Ab Initio Electron Densities Research Articles

Construct exchange-correlation functional via machine learning.

Density functional theory has been widely used in quantum mechanical simulations, but the search for a universal exchange-correlation (XC) functional has been elusive. Over the last two decades, machine-learning techniques have been introduced to approximate the XC functional or potential, and recent advances in deep learning have renewed interest in this approach. In this article, we review early efforts to use machine learning to approximate the XC functional, with a focus on the challenge of transferring knowledge from small molecules to larger systems. Recently, the transferability problem has been addressed through the use of quasi-local density-based descriptors, which are rooted in the holographic electron density theorem. We also discuss recent developments using deep-learning techniques that target high-level abinitio molecular energy and electron density for training. These efforts can be unified under a general framework, which will also be discussed from this perspective. Additionally, we explore the use of auxiliary machine-learning models for van der Waals interactions.

Predicting accurate ab initio DNA electron densities with equivariant neural networks

One of the fundamental limitations of accurately modeling biomolecules like DNA is the inability to perform quantum chemistry calculations on large molecular structures. We present a machine learning model based on an equivariant Euclidean neural network framework to obtain accurate ab initio electron densities for arbitrary DNA structures that are much too large for conventional quantum methods. The model is trained on representative B-DNA basepair steps that capture both base pairing and base stacking interactions. The model produces accurate electron densities for arbitrary B-DNA structures with typical errors of less than 1%. Crucially, the error does not increase with system size, which suggests that the model can extrapolate to large DNA structures with negligible loss of accuracy. The model also generalizes reasonably to other DNA structural motifs such as the A- and Z-DNA forms, despite being trained on only B-DNA configurations. The model is used to calculate electron densities of several large-scale DNA structures, and we show that the computational scaling for this model is essentially linear. We also show that this machine learning electron density model can be used to calculate accurate electrostatic potentials for DNA. These electrostatic potentials produce more accurate results compared with classical force fields and do not show the usual deficiencies at short range.

MrPIXEL: automated execution of Pixel calculations via the Mercury interface

The interpretation of crystal structures in terms of intermolecular interaction energies enables phase stability and polymorphism to be rationalized in terms of quantitative thermodynamic models, while also providing insight into the origin of physical and chemical properties including solubility, compressibility and host-guest formation. The Pixel method is a semi-empirical procedure for the calculation of intermolecular interactions and lattice energies based only on crystal structure information. Molecules are represented as blocks of undistorted ab initio molecular electron and nuclear densities subdivided into small volume elements called pixels. Electrostatic, polarization, dispersion and Pauli repulsion terms are calculated between pairs of pixels and nuclei in different molecules, with the accumulated sum equating to the intermolecular interaction energy, which is broken down into physically meaningful component terms. The MrPIXEL procedure enables Pixel calculations to be carried out with minimal user intervention from the graphical interface of Mercury, which is part of the software distributed with the Cambridge Structural Database (CSD). Following initial setup of a crystallographic model, one module assigns atom types and writes necessary input files. A second module then submits the required electron-density calculation either locally or to a remote server, downloads the results, and submits the Pixel calculation itself. Full lattice energy calculations can be performed for structures with up to two molecules in the crystallographic asymmetric unit. For more complex cases, only molecule-molecule energies are calculated. The program makes use of the CSD Python API, which is also distributed with the CSD.

Experimental and Theoretical Photoemission Study of Indole and Its Derivatives in the Gas Phase

The valence and core-level photoelectron spectra of gaseous indole, 2,3-dihydro-7-azaindole, and 3-formylindole have been investigated using VUV and soft X-ray radiation supported by both an ab initio electron propagator and density functional theory calculations. Three methods were used to calculate the outer valence band photoemission spectra: outer valence Green function, partial third order, and renormalized partial third order. While all gave an acceptable description of the valence spectra, the last method yielded very accurate agreement, especially for indole and 3-formylindole. The carbon, nitrogen, and oxygen 1s core-level spectra of these heterocycles were measured and assigned. The double ionization appearance potential for indole has been determined to be 21.8 ± 0.2 eV by C 1s and N 1s Auger photoelectron spectroscopy. Theoretical analysis identifies the doubly ionized states as a band consisting of two overlapping singlet states and one triplet state with dominant configurations corresponding to holes in the two uppermost molecular orbitals. One of the singlet states and the triplet state can be described as consisting largely of a single configuration, but other doubly ionized states are heavily mixed by configuration interactions. This work provides full assignment of the relative binding energies of the core level features and an analysis of the electronic structure of substituted indoles in comparison with the parent indole.

