arXiv subjects

James W. Furness

Publications and source records attributed to James W. Furness.

18 recordsLinked to original sources

arXiv2026

Meta-generalized gradient approximation made in the Hartree gauge

In density functional theory (DFT), exact constraints, fundamental mathematical properties of the exchange-correlation (XC) energy and its underlying XC hole, along with paradigm systems such as the uniform electron gas and the hydrogen atom have been instrumental in developing exchange- correlation (XC) density functional approximations (DFAs). However, since the spatial XC energy density is not uniquely defined, its exact constraints can only be formulated within a chosen gauge and are therefore seldom utilized in DFA construction. Here, we propose a meta-generalized gradient approximation for the exchange energy, explicitly constructed within the Hartree gauge, using the hydrogen atom's exchange energy density for gauge alignment in core and asymptotic regions. By formulating DFAs at the XC energy density level, this approach expands reference datasets for machine learning and establishes a foundation for more accurate nonlocal density functionals requiring gauge alignment.

cond-mat.mtrl-sci↗

arXiv2025

Advances and challenges of SCAN and r2SCAN density functionals in transition-metal compounds

Transition-metal compounds (TMCs) with open-shell d-electrons are characterized by a complex interplay of lattice, charge, orbital, and spin degrees of freedom, giving rise to a diverse range of fascinating applications. Often exhibiting exotic properties, these compounds are commonly classified as correlated systems due to strong inter-electronic interactions called Hubbard U. This inherent complexity presents significant challenges to Kohn-Sham density functional theory (KS-DFT), the most widely used electronic structure method in condensed matter physics and materials science. While KS-DFT is, in principle, exact for the ground-state total energy, its exchange-correlation energy must be approximated in practice. The mean-field nature of KS implementations, combined with the limitations of current exchange-correlation density functional approximations, has led to the perception that DFT is inadequate for correlated systems, particularly TMCs. Consequently, a common workaround involves augmenting DFT with an on-site Hubbard-like U correction. In recent years, the strongly constrained and appropriately normed (SCAN) density functional, along with its refined variant r2SCAN, has achieved remarkable progress in accurately describing the structural, energetic, electronic, magnetic, and vibrational properties of TMCs, challenging the traditional perception of DFT's limitations. This review explores the design principles of SCAN and r2SCAN, highlights their key advancements in studying TMCs, explains the mechanisms driving these improvements, and addresses the remaining challenges in this evolving field.

cond-mat.mtrl-sci↗

arXiv2024

Coupling-Constant Averaged Exchange-Correlation Hole for He, Li, Be, N, Ne Atoms from CCSD

Accurate approximation of the exchange-correlation (XC) energy in density functional theory (DFT) calculations is essential for reliably modelling electronic systems. Many such approximations are developed from models of the XC hole; accurate reference XC holes for real electronic systems are crucial for evaluating the accuracy of these models however the availability of reliable reference data is limited to a few systems. In this study, we employ the Lieb optimization with a coupled cluster singles and doubles (CCSD) reference to construct accurate coupling-constant averaged XC holes, resolved into individual exchange and correlation components, for five spherically symmetric atoms: He, Li, Be, N, and Ne. Alongside providing a new set of reference data for the construction and evaluation of model XC holes, we compare our data against the exchange and correlation hole models of the established LDA and PBE density functional approximations. Our analysis confirms the established rationalization for the limitations of LDA and the improvement observed with PBE in terms of the hole depth and its long-range decay, demonstrated in real-space for the series of spherically-symmetric atoms.

physics.chem-ph↗

arXiv2023

Capturing the electron-electron cusp with the coupling-constant averaged exchange-correlation hole: A case study for Hooke's atoms

