Kohn-Sham Density Functional Theory Research Articles

Density functional theory beyond the Born–Oppenheimer approximation: exact mapping onto an electronically non-interacting Kohn–Sham molecule

This work presents an alternative, general, and in-principle exact extension of electronic Kohn–Sham density functional theory (KS-DFT) to the fully quantum-mechanical molecular problem. Unlike in existing multi-component or exact-factorization-based DFTs of electrons and nuclei, both nuclear and electronic densities are mapped onto a fictitious electronically non-interacting molecule (referred to as KS molecule), where the electrons still interact with the nuclei. Moreover, in the present molecular KS-DFT, no assumption is made about the mathematical form (exactly factorized or not) of the molecular wavefunction. By expanding the KS molecular wavefunction à la Born–Huang, we obtain a self-consistent set of ‘KS beyond Born–Oppenheimer’ electronic equations coupled to nuclear equations that describe nuclei interacting among themselves and with non-interacting electrons. An exact adiabatic connection formula is derived for the Hartree-exchange-correlation energy of the electrons within the molecule and, on that basis, a practical adiabatic density-functional approximation is proposed and discussed.

Sparse-Stochastic Fragmented Exchange for Large-Scale Hybrid Time-Dependent Density Functional Theory Calculations.

We extend our recently developed sparse-stochastic fragmented exchange formalism for ground-state near-gap hybrid DFT to calculate absorption spectra within linear-response time-dependent generalized Kohn-Sham DFT (LR-GKS-TDDFT) for systems consisting of thousands of valence electrons within a grid-based/plane-wave representation. A mixed deterministic/fragmented-stochastic compression of the exchange kernel, here using long-range explicit exchange functionals, provides an efficient method for accurate optical spectra. Both real-time propagation as well as frequency-resolved Casida-equation-type approaches for spectra are presented, and the method is applied to large molecular dyes.

Tucker Tensor Approach for Accelerating Fock Exchange Computations in a Real-Space Finite-Element Discretization of Generalized Kohn-Sham Density Functional Theory.

The evaluation of Fock exchange is often the computationally most expensive part of hybrid functional density functional theory calculations in a systematically improvable, complete basis. In this work, we employ a Tucker tensor based approach that substantially accelerates the evaluation of the action of Fock exchange by transforming three-dimensional convolutional integrals into a tensor product of one-dimensional convolution integrals. Our numerical implementation uses a parallelization strategy that balances the memory and communication bottlenecks, alongside overlapping compute and communication operations to enhance computational efficiency and parallel scalability. The accuracy and computational efficiency are demonstrated on various systems, including Pt clusters of various sizes and a TiO2 cluster with 3684 electrons.

A DFT calculation of electronic structures, magnetic, and thermoelectric properties of the new equiatomic quaternary Heusler alloy RuTiCrSi

AbstractThe stabilities, mechanical, electronic, and magnetic properties of the new equiatomic quaternary Heusler alloy (EQHA) RuTiCrSi were investigated using the Kohn‐Sham DFT (KS‐DFT) calculations within the generalized gradient approach (GGA), the modified version of the exchange potential introduced by Becke and Johnson in addition to the GGA (mBJ‐GGA), and Heyd‐Scuseria‐Ernzerhof (HSE06) hybrid functional. The ground‐state equilibrium energy reveals that the ferromagnetic with type 2 structure is the more stable. The RuTiCrSi is energetically, mechanically, and dynamically stable. The calculated self‐consistent total magnetic moment is 2 μB and agrees well with the Slater‐Pauling rule of . The electronic structure results from mBJ‐GGA and HSE06 functionals show a half‐metallic behavior. A high Curie temperature is obtained using the mean‐field approximation. The thermoelectric response was calculated using the semi‐classical Boltzmann transport equation under constant relaxation time. The maximum value of Seebeck coefficient is observed at the ambient temperature of . It was also observed that the power factor increases significantly as temperature rises. Therefore, the new EQHA RuTiCrSi seems to be a potential candidate for spintronic thermoelectric applications.

