Vikram Gavini

Density functional theory (DFT) remains the most widely used electronic structure method. Although exact in principle, in practice, it relies on approximations to the exchange-correlation (XC) functional, which is known to be a unique functional of the electron density. Despite 50 years of active research, existing XC approximations remain far from general purpose chemical accuracy of various thermochemical and materials properties. In that light, the inverse DFT problem, of finding the exact XC potential corresponding to an accurate groundstate density, offers an insightful tool to understand the nature of the XC functional as well as aid in the development of more accurate functionals. However, solving the inverse DFT problem is fraught with several numerical challenges, such as non-uniqueness or spurious oscillations in the solution and non-convergence. We present invDFT as an open-source framework to address the outstanding challenges in inverse DFT and computed XC potentials solely from a target density. We do so by use of a systematically convergent differential finite-element basis—higher-order finite-elements for the Kohn-Sham orbitals and linear finite-elements for the XC potential—which together render the inverse DFT problem well-posed. We also employ necessary asymptotic corrections to the target density to avoid any unphysical oscillations in the resulting XC potential. We also employ several numerical and high-performance computing (HPC) advances that affords both efficiency and parallel scalability, on CPU-GPU hybrid architectures. We demonstrate the accuracy and scalability of invDFT using accurate full-configuration interaction (FCI) densities as well as model densities, ranging up to 100 electrons and spanning both weakly and strongly correlated molecules.

Density functional theory (DFT) remains the most widely used electronic structure method. Although exact in principle, in practice, it relies on approximations to the exchange-correlation (XC) functional, which is known to be a unique functional of the electron density. Despite 50 years of active research, existing XC approximations remain far from general purpose chemical accuracy of various thermochemical and materials properties. In that light, the inverse DFT problem, of finding the exact XC potential corresponding to an accurate groundstate density, offers an insightful tool to understand the nature of the XC functional as well as aid in the development of more accurate functionals. However, solving the inverse DFT problem is fraught with several numerical challenges, such as non-uniqueness or spurious oscillations in the solution and non-convergence. We present invDFT as an open-source framework to address the outstanding challenges in inverse DFT and computed XC potentials solely from a target density. We do so by use of a systematically convergent differential finite-element basis—higher-order finite-elements for the Kohn-Sham orbitals and linear finite-elements for the XC potential—which together render the inverse DFT problem well-posed. We also employ necessary asymptotic corrections to the target density to avoid any unphysical oscillations in the resulting XC potential. We also employ several numerical and high-performance computing (HPC) advances that affords both efficiency and parallel scalability, on CPU-GPU hybrid architectures. We demonstrate the accuracy and scalability of invDFT using accurate full-configuration interaction (FCI) densities as well as model densities, ranging up to 100 electrons and spanning both weakly and strongly correlated molecules.

Magnesium is the lightest structural alloy, yet its practical use is limited by its low ductility. Recent studies suggest ductility enhancement in dilute Mg alloys may stem from favorable solute modification ofpyramidal I/II screw dislocation core energy difference, activatingslip via a double cross-slip mechanism. This work conducts large-scale DFT calculations, reaching ~6,000 atoms, ofdislocation energetics in Mg and Mg-Y/Zn alloys. We find that relative solute strengthening effects on pyramidal I and II screw dislocation glide are crucial for cross-slip enhancement in Mg-Y, in contrast to prior investigations, that find solute-mediated dislocation-core energy modification as the main driver. Our predictions align with single- and poly-crystal experimental results and also capture the transition from pyramidal II to I preferred slip in Mg-Y.

Density functional theory (DFT) remains the most widely used electronic structure method. Although exact in principle, in practice, it relies on approximations to the exchange-correlation (XC) functional, which is known to be a unique functional of the electron density. Despite 50 years of active research, existing XC approximations remain far from general purpose chemical accuracy of various thermochemical and materials properties. In that light, the inverse DFT problem, of finding the exact XC potential corresponding to an accurate groundstate density, offers an insightful tool to understand the nature of the XC functional as well as aid in the development of more accurate functionals. However, solving the inverse DFT problem is fraught with several numerical challenges, such as non-uniqueness or spurious oscillations in the solution and non-convergence. We present invDFT as an open-source framework to address the outstanding challenges in inverse DFT and computed XC potentials solely from a target density. We do so by use of a systematically convergent finite-element basis and asymptotic corrections to the target density. We also employ several numerical and high-performance computing (HPC) advances that affords both efficiency and parallel scalability, on CPU-GPU hybrid architectures. We demonstrate the accuracy and scalability of invDFT using accurate full-configuration interaction (FCI) densities as well as model densities, ranging up to 100 electrons and spanning both weakly and strongly correlated molecules.

