Kohn-Sham Density Functional Theory Research Articles

Elastic properties of Janus transition metal dichalcogenide nanotubes from first principles

We calculate the elastic properties of Janus transition metal dichalcogenide (TMD) nanotubes using first principles Kohn-Sham density functional theory (DFT). Specifically, we perform electronic structure simulations that exploit the cyclic and helical symmetry in the system to compute the Young's moduli, Poisson's ratios, and torsional moduli for twenty-seven select armchair and zigzag Janus TMD nanotubes at their equilibrium diameters. We find the following trend in the moduli values: MSSe > MSTe > MSeTe, while their anisotropy with respect to armchair and zigzag configurations has the following ordering: MSTe > MSeTe > MSSe. This anisotropy and its ordering between the different groups is confirmed by computing the shear modulus from the torsional modulus using an isotropic elastic continuum model, and comparing it against the value predicted from the isotropic relation featuring the Young's modulus and Poisson's ratio. We also develop a model for the Young's and torsional moduli of Janus TMD nanotubes based on linear regression.

Using projection operators with maximum overlap methods to simplify challenging self-consistent field optimization.

Maximum overlap methods are effective tools for optimizing challenging ground- and excited-state wave functions using self-consistent field models such as Hartree-Fock and Kohn-Sham density functional theory. Nevertheless, such models have shown significant sensitivity to the user-defined initial guess of the target wave function. In this work, a projection operator framework is defined and used to provide a metric for non-aufbau orbital selection in maximum-overlap-methods. The resulting algorithms, termed the Projection-based Maximum Overlap Method (PMOM) and Projection-based Initial Maximum Overlap Method (PIMOM), are shown to perform exceptionally well when using simple user-defined target solutions based on occupied/virtual molecular orbital permutations. This work also presents a new metric that provides a simple and conceptually convenient measure of agreement between the desired target and the current or final SCF results during a calculation employing a maximum-overlap method.

Water in an External Electric Field: Comparing Charge Distribution Methods Using ReaxFF Simulations.

The growing interest in the effects of external electric fields on reactive processes requires predictive methods that can reach longer length and time scales than quantum mechanical simulations. Recently, many studies have included electric fields in ReaxFF, a widely used reactive molecular dynamics method. In the case of modeling an external electric field, the charge distribution method used in ReaxFF is critical. The most common charge distribution method used in previous studies of electric fields is the charge equilibration (QEq) method, which assumes that the system is a contiguous conductor and that charge transfer can occur across any distance. In contrast, many systems of interest are insulators or semiconductors, and long-distance charge transfer should not occur in response to a small difference in potential. This study focuses on the limitations of the QEq method in the context of water in an external electric field. We demonstrate that QEq can predict unphysical charge distributions and exhibits properties that do not converge as a function of system size. Furthermore, we show that electric fields within the recently developed atom-condensed Kohn-Sham density functional theory (DFT) approximated to the second-order (ACKS2) approach address the major limitations of electric fields in QEq. With ACKS2, we observe more physical charge distributions and properties that converge as a function of system size. We do not suggest that ACKS2 is perfect in all circumstances but rather show specific cases where it addresses the major shortcomings of QEq in the context of an external electric field.

Normalization of exact quasiparticle wave functions in the Green's function method guaranteed by the Ward identity