On-the-fly machine learned force fields for the study of warm dense matter: Application to diffusion and viscosity of CH

We develop a framework for on-the-fly machine learned force field (MLFF) molecular dynamics (MD) simulations of warm dense matter (WDM). In particular, we employ an MLFF scheme based on the kernel method and Bayesian linear regression, with the training data generated from the Kohn–Sham density functional theory (DFT) using the Gauss spectral quadrature method, within which we calculate energies, atomic forces, and stresses. We verify the accuracy of the formalism by comparing the predicted properties of warm dense carbon with recent Kohn–Sham DFT results in the literature. In so doing, we demonstrate that ab initio MD simulations of WDM can be accelerated by up to three orders of magnitude, while retaining ab initio accuracy. We apply this framework to calculate the diffusion coefficients and shear viscosity of CH at a density of 1 g/cm3 and temperatures in the range of 75 000–750 000 K. We find that the self- and inter-diffusion coefficients and the viscosity obey a power law with temperature, and that the diffusion coefficient results suggest a weak coupling between C and H in CH. In addition, we find agreement within standard deviation with previous results for C and CH but disagreement for H, demonstrating the need for ab initio calculations as presented here.

Transport coefficients of warm dense matter from Kohn-Sham density functional theory

Transport coefficients of warm dense matter from Kohn-Sham density functional theory

Consistent Analytical Second Derivatives of the Kohn-Sham DFT Energy in the Framework of the Conductor-Like Screening Model through Gaussian Charge Distributions.

The use of implicit solvation models such as the conductor-like screening model (COSMO) in quantum chemical calculations is very common, as both a rough estimate of solvation effects as well as a general tool for stabilizing ionic molecular structures. In order to generate a smooth potential energy surface as well as consistent gradients, it is necessary to apply the Gaussian charge model (GCM) for the COSMO charges. This work introduces an efficient implementation for consistent analytical second derivatives of the electronic energy with COSMO-GCM in the framework of the Kohn-Sham density functional theory. This is used to investigate the infrared spectroscopy of amino acids in aqueous solution, where the impact of pH on the molecular structure and vibrational spectra is examined. Furthermore, the structure and stability of selected all-metal aromatic cluster ions are assessed.

Machine learning nuclear orbital-free density functional based on Thomas–Fermi approach

Orbital-free density functional theory (DFT) is much more efficient than the orbital-dependent Kohn–Sham DFT due to the avoidance of the auxiliary one-body orbitals. The machine learning approach has been applied to build nuclear orbital-free DFT recently [Wu et al., Phys. Rev. C 105 (2022) L031303] and achieved more precise descriptions for nuclei than existing orbital-free DFTs. Here, improved machine learning nuclear orbital-free density functional is built by including the Thomas–Fermi approach as a basement. Performances of the functional are compared in detail with the ones based on the pure machine learning approach. It is found that with the Thomas–Fermi functional included, the machine-learning-based functional can achieve better performance in directly predicting the kinetic energies and in providing the ground-state properties by the self-consistent procedures.

Overcoming the barrier of orbital-free density functional theory for molecular systems using deep learning.

Orbital-free density functional theory (OFDFT) is a quantum chemistry formulation that has a lower cost scaling than the prevailing Kohn-Sham DFT, which is increasingly desired for contemporary molecular research. However, its accuracy is limited by the kinetic energy density functional, which is notoriously hard to approximate for non-periodic molecular systems. Here we propose M-OFDFT, an OFDFT approach capable of solving molecular systems using a deep learning functional model. We build the essential non-locality into the model, which is made affordable by the concise density representation as expansion coefficients under an atomic basis. With techniques to address unconventional learning challenges therein, M-OFDFT achieves a comparable accuracy to Kohn-Sham DFT on a wide range of molecules untouched by OFDFT before. More attractively, M-OFDFT extrapolates well to molecules much larger than those seen in training, which unleashes the appealing scaling of OFDFT for studying large molecules including proteins, representing an advancement of the accuracy-efficiency trade-off frontier in quantum chemistry.

