arXiv subjects

Andrea Grisafi

Publications and source records attributed to Andrea Grisafi.

At least 19 recordsLinked to original sources

arXiv2026

SALTED: a symmetry-adapted machine-learning program for predicting electron-densities in molecules and materials

SALTED provides an open-source Python package for machine learning the quantum-mechanical electron density, $n(\mathbf{r})$, in molecular and condensed-phase systems based on input atomic coordinates and species. The program adopts a linear atom-centered decomposition of the electron density, which makes it highly transferable across diverse atomistic configurations sharing similar chemical environments. Because of this representation choice, SALTED is naturally interfaced with state-of-the-art electronic-structure programs based on atomic orbitals, namely CP2K, FHI-aims, and PySCF, from which reference electron-density data can be generated and used to train a model. The learning algorithm is based on a symmetry-adapted extension of Gaussian process regression, making SALTED especially efficient in small-data regimes. Thanks to the implementation of vector-field kernel functions, SALTED can also learn the first-order response of the electron density to applied electric fields, $\partial n(\mathbf{r})/\partial \mathbf{E}$. The application of SALTED within computational workflows has already shown its utility in a wide variety of contexts, including the calculation of polarization vectors and polarizability tensors, the accurate evaluation of Coulomb forces in QM/MM molecular-dynamics simulations, and electronic-structure studies of large-scale 2D materials.

cond-mat.mtrl-sci↗

arXiv2026

Long-range electrostatics in atomistic machine learning: a physical perspective

The inclusion of long-range electrostatics in atomistic machine learning (ML) is receiving increasing attention for achieving quantum-mechanical accuracy in predicting a wide range of molecular and material properties. However, there is still no general prescription for how long-range physical effects should be incorporated into a model while preserving the well-established locality principles underlying most transferable ML representations. Here, we provide a physical perspective on this problem by discussing how distinct contributions to a system's electrostatics can be captured through different learning paradigms. Specifically, we distinguish between local charge models, which rely either on explicit charge-density decompositions or implicit auxiliary variables, and models in which a notion of nonlocality is deliberately introduced, either via self-consistent procedures or by using nonlocal descriptors and learning architectures. We further address the related aspect of incorporating finite-field effects through coupling to the system's polarization, relevant for applications involving an external electric bias. We conclude by discussing implications for simulations of electrochemical interfaces, where long-range electrostatics are essential to capture the interplay between charge redistribution, interfacial dynamics, and ionic screening, as well as for ionic transport phenomena, which, although less explored, appear far less sensitive to their inclusion.

cond-mat.mtrl-sci↗

arXiv2026

Exact Theory of Fermi-Energy Response at Metallic Interfaces

The response of the Fermi energy to external perturbations governs key physical observables at metallic interfaces. Although this response admits a local formulation in terms of the Fukui function, its evaluation has traditionally been limited by inherent approximations, fundamentally rooted in the difficulty of adding a finite charge in a periodic system. We present an exact resolution to this problem that leverages the screening properties of electronic conductors to compute Fukui functions via a finite electric field. The resulting linear-response theory yields strictly quadratic error scaling of Fermi-level shifts across representative platinum surfaces, achieving sub-meV accuracy up to fields of 0.1 V/\AA. The approach is further validated by reproducing work-function changes under molecular perturbations, and by providing mean-field estimates of electrode potentials that yield capacitance--voltage curves consistent with experiment. Our findings establish a rigorous foundation for a local theory relating electrostatic screening and Fermi-energy variations at metallic interfaces.

cond-mat.mtrl-sci↗

arXiv2025

Roadmap on Advancements of the FHI-aims Software Package

Electronic-structure theory is the foundation of the description of materials including multiscale modeling of their properties and functions. Obviously, without sufficient accuracy at the base, reliable predictions are unlikely at any level that follows. The software package FHI-aims has proven to be a game changer for accurate free-energy calculations because of its scalability, numerical precision, and its efficient handling of density functional theory (DFT) with hybrid functionals and van der Waals interactions. It treats molecules, clusters, and extended systems (solids and liquids) on an equal footing. Besides DFT, FHI-aims also includes quantum-chemistry methods, descriptions for excited states and vibrations, and calculations of various types of transport. Recent advancements address the integration of FHI-aims into an increasing number of workflows and various artificial intelligence (AI) methods. This Roadmap describes the state-of-the-art of FHI-aims and advancements that are currently ongoing or planned.

cond-mat.mtrl-sci↗

arXiv2025

Learning the Electrostatic Response of the Electron Density through a Symmetry-Adapted Vector Field Model