Chemical and mechanical degradation and mitigation strategies for Si anodes

Atomistic and mesoscopic models are used to analyze cracking and stresses produced during charge of Si nanoparticles covered by a thin SEI film. Mechanical stresses coupled to chemical effects are investigated with classical molecular dynamics simulations and with a mesoscopic model. Rupture of the surface film is the main cause of capacity fade and damage evolution is strongly influenced by the structure of the solid film. For example, high currents can cause rapid amorphization and help preserving the bond integrity. But large damage occurs after the current is above a threshold. In agreement with the atomistic results, mesoscopic modeling reveals that rupture of the surface film is the primary cause of capacity fading for amorphous silicon exhibiting single phase diffusion. It also suggests that conjugated silicon-film fracture in crystalline silicon with two-phase diffusion further exacerbates this deterioration. Fracture damage is slightly diminished by decreasing the Young's modulus of the brittle coating for both amorphous and crystalline silicon; however, controlling the large volumetric expansion induced stress on surface film is crucial towards improving silicon anodes. Mitigation strategies examined by ab initio molecular dynamics and electronic density functional theory simulations show passivation effects of graphene and graphene oxide on lithiated Si surfaces.

Ab initio structure determination from experimental fluctuation X-ray scattering data

Fluctuation X-ray scattering (FXS) is an emerging experimental technique in which X-ray solution scattering data are collected from particles in solution using ultrashort X-ray exposures generated by a free-electron laser (FEL). FXS experiments overcome the low data-to-parameter ratios associated with traditional solution scattering measurements by providing several orders of magnitude more information in the final processed data. Here we demonstrate the practical feasibility of FEL-based FXS on a biological multiple-particle system and describe data-processing techniques required to extract robust FXS data and significantly reduce the required number of snapshots needed by introducing an iterative noise-filtering technique. We showcase a successful ab initio electron density reconstruction from such an experiment, studying the Paramecium bursaria Chlorella virus (PBCV-1).

Magnetic properties of the CrMnFeCoNi high-entropy alloy

We present experimental data showing that the equiatomic CrMnFeCoNi high-entropy alloy undergoes two magnetic transformations at temperatures below 100 K while maintaining its fcc structure down to 3 K. The first transition, paramagnetic to spin glass, was detected at 93 K and the second transition of the ferromagnetic type occurred at 38 K. Field-assisted cooling below 38 K resulted in a systematic vertical shift of the hysteresis curves. Strength and direction of the associated magnetization bias was proportional to the strength and direction of the cooling field and shows a linear dependence with a slope of $0.006\ifmmode\pm\else\textpm\fi{}0.001 \mathrm{emu}\mathrm{T}$. The local magnetic moments of individual atoms in the CrMnFeCoNi quinary fcc random solid solution were investigated by ab initio (electronic density functional theory) calculations. Results of the numerical analysis suggest that, irrespective of the initial configuration of local magnetic moments, the magnetic moments associated with Cr atoms align antiferromagnetically with respect to a cumulative magnetic moment of their first coordination shell. The ab initio calculations further showed that the magnetic moments of Fe and Mn atoms remain strong (between 1.5 and $2\phantom{\rule{0.28em}{0ex}}{\ensuremath{\mu}}_{\mathrm{B}}$), while the local moments of Ni atoms effectively vanish. These results indicate that interactions of Mn- and/or Fe-located moments with the surrounding magnetic structure account for the observed macroscopic magnetization bias.

Transferable kriging machine learning models for the multipolar electrostatics of helical deca-alanine

We exploit the transferability of quantum topological atoms in the construction of a multipolar polarizable protein force field QCTFF. A helical oligopeptide of 10 alanine residues (103 atoms) has its total electrostatic energy predicted using the kriging machine learning method with a mean error of 6.4 kJ mol−1. This error is similar to that found in smaller molecules presented in past QCTFF publications. Kriging relates the molecular geometry to atomic multipole moments that describe the ab initio electron density. Atom types are constructed from similar atoms within the helix. As the atoms within a given atom type share a local chemical environment, they can share a kriging model with a reduced number of input descriptors (i.e. features). The feature reduction decreases the kriging training times by more than 23 times but increases the prediction error by only 1.3 %. In transferability tests, transferable models give a 5.7 % error when predicting moments of an atom outside the training set, compared to the 3.9 % error when tested against data belonging to atoms included in the training data. The transferable kriging models successfully predict atomic multipole moments with useful accuracy, opening an avenue to QCTFF modelling of a whole protein.