Machine Learning K-Means Clustering in Interpolative Separable Density Fitting Algorithm: Advancing Accurate and Efficient Cubic-Scaling Density Functional Perturbation Theory Calculations within Plane Waves.

Density functional perturbation theory (DFPT) is a crucial tool for accurately describing lattice dynamics. The adaptively compressed polarizability (ACP) method reduces the computational complexity of DFPT calculations from O(N4) to O(N3) by combining the interpolative separable density fitting (ISDF) algorithm. However, the conventional QR factorization with column pivoting (QRCP) algorithm, used for selecting the interpolation points in ISDF, not only incurs a high cubic-scaling computational cost, O(N3), but also leads to suboptimal convergence. This convergence issue is particularly pronounced when considering the complex interplay between the external potential and atomic displacement in ACP-based DFPT calculations. Here, we present a machine learning K-means clustering algorithm to select the interpolation points in ISDF, which offers a more efficient quadratic-scaling O(N2) alternative to the computationally intensive cubic-scaling O(N3) QRCP algorithm. We implement this efficient K-means-based ISDF algorithm to accelerate plane-wave DFPT calculations in KSSOLV, which is a MATLAB toolbox for performing Kohn-Sham density functional theory calculations within plane waves. We demonstrate that this K-means algorithm not only offers comparable accuracy to QRCP in ISDF but also achieves better convergence for ACP-based DFPT calculations. In particular, K-means can remarkably reduce the computational cost of selecting the interpolation points by nearly 2 orders of magnitude compared to QRCP in ISDF.

Massively parallel implementation of iterative eigensolvers in large-scale plane-wave density functional theory

The Kohn-sham density functional theory (DFT) is a powerful method to describe the electronic structures of molecules and solids in condensed matter physics, computational chemistry and materials science. However, large and accurate DFT calculations within plane waves process a cubic-scaling computational complexity, which is usually limited by expensive computation and communication costs. The rapid development of high performance computing (HPC) on leadership supercomputers brings new opportunities for developing plane-wave DFT calculations for large-scale systems. Here, we implement parallel iterative eigensolvers in large-scale plane-wave DFT calculations, including Davidson, locally optimal block preconditioned conjugate gradient (LOBPCG), projected preconditioned conjugate gradient (PPCG) and the Chebyshev subspace iteration (CheFSI) algorithms, and analyze the performance of these algorithms in massively parallel plane-wave computing tasks. We adopt a two-level parallelization strategy that combines the message passing interface (MPI) with open multi-processing (OpenMP) parallel programming to handle data exchange and matrix operations in the construction and diagonalization of large-scale Hamiltonian matrix within plane waves. Numerical results illustrate that these iterative eigensolvers can scale up to 42,592 processing cores with high peak performance of 30% on leadship supercomputers to study the electronic structures of bulk silicon systems containing 10,648 atoms. Program summaryProgram Title: Plane wave density functional theory (PWDFT)CPC Library link to program files:https://doi.org/10.17632/c8v2mx5vn4.1Developer's repository link:https://bitbucket.org/berkeleylab/scalesLicensing provisions: BSD 3-clauseProgramming language: C++Nature of problem: PWDFT is used for electronic structure calculations based on Kohn-Sham density functional theory. The key challenge to address is a constrained energy minimization problem, which can also be formulated as a nonlinear eigenvalue problem. MPI/OpenMP-based approaches are employed to provide multi-core acceleration for the study of the chemical and material properties of larger-scale molecules and solids.Solution method: PWDFT implements self-consistent field (SCF) iterations and direct constrained minimization algorithms with various acceleration strategies. It is written in C++ and offers parallel acceleration based on MPI/OpenMP.

Stretching Bonds without Breaking Symmetries in Density Functional Theory.

Kohn-Sham density functional theory (KS-DFT) stands out among electronic structure methods due to its balance of accuracy and computational efficiency. However, to achieve chemically accurate energies, standard density functional approximations in KS-DFT often need to break underlying symmetries, a long-standing "symmetry dilemma". By employing fragment spin densities as the main variables in calculations (rather than total molecular densities, as in KS-DFT), we present an embedding framework in which this symmetry dilemma is understood and partially resolved. The spatial overlap between fragment densities is used as the main ingredient to construct a simple, physically motivated approximation to a universal functional of the fragment densities. This "overlap approximation" is shown to significantly improve semilocal KS-DFT binding energies of molecules without artificially breaking either charge or spin symmetries. The approach is shown to be applicable to covalently bonded molecules and to systems of the "strongly correlated" type.