It has been a long-standing problem in $N$-electron systems as to how to solve the Dyson equation with the quasiparticle wave functions defined as $\ensuremath{\langle}\phantom{\rule{0.16em}{0ex}}{\mathrm{\ensuremath{\Psi}}}_{0}^{N}\phantom{\rule{0.16em}{0ex}}|\phantom{\rule{0.16em}{0ex}}{\ensuremath{\psi}}_{s}(\mathbit{r})\phantom{\rule{0.16em}{0ex}}|\phantom{\rule{0.16em}{0ex}}{\mathrm{\ensuremath{\Psi}}}_{\ensuremath{\nu}}^{N+1}\phantom{\rule{0.16em}{0ex}}\ensuremath{\rangle}$ and $\ensuremath{\langle}\phantom{\rule{0.16em}{0ex}}{\mathrm{\ensuremath{\Psi}}}_{\ensuremath{\mu}}^{N\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}|\phantom{\rule{0.16em}{0ex}}{\ensuremath{\psi}}_{s}(\mathbit{r})\phantom{\rule{0.16em}{0ex}}|\phantom{\rule{0.16em}{0ex}}{\mathrm{\ensuremath{\Psi}}}_{0}^{N}\phantom{\rule{0.16em}{0ex}}\ensuremath{\rangle}$, which are not mutually orthogonal and have a norm less than 1. We show that quasiparticle wave functions without multiple excitations can exactly be normalized to unity owing to the Ward identity and the vertex function in $(\mathbit{q},{\ensuremath{\omega}}^{\ensuremath{'}}\ensuremath{-}\ensuremath{\omega})\ensuremath{\rightarrow}0$, although they are not necessarily mutually orthogonal. Since they satisfy an eigenvalue equation with the hermitized self-energy due to Baym-Kadanoff's conservation laws, the present theory can be regarded as an extension of the Kohn-Sham density functional theory, with correlated, interacting, one-electron orbitals.

Symmetry Dilemma of Doubly Hybrid Density Functionals for Equilibrium Molecular Property Calculations.

In electronic structure theory, when an approximate wavefunction tends to artifactually break the symmetry of the exact Hamiltonian, the corresponding method is referred to as having a "symmetry dilemma" problem. Such types of artifacts were often reported when Hartree-Fock (HF) and the low-level post-HF methods were used, while the traditional Kohn-Sham density functional theory (KS-DFT) methods were usually found to be more resistant to this breakdown. In this work, we present a systematic study on the reliability of the doubly hybrid (DH) DFT methods for several violable cases. Almost all the commonly used B2PLYP-type (bDH) functionals are shown to have a severe "symmetry dilemma" problem and yield dramatically unreliable molecular properties, such as dipole moment, vibrational frequency, and static polarizability at the equilibrium geometry. A one-parameter bDH functional model study demonstrates that such a problem is a combined effect of the inappropriate portion of the HF exchange (over 50%) for the self-consistent field (SCF) calculation and the augmentation of the second-order perturbative contribution. It is remarkable that the XYG3-type (xDH) functionals show a good capability to resist the artifactual symmetry breaking and yield reliable molecular properties when the same critical cases are calculated. In the xDH, there are two functionals of different purposes, namely, the SCF functional and the energy functional, which have different amounts of the HF exchange and different portions of the correlation contributions. The success of the xDHs can be attributed to this flexibility in xDH construction to avoid using an improperly large portion of the HF exchange in the SCF functional. The insights gained in this work are of significance for the development of an improved DH functional.

Unity of Kohn-Sham density-functional theory and reduced-density-matrix-functional theory

This work presents a rigorous theory to unify the two independent theoretical frameworks of Kohn-Sham (KS) density-functional theory (DFT) and reduced-density-matrix-functional theory (RDMFT). The generalization of the KS orbitals to hypercomplex number systems leads to the hypercomplex KS (HCKS) theory, which extends the search space for the electron density in KS-DFT and reformulates the kinetic energy. The HCKS theory provides a general framework, and different dimensions of the HCKS orbitals lead to different HCKS methods, with KS-DFT and RDMFT being two cases corresponding to the smallest and largest dimensions. Furthermore, a series of tests show that HCKS can capture the multireference nature of strong correlation by dynamically varying fractional occupations, while maintaining the same computational scaling as the KS method. With great potential to overcome the fundamental limitations of the KS method, HCKS creates new possibilities for the development and application of DFT.

Breakdown of the ionization potential theorem of density functional theory in mesoscopic systems.