Optimized unrestricted Kohn–Sham potentials from ab initio spin densities

The reconstruction of the exchange–correlation potential from accurate ab initio electron densities can provide insights into the limitations of the currently available approximate functionals and provide guidance for devising improved approximations for density-functional theory (DFT). For open-shell systems, the spin density is introduced as an additional fundamental variable in spin-DFT. Here, we consider the reconstruction of the corresponding unrestricted Kohn–Sham (KS) potentials from accurate ab initio spin densities. In particular, we investigate whether it is possible to reconstruct the spin exchange–correlation potential, which determines the spin density in unrestricted KS-DFT, despite the numerical difficulties inherent to the optimization of potentials with finite orbital basis sets. We find that the recently developed scheme for unambiguously singling out an optimal optimized potential [Ch. R. Jacob, J. Chem. Phys. 135, 244102 (2011)10.1063/1.3670414] can provide such spin potentials accurately. This is demonstrated for two test cases, the lithium atom and the dioxygen molecule, and target (spin) densities from full configuration interaction and complete active space self-consistent field calculations, respectively.

Revealing Non‐covalent Interactions in Molecular Crystals through Their Experimental Electron Densities

Non-covalent interactions (NCI) define the rules underlying crystallisation, self-assembly and drug-receptor docking processes. A novel NCI descriptor, based on the reduced electron density gradient (RDG), that enables easy visualisation of the zones of the electron density (ED) involved in either the supposedly attractive (dispersive, hydrogen bonding) or allegedly repulsive (steric) intermolecular interactions, was recently developed by Johnson et al. Here, it is applied for the first time to EDs derived from single-crystal X-ray diffraction data. A computer code handling both experimental and ab initio EDs in the RDG-NCI perspective was purposely written. Three cases spanning a wide range of NCI classes were analysed: 1) benzene, as the prototype of stacking and weak CH···π interactions; 2) austdiol, a heavily functionalised fungal metabolite with a complex hydrogen-bonding network; 3) two polymorphs of the heteroatom-rich anti-ulcer drug famotidine, with van der Waals and hydrogen-bond contacts between N- and S-containing groups. Even when applied to experimental EDs, the RDG index is a valuable NCI descriptor that can highlight their different nature and strength and provide results of comparable quality to ab initio approaches. Combining the RDG-NCI study with Bader's ED approach was a key step forward, as the RDG index can depict inherently delocalised interactions in terms of extended and flat RDG isosurfaces, in contrast to the bond path analysis, which is often bounded to a too localised and possibly discontinuous (yes/no) description. Conversely, the topological tool can provide quantitative insight into the simple, qualitative NCI picture offered by the RDG index. Hopefully, this study may pave the way to a deeper analysis of weak interactions in proteins using structural and ED information from experiment.

A model of phase transitions in double-well Morse potential: Application to hydrogen bond

A model of phase transitions in double-well Morse potential is developed. Application of this model to the hydrogen bond is based on ab initio electron density calculations, which proved that the predominant contribution to the hydrogen bond energy originates from the interaction of proton with the electron shells of hydrogen-bonded atoms. This model uses a double-well Morse potential for proton. Analytical expressions for the hydrogen bond energy and the frequency of O–H stretching vibrations were obtained. Experimental data on the dependence of O–H vibration frequency on the bond length were successfully fitted with model-predicted dependences in classical and quantum mechanics approaches. Unlike empirical exponential function often used previously for dependence of O–H vibration frequency on the hydrogen bond length (Libowitzky, Mon. Chem., 1999, vol.130, 1047), the dependence reported here is theoretically substantiated.

Atomic multipoles: Electrostatic potential fit, local reference axis systems, and conformational dependence

Currently, all standard force fields for biomolecular simulations use point charges to model intermolecular electrostatic interactions. This is a fast and simple approach but has deficiencies when the electrostatic potential (ESP) is compared to that from ab initio methods. Here, we show how atomic multipoles can be rigorously implemented into common biomolecular force fields. For this, a comprehensive set of local reference axis systems is introduced, which represents a universal solution for treating atom-centered multipoles for all small organic molecules and proteins. Furthermore, we introduce a new method for fitting atomic multipole moments to the quantum mechanically derived ESP. This methods yields a 50-90% error reduction compared to both point charges fit to the ESP and multipoles directly calculated from the ab initio electron density. It is shown that it is necessary to directly fit the multipole moments of conformational ensembles to the ESP. Ignoring the conformational dependence or averaging over parameters from different conformations dramatically deteriorates the results obtained with atomic multipole moments, rendering multipoles worse than partial charges.

