Density Functional Theory Reference Research Articles

Exploring the Kinetics of Oxygen Reduction Reaction in Relation to Pitting Corrosion Resistance in Fe-Cr Alloys

Pitting corrosion, a major concern in materials science and engineering, threatens critical metallic structures and components. Its implications reach across daily life and industries such as energy, transportation, and infrastructure, potentially causing environmental harm, economic losses, and even loss of life. This complex process is influenced by factors including material composition, local environment, and mechanical stresses.1 Once initiated, pit propagation rates are largely dependent on the magnitude of the supporting cathodic current available from the oxygen reduction reaction (ORR) occurring on the external passive film.2 In Fe-Cr alloys, the ORR occurs on this film, undergoing a mixed diffusion and kinetic-controlled process. The number of electrons involved and the corrosion rate are determined by the thermodynamically stable state of the passive film.This research studies the ORR kinetics on FeCr alloys fabricated by arc-melting, using both computational and experimental methods. The rotating disc electrode technique was employed across various Fe:Cr alloys in alkaline and neutral electrolytes. The Koutecky-Levich analysis showed a dominant four-electron ORR pathway in all tested Fe-Cr alloys, with the ORR significantly inhibited by higher proportions of Cr2O3 in the film, suggesting a correlation with high chromium content. Experimental ORR overpotentials, when combined with theoretical potential-pH (Pourbaix) diagrams, helped discern the likely characteristics of the passive films on the alloys. It was deduced that the catalytic properties of potential passive films increased in the order Cr2O3 < Fe3O4 < Fe2O3 < FeCr2O4. These findings, excellently aligned with density functional theory (DFT) modelling, underscore the role of increased chromium levels in slowing pitting progression by suppressing the ORR.In summary, this research offers distinctive insights into the correlation between the kinetics of the ORR and the resistance to localized corrosion in Fe-Cr alloys, which enhances our understanding of the underlying mechanisms of pitting corrosion. Keywords FeCr alloy, pitting corrosion, ORR, rotating disc electrode, DFT Reference [1] B. Zhang, J. Wang, B. Wu, X. W. Guo, Y. J. Wang, D. Chen, Y. C. Zhang, K. Du, E. E. Oguzie, and X. L. Ma, Nat. Commun. (2018) 9, 2559.[2] G. T. Burstein, P. C. Pistorius, and S. P. Mattin, Corros. Sci. (1993) 35, 57.

Multiconfigurational Correlation at DFT + U Cost: On-Site Electron-Electron Interactions Yield a Block-Localized Configuration Interaction Hamiltonian.

This work presents a first-principles wavefunction-in-DFT approach based on the Hubbard density functional theory (DFT) + U method. This approach begins with the standard DFT reference system of noninteracting electrons and introduces an electron-electron interaction projected onto DFT+U-type atomic states. The reference system's configuration interaction Hamiltonian is block-localized to these states and can be expressed in terms of state occupation numbers, state self-energies (which correspond to unscreened Hubbard U values), and the promotion energies of doubly excited Slater determinants. Simple approximations for the promotion energies provide multiconfigurational correlation energies without requiring explicit orbital localization/transform. Numerical results for fractionally occupied chromium atom, bonded chromium dimer, dissociating covalent bonds, and large active spaces show that the approach provides beyond-zero-sum accuracy at computational cost comparable to standard DFT+U.

Machine-learned acceleration for molecular dynamics in CASTEP.

Machine learning (ML) methods are of rapidly growing interest for materials modeling, and yet, the use of ML interatomic potentials for new systems is often more demanding than that of established density-functional theory (DFT) packages. Here, we describe computational methodology to combine the CASTEP first-principles simulation software with the on-the-fly fitting and evaluation of ML interatomic potential models. Our approach is based on regular checking against DFT reference data, which provides a direct measure of the accuracy of the evolving ML model. We discuss the general framework and the specific solutions implemented, and we present an example application to high-temperature molecular-dynamics simulations of carbon nanostructures. The code is freely available for academic research.

A non-self-consistent tight-binding electronic structure potential in a polarized double-ζ basis set for all spd-block elements up to Z = 86.