Unusually large energy errors of semi-local density functional approximations (DFAs) for molecules are often strongly reduced by using the Hartree-Fock (HF) electron density instead of the self-consistent DFA density. For reaction barriers and water clusters, some of us earlier found that HF-density functional theory (DFT) succeeds not because the HF density is accurate but due to the cancellation of negative functional-driven error (FE) by positive density-driven error (DE). Since DE, as defined here, is biased toward the self-consistent DFA density and against the HF density, the DE of the HF density is referred to as non-variational density over-localization (NVDO). In this work, we show that interaction energy errors in halogen- and chalcogen-bonded complexes in the B30 dataset are not dominated by density-driven error. Instead, HF-DFT again succeeds through FE-NVDO cancellation. Benchmark Kohn-Sham inversions of coupled-cluster densities for NH3⋯ClF, Cl-⋯ClF, Cl-⋯SF2, Cl-⋯SCF2, and Cl-⋯PF3 provide strong evidence for this cancellation. For additional complexes, we employ the long-range-corrected hybrid LCωPBE as a proxy for electron-transfer errors in the exact density. We also examine several self-interaction correction (SIC) methods and find significant improvement from FLOSIC. We point out common features of the density errors in the NH3⋯ClF and Cl-⋯ClF complexes and three transition states, arguing that significant density-driven errors of energy arise only from electron-transfer errors. We also highlight a common feature in our present and previous work: long bonds can lead to non-negligible functional-driven self-interaction error of the energy from otherwise accurate semi-local functionals in transition states, water clusters, and halogen or chalcogen bonds.

Contains some additional grpahs and data tables to support the results and conclusions made in original manuscript.

Contains some additional grpahs and data tables to support the results and conclusions made in original manuscript.

Density functional theory (DFT) is widely used to describe electronic structure in chemistry, physics, and materials science. Its accuracy is constrained by the exchange-correlation (XC) functional, which remains an approximation in all practical implementations. In contrast, wavefunction theory (WFT) offers a systematically improvable description of electron correlation, albeit at a higher computational cost. The complementary strengths of DFT and WFT have motivated efforts to connect the two. Historically, such connections have centered on total energies and electron densities, but recent advances have expanded these bridges to include XC potentials and energy densities. This review highlights strategies for translating quantities from WFT to DFT, with a focus on extracting XC potentials and energy densities from wavefunctions. Challenges in using finite basis sets, and potential solutions to this problem, are highlighted. These approaches offer insights into the structure of the exact XC functional and practical tools for developing next-generation approximations with improved accuracy and generalizability.

Magnesium is the lightest structural alloy, yet its practical use is limited by its low ductility. Recent studies suggest ductility enhancement in dilute Mg alloys may stem from favorable solute modification of pyramidal I/II screw dislocation core energy difference, activating slip via a double cross-slip mechanism. This work conducts large-scale DFT calculations, reaching ~6,000 atoms, of dislocation energetics in Mg and Mg-Y/Zn alloys. We find that relative solute strengthening effects on pyramidal I and II screw dislocation glide are crucial for cross-slip enhancement in Mg-Y, in contrast to prior investigations, that find solute-mediated dislocation-core energy modification as the main driver. Our predictions align with single- and poly-crystal experimental results and also capture the transition from pyramidal II to I preferred slip in Mg-Y.

Magnesium is the lightest structural alloy, yet its practical use is limited by its low ductility. Recent studies suggest ductility enhancement in dilute Mg alloys may stem from favorable solute modification of <c+a> pyramidal I/II screw dislocation core energy difference, activating <c+a> slip via a double cross-slip mechanism. This work conducts large-scale DFT calculations, reaching ~6,000 atoms, of <c+a> dislocation energetics in Mg and Mg-Y/Zn alloys. We find that relative solute strengthening effects on pyramidal I and II screw dislocation glide are crucial for cross-slip enhancement in Mg-Y, in contrast to prior investigations, that find solute-mediated dislocation-core energy modification as the main driver. Our predictions align with single- and poly-crystal experimental results and also capture the transition from pyramidal II to I preferred slip in Mg-Y.