The ionization potential (IP)-theorem of Kohn-Sham (KS) density functional theory (DFT) states that the energy of the highest occupied molecular orbital (HOMO) ϵHOMO equals the negative of the first IP, thus ascribing a physical meaning to one of the eigenvalues of the KS Hamiltonian. We scrutinize the fact that the validity of the IP-theorem relies critically on the electron density n(r), far from the system, to be determined by HOMO only, behaving as n(r)∼r→∞e-2-2ϵHOMOr. While this behavior always holds for finite systems, it does not hold for mesoscopic ones, such as quasi-two-dimensional (Q2D) electron gas or Q2D crystals. We show that this leads to the violation of the IP-theorem for the latter class of systems. This finding has a strong bearing on the role of the KS valence band with respect to the work-function problem in the mesoscopic case. Based on our results, we introduce a concept of the IP band structure as an observable alternative to its unphysical KS counterpart. A practical method of the determination of the IP band structure in terms of DFT quantities is provided.

Constructing and representing exchange-correlation holes through artificial neural networks.

One strategy to construct approximations to the exchange-correlation (XC) energy EXC of Kohn-Sham density functional theory relies on physical constraints satisfied by the XC hole ρXC(r, u). In the XC hole, the reference charge is located at r and u is the electron-electron separation. With mathematical intuition, a given set of physical constraints can be expressed in a formula, yielding an approximation to ρXC(r, u) and the corresponding EXC. Here, we adapt machine learning algorithms to partially automate the construction of X and XC holes. While machine learning usually relies on finding patterns in datasets and does not require physical insight, we focus entirely on the latter and develop a tool (ExMachina), consisting of the basic equations and their implementation, for the machine generation of approximations. To illustrate ExMachina, we apply it to calculate various model holes and show how to go beyond existing approximations.

Short-Range Imbalances in the AMBER Lennard-Jones Potential for (Deoxy)Ribose···Nucleobase Lone-Pair···π Contacts in Nucleic Acids.

The lone-pair···π (lp···π) (deoxy)ribose···nucleobase stacking is a recurring interaction in Z-DNA and RNAs that is characterized by sub-van der Waals lp···π contacts (<3.0 Å). It is a part of the structural signature of CpG Z-step motifs in Z-DNA and r(UNCG) tetraloops that are known to behave poorly in molecular dynamics (MD) simulations. Although the exact origin of the MD simulation issues remains unclear, a significant part of the problem might be due to an imbalanced description of nonbonded interactions, including the characteristic lp···π stacking. To gain insights into the links between lp···π stacking and MD, we present an in-depth comparison between accurate large-basis-set double-hybrid Kohn-Sham density functional theory calculations DSD-BLYP-D3/ma-def2-QZVPP (DHDF-D3) and data obtained with the nonbonded potential of the AMBER force field (AFF) for NpN Z-steps (N = G, A, C, and U). Among other differences, we found that the AFF overestimates the DHDF-D3 lp···π distances by ∼0.1-0.2 Å, while the deviation between the DHDF-D3 and AFF descriptions sharply increases in the short-range region of the interaction. Based on atom-in-molecule polarizabilities and symmetry-adapted perturbation theory analysis, we inferred that the DHDF-D3 versus AFF differences partly originate in identical nucleobase carbon atom Lennard-Jones (LJ) parameters despite the presence/absence of connected electron-withdrawing groups that lead to different effective volumes or vdW radii. Thus, to precisely model the very short CpG lp···π contact distances, we recommend revision of the nucleobase atom LJ parameters. Additionally, we suggest that the large discrepancy between DHDF-D3 and AFF short-range repulsive part of the interaction energy potential may significantly contribute to the poor performances of MD simulations of nucleic acid systems containing Z-steps. Understanding where, and if possible why, the point-charge-type effective potentials reach their limits is vital for developing next-generation FFs and for addressing specific issues in contemporary MD simulations.