Existing semiempirical molecular orbital methods suffer from the usually minimal atomic-orbital (AO) basis set used to simplify the calculations. Here, a completely new and consistently parameterized tight-binding electronic structure Hamiltonian evaluated in a deeply contracted, properly polarized valence double-zeta basis set (vDZP) is described. The inner-shell electrons are accounted for by standard, large-core effective potentials and approximations to them. The primary target of this so-called density matrix tight-binding method is to reproduce the one-particle density matrix P of a molecular ωB97X-V range-separated hybrid density functional theory (DFT) calculation in exactly the same basis set. Additional properties considered are orbital energies, dipole polarizabilities and dipole moments, and dipole polarizability derivatives. The key features of the method are as follows: (a) it is non-self-consistent with an overall fixed number of only three required matrix diagonalizations; (b) only AO overlap integrals are needed to construct the effective Hamiltonian matrix; (c) new P-dependent terms emulating non-local exchange are included; and (d) only element-specific empirical parameters (about 50 per element) need to be determined. The method globally achieves a high accuracy for the target properties at a speedup compared to the ωB97X-V/vDZP reference of about 3-4 orders of magnitude. It performs robustly for difficult transition metal complexes, for highly charged or zwitterionic systems, and for chemically unusual bonding situations, indicating a generally robust approximation of the (self-consistent) Kohn-Sham potential. As an example application, the vibrational Raman spectrum of an entire protein with 327 atoms with respect to the DFT reference calculation is shown. This method may be used out-of-the-box to generate molecular/atomic features for machine learning applications or as the basis for accurate high-speed DFT methods.

A variational formulation of the Harris functional as a correction to approximate Kohn-Sham density functional theory.

Accurate descriptions of intermolecular interactions are of great importance in simulations of molecular liquids. We present an electronic structure method that combines the accuracy of the Harris functional approach with the computational efficiency of approximately linear-scaling density functional theory (DFT). The non-variational nature of the Harris functional has been addressed by constructing a Lagrangian energy functional, which restores the variational condition by imposing stationarity with respect to the reference density. The associated linear response equations may be treated with linear-scaling efficiency in an atomic orbital based scheme. Key ingredients to describe the structural and dynamical properties of molecular systems are the forces acting on the atoms and the stress tensor. These first-order derivatives of the Harris Lagrangian have been derived and implemented in consistence with the energy correction. The proposed method allows for simulations with accuracies close to the Kohn-Sham DFT reference. Embedded in the CP2K program package, the method is designed to enable ab initio molecular dynamics simulations of molecular solutions for system sizes of several thousand atoms. Available subsystem DFT methods may be used to provide the reference density required for the energy correction at near linear-scaling efficiency. As an example of production applications, we applied the method to molecular dynamics simulations of the binary mixtures cyclohexane-methanol and toluene-methanol, performed within the isobaric-isothermal ensemble, to investigate the hydrogen bonding network in these non-ideal mixtures.

Data-driven many-body potentials from density functional theory for aqueous phase chemistry

Density functional theory (DFT) has been applied to modeling molecular interactions in water for over three decades. The ubiquity of water in chemical and biological processes demands a unified understanding of its physics, from the single molecule to the thermodynamic limit and everything in between. Recent advances in the development of data-driven and machine-learning potentials have accelerated simulation of water and aqueous systems with DFT accuracy. However, anomalous properties of water in the condensed phase, where a rigorous treatment of both local and non-local many-body (MB) interactions is in order, are often unsatisfactory or partially missing in DFT models of water. In this review, we discuss the modeling of water and aqueous systems based on DFT and provide a comprehensive description of a general theoretical/computational framework for the development of data-driven many-body potentials from DFT reference data. This framework, coined MB-DFT, readily enables efficient many-body molecular dynamics (MD) simulations of small molecules, in both gas and condensed phases, while preserving the accuracy of the underlying DFT model. Theoretical considerations are emphasized, including the role that the delocalization error plays in MB-DFT potentials of water and the possibility to elevate DFT and MB-DFT to near-chemical-accuracy through a density-corrected formalism. The development of the MB-DFT framework is described in detail, along with its application in MB-MD simulations and recent extension to the modeling of reactive processes in solution within a quantum mechanics/MB molecular mechanics (QM/MB-MM) scheme, using water as a prototypical solvent. Finally, we identify open challenges and discuss future directions for MB-DFT and QM/MB-MM simulations in condensed phases.

