Plane-wave pseudopotential implementation and performance of SCAN meta-GGA exchange-correlation functional for extended systems

Uncertainty of DFT Calculated Mechanical and Structural Properties of Solids due to Incompatibility of Pseudopotentials and Exchange-Correlation Functionals

The demand for pseudopotentials constructed for a given exchange-correlation (XC) functional far exceeds the supply, necessitating the use of those commonly available. The number of XC functionals currently available is in the hundreds, if not thousands, and the majority of pseudopotentials have been generated for LDA and PBE. The objective of this study is to identify the error in the determination of the mechanical and structural properties (lattice constant, cohesive energy, surface energy, elastic constants, and bulk modulus) of crystals calculated by DFT with such inconsistency. Additionally, this study aims to estimate the performance of popular XC functionals (LDA, PBE, PBEsol, and SCAN) for these calculations in a consistent manner.

Theoretical insights into off-stoichiometric Zr(x)Ti(1-x)IrSb half-Heusler alloys: a first principle calculations

This study presents a theoretical investigation into the phase stability, electronic, and optical properties of off-stoichiometricZrxTi1-xIrSb(x= 0, 0.0625, 0.1875, 0.25, 0.50, 0.75, 1) compounds. Using first-principles calculations, we explore how varying Zr and Ti concentrations can tune the electronic and optical properties of these half-Heusler alloys. The Structural, optical, and electronic properties were meticulously analyzed with both the GGA-PBE and Meta-GGA-SCAN approximations, as implemented in the ViennaAb initioSimulation Package (VASP). The dynamical stability of these compounds was assessed using the Phonopy package. Our findings reveal that these alloys exhibit semiconductor behavior with tunable band gaps, and their optical properties show significant variation across different compositions, particularly in the visible light range. The compounds also demonstrate robust dynamical stability, indicating their potential for practical applications in electronic and optoelectronic devices. These results underscore the versatility ofZrxTi1-xIrSballoys and highlight their promise for next-generation technology.

Understanding Strain and Failure of a Knot in Polyethylene Using Molecular Dynamics with Machine-Learned Potentials

A neural network potential (NNP) has been developed by fitting to ab initio electronic structure data on hydrocarbons and is used to study failure of linear and knotted polyethylene (PE) chains. A linear PE chain must be highly strained before breaking as the stress is equally distributed across the chain. In contrast, the stress in a PE chain with a 31 or overhand knot, accumulates at the knot's entrance/exit. We find the strain energy is greatest when the bond length and angle are strained simultaneously, and that the knot weakens the chain by increasing the variance of the C-C-C angle, thereby allowing rupture at lower bond strains. We extend our analysis to both 51 and 52 knots and find that both break at the entrance/exit of a loop. Notably, molecular scale PE knots exhibit many of the same characteristics as knots in a macroscopic rope, with stick-slip phenomena upon tightening and similar points of failure.

Efficient exact exchange using Wannier functions and other related developments in planewave-pseudopotential implementation of RT-TDDFT

The plane-wave pseudopotential (PW-PP) formalism is widely used for the first-principles electronic structure calculation of extended periodic systems. The PW-PP approach has also been adapted for real-time time-dependent density functional theory (RT-TDDFT) to investigate time-dependent electronic dynamical phenomena. In this work, we detail recent advances in the PW-PP formalism for RT-TDDFT, particularly how maximally localized Wannier functions (MLWFs) are used to accelerate simulations using the exact exchange. We also discuss several related developments, including an anti-Hermitian correction for the time-dependent MLWFs (TD-MLWFs) when a time-dependent electric field is applied, the refinement procedure for TD-MLWFs, comparison of the velocity and length gauge approaches for applying an electric field, and elimination of long-range electrostatic interaction, as well as usage of a complex absorbing potential for modeling isolated systems when using the PW-PP formalism.

Neutron scattering and neural-network quantum molecular dynamics investigation of the vibrations of ammonia along the solid-to-liquid transition

Vibrational spectroscopy allows us to understand complex physical and chemical interactions of molecular crystals and liquids such as ammonia, which has recently emerged as a strong hydrogen fuel candidate to support a sustainable society. We report inelastic neutron scattering measurement of vibrational properties of ammonia along the solid-to-liquid phase transition with high enough resolution for direct comparisons to ab-initio simulations. Theoretical analysis reveals the essential role of nuclear quantum effects (NQEs) for correctly describing the intermolecular spectrum as well as high energy intramolecular N-H stretching modes. This is achieved by training neural network models using ab-initio path-integral molecular dynamics (PIMD) simulations, thereby encompassing large spatiotemporal trajectories required to resolve low energy dynamics while retaining NQEs. Our results not only establish the role of NQEs in ammonia but also provide general computational frameworks to study complex molecular systems with NQEs.