A current challenge in atomistic machine learning is that of efficiently predicting the response of the electron density under electric fields. We address this challenge with symmetry-adapted kernel functions that are specifically derived to account for the rotational symmetry of a three-dimensional vector field. We demonstrate the equivariance of the method on a set of rotated water molecules and show its high efficiency with respect to number of training configurations and features for liquid water and naphthalene crystals. We conclude showcasing applications for relaxed configurations of gold nanoparticles, reproducing the scaling law of the electronic polarizability with size, up to systems with more than 2000 atoms. By deriving a natural extension to equivariant learning models of the electron density, our method provides an accurate and inexpensive strategy to predict the electrostatic response of molecules and materials.

cond-mat.mtrl-sci↗

arXiv2024

Accelerating QM/MM simulations of electrochemical interfaces through machine learning of electronic charge densities

A crucial aspect in the simulation of electrochemical interfaces consists in treating the distribution of electronic charge of electrode materials that are put in contact with an electrolyte solution. Recently, it has been shown how a machine-learning method that specifically targets the electronic charge density, also known as SALTED, can be used to predict the long-range response of metal electrodes in model electrochemical cells. In this work, we provide a full integration of SALTED with MetalWalls, a program for performing classical simulations of electrochemical systems. We do so by deriving a spherical harmonics extension of the Ewald summation method, which allows us to efficiently compute the electric field originated by the predicted electrode charge distribution. We show how to use this method to drive the molecular dynamics of an aqueous electrolyte solution under the quantum electric field of a gold electrode, which is matched to the accuracy of density-functional theory. Notably, we find that the resulting atomic forces present a small error of the order of 1 meV/Å, demonstrating the great effectiveness of adopting an electron-density path in predicting the electrostatics of the system. Upon running the data-driven dynamics over about 3 ns, we observe qualitative differences in the interfacial distribution of the electrolyte with respect to the results of a classical simulation. By greatly accelerating quantum-mechanics/molecular-mechanics approaches applied to electrochemical systems, our method opens the door to nanoseconds timescales in the accurate atomistic description of the electrical double layer.

cond-mat.mtrl-sci↗

arXiv2023

Predicting the Charge Density Response in Metal Electrodes

The computational study of energy storage and conversion processes calls for simulation techniques that can reproduce the electronic response of metal electrodes under electric fields. Despite recent advancements in machine-learning methods applied to electronic-structure properties, predicting the non-local behavior of the charge density in electronic conductors remains a major open challenge. We combine long-range and equivariant kernel methods to predict the Kohn-Sham electron density of metal electrodes in response to various kinds of electric field perturbations. By taking slabs of gold as an example, we first show how the non-local electronic polarization generated by the interaction with an ionic species can be accurately reproduced in electrodes of arbitrary thickness. A finite-field extension of the method is then introduced, which allows us to predict the charge transfer and the electrostatic potential drop induced by the application of a homogeneous and constant electric field. Finally, we demonstrate the capability of the method to reproduce the charge-density response in a gold/electrolyte capacitor under an applied voltage, predicting the system polarization with a greater accuracy than state-of-the-art classical atomic-charge models.

cond-mat.mtrl-sci↗

arXiv2023

Effect of a Temperature Gradient on the Screening Properties of Ionic Fluids

The electrostatic screening properties of ionic fluids are of paramount importance in countless physical processes. Yet, the behavior of ionic conductors out of thermal equilibrium has to date mainly been studied in the context of thermodiffusion phenomena by virtue of direct extensions of Debye-Hückel theories. We investigate how the static response of a symmetric ionic fluid is influenced by the presence of a thermal gradient by introducing a theory of electrostatic screening under a stationary temperature profile. By borrowing mathematical methods commonly used in the semiclassical approximation of quantum particles, we find analytical solutions to the asymptotic decay of the charge density which can be used to describe the non-equilibrium response of the system to external charge perturbations and for arbitrary ionic concentrations. Notably, a transition between monotonic and oscillatory screening regimes is observed as an effect of the temperature variation which generalizes known results of thermal equilibrium to out of equilibrium conditions. A final quantitative example on the screening of charged surfaces in aqueous electrolytes shows that the deviation from thermal equilibrium predicted by our solutions is generally larger than thermodiffusion effects, and should therefore be taken into account for a comprehensive description of the electrical double layer. Our findings pave the way to the rigorous treatment of non-equilibrium steady states in ionic systems with potential applications to the study of energy materials, nanostructured systems and waste-heat-recovery technologies.

cond-mat.stat-mech↗

arXiv2022

Electronic-structure properties from atom-centered predictions of the electron density