Selectivity in Catalytic Asymmetric Formal [3 + 3] Annulation of 2-Enoyl-pyridine N-Oxide with Benzyl Methyl Ketone

The asymmetric formal [3 + 3] annulation process of (E)-2-(3-phenylacryloyl)pyridine N-oxide with benzyl methyl ketone was investigated. The possibility of a stereoselective outcome was checked using salts of natural amino acids, as well as chiral bifunctional derivatives containing amino groups and thiourea or squaramide fragments as organocatalysts. Different types of organocatalysts applied led to opposite enantiomers of 2-(3-oxo-4,5-diphenyl-cyclohex-1-en-yl)pyridine 1-oxide (up to 60% ee). Spectroscopic analysis of the isolated product and analysis of the reaction course was carried out, taking into account the obtained regio- and stereoselectivity. In order to verify the postulated results, calculations of the energy of the intermediate reaction products and the final product using the Kohn–Sham Density Functional Theory (KS-DFT) were made.

Variational Pair-Density Functional Theory: Dealing with Strong Correlation at the Protein Scale.

Multiconfigurational pair-density functional theory (MC-PDFT) offers a promising solution to the challenges faced by traditional density functional theory (DFT) in addressing molecular systems containing transition metals, open-shells, or strong correlations in general. By utilizing both the density and on-top pair-density, MC-PDFT can make use of a more flexible multiconfigurational wave function to capture the necessary static correlation, while the pair-density functional also includes the effect of dynamic correlation. So far, MC-PDFT has been used after a multiconfigurational self-consistent field (MCSCF) step, using the orbitals and configuration interaction coefficients from the converged MCSCF wave function to compute PDFT energies and properties. Here, instead, we propose to perform a direct optimization of the wave function using the pair-density functionals, resulting in a variational formulation of MC-PDFT. We derive the expressions for the wave function gradient and illustrate their similarity to standard MCSCF equations. Furthermore, we illustrate the accuracy on a set of singlet-triplet gaps as well as dissociation curves. Our findings highlight one of MC-PDFT's standout features: a reduced dependency on the active space size compared to conventional multiconfigurational wave function methodologies. Additionally, we show that the computational cost of MC-PDFT is potentially lower than MCSCF and often on-par with standard Kohn-Sham DFT, which is demonstrated by performing a MC-PDFT calculation of the entire ferredoxin protein with 1447 atoms and nearly 12000 basis functions.

Improved Self-consistent Field Iteration for Kohn–Sham Density Functional Theory

Improved Self-consistent Field Iteration for Kohn–Sham Density Functional Theory

Spectral approximation scheme for a hybrid, spin-density Kohn–Sham density-functional theory in an external (nonuniform) magnetic field and a collinear exchange-correlation energy

AbstractWe provide a mathematical justification of a spectral approximation scheme known as spectral binning for the Kohn–Sham spin density-functional theory in the presence of an external (nonuniform) magnetic field and a collinear exchange-correlation energy term. We use an extended density-only formulation for modeling the magnetic system. No current densities enter the description in this formulation, but the particle density is split into different spin components. By restricting the exchange-correlation energy functional to be of a collinear LSDA form, we prove a series of results which enable us to mathematically justify the spectral binning scheme using the method of Gamma-convergence, in conjunction with auxiliary steps involving recasting the electrostatic potentials, justifying the spectral approximation by making a spectral decomposition of the Hamiltonian and “linearizing" the latter Hamiltonian.

A comparison of QTP functionals against coupled-cluster methods for EAs of small organic molecules.