A Deep Neural Network Potential for Water Confined in Graphene Nanocapillaries

Water under nanoconfinement exhibits structural and dynamical properties remarkably different from those of bulk water, and empirical potential-based molecular dynamics has played an important role in furthering our understanding of the behavior of confined water. However, existing potentials for water were commonly parametrized based on the properties of the bulk water and may be unreliable for describing nanoconfined water. Here, we develop a machine learning potential for water confined in graphene nanocapillaries using deep neural networks trained on quantum mechanical density-functional theory (DFT) calculations. This deep neural network potential offers near-DFT accuracy in terms of potential energy and atomic forces but at a computational cost much lower than DFT-based ab initio molecular dynamics methods. In particular, this potential reproduces well the DFT reference for a wide range of properties, including O–H bond length distribution, density distribution, radial distribution functions, hydrogen bonding, etc. The developed deep neural network potential opens the door to simulations of nanoconfined water with large system sizes and time scales at near-DFT accuracy.

Ultrafast estimation of electronic couplings for electron transfer between pi-conjugated organic molecules. II.

The development of highly efficient methods for the calculation of electronic coupling matrix elements between the electron donor and acceptor is an important goal in theoretical organic semiconductor research. In Paper I [F. Gajdos, S. Valner, F. Hoffmann, J. Spencer, M. Breuer, A. Kubas, M. Dupuis, and J. Blumberger, J. Chem. Theory Comput. 10, 4653 (2014)], we introduced the analytic overlap method (AOM) for this purpose, which is an ultrafast electronic coupling estimator parameterized to and orders of magnitude faster than density functional theory (DFT) calculations at a reasonably small loss in accuracy. In this work, we reparameterize and extend the AOM to molecules containing nitrogen, oxygen, fluorine, and sulfur heteroatoms using 921 dimer configurations from the recently introduced HAB79 dataset. We find again a very good linear correlation between the frontier orbital overlap, calculated ultrafast in an optimized minimum Slater basis, and DFT reference electronic couplings. The new parameterization scheme is shown to be transferable to sulfur-containing polyaromatic hydrocarbons in experimentally resolved dimeric configurations. Our extension of the AOM enables high-throughput screening of very large databases of chemically diverse organic crystal structures and the application of computationally intense non-adiabatic molecular dynamics methods to charge transport in state-of-the-art organic semiconductors, e.g., non-fullerene acceptors.

Single-Point Hessian Calculations for Improved Vibrational Frequencies and Rigid-Rotor-Harmonic-Oscillator Thermodynamics.

The calculation of harmonic vibrational frequencies (HVF) to interpret infrared (IR) spectra and to convert molecular energies to free energies is one of the essential steps in computational chemistry. A prerequisite for accurate thermostatistics so far was to optimize the molecular input structures in order to avoid imaginary frequencies, which inevitably leads to changes in the geometry if different theoretical levels are applied for geometry optimization and frequency calculations. In this work, we propose a new method termed single-point Hessian (SPH) for the computation of HVF and thermodynamic contributions to the free energy within the modified rigid-rotor-harmonic-oscillator approximation for general nonequilibrium molecular geometries. The key ingredient is the application of a biasing potential given as Gaussian functions expressed with the root-mean-square-deviation (RMSD) in Cartesian space in order to retain the initial geometry. The theory derived herein is generally applicable to quantum mechanical (QM), semiempirical QM, and force-field (FF) methods. Besides a detailed description of the underlying theory including the important back-correction of the biased HVF, the SPH approach is tested for reaction paths, molecular dynamics snapshots of crambin, and supramolecular association free energies in comparison to high-level density functional theory (DFT) values. Furthermore, the effect on IR spectra is investigated for organic dimers and transition-metal complexes revealing improved spectra at low theoretical levels. On average, DFT reference free energies are better reproduced by the newly developed SPH scheme than by conventional calculations on freely optimized geometries or without any relaxation.

Efficient Computation of Free Energy Contributions for Association Reactions of Large Molecules.

