A Transferable Machine-Learning Model of the Electron Density

The electronic charge density plays a central role in determining the behavior of matter at the atomic scale, but its computational evaluation requires demanding electronic-structure calculations. We introduce an atom-centered, symmetry-adapted framework to machine-learn the valence charge density based on a small number of reference calculations. The model is highly transferable, meaning it can be trained on electronic-structure data of small molecules and used to predict the charge density of larger compounds with low, linear-scaling cost. Applications are shown for various hydrocarbon molecules of increasing complexity and flexibility, and demonstrate the accuracy of the model when predicting the density on octane and octatetraene after training exclusively on butane and butadiene. This transferable, data-driven model can be used to interpret experiments, initialize electronic structure calculations, and compute electrostatic interactions in molecules and condensed-phase systems

Electrostatic interactions in host-guest complexes 2

In this article the quantum chemically calculated charge density distribution of 18-crown-6 and the K+ 18-crown-6 complex are compared with the charge density distribution of smaller molecules and corresponding complexes which can be considered as fragments of the 18-crown-6 molecule. An analysis of the charge density distribution in terms of atomic charge distribution according to the stockholder recipe gives accurate rules for the transferability of the charge density distribution. This gives us the possibility to construct the charge density distribution of large molecules out of accurate large basis set results on small molecules

Nanoplasmonics simulations at the basis set limit through completeness-optimized, local numerical basis sets

We present an approach for generating local numerical basis sets of improving accuracy for first-principles nanoplasmonics simulations within time-dependent density functional theory. The method is demonstrated for copper, silver, and gold nanoparticles that are of experimental interest but computationally demanding due to the semi-core d-electrons that affect their plasmonic response. The basis sets are constructed by augmenting numerical atomic orbital basis sets by truncated Gaussian-type orbitals generated by the completeness-optimization scheme, which is applied to the photoabsorption spectra of homoatomic metal atom dimers. We obtain basis sets of improving accuracy up to the complete basis set limit and demonstrate that the performance of the basis sets transfers to simulations of larger nanoparticles and nanoalloys as well as to calculations with various exchange-correlation functionals. This work promotes the use of the local basis set approach of controllable accuracy in first-principles nanoplasmonics simulations and beyond.Comment: 11 pages, 6 figure

Computation of charge distribution and electrostatic potential in silicates with the use of chemical potential equalization models

New parameters for the electronegativity equalization model (EEM) and the split-charge equilibration (SQE) model are calibrated for silicate materials, based on an extensive training set of representative isolated systems. In total, four calibrations are carried out, two for each model, either using iterative Hirshfeld (HI) charges or ESP grid data computed with density functional theory (DFT) as a reference. Both the static (ground state) reference quantities and their responses to uniform electric fields are included in the fitting procedure. The EEM model fails to describe the response data, whereas the SQE model quantitatively reproduces all of the training data. For the ESP-based parameters, we found that the reference ESP data are only useful at those grid points where the electron density is lower than 0.001 a.u. The density value correlates with a distance criterion used for selecting grid points in common ESP fitting schemes. All parameters are validated with DFT computations on an independent set of isolated systems (similar to the training set), and on a set of periodic systems including dense and microporous crystalline silica structures, zirconia, and zirconium silicate. Although the transferability of the parameters to new isolated systems poses no difficulties, the atomic hardness parameters in the HI-based models must be corrected to obtain accurate results for periodic systems. The SQE/ESP model permits the calculation of the ESP with similar accuracy in both isolated and periodic systems

The ReaxFF reactive force-field : development, applications and future directions

The reactive force-field (ReaxFF) interatomic potential is a powerful computational tool for exploring, developing and optimizing material properties. Methods based on the principles of quantum mechanics (QM), while offering valuable theoretical guidance at the electronic level, are often too computationally intense for simulations that consider the full dynamic evolution of a system. Alternatively, empirical interatomic potentials that are based on classical principles require significantly fewer computational resources, which enables simulations to better describe dynamic processes over longer timeframes and on larger scales. Such methods, however, typically require a predefined connectivity between atoms, precluding simulations that involve reactive events. The ReaxFF method was developed to help bridge this gap. Approaching the gap from the classical side, ReaxFF casts the empirical interatomic potential within a bond-order formalism, thus implicitly describing chemical bonding without expensive QM calculations. This article provides an overview of the development, application, and future directions of the ReaxFF method