In density functional theory the exchange-correlation (XC) energy functional can be defined exactly through the coupling-constant ($λ$) averaged XC hole $\bar{n}_\text{xc}(\mathbf{r},\mathbf{r}')$, representing the probability depletion of finding an electron at $\mathbf{r}$ due to an electron at $\mathbf{r}$. Accurate knowledge of $\bar{n}_\text{xc}(\mathbf{r},\mathbf{r}')$ has been crucial for developing various XC energy density functional approximations and understanding their performance for real molecules and materials. However, there are very few systems for which accurate XC holes have been calculated, since this requires evaluating the one- and two-particle reduced density matrices for a reference wave function over a range of $λ$ whilst the electron density remains fixed at the physical ($λ=1$) density. Although the coupled-cluster singles and doubles (CCSD) method can yield exact results for a two-electron system in the complete basis set limit, it cannot capture the electron-electron cusp with commonly used finite basis sets. In this study, focusing on the Hooke's atom as a two-electron model system for which certain analytic solutions are known, we examine the effect of this cusp error on the XC hole calculated using CCSD. The Lieb functional is calculated at a range of coupling constants to determine the $λ$-integrated XC hole. Our results indicate that, for the Hooke's atoms, the error introduced by the description of the electron-electron cusp using Gaussian basis sets at the CCSD level is negligible compared to the basis set incompleteness error. The system-, angle- and coupling-constant-averaged XC hole is calculated using the same approach and provides a benchmark against which the Perdew-Burke-Ernzerhof (PBE) and local density approximation (LDA) XC hole models are assessed.

physics.chem-ph↗

arXiv2023

Comparative Density Functional Theory Study of Magnetic Exchange Coupling in Di-nuclear Transition Metal Complexes

Multi-center transition metal complexes (MCTMs) with magnetically interacting ions have been proposed as components for information processing devices and storage units. For any practical application of MCTMs as magnetic units, it is crucial to characterize their magnetic behavior, and in particular the isotropic magnetic exchange coupling, J, between its magnetic centers. Due to the large size of typical MCTMs, density functional theory (DFT) is the only practical electronic structure method for evaluating the J coupling. Here we assess the accuracy of different density functional approximations for predicting the magnetic couplings of seven di-metal transition metal complexes with known reliable experimental J couplings spanning from ferromagnetic to strong antiferromagnetic. The density functionals considered include global hybrid functionals which mix semilocal density functional approximations and exact exchange with a fixed admixing parameter, six local hybrid functionals where the admixing parameters are extended to be spatially dependent, the SCAN and r$^2$SCAN meta-generalized gradient approximations (GGAs), and two widely used GGAs. We found that global hybrids have a tendency to over-correct the error in magnetic coupling parameters from the Perdew-Burke-Ernzerhof (PBE) GGA, while the performance of local hybrid density functionals is scattered without a clear trend, suggesting that more efforts are needed for the extension from global to local hybrid density functionals for this particular property. The SCAN and r$^2$SCAN meta-GGAs are found to perform as well or better than the global and local hybrids on most tested complexes. We further analyze the charge density redistribution of meta-GGAs as well as global and local hybrid density functionals with respect to that of PBE, in connection to the self-interaction error (SIE) or delocalization error.

physics.chem-ph↗

arXiv2023

Emergence of competing electronic states from non-integer nuclear charges

Understanding many-electron phenomena with competing near-degenerate electronic states is of fundamental importance to chemistry and condensed matter physics. One of the most significant challenges for exploring such many-electron phenomena is the necessity for large system sizes in order to realize competing states, far beyond those practical for first-principles methods. Here, we show how allowing non-integer nuclear charges expands the space of computationally tractable electron systems that host competing electronic states. The emergence of competing electronic states from non-integer nuclear charges is exemplified in the simple 2-electron H_{2} molecule and used to examine the microscopic structure of doped quasi-1D cuprate chains, showing how non-integer nuclear charges can open a window for first-principles calculations of difficult many-electron phenomena.

cond-mat.str-el↗

arXiv2022

Testing the r$^2$SCAN density functional for the thermodynamic stability of solids with and without a van der Waals correction