Modern density functional theory (DFT) methods are capable of providing accurate association energies for supramolecular systems and even protein-ligand complexes. However, the calculation of the essential harmonic vibrational frequencies needed to obtain free energies is often too computationally demanding. In this work, the corresponding thermostatistical contributions are computed in the well-established (modified) rigid-rotor-harmonic-oscillator approximation with structures and frequencies taken from low-cost quantum chemical methods, namely, GFN2-xTB and PM6-D3H4. Additionally, a recently developed new general force field (GFN-FF) is tested for this purpose. DFT reference values for 59 complexes composed of three standard noncovalent and supramolecular benchmark sets (S22, L7, and S30L) are used in the evaluation. Overall, the accuracy of the low-cost methods is remarkable with typical deviations of only 0.5-2 kcal mol-1 (5-10%) from the DFT reference values. In particular, the performance of the GFN-FF is promising considering the acceleration of 5 and 2-3 orders of magnitude compared to DFT and GFN2-xTB, respectively. This opens new perspectives for computing thermodynamic properties of, e.g., biomacromolecules as shown, for example, for the binding of retinol and rivaroxaban in protein complexes consisting of ≤4700 atoms.

An accurate and transferable machine learning potential for carbon.

We present an accurate machine learning (ML) model for atomistic simulations of carbon, constructed using the Gaussian approximation potential (GAP) methodology. The potential, named GAP-20, describes the properties of the bulk crystalline and amorphous phases, crystal surfaces, and defect structures with an accuracy approaching that of direct ab initio simulation, but at a significantly reduced cost. We combine structural databases for amorphous carbon and graphene, which we extend substantially by adding suitable configurations, for example, for defects in graphene and other nanostructures. The final potential is fitted to reference data computed using the optB88-vdW density functional theory (DFT) functional. Dispersion interactions, which are crucial to describe multilayer carbonaceous materials, are therefore implicitly included. We additionally account for long-range dispersion interactions using a semianalytical two-body term and show that an improved model can be obtained through an optimization of the many-body smooth overlap of atomic positions descriptor. We rigorously test the potential on lattice parameters, bond lengths, formation energies, and phonon dispersions of numerous carbon allotropes. We compare the formation energies of an extensive set of defect structures, surfaces, and surface reconstructions to DFT reference calculations. The present work demonstrates the ability to combine, in the same ML model, the previously attained flexibility required for amorphous carbon [V. L. Deringer and G. Csányi, Phys. Rev. B 95, 094203 (2017)] with the high numerical accuracy necessary for crystalline graphene [Rowe et al., Phys. Rev. B 97, 054303 (2018)], thereby providing an interatomic potential that will be applicable to a wide range of applications concerning diverse forms of bulk and nanostructured carbon.

Computational Assessment of MLCT versus MC Stabilities in First-to-Third-Row d6 Pseudo-Octahedral Transition Metal Complexes.

An accurate modeling of metal-to-ligand-charge-transfer (MLCT) and metal-centered (MC) excited state energies is key to predict the photoinduced response in transition metal complexes (TMCs). Herein, the importance of the ground state and excited state reference geometries is addressed for three-prototype d6 pseudo-octahedral TMCs, each displaying a different potential energy landscape of MLCT versus MC relative stabilities. Several functionals are used within the time-dependent density functional theory (TDDFT), as well as multireference wave-function theory (MS-CASPT2), applied to [Mn(im)(CO)3 (phen)]+ , [Ru(im)2 (bpy)2 ]2+ , and [Re(im)(CO)3 (phen)]+ , (im: imidazole, bpy: bypiridine, phen: phenantroline). The results revel that TDDFT is robust except when using B3LYP functional for first-row d6 TMCs. In contrast, MS-CASPT2 calculations are strongly biased in those cases with competitive MLCT/MC states. The results reinforce the reliability of B3LYP to describe the excited states in d6 TMCs, but question the validity of assessing the density functional theory (DFT)/TDDFT performance via direct comparison with MS-CASPT2 performed at the same DFT reference geometry as a standard strategy. © 2019 Wiley Periodicals, Inc.