Potential explanation of charge response of magnetization in nanoporous systems

An example of technologically promising magnetoelectric effects in nanostructures is the reversible tuning of the magnetic properties of nanoporous systems by charging them in an electrolyte. So far this effect, which has been observed experimentally in various metallic nanoporous materials, has been tentatively related to two different microscopic mechanisms: the filling of the electronic $d$ band upon charging, or the magnetoelastic response to charge-induced structural changes of the nanoparticles which form the nanoporous systems. In the present paper a potential mechanism is introduced which is related to a change in the magnetic surface anisotropy of the nanoparticle upon charging. An essential assumption of the mechanism is that only those surfaces of the nanoparticle which are not in the grain-boundary contact with the neighboring nanoparticles of the nanoporous material are charged in the electrolyte. This is underpinned by computer simulations on the atomic level with information on the charge response of the magnetic surface anisotropy from ab initio electron density functional calculations.

The pressure-induced ringwoodite to Mg-perovskite and periclase post-spinel phase transition: a Bader’s topological analysis of the ab initio electron densities

In order to characterize the pressure-induced decomposition of ringwoodite (γ-Mg2SiO4), the topological analysis of the electron density ρ(r), based upon the theory of atoms in molecules (AIM) developed by Bader in the framework of the catastrophe theory, has been performed. Calculations have been carried out by means of the ab initio CRYSTAL09 code at the HF/DFT level, using Hamiltonians based on the Becke- LYP scheme containing hybrid Hartree–Fock/density functional exchange–correlation terms. The equation of state at 0 K has been constructed for the three phases involved in the post-spinel phase transition (ringwoodite → Mg-perovskite + periclase) occurring at the transition zone–lower mantel boundary. The topological results show that the decomposition of the ringwoodite at high pressures is caused by a conflict catastrophe. Furthermore, topological evidences of the central role played by the oxygen atoms to facilitate the pressure-induced ringwoodite decomposition and the subsequent phase transition have been noticed.

Understanding the Surface Potential of Water

We have resolved the inconsistency in quantifying the surface potential at the liquid-vapor interface when using explicit ab initio electronic charge density and effective atomic partial charge models of liquid water. This is related, in part, to the fact that the resulting electric potentials from partial-charge models and ab initio charge distributions are quite different except for those regions of space between the molecules. We show that the electrostatic surface potential from a quantum mechanical charge distribution compares well to high-energy electron diffraction and electron holography measurements, as opposed to the comparison with electrochemical measurements. We suggest that certain regions of space be excluded when comparing computed surface potentials with electrochemical measurements. This work describes a novel interpretation of ab initio computed surface potentials through high-energy electron holography measurements as useful benchmarks toward a better understanding of electrochemistry.

A Discussion of the pH-Dependent Protonation Behaviors of Poly(2-(dimethylamino)ethyl methacrylate) (PDMAEMA) and Poly(ethylenimine-ran-2-ethyl-2-oxazoline) (P(EI-r-EOz))

In this article, we present results of our experimental and atomistic simulation studies of the pH-dependent protonation behaviors of poly(2-(dimethylamino)ethyl methacrylate) (PDMAEMA) and poly(ethylenimine) (PEI). The potentiometric titration profiles of the PDMAEMA polymer and its unpolymerized monomer (i.e., DMAEMA) were measured under identical conditions in order to study the influence of the covalent linkage of the amine groups on their protonation behavior. The titration curves of poly(ethylenimine-ran-2-ethyl-2-oxazoline) (P(EI-r-EOz)) random copolymers with varying monomer composition were measured in order to study the effect of the spacing between the EI monomers on the protonation behavior of the P(EI-r-EOz) copolymer. The results of these two sets of measurements demonstrate that the connectivity and tight spacing between amine groups in a polyamine chain causes the retardation of the protonation of the amine groups relative to the same compounds in their isolated state. The same titration measurements were also performed with added NaCl. The results of these measurements demonstrate that added NaCl weakens the electrostatic repulsion between charged amine groups in a polyamine chain and thus enhances the protonation of the chain, and this effect is quite significant at a physiological NaCl concentration of 150 mM. However, on the quantitative level, the effect of added NaCl was found to be very different between the PDMAEMA and P(EI-r-EOz) cases. In PDMAEMA, since the amine groups are located at the termini of the side chains, the interaction between adjacent charged monomers occurs through the aqueous medium, and therefore at a sufficiently high concentration of added NaCl, the amine groups on the chain behave almost identically to their unpolymerized equivalents. In contrast, the electrostatic interaction between two closely spaced charged EI monomers in a P(EI-r-EOz) chain is significantly less influenced by a change of the ionic strength of the medium, because it is dominated by the local dielectric property of the polymer segment located between the charged monomers. This interpretation is further supported by ab initio electron density functional theory (DFT) calculations on model oligomeric compounds whose structures imitate the repeat unit structures of the polymers. Lastly, in connection with potential applications of the PEI and PDMAEMA polymers in gene delivery technologies, it was also examined how complexation with negatively charged polymers at the physiological NaCl concentration (150 mM) impacts the protonation behaviors of the polyamines. We found that the oppositely charged polyanion greatly stabilizes the protonated form of the amine groups on the polyamine chain. However, the proton buffering capacity of the polyamine in the complexed form under the influence of added 150 mM NaCl for the intracellularly relevant pH change was found to be significantly lower than that of the pure polyamine in the uncomplexed state with no added salt.