Unusually large energy errors of semi-local density functional approximations (DFAs) for molecules are often strongly reduced by using the Hartree-Fock (HF) electron density instead of the self-consistent DFA density. For reaction barriers and water clusters, some of us earlier found that HF-DFT succeeds not because the HF density is accurate, but due to cancellation of negative functional-driven error (FE) by positive density-driven error (DE). Since DE, as defined here, is biased toward the self-consistent DFA density and against the HF density, the DE of the HF density is referred to as non-variational density over-localization (NVDO). In this work, we show that interaction energy errors in halogen- and chalcogen-bonded complexes in the B30 data set are not dominated by density-driven error. Instead, HF-DFT again succeeds through FE-NVDO cancellation. Benchmark Kohn-Sham inversions of coupled-cluster densities for NH3...ClF, Cl-...ClF, Cl-...SF2, Cl-...SCF2, and Cl-...PF3 provide strong evidence for this cancellation. For additional complexes, we employ the long-range-corrected hybrid LCωPBE as a proxy for electron-transfer errors in the exact density. We also examine several self-interaction correction (SIC) methods and find significant improvement from FLOSIC. We point out common features of the density errors in the NH3...ClF, Cl-...ClF complexes and three transition states, arguing that significant density-driven errors of energy arise only from electron-transfer errors. We also highlight a common feature in our present and previous work: Long bonds can lead to non-negligible functional-driven self-interaction error of the energy from otherwise-accurate semi-local functionals in transition states, water clusters, and halogen or chalcogen bonds.

Unusually large energy errors of semi-local density functional approximations (DFAs) for molecules are often strongly reduced by using the Hartree-Fock (HF) electron density instead of the self-consistent DFA density. For reaction barriers and water clusters, some of us earlier found that HF-DFT succeeds not because the HF density is accurate, but due to cancellation of negative functional-driven error (FE) by positive density-driven error (DE). Since DE, as defined here, is biased toward the self-consistent DFA density and against the HF density, the DE of the HF density is referred to as non-variational density over-localization (NVDO). In this work, we show that interaction energy errors in halogen- and chalcogen-bonded complexes in the B30 data set are not dominated by density-driven error. Instead, HF-DFT again succeeds through FE-NVDO cancellation. Benchmark Kohn-Sham inversions of coupled-cluster densities for NH3...ClF, Cl-...ClF, Cl-...SF2, Cl-...SCF2, and Cl-...PF3 provide strong evidence for this cancellation. For additional complexes, we employ the long-range-corrected hybrid LCωPBE as a proxy for electron-transfer errors in the exact density. We also examine several self-interaction correction (SIC) methods and find significant improvement from FLOSIC. We point out common features of the density errors in the NH3...ClF, Cl-...ClF complexes and three transition states, arguing that significant density-driven errors of energy arise only from electron-transfer errors. We also highlight a common feature in our present and previous work: Long bonds can lead to non-negligible functional-driven self-interaction error of the energy from otherwise-accurate semi-local functionals in transition states, water clusters, and halogen or chalcogen bonds.

Unusually large energy errors of semi-local density functional approximations (DFAs) for molecules are often strongly reduced by using the Hartree–Fock (HF) electron density instead of the self-consistent DFA density. For reaction barriers and water clusters, some of us earlier found that HF-DFT succeeds not because the HF density is accurate, but due to cancellation of negative functional-driven error (FE) by positive density-driven error (DE). Since DE, as defined here, is biased toward the self-consistent DFA density and against the HF density, the DE of the HF density is referred to as non-variational density over-localization (NVDO). In this work, we show that interaction energy errors in halogen- and chalcogen-bonded complexes in the B30 data set are not dominated by density-driven error. Instead, HF-DFT again succeeds through FE–DE cancellation. Benchmark Kohn–Sham inversions of coupled-cluster densities for NH3…ClF, Cl-…ClF, Cl-…SF2, Cl-...SCF2, and Cl-…PF3 provide strong evidence for this cancellation. For additional complexes, we employ the long-range-corrected hybrid LCωPBE as a proxy for electron-transfer errors in the exact density. We also examine several self-interaction correction (SIC) methods and find significant improvement from FLOSIC. We point out common features of the density errors in the NH3…ClF, Cl-…ClF complexes and three transition states, arguing that significant density-driven errors of energy arise only from electron-transfer errors. We also highlight a common feature in our present and previous work: long bonds can lead to non-negligible functional-driven self-interaction error of the energy from otherwise-accurate semi-local functionals in transition states, water clusters, and halogen or chalcogen bonds.