The electron density of a molecule or material has recently received major attention as a target quantity of machine-learning models. A natural choice to construct a model that yields transferable and linear-scaling predictions is to represent the scalar field using a multi-centered atomic basis analogous to that routinely used in density fitting approximations. However, the non-orthogonality of the basis poses challenges for the learning exercise, as it requires accounting for all the atomic density components at once. We devise a gradient-based approach to directly minimize the loss function of the regression problem in an optimized and highly sparse feature space. In so doing, we overcome the limitations associated with adopting an atom-centered model to learn the electron density over arbitrarily complex datasets, obtaining extremely accurate predictions. The enhanced framework is tested on 32-molecule periodic cells of liquid water, presenting enough complexity to require an optimal balance between accuracy and computational efficiency. We show that starting from the predicted density a single Kohn-Sham diagonalization step can be performed to access total energy components that carry an error of just 0.1 meV/atom with respect to the reference density functional calculations. Finally, we test our method on the highly heterogeneous QM9 benchmark dataset, showing that a small fraction of the training data is enough to derive ground-state total energies within chemical accuracy.

physics.chem-ph↗

arXiv2021

Learning electron densities in the condensed phase

We introduce a local machine-learning method for predicting the electron densities of periodic systems. The framework is based on a numerical, atom-centred auxiliary basis, which enables an accurate expansion of the all-electron density in a form suitable for learning isolated and periodic systems alike. We show that using this formulation the electron densities of metals, semiconductors and molecular crystals can all be accurately predicted using symmetry-adapted Gaussian process regression models, properly adjusted for the non-orthogonal nature of the basis. These predicted densities enable the efficient calculation of electronic properties which present errors on the order of tens of meV/atom when compared to ab initio density-functional calculations. We demonstrate the key power of this approach by using a model trained on ice unit cells containing only 4 water molecules to predict the electron densities of cells containing up to 512 molecules, and see no increase in the magnitude of the errors of derived electronic properties when increasing the system size. Indeed, we find that these extrapolated derived energies are more accurate than those predicted using a direct machine-learning model. Finally, on heterogeneous datasets SALTED can predict electron densities with errors below 4%.

physics.chem-ph↗

arXiv2021

Physics-inspired structural representations for molecules and materials

The first step in the construction of a regression model or a data-driven analysis, aiming to predict or elucidate the relationship between the atomic scale structure of matter and its properties, involves transforming the Cartesian coordinates of the atoms into a suitable representation. The development of atomic-scale representations has played, and continues to play, a central role in the success of machine-learning methods for chemistry and materials science. This review summarizes the current understanding of the nature and characteristics of the most commonly used structural and chemical descriptions of atomistic structures, highlighting the deep underlying connections between different frameworks, and the ideas that lead to computationally efficient and universally applicable models. It emphasizes the link between properties, structures, their physical chemistry and their mathematical description, provides examples of recent applications to a diverse set of chemical and materials science problems, and outlines the open questions and the most promising research directions in the field.

physics.chem-ph↗

arXiv2020

Multi-scale approach for the prediction of atomic scale properties

Electronic nearsightedness is one of the fundamental principles governing the behavior of condensed matter and supporting its description in terms of local entities such as chemical bonds. Locality also underlies the tremendous success of machine-learning schemes that predict quantum mechanical observables -- such as the cohesive energy, the electron density, or a variety of response properties -- as a sum of atom-centred contributions, based on a short-range representation of atomic environments. One of the main shortcomings of these approaches is their inability to capture physical effects, ranging from electrostatic interactions to quantum delocalization, which have a long-range nature. Here we show how to build a multi-scale scheme that combines in the same framework local and non-local information, overcoming such limitations. We show that the simplest version of such features can be put in formal correspondence with a multipole expansion of permanent electrostatics. The data-driven nature of the model construction, however, makes this simple form suitable to tackle also different types of delocalized and collective effects. We present several examples that range from molecular physics, to surface science and biophysics, demonstrating the ability of this multi-scale approach to model interactions driven by electrostatics, polarization and dispersion, as well as the cooperative behavior of dielectric response functions.

physics.comp-ph↗

arXiv2019

Using Gaussian Process Regression to Simulate the Vibrational Raman Spectra of Molecular Crystals

Vibrational properties of molecular crystals are constantly used as structural fingerprints, in order to identify both the chemical nature and the structural arrangement of molecules. The simulation of these properties is typically very costly, especially when dealing with response properties of materials to e.g. electric fields, which require a good description of the perturbed electronic density. In this work, we use Gaussian process regression (GPR) to predict the static polarizability and dielectric susceptibility of molecules and molecular crystals. We combine this framework with ab initio molecular dynamics to predict their anharmonic vibrational Raman spectra. We stress the importance of data representation, symmetry, and locality, by comparing the performance of different flavors of GPR. In particular, we show the advantages of using a recently developed symmetry-adapted version of GPR. As an examplary application, we choose Paracetamol as an isolated molecule and in different crystal forms. We obtain accurate vibrational Raman spectra in all cases with less than 1000 training points, and obtain improvements when using a GPR trained on the molecular monomer as a baseline for the crystal GPR models. Finally, we show that our methodology is transferable across polymorphic forms: we can train the model on data for one structure, and still be able to accurately predict the spectrum for a second polymorph. This procedure provides an independent route to access electronic structure properties when performing force-evaluations on empirical force-fields or machine-learned potential energy surfaces.

