum

Abstract: We examine the recently derived quantum-mechanical relation between atomic polarizabilities and equilibrium internuclear distances in van der Waals (vdW) bonded diatomic systems [Phys Rev Lett {\bf 121}, 183401 (2018)] For homonuclear dimers, this relation is described by the compact formula $\alpha_{\rm m}^{\rm q} = \Phi R_{\rm vdW}^7$, where the constant factor in front of the vdW radius was determined empirically Here, we derive $\Phi = (4\pi\epsilon_0/a_0^4) \times \alpha^{4/3}$ expressed in terms of the vacuum electric permittivity $\epsilon_0$, the Bohr radius $a_0$, and the fine-structure constant $\alpha$ The validity of the obtained formula is confirmed by estimating the value of the fine-structure constant from non-relativistic quantum-mechanical calculations of atomic polarizabilities and equilibrium internuclear vdW distances The presented derivation allows to interpret the fine-structure constant as the ratio between the polarizability densities of vacuum and matter, whereas the vdW radius becomes a geometrical length scale of atoms endowed by the vacuum field

Machine learning force fields and coarse-grained variables in molecular dynamics: application to materials and biological systems

Abstract: Machine learning encompasses a set of tools and algorithms which are now becoming popular in almost all scientific and technological fields. This is true for molecular dynamics as well, where machine learning offers promises of extracting valuable information from the enormous amounts of data generated by simulation of complex systems. We provide here a review of our current understanding of goals, benefits, and limitations of machine learning techniques for computational studies on atomistic systems, focusing on the construction of empirical force fields from ab-initio databases and the determination of reaction coordinates for free energy computation and enhanced sampling.

Molecular basis for SARS-CoV-2 spike affinity for human ACE2 receptor

Abstract: Severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) has caused substantially more infections, deaths, and economic disruptions than the 2002-2003 SARS-CoV. The key to understanding SARS-CoV-2’s higher infectivity may lie in its host receptor recognition mechanism. This is because experiments show that the human ACE2 protein, which serves as the primary receptor for both CoVs, binds to CoV-2’s spike protein 5-20 fold stronger than SARS-CoV’s spike protein. The molecular basis for this difference in binding affinity, however, remains unexplained and, in fact, a comparison of X-ray structures leads to an opposite proposition. To gain insight, we use all-atom molecular dynamics simulations. Free energy calculations indicate that CoV-2’s higher affinity is due primarily to differences in specific spike residues that are local to the spike-ACE2 interface, although there are allosteric effects in binding. Comparative analysis of equilibrium simulations reveals that while both CoV and CoV-2 spike-ACE2 complexes have similar interfacial topologies, CoV-2’s spike protein engages in greater numbers, combinatorics and probabilities of hydrogen bonds and salt bridges with ACE2. We attribute CoV-2’s higher affinity to these differences in polar contacts, and these findings also highlight the importance of thermal structural fluctuations in spike-ACE2 complexation. We anticipate that these findings will also inform the design of spike-ACE2 peptide blockers that, like in the cases of HIV and Influenza, can serve as antivirals.