The dynamic behavior of a liquid ethanol–water mixture: a perspective from quantum chemical topology

Quantum Chemical Topology (QCT) is used to reveal the dynamics of atom-atom interactions in a liquid. A molecular dynamics simulation was carried out on an ethanol-water liquid mixture at its azeotropic concentration (X(ethanol)=0.899), using high-rank multipolar electrostatics. A thousand (ethanol)(9)-water heterodecamers, respecting the water-ethanol ratio of the azeotropic mixture, were extracted from the simulation. Ab initio electron densities were computed at the B3LYP/6-31+G(d) level for these molecular clusters. A video shows the dynamical behavior of a pattern of bond critical points and atomic interaction lines, fluctuating over 1 ns. A bond critical point distribution revealed the fluctuating behavior of water and ethanol molecules in terms of O-H···O, C-H···O and H···H interactions. Interestingly, the water molecule formed one to six C-H···O and one to four O-H···O interactions as a proton acceptor. We found that the more localized a dynamical bond critical point distribution, the higher the average electron density at its bond critical points. The formation of multiple C-H···O interactions affected the shape of the oxygen basin of the water molecule, which is shown in three dimensions. The hydrogen atoms of water strongly preferred to form H···H interactions with ethanol's alkyl hydrogen atoms over its hydroxyl hydrogen.

Modeling the Photovoltage of Doped Si Surfaces

Doped Si(111) surfaces have been modeled with a Si slab, and their photovoltage has been calculated with a combination of ab initio electronic structure and density matrix treatments from the steady state solution of the electronic density matrix (DM) for electrons interacting with thermalized lattice vibrations. Densities of electronic states and photovoltage spectra of the silicon surfaces are drastically affected by the presence of p or n doping. We report results on the effect of surface doping by group III (B, Al, and Ga) and group V (N, P, and As) elements, of interest in the study of surface optical properties, for concentrations of doping atoms in the host lattice in the range of 0.5−1.5%, obtained from slab atomic models with several hundred atoms. Analysis of the results provides insight on trends relevant to the absorption of near IR, visible, and near UV light and to measurements of photovoltages and shows some of the trends found for doped bulk Si in experiments at lower dopant densities.

Simulation of liquid imidazole using a high-rank quantum topological electrostatic potential

Rigid body molecular dynamics simulations were carried out on pure liquid imidazole at four different temperatures and at 1 atm. Imidazole, which is important both in life science and materials science, is one of the simplest molecules to possess both a lone pair and a π system. These two features are known to benefit from multipolar electrostatics. Here the electrostatic interaction is governed by atomic multipole moments obtained from topologically partitioned ab initio electron densities. The non-electrostatic terms are modeled with Lennard-Jones parameters adjusted to fit the experimental liquid density. All σ values are incrementally increased by one single scaling factor. We report on how the presence of multipolar electrostatics influences the local structure, dynamics and thermodynamics of the liquid compared to electrostatics by atomic point charges. The point charge force field exaggerates the number of π-stacked dimers in the liquid, and underestimates the number of hydrogen-bonded dimers. The effect of the temperature on the local structure of liquid imidazole was analysed using radial and spatial distribution functions.

IONIZATION AND FRAGMENTATION OF ANTHRACENE UPON INTERACTION WITH keV PROTONS AND α PARTICLES

The interaction of keV ions with polyaromatic hydrocarbons is dominated by charge exchange and electronic stopping. We have studied the response of the polyaromatic hydrocarbon anthracene (C14H10) upon keV H+ and He2+ impact using high-resolution time-of-flight mass spectrometry. Extensive fragmentation into small C n H q+ m as well as formation of up to triply charged parent ions is observed. Ab initio electron densities are used to calculate the molecular excitation due to electronic stopping. Fragment yields increase with the increase of electronic stopping as a function of projectile velocity. For equal electronic stopping, He2+ is found to induce more fragmentation than H+. The difference in fragmentation is concluded to be due to two electron processes, which are relevant channels only for He2+.