physics.comp-ph↗

arXiv2019

Incorporating long-range physics in atomic-scale machine learning

The most successful and popular machine learning models of atomic-scale properties derive their transferability from a locality ansatz. The properties of a large molecule or a bulk material are written as a sum over contributions that depend on the configurations within finite atom-centered environments. The obvious downside of this approach is that it cannot capture non-local, non-additive effects such as those arising due to long-range electrostatics or quantum interference. We propose a solution to this problem by introducing non-local representations of the system that are remapped as feature vectors that are defined locally and are equivariant in O(3). We consider in particular one form that has the same asymptotic behavior as the electrostatic potential. We demonstrate that this framework can capture non-local, long-range physics by building a model for the electrostatic energy of randomly distributed point-charges, for the unrelaxed binding curves of charged organic molecular dimers, and for the electronic dielectric response of liquid water. By combining a representation of the system that is sensitive to long-range correlations with the transferability of an atom-centered additive model, this method outperforms current state-of-the-art machine-learning schemes, and provides a conceptual framework to incorporate non-local physics into atomistic machine learning.

physics.chem-ph↗

arXiv2019

Atomic-scale representation and statistical learning of tensorial properties

This chapter discusses the importance of incorporating three-dimensional symmetries in the context of statistical learning models geared towards the interpolation of the tensorial properties of atomic-scale structures. We focus on Gaussian process regression, and in particular on the construction of structural representations, and the associated kernel functions, that are endowed with the geometric covariance properties compatible with those of the learning targets. We summarize the general formulation of such a symmetry-adapted Gaussian process regression model, and how it can be implemented based on a scheme that generalizes the popular smooth overlap of atomic positions representation. We give examples of the performance of this framework when learning the polarizability and the ground-state electron density of a molecule.

physics.chem-ph↗

arXiv2018

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.

physics.chem-ph↗

arXiv2018

Accurate molecular polarizabilities with coupled-cluster theory and machine learning

The molecular polarizability describes the tendency of a molecule to deform or polarize in response to an applied electric field. As such, this quantity governs key intra- and inter-molecular interactions such as induction and dispersion, plays a key role in determining the spectroscopic signatures of molecules, and is an essential ingredient in polarizable force fields and other empirical models for collective interactions. Compared to other ground-state properties, an accurate and reliable prediction of the molecular polarizability is considerably more difficult as this response quantity is quite sensitive to the description of the underlying molecular electronic structure. In this work, we present state-of-the-art quantum mechanical calculations of the static dipole polarizability tensors of 7,211 small organic molecules computed using linear-response coupled-cluster singles and doubles theory (LR-CCSD). Using a symmetry-adapted machine-learning based approach, we demonstrate that it is possible to predict the molecular polarizability with LR-CCSD accuracy at a negligible computational cost. The employed model is quite robust and transferable, yielding molecular polarizabilities for a diverse set of 52 larger molecules (which includes challenging conjugated systems, carbohydrates, small drugs, amino acids, nucleobases, and hydrocarbon isomers) at an accuracy that exceeds that of hybrid density functional theory (DFT). The atom-centered decomposition implicit in our machine-learning approach offers some insight into the shortcomings of DFT in the prediction of this fundamental quantity of interest.

physics.chem-ph↗

arXiv2017

Symmetry-Adapted Machine-Learning for Tensorial Properties of Atomistic Systems

Statistical learning methods show great promise in providing an accurate prediction of materials and molecular properties, while minimizing the need for computationally demanding electronic structure calculations. The accuracy and transferability of these models are increased significantly by encoding into the learning procedure the fundamental symmetries of rotational and permutational invariance of scalar properties. However, the prediction of tensorial properties requires that the model respects the appropriate geometric transformations, rather than invariance, when the reference frame is rotated. We introduce a formalism that can be used to perform machine-learning of tensorial properties of arbitrary rank for general molecular geometries. To demonstrate it, we derive a tensor kernel adapted to rotational symmetry, which is the natural generalization of the smooth overlap of atomic positions (SOAP) kernel commonly used for the prediction of scalar properties at the atomic scale. The performance and generality of the approach is demonstrated by learning the instantaneous electrical response of water oligomers of increasing complexity, from the isolated molecule to the condensed phase.

cond-mat.mtrl-sci↗