Phase transitions of choline dihydrogen phosphate: A vibrational spectroscopy and periodic DFT study

Choline dihydrogen phosphate, [Chol][H2PO4], is a proton-conducting ionic plastic crystal exhibiting a complicated sequence of phase transitions. Here, we address the argument in the literature around the thermal properties of [Chol][H2PO4] using Raman and infrared microspectroscopy. The known structure of the low-temperature crystal, which contains the anti-conformer of [Chol]+ and hydrogen-bonded dimers of anions, was used to do periodic density functional theory calculations of the vibrational frequencies. Raman spectra indicate that the solid-solid transition at 20 °C is linked to a conformational change to the gauche [Chol] conformer with a concurrent local rearrangement of the anions. The distinct bands of lattice modes in the low-frequency range of the Raman spectra vanish at the 20 °C transition. Given the ease with which metastable crystals can be produced, Raman mappings demonstrate that a sample of [Chol][H2PO4] at ambient temperature can contain a combination of anti- and gauche conformers. Heating to 120 °C causes continuous changes in the local environment of anions rather than melting as suggested by a recent calorimetric investigation of [Chol][H2PO4]. The monotonic change in vibrational spectra is consistent with earlier observations of a very small entropy of fusion and no abrupt jump in the temperature dependence of ionic conductivity along the phase transitions of [Chol][H2PO4].

Real-Time Time-Dependent Density Functional Theory for Simulating Nonequilibrium Electron Dynamics

The explicit real-time propagation approach for time-dependent density functional theory (RT-TDDFT) has increasingly become a popular first-principles computational method for modeling various time-dependent electronic properties of complex chemical systems. In this Perspective, we provide a nontechnical discussion of how this first-principles simulation approach has been used to gain novel physical insights into nonequilibrium electron dynamics phenomena in recent years. Following a concise overview of the RT-TDDFT methodology from a practical standpoint, we discuss our recent studies on the electronic stopping of DNA in water and the Floquet topological phase as examples. Our discussion focuses on how RT-TDDFT simulations played a unique role in deriving new scientific understandings. We then discuss existing challenges and some new advances at the frontier of RT-TDDFT method development for studying increasingly complex dynamic phenomena and systems.

Electrostatic Gating of Phosphorene Polymorphs

The ability to directly monitor the states of electrons in modern field-effect transistors (FETs) could transform our understanding of the physics and improve the function of related devices. In particular, phosphorene allotropes present a fertile landscape for the development of high-performance FETs. Using density functional theory-based methods, we have systematically investigated the influence of electrostatic gating on the structures, stabilities, and fundamental electronic properties of pristine and carbon-doped monolayer (bilayer) phosphorene allotropes. The remarkable flexibility of phosphorene allotropes, arising from intra- and interlayer van der Waals interactions, causes a good resilience up to equivalent gate potential of two electrons per unit cell. The resilience depends on the stacking details in such a way that rotated bilayers show considerably higher thermodynamical stability than the unrotated ones, even at a high gate potential. In addition, a semiconductor to metal phase transition is observed in some of the rotated and carbon-doped structures with increased electronic transport relative to graphene in the context of real space Green's function formalism.

Meta-generalized gradient approximations in time dependent generalized Kohn-Sham theory: Importance of the current density correction

We revisit the use of Meta-Generalized Gradient Approximations (mGGAs) in time-dependent density functional theory, reviewing conceptual questions and solving the generalized Kohn-Sham equations by real-time propagation. After discussing the technical aspects of using mGGAs in combination with pseudopotentials and comparing real-space and basis set results, we focus on investigating the importance of the current-density based gauge invariance correction. For the two modern mGGAs that we investigate in this work, TASK and r2SCAN, we observe that for some systems, the current density correction leads to negligible changes, but for others, it changes excitation energies by up to 40% and more than 0.8 eV. In the cases that we study, the agreement with the reference data is improved by the current density correction.