Abstract Twisted multilayer graphene, characterized by its moiré patterns arising from inter-layer rotational misalignment, serves as a rich platform for exploring quantum phenomena. Machine learning interatomic potentials (MLIPs) are a promising approach to model such systems. Our work develops a method to generate training and test datasets for fitting MLIPs that capture all possible misalignments but remain small-scale to facilitate efficient data generation and parameter estimation. To achieve this, we generate configurations with periodic boundary conditions suitable for density functional theory calculations, and then introduce an internal twist and shift within those supercell structures. Using this technique, supplemented with an active learning workflow, we fit an Atomic Cluster Expansion potential for simulating twisted multilayer graphene and test it for accuracy and robustness on a range of simulation tasks.

Finding accurate exchange-correlation (XC) functionals remains the defining challenge in density functional theory (DFT). Despite 40 years of active development, attaining general purpose chemical accuracy is still elusive with existing functionals. We present a data-driven pathway to learn the XC functional by using the exact density, XC energy, and XC potential. While the exact densities are obtained from accurate configuration interaction (CI), the exact XC energies and XC potentials are obtained via inverse DFT calculations on the CI densities. We demonstrate how simple neural network (NN)-based local density approximation (LDA) and generalized gradient approximation (GGA), trained on just five atoms and two molecules, provide remarkable improvement in total energies and densities. Particularly, the NN-based GGA functional attains similar accuracy as the higher rung SCAN meta-GGA on various thermochemistry datasets. These results underscore the promise of using the XC potential in modeling XC functionals and can pave the way for systematic learning of increasingly accurate XC functionals.

Semi-local functionals are often more accurate for energies when evaluated on the Hartree-Fock (HF) density than on their own self-consistent densities. HF densities are known to greatly reduce or overcorrect the charge-delocalization error associated with semi-local functionals. Over the last decade, this Hartree-Fock density functional theory (HF-DFT) has been systematized as density corrected DFT (DC-DFT), demonstrating remarkable success: improved chemical barrier heights, near chemical accuracy in water cluster binding energies, highly accurate interaction energies for halogenand chalcogen bonded systems, and more. For reaction barriers and water clusters, some of us found earlier that HFDFT works, not because the HF density is accurate but because of cancellation of negative functional-driven error (FE) by positive density-driven error (DE). In this work, we present evidence that interaction energy errors in halogen and chalcogen bonded molecular complexes in the B30 data set are not primarily driven by density errors, and that the success of HF-DFT for these weakly bonded molecular complexes results from a similar cancellation of FE by DE. Our benchmark Kohn-Sham inversion of the coupled cluster densities for NH3 · · ·ClF, Cl− · · ·SF2 and Cl− · · ·SCF2 presents strong evidence for this error cancellation. For most of the complexes, we employ proxies for the electron transfer in the exact density: the LCωPBE long-range-corrected hybrid and the r2SCAN50 global hybrid. We further investigate several self-interaction correction (SIC) methods for these weakly bonded systems, finding significant improvement from FLOSIC. In the conclusions section, we point out the common feature in our present and previous work: Long bonds can lead to non-negligible functional-driven self-interaction error of the energy from otherwise-accurate semi-local functionals in transition states, water clusters, and halogen or chalcogen bonds.

Twisted multilayer graphene, characterized by its moiré patterns arising from inter-layer rotational misalignment, serves as a rich platform for exploring quantum phenomena. Machine learning interatomic potentials (MLIPs) are a promising approach to model such systems. Our work develops a method to generate training and test datasets for fitting MLIPs that capture all possible misalignments but remain small-scale to facilitate efficient data generation and parameter estimation. To achieve this, we generate configurations with periodic boundary conditions suitable for DFT calculations, and then introduce an internal twist and shift within those supercell structures. Using this technique, supplemented with an active learning workflow, we fit an Atomic Cluster Expansion potential for simulating twisted multilayer graphene and test it for accuracy and robustness on a range of simulation tasks.