Toward transferable interatomic van der Waals interactions without electrons: The role of multipole electrostatics and many-body dispersion

We estimate polarizabilities of atoms in molecules without electron density, using a Voronoi tesselation approach instead of conventional density partitioning schemes. The resulting atomic dispersion coefficients are calculated, as well as many-body dispersion effects on intermolecular potential energies. We also estimate contributions from multipole electrostatics and compare them to dispersion. We assess the performance of the resulting intermolecular interaction model from dispersion and electrostatics for more than 1,300 neutral and charged, small organic molecular dimers. Applications to water clusters, the benzene crystal, the anti-cancer drug ellipticine---intercalated between two Watson-Crick DNA base pairs, as well as six macro-molecular host-guest complexes highlight the potential of this method and help to identify points of future improvement. The mean absolute error made by the combination of static electrostatics with many-body dispersion reduces at larger distances, while it plateaus for two-body dispersion, in conflict with the common assumption that the simple $1/R^6$ correction will yield proper dissociative tails. Overall, the method achieves an accuracy well within conventional molecular force fields while exhibiting a simple parametrization protocol.Comment: 13 pages, 8 figure

Molecular Force Fields with Gradient-Domain Machine Learning: Construction and Application to Dynamics of Small Molecules with Coupled Cluster Forces

We present the construction of molecular force fields for small molecules (less than 25 atoms) using the recently developed symmetrized gradient-domain machine learning (sGDML) approach [Chmiela et al., Nat. Commun. 9, 3887 (2018); Sci. Adv. 3, e1603015 (2017)]. This approach is able to accurately reconstruct complex high-dimensional potential-energy surfaces from just a few 100s of molecular conformations extracted from ab initio molecular dynamics trajectories. The data efficiency of the sGDML approach implies that atomic forces for these conformations can be computed with high-level wavefunction-based approaches, such as the "gold standard" CCSD(T) method. We demonstrate that the flexible nature of the sGDML model recovers local and non-local electronic interactions (e.g. H-bonding, proton transfer, lone pairs, changes in hybridization states, steric repulsion and $n\to\pi^*$ interactions) without imposing any restriction on the nature of interatomic potentials. The analysis of sGDML molecular dynamics trajectories yields new qualitative insights into dynamics and spectroscopy of small molecules close to spectroscopic accuracy

Minimal Basis Iterative Stockholder: Atoms in Molecules for Force-Field Development

Atomic partial charges appear in the Coulomb term of many force-field models and can be derived from electronic structure calculations with a myriad of atoms-in-molecules (AIM) methods. More advanced models have also been proposed, using the distributed nature of the electron cloud and atomic multipoles. In this work, an electrostatic force field is defined through a concise approximation of the electron density, for which the Coulomb interaction is trivially evaluated. This approximate "pro-density" is expanded in a minimal basis of atom-centered s-type Slater density functions, whose parameters are optimized by minimizing the Kullback-Leibler divergence of the pro-density from a reference electron density, e.g. obtained from an electronic structure calculation. The proposed method, Minimal Basis Iterative Stockholder (MBIS), is a variant of the Hirshfeld AIM method but it can also be used as a density-fitting technique. An iterative algorithm to refine the pro-density is easily implemented with a linear-scaling computational cost, enabling applications to supramolecular systems. The benefits of the MBIS method are demonstrated with systematic applications to molecular databases and extended models of condensed phases. A comparison to 14 other AIM methods shows its effectiveness when modeling electrostatic interactions. MBIS is also suitable for rescaling atomic polarizabilities in the Tkatchenko-Sheffler scheme for dispersion interactions.Comment: 61 pages, 12 figures, 2 table