Implementation of the meta-GGA exchange-correlation functional in numerical atomic orbital basis: With systematic testing on SCAN, rSCAN, and r2SCAN functionals

Kohn-Sham density functional theory (DFT) is nowadays widely used for electronic structure theory simulations, and the accuracy and efficiency of DFT rely on approximations of the exchange-correlation functional. By including the kinetic energy density τ, the meta-generalized-gradient approximation (meta-GGA) family of functionals achieves better accuracy and flexibility while retaining the efficiency of semi-local functionals. For example, the strongly constrained and appropriately normed (SCAN) meta-GGA functional has been proven to yield accurate results for solid and molecular systems. We implement meta-GGA functionals with both numerical atomic orbitals and plane wave bases in the ABACUS package. Apart from the exchange-correlation potential, we also discuss the evaluation of force and stress. To validate our implementation, we perform finite-difference tests and convergence tests with the SCAN, rSCAN, and r2SCAN meta-GGA functionals. We further test water hexamers, weakly interacting molecules from the S22 dataset, as well as 13 semiconductors using the three functionals. The results show satisfactory agreement with previous calculations and available experimental values.

Accuracy of a Recent Regularized Nuclear Potential

F. Gygi recently suggested an analytic, norm-conserving, regularized nuclear potential to enable all-electron plane-wave calculations [Gygi J. Chem. Theory Comput. 2023, 19, 1300-1309.]. This potential V(r) is determined by inverting the Schrödinger equation for the wave function Ansatz ϕ(r) = exp[-h(r)]/√π with h(r) = r erf(ar) + b exp(-a2r2), where a and b are parameters. Gygi fixes b by demanding ϕ to be normalized, with the value b(a) depending on the strength of the regularization controlled by a. We begin this work by re-examining the determination of b(a) and find that the original 10-decimal tabulations of Gygi are only correct to 5 decimals, leading to normalization errors in the order of 10-10. In contrast, we show that a simple 100-point radial quadrature scheme not only ensures at least 10 correct decimals of b but also leads to machine-precision level satisfaction of the normalization condition. Moreover, we extend Gygi's plane-wave study by examining the accuracy of V(r) with high-precision finite element calculations with Hartree-Fock and LDA, GGA, and meta-GGA functionals on first- to fifth-period atoms. We find that although the convergence of the total energy appears slow in the regularization parameter a, orbital energies and shapes are indeed reproduced accurately by the regularized potential even with relatively small values of a, as compared to results obtained with a point nucleus. The accuracy of the potential is furthermore studied with s-d excitation energies of Sc-Cu as well as ionization potentials of He-Kr, which are found to converge to sub-meV precision with a = 4. The findings of this work are in full support of Gygi's contribution, indicating that all-electron plane-wave calculations can be accurately performed with the regularized nuclear potential.

Meta-GGA Density Functional Calculations on Atoms with Spherically Symmetric Densities in the Finite Element Formalism

Density functional calculations on atoms are often used for determining accurate initial guesses as well as generating various types of pseudopotential approximations and efficient atomic-orbital basis sets for polyatomic calculations. To reach the best accuracy for these purposes, the atomic calculations should employ the same density functional as the polyatomic calculation. Atomic density functional calculations are typically carried out employing spherically symmetric densities, corresponding to the use of fractional orbital occupations. We have described their implementation for density functional approximations (DFAs) belonging to the local density approximation (LDA) and generalized gradient approximation (GGA) levels of theory as well as Hartree-Fock (HF) and range-separated exact exchange [Lehtola, S. Phys. Rev. A 2020, 101, 012516]. In this work, we describe the extension to meta-GGA functionals using the generalized Kohn-Sham scheme, in which the energy is minimized with respect to the orbitals, which in turn are expanded in the finite element formalism with high-order numerical basis functions. Furnished with the new implementation, we continue our recent work on the numerical well-behavedness of recent meta-GGA functionals [Lehtola, S.; Marques, M. A. L. J. Chem. Phys. 2022, 157, 174114]. We pursue complete basis set (CBS) limit energies for recent density functionals and find many to be ill-behaved for the Li and Na atoms. We report basis set truncation errors (BSTEs) of some commonly used Gaussian basis sets for these density functionals and find the BSTEs to be strongly functional dependent. We also discuss the importance of density thresholding in DFAs and find that all of the functionals studied in this work yield total energies converged to 0.1 μEh when densities smaller than 10-11a0-3 are screened out.