The aperiodic order of quasicrystals bridges the amorphous and crystalline regime, so it has remained unclear whether quasicrystals are metastable or stable phases of matter. Density functional theory is often used to evaluate thermodynamic stability, but quasicrystals are long-range aperiodic and their energies cannot be calculated using conventional ab initio methods. Here, we perform first-principles calculations on quasicrystal nanoparticles of increasing size, from which we can directly extrapolate their bulk and surface energies. Using this technique, we determine with high confidence that the icosahedral quasicrystals ScZn7.33 and YbCd5.7 are ground-state phases, thus revealing that translational symmetry is not a necessary condition for the zero-temperature stability of inorganic solids. Although we found the ScZn7.33 quasicrystal to be thermodynamically stable, we show on a mixed thermodynamic and kinetic phase diagram that its solidification from the melt is limited by nucleation, which illustrates why even stable materials may be kinetically challenging to grow. Our techniques broadly open the door to first-principles investigations into the structure–bonding–stability relationships of aperiodic materials. Traditionally, density functional theory could not describe quasicrystals as they lack translational symmetry. An ab initio approach now establishes that the quasicrystalline structures of ScZn7.33 and YbCd5.7 are true ground states.

The Ryabinkin-Kohut-Staroverov (RKS) and Kanungo-Zimmerman-Gavini (KZG) methods offer two approaches to find exchange-correlation (XC) potentials from ground state densities. The RKS method utilizes the one- and two-particle reduced density matrices to alleviate any numerical artifacts stemming from a finite basis (e.g., Gaussian- or Slater-type orbitals). The KZG approach relies solely on the density to find the XC potential by combining a systematically convergent finite-element basis with appropriate asymptotic correction on the target density. The RKS method, being designed for a finite basis, offers computational efficiency. The KZG method, using a complete basis, provides higher accuracy. In this work, we combine both methods to simultaneously afford accuracy and efficiency. In particular, we use the RKS solution as an initial guess for the KZG method to attain a significant 3-11× speedup. This work also presents a direct comparison of the XC potentials from the RKS and the KZG method and their relative accuracy on various weakly and strongly correlated molecules, using their ground state solutions from accurate configuration interaction calculations solved in a Slater orbital basis.

This work examines the impact of locally imposed constraints in Density Functional Theory (DFT). Using a metric referred to as the extent of violation index (EVI), we quantify how well exchange-correlation functionals adhere to local constraints. Applying EVIs to a diverse set of molecules for GGA functionals reveals constraint violations, particularly for semi-empirical functionals. We leverage EVIs to explore potential connections between these violations and errors in chemical properties. While no correlation is observed for atomization energies, a significant statistical correlation emerges between EVIs and total energies. Similarly, the analysis of reaction energies suggests weak positive correlations for specific constraints. However, definitive conclusions about error cancellation mechanisms cannot be made at this time. These observations revealed by EVIs may be useful for consideration when designing future generations of semilocal functionals.

We propose a computationally efficient and systematically convergent approach for elastodynamics simulations. We recast the second-order dynamical equation of elastodynamics into an equivalent first-order system of coupled equations, so as to express the solution in the form of a Magnus expansion. With any spatial discretization, it entails computing the exponential of a matrix acting upon a vector. We employ an adaptive Krylov subspace approach to inexpensively and accurately evaluate the action of the exponential matrix on a vector. In particular, we use an apriori error estimate to predict the optimal Krylov subspace size required for each time-step size. We show that the Magnus expansion truncated after its first term provides quadratic and superquadratic convergence in the time-step for nonlinear and linear elastodynamics, respectively. We demonstrate the accuracy and efficiency of the proposed method for one linear (linear cantilever beam) and three nonlinear (nonlinear cantilever beam , soft tissue elastomer , and hyperelastic rubber) benchmark systems. For a desired accuracy in energy, displacement, and velocity, our method allows for 10 − 100 × larger time-steps than conventional time-marching schemes such as Newmark- β method. Computationally, it translates to a ∼ 1000 × and ∼ 10 − 100 × speed-up over conventional time-marching schemes for linear and nonlinear elastodynamics, respectively.