Transferability of interatomic potentials for molybdenum and silicon

Interatomic potentials are widely used in computational materials science, in particular for simulations that are too computationally expensive for density functional theory (DFT). Most interatomic potentials have a limited application range and often there is very limited information available regarding their performance for specific simulations. We carried out high-throughput calculations for molybdenum and silicon with DFT and a number of interatomic potentials. We compare the DFT reference calculations and experimental data to the predictions of the interatomic potentials. We focus on a large number of basic materials properties, including the cohesive energy, atomic volume, elastic coefficients, vibrational properties, thermodynamic properties, surface energies and vacancy formation energies, which enables a detailed discussion of the performance of the different potentials. We further analyze correlations between properties as obtained from DFT calculations and how interatomic potentials reproduce these correlations, and suggest a general measure for quantifying the accuracy and transferability of an interatomic potential. From our analysis we do not establish a clearcut ranking of the potentials as each potential has its strengths and weaknesses. It is therefore essential to assess the properties of a potential carefully before application of the potential in a specific simulation. The data presented here will be useful for selecting a potential for simulations of Mo or Si.

Multiscale model for disordered hybrid perovskites: The concept of organic cation pair modes

We have studied the properties of the prototype hybrid organic-inorganic perovskite $\text{CH}_3^{}\text{NH}_3^{}\text{PbI}_3^{}$ using relativistic density functional theory (DFT). For our analysis we introduce the concept of $\text{CH}_3^{}\text{NH}_3^+$ "pair modes", that is, characteristic relative orientations of two neighboring $\text{CH}_3^{}\text{NH}_3^+$ cations. In our previous work [Phys. Rev. B \textbf{94}, 045201 (2016)] we identified two preferential orientations that a single $\text{CH}_3^{}\text{NH}_3^+$ cation adopts in a unit cell. The total number of relevant pairs can be reduced from the resulting 196 combinations to only 25 by applying symmetry operations. DFT results of several $2\!\times\!2\!\times\!2$ supercell models reveal the dependence of the total energy, band gap and band structure on the distribution of $\text{CH}_3^{}\text{NH}_3^+$ cations and the pair modes. We have then analyzed the pair-mode distribution of a series of $4\!\times\!4\!\times\!4$ supercell models with disordered $\text{CH}_3^{}\text{NH}_3^+$ cations. Our results show that diagonally-oriented $\text{CH}_3^{}\text{NH}_3^+$ cations are rare in optimized $\text{CH}_3^{}\text{NH}_3^{}\text{PbI}_3^{}$ supercell structures. In the prevailing pair modes, the $\text{C--N}$ bonds of the two neighboring $\text{CH}_3^{}\text{NH}_3^+$ cations are aligned approximately vertically. Furthermore, we fit the coefficients of a pair-mode expansion to our supercell DFT reference structures. The pair-mode model can then be used to quickly estimate the energies of disordered perovskite structures. Our pair-mode concept provides combined atomistic-statistical insight into disordered structures in bulk hybrid perovskite materials.

Gaussian approximation potential modeling of lithium intercalation in carbon nanostructures.

We demonstrate how machine-learning based interatomic potentials can be used to model guest atoms in host structures. Specifically, we generate Gaussian approximation potential (GAP) models for the interaction of lithium atoms with graphene, graphite, and disordered carbon nanostructures, based on reference density functional theory data. Rather than treating the full Li-C system, we demonstrate how the energy and force differences arising from Li intercalation can be modeled and then added to a (prexisting and unmodified) GAP model of pure elemental carbon. Furthermore, we show the benefit of using an explicit pair potential fit to capture "effective" Li-Li interactions and to improve the performance of the GAP model. This provides proof-of-concept for modeling guest atoms in host frameworks with machine-learning based potentials and in the longer run is promising for carrying out detailed atomistic studies of battery materials.

Prediction Errors of Molecular Machine Learning Models Lower than Hybrid DFT Error