Simulating electronic excitation and dynamics with real-time propagation approach to TDDFT within plane-wave pseudopotential formulation

We give a perspective on simulating electronic excitation and dynamics using the real-time propagation approach to time-dependent density functional theory (RT-TDDFT) in the plane-wave pseudopotential formulation. RT-TDDFT is implemented in various numerical formalisms in recent years, and its practical application often dictates the most appropriate implementation of the theory. We discuss recent developments and challenges, emphasizing numerical aspects of studying real systems. Several applications of RT-TDDFT simulation are discussed to highlight how the approach is used to study interesting electronic excitation and dynamics phenomena in recent years.

Nuclear Quantum Effect and Its Temperature Dependence in Liquid Water from Random Phase Approximation via Artificial Neural Network

We report structural and dynamical properties of liquid water described by the random phase approximation (RPA) correlation together with the exact exchange energy (EXX) within density functional theory. By utilizing thermostated ring polymer molecular dynamics, we examine the nuclear quantum effects and their temperature dependence. We circumvent the computational limitation of performing direct first-principles molecular dynamics simulation at this high level of electronic structure theory by adapting an artificial neural network model. We show that the EXX+RPA level of theory accurately describes liquid water in terms of both dynamical and structural properties.

Modeling solvation effects on absorption and fluorescence spectra of indole in aqueous solution

Modeling the optical spectra of molecules in solution presents a challenge, so it is important to understand which of the solvation effects (i.e., electrostatics, mutual polarization, and hydrogen bonding interactions between solute and solvent molecules) are crucial in reproducing the various features of the absorption and fluorescence spectra and to identify a sufficient theoretical model that accurately captures these effects with minimal computational cost. In this study, we use various implicit and explicit solvation models, such as molecular dynamics coupled with non-polarizable and polarizable force fields, as well as Car-Parrinello molecular dynamics, to model the absorption and fluorescence spectra of indole in aqueous solution. The excited states are computed using the equation of motion coupled cluster with single and double excitations combined with the effective fragment potential to represent water molecules, which we found to be a computationally efficient approach for modeling large solute-solvent clusters at a high level of quantum theory. We find that modeling mutual polarization, compared to other solvation effects, is a dominating factor for accurately reproducing the position of the peaks and spectral line shape of the absorption spectrum of indole in solution. We present an in-depth analysis of the influence that different solvation models have on the electronic excited states responsible for the features of the absorption spectra. Modeling fluorescence is more challenging since it is hard to reproduce even the correct emitting state, and force field parameters need to be re-evaluated.

Accurate and Numerically Efficient r2SCAN Meta-Generalized Gradient Approximation

The recently proposed rSCAN functional [ J. Chem. Phys. 2019 150, 161101] is a regularized form of the SCAN functional [ Phys. Rev. Lett. 2015 115, 036402] that improves SCAN's numerical performance at the expense of breaking constraints known from the exact exchange-correlation functional. We construct a new meta-generalized gradient approximation by restoring exact constraint adherence to rSCAN. The resulting functional maintains rSCAN's numerical performance while restoring the transferable accuracy of SCAN.

Validation of Pseudopotential Calculations for the Electronic Band Gap of Solids

Nowadays pseudopotential (PP) density functional theory calculations constitute the standard approach to tackle solid-state electronic problems. These rely on distributed PP tables that were built from all-electron atomic calculations using few popular semilocal exchange-correlation functionals, while PPs based on more modern functionals, such as meta-generalized gradient approximation and hybrid functionals, or for many-body methods, such as GW, are often not available. Because of this, employing PPs created with inconsistent exchange-correlation functionals has become a common practice. Our aim is to quantify systematically the error in the determination of the electronic band gap when cross-functional PP calculations are performed. To this end, we compare band gaps obtained with norm-conserving PPs or the projector-augmented wave method with all-electron calculations for a large data set of 473 solids. We focus, in particular, on density functionals that were designed specifically for band gap calculations. On average, the absolute error is about 0.1 eV, yielding absolute relative errors in the 5-10% range. Considering that typical errors stemming from the choice of the functional are usually larger, we conclude that the effect of choosing an inconsistent PP is rather harmless for most applications. However, we find specific cases where absolute errors can be larger than 1 eV or others where relative errors can amount to a large fraction of the band gap.