Finding accurate exchange-correlation (XC) functionals remains the defining challenge in density functional theory (DFT). Despite 40 years of active development, the desired chemical accuracy is still elusive with existing functionals. We present a data-driven pathway to learn the XC functionals by utilizing the exact density, XC energy, and XC potential. While the exact densities are obtained from accurate configuration interaction (CI), the exact XC energies and XC potentials are obtained via inverse DFT calculations on the CI densities. We demonstrate how simple neural network (NN) based local density approximation (LDA) and generalized gradient approximation (GGA), trained on just five atoms and two molecules, provide remarkable improvement in total energies, densities, atomization energies, and barrier heights for hundreds of molecules outside the training set. Particularly, the NN-based GGA functional attains similar accuracy as the higher rung SCAN meta-GGA, highlighting the promise of using the XC potential in modeling XC functionals. We expect this approach to pave the way for systematic learning of increasingly accurate and sophisticated XC functionals.

The Ryabinkin-Kohut-Staroverov (RKS) and Kanungo-Zimmerman-Gavini (KZG) methods offer two approaches to find exchange-correlation (XC) potentials from ground state densities. The RKS method utilizes the one- and two-particle reduced density matrices to alleviate any numerical artifacts stemming from a finite basis (e.g., Gaussian- or Slater-type orbitals). The KZG approach relies solely on the density to find the XC potential, by combining a systematically convergent finite-element basis with appropriate asymptotic correction on the target density. The RKS method, being designed for a finite basis, offers computational efficiency. The KZG method, using a complete basis, provides higher accuracy. In this work, we combine both the methods to simultaneously afford accuracy and efficiency. In particular, we use the RKS solution as initial guess to the KZG method to attain a significant $3-11\times$ speedup. This work also presents a direct comparison of the XC potentials from the RKS and the KZG method and their relative accuracy on various weakly and strongly correlated molecules, using their ground state solutions from accurate configuration interaction calculations solved in a Slater orbital basis.

MiMiC is a framework for performing multiscale simulations in which loosely coupled external programs describe individual subsystems at different resolutions and levels of theory. To make it highly efficient and flexible, we adopt an interoperable approach based on a multiple-program multiple-data (MPMD) paradigm, serving as an intermediary responsible for fast data exchange and interactions between the subsystems. The main goal of MiMiC is to avoid interfering with the underlying parallelization of the external programs, including the operability on hybrid architectures (e.g., CPU/GPU), and keep their setup and execution as close as possible to the original. At the moment, MiMiC offers an efficient implementation of electrostatic embedding quantum mechanics/molecular mechanics (QM/MM) that has demonstrated unprecedented parallel scaling in simulations of large biomolecules using CPMD and GROMACS as QM and MM engines, respectively. However, as it is designed for high flexibility with general multiscale models in mind, it can be straightforwardly extended beyond QM/MM. In this article, we illustrate the software design and the features of the framework, which make it a compelling choice for multiscale simulations in the upcoming era of exascale high-performance computing.

Bolstered by recent calculations of exact functional-driven errors (FEs) and density-driven errors (DEs) of semilocal density functionals in the water dimer binding energy [ Kanungo, B. J. Phys. Chem. Lett. 2024, 15, 323–328], we investigate approximate FEs and DEs in neutral water clusters containing up to 20 monomers, charged water clusters, and alkali- and halide-water clusters. Our proxy for the exact density is r 2 SCAN 50, a 50% global hybrid of exact exchange with r 2 SCAN, which may be less correct than r 2 SCAN for the compact water monomer but importantly more correct for long-range electron transfers in the noncompact water clusters. We show that SCAN makes substantially larger FEs for neutral water clusters than r 2 SCAN, while both make essentially the same DEs. Unlike the case for barrier heights, these FEs are small in a relative sense and become large in an absolute sense only due to an increase in cluster size. SCAN@HF, short for SCAN evaluated on the Hartree–Fock (HF) density, produces a cancellation of errors that makes it chemically accurate for predicting the absolute binding energies of water clusters. Likewise, adding a long-range dispersion correction to r 2 SCAN@HF, as in the composite method HF-r 2 SCAN-DC4, makes its FE more negative than in r 2 SCAN@HF, permitting a near-perfect cancellation of FE and DE. r 2 SCAN by itself (and even more so, r 2 SCAN evaluated on the r 2 SCAN 50 density), is almost perfect for the energy differences between water hexamers, and thus probably also for liquid water away from the boiling point. Thus, the accuracy of composite methods like SCAN@HF and HF-r 2 SCAN-DC4 is not due to the HF density being closer to the exact density, but to a compensation of errors from its greater degree of localization. We also give an argument for the approximate reliability of this unconventional error cancellation for diverse molecular properties. Finally, we confirm this unconventional error cancellation for the SCAN description of the water trimer via Kohn–Sham inversion of the CCSD(T) density.