Third order non-linear optical susceptibilities[formula omitted]of yttria stabilized cubic hafnium(IV) oxide

This work reports for the first time theoretical third order nonlinear optical susceptibilities of YSH bulk phases which are key properties for telecommunication technologies and integrated photonic devices. Our outcomes, relying on coupled perturbed Kohn-Sham density functional theory expose that the NLO capacity of YSH should be similar to another material of this family, namely, yttria stabilized zirconia that has been proposed as a promising candidate for integrated photonics by Marcaud et al. (2020). Finally, evidence implying important vibrational contributions to the optical nonlinearities of the systems are revealed and analyzed.

Dissociation limit in Kohn–Sham density functional theory

We consider the dissociation limit for molecules of the type X2 in the Kohn–Sham density functional theory setting, where X can be any element with N electrons. We prove that when the two atoms in the system are torn infinitely far apart, the energy of the system converges to minα∈[0,N](IαX+I2N−αX), where IαX denotes the energy of the atom with α electrons surrounding it. Depending on the “strength” of the exchange this minimum might not be equal to the symmetric splitting 2INX. We show numerically that for the H2-molecule with Dirac exchange this gives the expected result of twice the energy of a H-atom 2I1H.

Generalized Method for Charge-Transfer Equilibration in Reactive Molecular Dynamics.

Variable charge models (e.g., electronegativity equalization method (EEM), charge equilibration (QEq), electrostatic plus (ES+)) used in reactive molecular dynamics simulations often inherently impose a global charge transfer between atoms (approximating each system as an ideal metal). Consequently, most surface processes (e.g., adsorption, desorption, deposition, sputtering) are affected, potentially causing dubious dynamics. This issue has been addressed by certain split charge variants (i.e., split charge equilibration (SQE), redoxSQE) through a distance-dependent bond hardness, by the atomic charge ACKS2 and QTPIE models, which are based on the Kohn-Sham density functional theory, as well as by an electronegativity screening extension to the QEq model (approximating each system as an ideal insulator). In a brief review of the QEq and the QTPIE model, their applicability for studying surface interactions is assessed in this work. Following this evaluation, a revised generalization of the QEq and QTPIE models is proposed and formulated, called the charge-transfer equilibration model or in short the QTE model. This method is based on the equilibration of charge-transfer variables, which locally constrain the split charge transfer per unit time (i.e., due to overlapping orbitals) without any kind of bond hardness specification. Furthermore, a formalism relying solely on atomic charges is obtained by a respective transformation, employing an extended Lagrangian method. We moreover propose a mirror boundary condition and its implementation to accelerate surface investigations. The models proposed in this work facilitate reactive molecular dynamics simulations, which describe various materials and surface phenomena appropriately.

KSSOLV-GPU: An efficient GPU-enabled MATLAB toolbox for solving the Kohn-Sham equations within density functional theory in plane-wave basis set

KSSOLV (Kohn-Sham Solver) is a MATLAB (Matrix Laboratory) tool-box for solving the Kohn-Sham density functional theory (KS-DFT) with the plane-wave basis set. In the KS-DFT calculations, the most expensive part is commonly the diagonalization of Kohn-Sham Hamiltonian in the self-consistent field (SCF) scheme. To enable a personal computer to perform medium-sized KS-DFT calculations that contain hundreds of atoms, we present a hybrid CPU-GPU implementation to accelerate the iterative diagonalization algorithms implemented in KSSOLV by using the MATLAB built-in Parallel Computing Toolbox. We compare the performance of KSSOLV-GPU on three types of GPU, including RTX3090, V100, and A100, with conventional CPU implementation of KSSOLV respectively and numerical results demonstrate that hybrid CPU-GPU implementation can achieve a speedup of about 10 times compared with sequential CPU calculations for bulk silicon systems containing up to 128 atoms.

The relevance of electronic perturbations in the warm dense electron gas.