EA-EOM-CCSD electron affinities and LUMO energies of various Kohn-Sham density functional theory (DFT) methods are calculated for an a priori IP benchmark set of 64 small, closed-shell molecules. The purpose of these calculations was to investigate whether the QTP KS-DFT functionals can emulate EA-EOM-CC with only a mean-field approximation. We show that the accuracy of DFT-relative to CCSD-improves significantly when elements of correlated orbital theory are introduced into the parameterization to define the QTP family of functionals. In particular, QTP(02), which has only a single range separation parameter, provides results accurate to a MAD of <0.15eV for the whole set of 64 molecules compared to EA-EOM-CCSD, far exceeding the results from the non-QTP family of density functionals.

Development of a machine learning finite-range nonlocal density functional.

Kohn-Sham density functional theory has been the most popular method in electronic structure calculations. To fulfill the increasing accuracy requirements, new approximate functionals are needed to address key issues in existing approximations. It is well known that nonlocal components are crucial. Current nonlocal functionals mostly require orbital dependence such as in Hartree-Fock exchange and many-body perturbation correlation energy, which, however, leads to higher computational costs. Deviating from this pathway, we describe functional nonlocality in a new approach. By partitioning the total density to atom-centered local densities, a many-body expansion is proposed. This many-body expansion can be truncated at one-body contributions, if a base functional is used and an energy correction is approximated. The contribution from each atom-centered local density is a single finite-range nonlocal functional that is universal for all atoms. We then use machine learning to develop this universal atom-centered functional. Parameters in this functional are determined by fitting to data that are produced by high-level theories. Extensive tests on several different test sets, which include reaction energies, reaction barrier heights, and non-covalent interaction energies, show that the new functional, with only the density as the basic variable, can produce results comparable to the best-performing double-hybrid functionals, (for example, for the thermochemistry test set selected from the GMTKN55 database, BLYP based machine learning functional gives a weighted total mean absolute deviations of 3.33kcal/mol, while DSD-BLYP-D3(BJ) gives 3.28kcal/mol) with a lower computational cost. This opens a new pathway to nonlocal functional development and applications.

Combining stochastic density functional theory with deep potential molecular dynamics to study warm dense matter

In traditional finite-temperature Kohn–Sham density functional theory (KSDFT), the partial occupation of a large number of high-energy KS eigenstates restricts the use of first-principles molecular dynamics methods at extremely high temperatures. However, stochastic density functional theory (SDFT) can overcome this limitation. Recently, SDFT and the related mixed stochastic–deterministic density functional theory, based on a plane-wave basis set, have been implemented in the first-principles electronic structure software ABACUS [Q. Liu and M. Chen, Phys. Rev. B 106, 125132 (2022)]. In this study, we combine SDFT with the Born–Oppenheimer molecular dynamics method to investigate systems with temperatures ranging from a few tens of eV to 1000 eV. Importantly, we train machine-learning-based interatomic models using the SDFT data and employ these deep potential models to simulate large-scale systems with long trajectories. Subsequently, we compute and analyze the structural properties, dynamic properties, and transport coefficients of warm dense matter.

Widening of the fundamental gap in cluster GW for metal-molecular interfaces.

The GW approximation is very promising for an accurate first-principles description of charged excitations in single-molecule-metal interfaces. In the cluster approach for electronic transport across molecules, the infinite metal (with an adsorbed molecule) is replaced by a finite cluster whose volume should be incrementally increased to test the approach to the thermodynamic limit. Here we show that in GW, the approach to the thermodynamic limit will be much slower than in Kohn-Sham density-functional theory (DFT) because of the Coulomb interaction. To demonstrate this statement, we investigate spectral gaps in an ensemble of disordered sodium clusters in Kohn-Sham DFT, quasiparticle eigenvalue-self-consistent GW and Hartree-Fock. The fundamental gaps (i.e. difference between the lowest unoccupied and highest occupied level) in GW scale as N-1/3 on average, where N is the number of atoms. We demonstrate that this slow decrease artificially depletes the density of states at the Fermi level when the cluster is used to simulate a semi-infinite electrode. Therefore, the GW method cannot be taken as an out-of-the-box improvement of the DFT in cluster geometries, unless careful convergence checks are performed.