We investigate the impact of choosing regressors and molecular representations for the construction of fast machine learning (ML) models of 13 electronic ground-state properties of organic molecules. The performance of each regressor/representation/property combination is assessed using learning curves which report out-of-sample errors as a function of training set size with up to ∼118k distinct molecules. Molecular structures and properties at the hybrid density functional theory (DFT) level of theory come from the QM9 database [ Ramakrishnan et al. Sci. Data 2014 , 1 , 140022 ] and include enthalpies and free energies of atomization, HOMO/LUMO energies and gap, dipole moment, polarizability, zero point vibrational energy, heat capacity, and the highest fundamental vibrational frequency. Various molecular representations have been studied (Coulomb matrix, bag of bonds, BAML and ECFP4, molecular graphs (MG)), as well as newly developed distribution based variants including histograms of distances (HD), angles (HDA/MARAD), and dihedrals (HDAD). Regressors include linear models (Bayesian ridge regression (BR) and linear regression with elastic net regularization (EN)), random forest (RF), kernel ridge regression (KRR), and two types of neural networks, graph convolutions (GC) and gated graph networks (GG). Out-of sample errors are strongly dependent on the choice of representation and regressor and molecular property. Electronic properties are typically best accounted for by MG and GC, while energetic properties are better described by HDAD and KRR. The specific combinations with the lowest out-of-sample errors in the ∼118k training set size limit are (free) energies and enthalpies of atomization (HDAD/KRR), HOMO/LUMO eigenvalue and gap (MG/GC), dipole moment (MG/GC), static polarizability (MG/GG), zero point vibrational energy (HDAD/KRR), heat capacity at room temperature (HDAD/KRR), and highest fundamental vibrational frequency (BAML/RF). We present numerical evidence that ML model predictions deviate from DFT (B3LYP) less than DFT (B3LYP) deviates from experiment for all properties. Furthermore, out-of-sample prediction errors with respect to hybrid DFT reference are on par with, or close to, chemical accuracy. The results suggest that ML models could be more accurate than hybrid DFT if explicitly electron correlated quantum (or experimental) data were available.

In-Situ and First Principles Characterization of Alpha-Manganese Oxide (MnO2)

Alpha manganese oxide (α-MnO2) is of interest as a cathode material for lithium-ion batteries and as an electrode/electrocatalyst for hybrid Li-ion/Li-O2 systems. It has a tunnel structure with large 2x2 channels that accommodate different species such as Ba2+, K+, NH4 +, or H3O+/H2O. Characterization and modeling of the insertion and removal of Li, oxygen, and H3O+/H2O species under electrochemical cycling and heating is important for understanding how MnO2 acts as a hybrid Li-ion/Li-O2 battery material. In this talk, we will discuss our work in using in-situ synchrotron X-ray diffraction (XRD), X-ray absorption near-edge spectroscopy (XANES), in-situ UV resonance Raman spectroscopy, and density functional theory (DFT) calculations, to unravel the changes in α-MnO2during electrochemical cycling as well as dehydration process. We found evidence of oxygen incorporation and partial removal during electrochemical cycling, as well as two-stage water removal during heating. Both processes involve facile oxygen diffusion through the center of 2x2 tunnels. Keywords: MnO2, in-situ XRD, DFT Reference: Z.-Z. Yang, D. Ford, J.-S. Park, Y. Ren, S. Kim, H. Kim, T. Fister, M. K. Y. Chan,# M. M. Thackeray,# “Probing the release and uptake of water in α-MnO2•xH2O,” Chemistry of Materials 29, 1507–1517 (2017).Z. Yang, L. Trahey, Y. Ren, M. K. Y. Chan,# C. Lin, J. Okasinski, and M. M. Thackeray, “In-Situ High-Energy Synchrotron X-ray Diffraction Studies and First Principles Modeling of α-MnO2 Electrodes in Li-O2 and Li-ion Coin Cells,” Journal of Materials Chemistry A 3, 7389-7398 (2015). Acknowledgements: This work was supported as a part of the Center for Electrochemical Energy Science, an Energy Frontier Research Center funded by the US Department of Energy, Office of Science, Basic Energy Sciences under award number DE-AC02–06CH11. Use of the Advanced Photon Source, a US DOE Office of Science User Facility operated by Argonne National Laboratory, was supported by DOE under Contract No. DE-AC02-06CH11357. Use of the Center for Nanoscale Materials, an Office of Science user facility, was supported by the U. S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357. This research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. Figure 1

Charge-Transfer Modified Embedded-Atom Method for LiNi1-x-YCoxMnyO2 Cathode Materials