Warm dense matter (WDM) has emerged as one of the frontiers of both experimental physics and theoretical physics and is a challenging traditional concept of plasma, atomic, and condensed-matter physics. While it has become common practice to model correlated electrons in WDM within the framework of Kohn-Sham density functional theory, quantitative benchmarks of exchange-correlation (XC) functionals under WDM conditions are yet incomplete. Here, we present the first assessment of common XC functionals against exact path-integral Monte Carlo calculations of the harmonically perturbed thermal electron gas. This system is directly related to the numerical modeling of x-ray scattering experiments on warm dense samples. Our assessment yields the parameter space where common XC functionals are applicable. More importantly, we pinpointwhere the tested XC functionals fail when perturbations on the electronic structure are imposed. We indicate the lack of XC functionals that take into account the needs of WDM physics in terms of perturbed electronic structures.

Modeling Liquid Water by Climbing up Jacob's Ladder in Density Functional Theory Facilitated by Using Deep Neural Network Potentials.

Within the framework of Kohn-Sham density functional theory (DFT), the ability to provide good predictions of water properties by employing a strongly constrained and appropriately normed (SCAN) functional has been extensively demonstrated in recent years. Here, we further advance the modeling of water by building a more accurate model on the fourth rung of Jacob's ladder with the hybrid functional, SCAN0. In particular, we carry out both classical and Feynman path-integral molecular dynamics calculations of water with the SCAN0 functional and the isobaric-isothermal ensemble. To generate the equilibrated structure of water, a deep neural network potential is trained from the atomic potential energy surface based on ab initio data obtained from SCAN0 DFT calculations. For the electronic properties of water, a separate deep neural network potential is trained by using the Deep Wannier method based on the maximally localized Wannier functions of the equilibrated trajectory at the SCAN0 level. The structural, dynamic, and electric properties of water were analyzed. The hydrogen-bond structures, density, infrared spectra, diffusion coefficients, and dielectric constants of water, in the electronic ground state, are computed by using a large simulation box and long simulation time. For the properties involving electronic excitations, we apply the GW approximation within many-body perturbation theory to calculate the quasiparticle density of states and bandgap of water. Compared to the SCAN functional, mixing exact exchange mitigates the self-interaction error in the meta-generalized-gradient approximation and further softens liquid water toward the experimental direction. For most of the water properties, the SCAN0 functional shows a systematic improvement over the SCAN functional. However, some important discrepancies remain. The H-bond network predicted by the SCAN0 functional is still slightly overstructured compared to the experimental results.

Learning the Exchange-Correlation Functional from Nature with Fully Differentiable Density Functional Theory.

Improving the predictive capability of molecular properties in abinitio simulations is essential for advanced material discovery. Despite recent progress making use of machine learning, utilizing deep neural networks to improve quantum chemistry modeling remains severely limited by the scarcity and heterogeneity of appropriate experimental data. Here we show how training a neural network to replace the exchange-correlation functional within a fully differentiable three-dimensional Kohn-Sham density functional theory framework can greatly improve simulation accuracy. Using only eight experimental data points on diatomic molecules, our trained exchange-correlation networks enable improved prediction accuracy of atomization energies across a collection of 104molecules containing new bonds, and atoms, that are not present in the training dataset.

Subsystem Density Functional Theory Augmented by a Delta Learning Approach to Achieve Kohn-Sham Accuracy.

Simulations based on electronic structure theory naturally include polarization and have no transferability problems. In particular, Kohn-Sham density functional theory (KS-DFT) has become the method of reference for ab initio molecular dynamics simulations of condensed matter systems. However, the high computational cost often poses strict limits on the affordable system size as well as on the extension of sampling (number of configurations). In this work, we propose an improvement to the subsystem density functional theory approach, known as the Kim-Gordon (KG) scheme, thus enabling the sampling of configurations for condensed molecular systems keeping the KS-DFT level accuracy at a fraction of computer time. Our scheme compensates the known KG shortcomings of the electronic kinetic energy term by adding a simple correction and can match KS-DFT accuracy in energies and forces. The computationally cheap correction is determined by means of a machine learning procedure. The proposed KG scheme is applied within a linear scaling self-consistent field formalism and is assessed by a series of molecular dynamics simulations of liquid water under different conditions. Although system-dependent, the correction is transferable between system sizes and temperatures.