Improved description of hematite surfaces by the SCAN functional

Controversies on the surface termination of α-Fe₂O₃ (0001) focus on its surface stoichiometry dependence on the oxygen chemical potential. Density functional theory (DFT) calculations applying the commonly accepted Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional to a strongly correlated system predict the best matching surface termination, but would produce a delocalization error, resulting in an inappropriate bandgap, and thus are not applicable for comprehensive hematite system studies. Besides, the widely applied PBE+U scheme cannot provide evidence for existence of some of the successfully synthesized stoichiometric α-Fe₂O₃ (0001) surfaces. Hence, a better scheme is needed for hematite DFT studies. This work investigates whether the strongly constrained and appropriately normed (SCAN) approximation reported by Perdew et al. could provide an improved result for the as-mentioned problem, and whether SCAN can be applied to hematite systems. By comparing the results calculated with the PBE, SCAN, PBE+U, and SCAN+U schemes, we find that SCAN and SCAN+U improves the description of the electronic structure of different stoichiometric α-Fe₂O₃ (0001) surfaces with respect to the PBE results, and that they give a consistent prediction of the surface terminations. Besides, the bulk lattice constants and the bulk density of states are also improved with the SCAN functional. This study provides a general characterization of the α-Fe₂O₃ (0001) surfaces and rationalizes how the SCAN approximation improves the results of hematite surface calculations.

Localization in the SCAN meta-generalized gradient approximation functional leading to broken symmetry ground states for graphene and benzene

SCAN over localizes orbitals leading to spin symmetry broken ground states in graphene and benzene.

K-Shell Core-Electron Excitations in Electronic Stopping of Protons in Water from First Principles

Understanding the role of core-electron excitation in liquid water under proton irradiation has become important due to the growing use of proton beams in radiation oncology. Using a first-principles, nonequilibrium simulation approach based on real-time, time-dependent density functional theory, we determine the electronic stopping power, the velocity-dependent energy transfer rate from irradiating ions to electrons. The electronic stopping power curve agrees quantitatively with experimental data over the velocity range available. At the same time, significant differences are observed between our first-principles result and commonly used perturbation theoretic models. Excitations of the water molecules' oxygen core electrons are a crucial factor in determining the electronic stopping power curve beyond its maximum. The core-electron contribution is responsible for as much as one third of the stopping power at the high proton velocity of 8.0 a.u. (1.6 MeV). K-shell core-electron excitations not only provide an additional channel for the energy transfer-they also significantly influence the valence electron excitations. In the excitation process, generated holes remain highly localized within a few angstroms around the irradiating proton path, whereas electrons are excited away from the path. In spite of their great contribution to the stopping power, K-shell electrons play a rather minor role in terms of the excitation density; only 1% of the hole population composes K-shell holes, even at the high proton velocity of 8.0 a.u. The excitation behavior revealed is distinctly different from that of photon-based ionizing radiation such as x or γ rays.

Regularized SCAN functional

We propose modifications to the functional form of the Strongly Constrained and Appropriately Normed (SCAN) density functional to eliminate numerical instabilities. This is necessary to allow reliable, automatic generation of pseudopotentials (including projector augmented-wave potentials). The regularized SCAN is designed to match the original form very closely, and we show that its performance remains comparable.

Nuclear quantum effect with pure anharmonicity and the anomalous thermal expansion of silicon

Despite the widespread use of silicon in modern technology, its peculiar thermal expansion is not well understood. Adapting harmonic phonons to the specific volume at temperature, the quasiharmonic approximation, has become accepted for simulating the thermal expansion, but has given ambiguous interpretations for microscopic mechanisms. To test atomistic mechanisms, we performed inelastic neutron scattering experiments from 100 K to 1,500 K on a single crystal of silicon to measure the changes in phonon frequencies. Our state-of-the-art ab initio calculations, which fully account for phonon anharmonicity and nuclear quantum effects, reproduced the measured shifts of individual phonons with temperature, whereas quasiharmonic shifts were mostly of the wrong sign. Surprisingly, the accepted quasiharmonic model was found to predict the thermal expansion owing to a large cancellation of contributions from individual phonons.