A central aim of materials discovery is an accurate and numerically reliable description of thermodynamic properties, such as the enthalpies of formation and decomposition. The r$^2$SCAN revision of the strongly constrained and appropriately normed (SCAN) meta-generalized gradient approximation (meta-GGA) balances numerical stability with high general accuracy. To assess the r$^2$SCAN description of solid-state thermodynamics, we evaluate the formation and decomposition enthalpies, equilibrium volumes, and fundamental bandgaps of more than 1,000 solids using r$^2$SCAN, SCAN, and PBE, as well as two dispersion-corrected variants, SCAN+rVV10 and r$^2$SCAN+rVV10. We show that r$^2$SCAN achieves accuracy comparable to SCAN and often improves upon SCAN's already excellent accuracy. Whereas SCAN+rVV10 is often observed to worsen the formation enthalpies of SCAN, and makes no substantial correction to SCAN's cell volume predictions, r$^2$SCAN+rVV10 predicts marginally less-accurate formation enthalpies than r$^2$SCAN, and slightly more-accurate cell volumes than r$^2$SCAN. The average absolute errors in predicted formation enthalpies are found to decrease by a factor of 1.5 to 2.5 from the GGA level to the meta-GGA level. Smaller decreases in error are observed for decomposition enthalpies. For formation enthalpies r$^2$SCAN improves over SCAN for intermetallic systems. For a few classes of systems -- transition metals, intermetallics, weakly-bound solids, and enthalpies of decomposition into compounds -- GGAs are comparable to meta-GGAs. In total, r$^2$SCAN and r$^2$SCAN+rVV10 can be recommended as stable, general-purpose meta-GGAs for materials discovery.

cond-mat.mtrl-sci↗

arXiv2022

Workhorse minimally-empirical dispersion-corrected density functional, with tests for weakly-bound systems: r$^{2}$SCAN+rVV10

SCAN+rVV10 has been demonstrated to be a versatile van der Waals (vdW) density functional that delivers good predictions of both energetic and structural properties for many types of bonding. Recently, the r$^{2}$SCAN functional has been devised as a revised form of SCAN with improved numerical stability. In this work, we refit the rVV10 functional to optimize the r$^{2}$SCAN+rVV10 vdW density functional, and test its performance for molecular interactions and layered materials. Our molecular tests demonstrate that r$^{2}$SCAN+rVV10 outperforms its predecessor SCAN+rVV10 in both efficiency (numerical stability) and accuracy. This good performance is also found in lattice constant predictions. In comparison with benchmark results from higher-level theories or experiments, r$^{2}$SCAN+rVV10 yields excellent interlayer binding energies and phonon dispersions for layered materials.

cond-mat.mtrl-sci↗

arXiv2022

Exact constraints and appropriate norms in machine learned exchange-correlation functionals

Machine learning techniques have received growing attention as an alternative strategy for developing general-purpose density functional approximations, augmenting the historically successful approach of human designed functionals derived to obey mathematical constraints known for the exact exchange-correlation functional. More recently efforts have been made to reconcile the two techniques, integrating machine learning and exact-constraint satisfaction. We continue this integrated approach, designing a deep neural network that exploits the exact constraint and appropriate norm philosophy to deorbitalize the strongly constrained and appropriately normed SCAN functional. The deep neural network is trained to replicate the SCAN functional from only electron density and local derivative information, avoiding use of the orbital dependent kinetic energy density. The performance and transferability of the machine learned functional are demonstrated for molecular and periodic systems.

physics.chem-ph↗

arXiv2022

Sensitivity of the electronic and magnetic structures of cuprate superconductors to density functional approximations

We discuss the crystal, electronic, and magnetic structures of $\mathrm{La_{2-x}Sr_{x}CuO_{4}}$ (LSCO) for $x=0.0$ and $x=0.25$ employing 13 density functional approximations, representing the local, semi-local, and hybrid exchange-correlation approximations within the Perdew-Schmidt hierarchy. The meta-generalized gradient approximation (meta-GGA) class of functionals is found to perform well in capturing the key properties of LSCO, a prototypical high-temperature cuprate superconductor. In contrast, the local-spin-density approximation, GGA, and the hybrid density functional fail to capture the metal-insulator transition under doping.