Achieving performance portability in Gaussian basis set density functional theory on accelerator based architectures in NWChemEx

The numerical integration of the exchange–correlation (XC) potential is one of the primary computational bottlenecks in Gaussian basis set Kohn–Sham density functional theory (KS-DFT). To achieve optimal performance and accuracy, care must be taken in this numerical integration to preserve local sparsity as to allow for near linear weak scaling with system size. This leads to an integration scheme with several performance critical kernels which must be hand optimized for each architecture of interest. As the set of available accelerator hardware goes more diverse, a key challenge for developers of KS-DFT software is to maintain performance portability across a wide range of computational architectures. In this work, we examine a modular software design pattern which decouples the implementation details of performance critical kernels from the expression of high-level algorithmic workflows in a device-agnostic language such as C++; thus allowing for developers to target existing and emerging accelerator hardware within a single code base. We consider the efficacy of such a design pattern in the numerical integration of the XC potential by demonstrating its ability to achieve performance portability across a set of accelerator architectures which are representative of those on current and future U.S. Department of Energy Leadership Computing Facilities.

Possible Steps of the Carboxylation of Ribulose-1,5-biphosphate from Intermediates: 2,3-Enediol versus 1,2-Enol.

Ribulose 1,5-bisphosphate (RuBP) undergoes enolization to initiate fixation of atmospheric carbon dioxide in the plant carbon cycle. The known model assumes the binding of RuBP to the Rubisco active site with the subsequent formation of 2,3-enediol (2,3,4-trihydroxypent-2-ene-1,5-diyl diphosphate). In the present study, it is assumed that 1,2-enol (2,3,4-trihydroxypent-1-ene-1,5-diyl diphosphate) can be formed in the enolization step to initiate the carboxylation reaction. We have used Kohn–Sham density functional theory on WB97X-D3/Def2-TZVP levels to compare the reaction barriers in the two ways. We considered the pathways of carboxylation of 1/2-ene (mono/di)ol via the C1 and C2 carbons without taking into account the binding of RuBP to the magnesium ion. Calculations of Gibbs free energies confirm the equal probability of the formation of 2,3-enediol and 1,2-enol. Quantum–chemical modeling of enolization and carboxylation reactions supports the important role of the bridging water molecule and diphosphate groups, which provide proton transfer and lower reaction barriers. The results show that carbon dioxide fixation can occur without a magnesium ion, and binding with C1 can have a lower barrier (~12 kcal/mol) than with C2 (~23 kcal/mol).

How to Identify Lone Pairs, Van der Waals Gaps, and Metavalent Bonding Using Charge and Pair Density Methods: From Elemental Chalcogens to Lead Chalcogenides and Phase‐Change Materials

Lone pairs explain the structure of many molecular solids, as well as the chain‐like or layered structures encountered in many chalcogenide crystals. Such chalcogenides have enabled a plethora of applications, including phase‐change memories, thermoelectrics, topological insulators or photoconductors. In many of these, lone pairs also are invoked to explain the unconventional material properties. The presence of so‐called van der Waals gaps in layered chalcogenides and their low thermal conductivity have also been linked to lone pairs. However, for some of these systems, a second view of bonding has been proposed, where atoms are held together across the interlayer spacing by shared electrons. To clarify this situation, herein, several systems for which lone pairs have been frequently emphasized are reinvestigated theoretically. By comparing the charge and electron localization analysis in terms of a Hartree–Fock‐like pair density obtained from Kohn–Sham density functional theory (KS‐DFT), it is verified that the structure of several chalcogenides is governed by the presence of lone pairs, whereas others are not. As an example, crystalline Se is demonstrated to form a structure with two covalent bonds and a lone pair, whereas metavalenty bonds are the essential characteristics of crystalline Sb, crystalline Te being an intermediate case.