Benefiting from the high voltage and high capacity, transition metal (TM) layered oxides LiNi1-x-yCoxMnyO2 (NCM) constitute a very attractive family of compounds for the positive electrode of Li-ion batteries. Full quantum simulations such as density functional theory (DFT) method have provided many accurate atomic and electronic structure information, but these understanding is limited to a very small system size of 100-1000 atoms. For micro-scale structures simulations, e.g. , multiple phases and interfaces in-between, a large-scale simulation method that can simulate 1000-10000 atoms is required. However, high challenges are faced to develop such method for cathode materials, due to the complex TM-O bonding nature with both ionic and covalent components, the diverse interactions in a quinary system, and the continuous charge state variations during delithiation. In this work, we have developed a multi-scale simulation method for NCM cathode materials, based on Charge-Transfer Modified Embedded-Atom Method (CT-MEAM), in which both the long range Coulomb interaction due to charge transfer and the short range non-ionic interaction can be well described. Properties derived from this method match quite well with the corresponding DFT reference work and essential atomic structure behaviors have been modeled, including NCM interfaces, defect structures, size effects, and corresponding TM distribution interactions, etc. The presented simulation method can help facilitate large-scale atomic calculations required for the optimal design of NCM oxides applications.

Development of Classical Molecule–Surface Interaction Potentials Based on Density Functional Theory Calculations: Investigation of Force Field Representability

A simple classical force field, based only on Coulomb and Lennard-Jones potentials, was developed to describe the interaction of an ethanol molecule physisorbed on the α-alumina (0001) surface. A range of adsorption structures were calculated using density functional theory (DFT) and these results were used for the force field parametrization. This system has a very inhomogeneous adsorption energy landscape, and the importance of the choice of data set used for fitting the force field was investigated. It was found that a Lennard-Jones and Coulombic potential can describe the ethanol–alumina interaction in reasonable qualitative agreement with the DFT reference data, provided that the data set was representative of both short- and long-range interactions and high- and low-energy configurations. Using a few distance-dependent adsorption energy curves at different surface sites gives the best compromise between computing time and accuracy of a Lennard-Jones based force field. This approach demonstrates a systematic way to test the quality of a force field and provides insight into how to improve upon the representability for a complex adsorption energy landscape.

Electric field gradients in Hg compounds: Molecular orbital (MO) analysis and comparison of 4-component and 2-component (ZORA) methods

We examine the performance of Density Functional Theory (DFT) approaches based on the Zeroth-Order Regular Approximation (ZORA) Hamiltonian (with and without inclusion of spin-orbit coupling) for predictions of electric field gradients (EFGs) at the heavy atom Hg nucleus. This is achieved by comparing with benchmark DFT and CCSD-T data (Arcisauskaite et al., Phys. Chem. Chem. Phys., 2012, 14, 2651-2657) obtained from 4-component Dirac-Coulomb Hamiltonian calculations. The investigated set of molecules comprises linear HgL(2) (L = Cl, Br, I, CH(3)) and bent HgCl(2) mercury compounds as well as the trigonal planar [HgCl(3)](-) system. In 4-component calculations we used the dyall.cv3z basis set for Hg, Br, I and the cc-pCVTZ basis set for H, C, Cl, whereas in ZORA calculations we used the QZ4P basis set for all the atoms. ZORA-4 reproduces the fully relativistic 4-component DFT reference values within 6% for all studied Hg compounds and employed functionals (BH&H, BP86, PBE0), whereas scalar relativistic (SR)-ZORA-4 results show deviations of up to 15%. Compared to our 4-component CCSD-T benchmark the BH&H functional performs best at both 4-component and ZORA levels. We furthermore observe that changes in the largest component of the diagonalised EFG tensor, V(zz), of linear HgCl(2) show a slightly stronger dependence than the r(-3) scaling upon bond length r(Hg-Cl) alterations. The 4-component/BH&H V(zz) value of -9.26 a.u. for a bent HgCl(2) (∠Cl-Hg-Cl = 120°) is close to -9.60 a.u. obtained for the linear HgCl(2) structure. Thus a point charge model for EFG calculations completely fails in this case. By means of a projection analysis of molecular orbital (MO) contributions to V(zz) in terms of the atomic constituents, we conclude that this is due to the increased importance of the Hg 5d orbitals upon bending HgCl(2) compared to the linear HgCl(2) structure. Changing ligand leads to only minor changes in V(zz) (from -9.60 a.u. (HgCl(2)) to -8.85 a.u. (HgI(2)) at the 4-component/BH&H level). This appears to be due to cancellation of contributions with opposite signs to V(zz) arising from: (i) increasing electron donation from occupied ligand orbitals to the formally empty Hg 6p orbitals and (ii) an increasing bond length and a decreasing negative charge on the ligand along the series.