cond-mat.supr-con↗

arXiv2021

Construction of meta-GGA functionals through restoration of exact constraint adherence to regularized SCAN functionals

The SCAN meta-GGA exchange-correlation functional [Phys. Rev. Lett. 115, 036402 (2015)] is constructed as a chemical environment-determined interpolation between two separate energy densities: one describes single orbital electron densities accurately, and another describes slowly-varying densities accurately. To conserve constraints known for the exact exchange-correlation functional, the derivatives of this interpolation vanish in the slowly-varying limit. While theoretically convenient, this choice introduces numerical challenges that degrade the functional's efficiency. We have recently reported a modification to the SCAN functional, termed r$^2$SCAN [J. Phys. Chem. Lett. 11, 8208 (2020)] that introduces two regularizations into SCAN which improve its numerical performance at the expense of not recovering the fourth order term of the slowly-varying density gradient expansion for exchange. Here we show the derivation of a progression of functionals (rSCAN, r++SCAN, r$^2$SCAN, and r$^4$SCAN) with increasing adherence to exact conditions while maintaining a smooth interpolation. The greater smoothness of r$^2$SCAN seems to lead to better general accuracy than the additional exact constraint of SCAN or r$^4$SCAN does.

cond-mat.mtrl-sci↗

arXiv2021

Reliable lattice dynamics from an efficient density functional

First principles predictions of lattice dynamics are of vital importance for a broad range of topics in materials science and condensed matter physics. The large-scale nature of lattice dynamics calculations and the desire to design novel materials with distinct properties demands that first principles predictions are accurate, transferable, efficient, and reliable for a wide variety of materials. In this work, we demonstrate that the recently constructed r2SCAN density functional meets this need for general systems by demonstrating phonon dispersions for typical systems with distinct chemical characteristics. The functional's performance opens a door for phonon-mediated materials discovery from first principles calculations.

cond-mat.mtrl-sci↗

arXiv2020

r2SCAN-D4: Dispersion corrected meta-generalized gradient approximation for general chemical applications

We combine a regularized variant of the strongly constrained and appropriately normed semilocal density functional [J. Sun, A. Ruzsinszky, and J. P. Perdew, Phys. Rev. Lett. 115, 036402 (2015)] with the latest generation semi-classical London dispersion correction. The resulting density functional approximation r2SCAN-D4 has the speed of generalized gradient approximations while approaching the accuracy of hybrid functionals for general chemical applications. We demonstrate its numerical robustness in real-life settings and benchmark molecular geometries, general main group and organo-metallic thermochemistry, as well as non-covalent interactions in supramolecular complexes and molecular crystals. Main group and transition metal bond lengths have errors of just 0.8%, which is competitive with hybrid functionals for main group molecules and outperforms them for transition metal complexes. The weighted mean absolute deviation (WTMAD2) on the large GMTKN55 database of chemical properties is exceptionally small at 7.5 kcal/mol. This also holds for metal organic reactions with an MAD of 3.3 kcal/mol. The versatile applicability to organic and metal-organic systems transfers to condensed systems, where lattice energies of molecular crystals are within chemical accuracy (errors <1 kcal/mol).

physics.chem-ph↗

arXiv2020

Accurate and numerically efficient r$^2$SCAN meta-generalized gradient approximation

The recently proposed rSCAN functional [J. Chem. Phys. 150, 161101 (2019)] is a regularized form of the SCAN functional [Phys. Rev. Lett. 115, 036402 (2015)] 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.

cond-mat.mtrl-sci↗

arXiv2020

First-Principles Calculation of Spin and Orbital Contributions to Magnetically Ordered Moments in Sr$_{2}$IrO$_{4}$

We show how an accurate first-principles treatment of the canted-antiferromagnetic ground state of Sr$_2$IrO$_4$, a prototypical $5d$ correlated spin-orbit coupled material, can be obtained without invoking any free parameters such as the Hubbard U or tuning the spin-orbit coupling strength. Our theoretically predicted iridium magnetic moment of 0.250 $μ_B$, canted by 12.6$^{\circ}$ off the a-axis, is in accord with experimental results. By resolving the magnetic moments into their spin and orbital components, we show that our theoretically obtained variation of the magnetic scattering amplitude $ $ as a function of the polarization angle is consistent with recent non-resonant magnetic x-ray scattering measurements. The computed value of the band gap (55 meV) is also in line with the corresponding experimental values. A comparison of the band structure to that of the cuprates suggests the presence of incommensurate charge-density wave phases in Sr$_{2}$IrO$_{4}$.

cond-mat.str-el↗

arXiv2018

Landscape of competing stripe and magnetic phases in cuprates

Realistic modeling of competing phases in complex quantum materials has proven extremely challenging. For example, much of the existing density-functional-theory-based first-principles framework fails in the cuprate superconductors. Various many-body approaches involve generic model Hamiltonians and do not account for the couplings between spin, charge, and lattice. Here, by deploying the recently constructed strongly-constrained-and-appropriately-normed density functional, we show how landscapes of competing stripe and magnetic phases can be addressed on a first-principles basis in YBa2Cu3O6 and YBa2Cu3O7 as archetype cuprate compounds. We invoke no free parameters such as the Hubbard U, which has been the basis of much of the cuprate literature. Lattice degrees of freedom are found to be crucially important in stabilizing the various phases.

cond-mat.supr-con↗

arXiv2018

Antiferromagnetic Ground State of La$_{2}$CuO$_{4}$: A Parameter-free Ab Initio Description

We show how an accurate first-principles treatment of the antiferromagnetic (AFM) ground state of La$_2$CuO$_4$ can be obtained without invoking any free parameters such as the Hubbard $U$. The magnitude and orientation of our theoretically predicted magnetic moment of $0.495 μ_{B}$ on Cu-sites along the (100) direction are in excellent accord with experimental results. The computed values of the band gap (1.00 eV) and the exchange-coupling (-138 meV) match the corresponding experimental values. We identify interesting band splittings below the Fermi energy, including an appreciable Hund's splitting of 1.25 eV. The magnetic form factor obtained from neutron scattering experiments is also well described by our calculations. Our study opens up a new pathway for first-principles investigations of electronic and atomic structures and phase diagrams of cuprates and other complex materials.

cond-mat.str-el↗

arXiv2015

Current Density-Functional Theory using meta-Generalized Gradient Exchange--Correlation Functionals

We present the self-consistent implementation of current-dependent (hybrid) meta generalized gradient approximation (mGGA) density functionals using London atomic orbitals. A previously proposed generalized kinetic energy density is utilized to implement mGGAs in the framework of Kohn--Sham current density-functional theory (KS-CDFT). A unique feature of the non-perturbative implementation of these functionals is the ability to seamlessly explore a wide range of magnetic fields up to 1 a.u. ($\sim 235000$T) in strength. CDFT functionals based on the TPSS and B98 forms are investigated and their performance is assessed by comparison with accurate CCSD(T) data. In the weak field regime magnetic properties such as magnetizabilities and NMR shielding constants show modest but systematic improvements over GGA functionals. However, in strong field regime the mGGA based forms lead to a significantly improved description of the recently proposed perpendicular paramagnetic bonding mechanism, comparing well with CCSD(T) data. In contrast to functionals based on the vorticity these forms are found to be numerically stable and their accuracy at high field suggests the extension of mGGAs to CDFT via the generalized kinetic energy density should provide a useful starting point for further development of CDFT approximations.

physics.chem-ph↗