We propose a computationally efficient and systematically convergent approach for elastodynamics simulations. We recast the second-order dynamical equation of elastodynamics into an equivalent first-order system of coupled equations, so as to express the solution in the form of a Magnus expansion. With any spatial discretization, it entails computing the exponential of a matrix acting upon a vector. We employ an adaptive Krylov subspace approach to inexpensively and and accurately evaluate the action of the exponential matrix on a vector. In particular, we use an apriori error estimate to predict the optimal Kyrlov subspace size required for each time-step size. We show that the Magnus expansion truncated after its first term provides quadratic and superquadratic convergence in the time-step for nonlinear and linear elastodynamics, respectively. We demonstrate the accuracy and efficiency of the proposed method for one linear (linear cantilever beam) and three nonlinear (nonlinear cantilever beam, soft tissue elastomer, and hyperelastic rubber) benchmark systems. For a desired accuracy in energy, displacement, and velocity, our method allows for $10-100\times$ larger time-steps than conventional time-marching schemes such as Newmark-$β$ method. Computationally, it translates to a $\sim$$1000\times$ and $\sim$$10-100\times$ speed-up over conventional time-marching schemes for linear and nonlinear elastodynamics, respectively.

Bolstered by recent calculations of exact functional-driven errors (FEs) and density-driven errors (DEs) of semi-local density functionals in the water dimer binding energy [Kanungo et al., J. Phys. Chem. Lett. 2023, 15, 323], we investigate approximate FEs and DEs in neutral water clusters containing up to 20 monomers, charged water clusters, and alkali- and halide-water clusters. Our proxy for the exact density is r2SCAN50, a 50% global hybrid of exact exchange with r2SCAN, which may be less correct than r2SCAN for the compact water monomer but importantly more correct for long-range electron transfers in the non-compact water clusters. We show that SCAN makes substantially larger FEs for neutral water clusters than r2SCAN, while both make essentially the same DEs. Unlike the case for barrier heights, these FEs are small in a relative sense, and become large in an absolute sense only due to an increase in cluster size. SCAN@HF produces a cancellation of errors that makes it chemically accurate for predicting the absolute binding energies of water clusters. Likewise, adding a long-range dispersion correction to r2SCAN@HF, as in the composite method HF-r2SCAN-DC4, makes its FE more negative than in r2SCAN@HF, permitting a near-perfect cancellation of FE and DE. r2SCAN by itself (and even more so, r2SCAN evaluated on the r2SCAN50 density), is almost perfect for the energy differences between water hexamers, and thus probably also for liquid water away from the boiling point. Thus the accuracy of composite methods like SCAN@HF and HF-r2SCAN-DC4 is not due to the HF density being closer to the exact density, but to a compensation of errors from its greater degree of localization. We also give an argument for the approximate reliability of this unconventional error cancellation for diverse molecular properties. Finally, we confirm this unconventional error cancellation for the SCAN description of the water trimer via Kohn-Sham inversion of the CCSD(T) density.

High Resolution Image Download MS PowerPoint Slide 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 TiO 2 cluster with 3684 electrons.

Are quasicrystals stable or metastable? Density functional theory (DFT) is often used to evaluate thermodynamic stability, but quasicrystals are long-range aperiodic and their energies cannot be calculated using conventional ab initio methods. Here, we perform first-principles calculations on quasicrystal nanoparticles of increasing sizes, from which we can directly extrapolate their bulk and surface energies. Using this technique, we determine with high confidence that the icosahedral quasicrystals ScZn7.33 and YbCd5.7 are ground-state phases--revealing that translational symmetry is not a necessary condition for the T = 0 K stability of inorganic solids. Although we find the ScZn7.33 quasicrystal to be thermodynamically stable, we show on a mixed thermodynamic and kinetic phase diagram that its solidification from the melt is nucleation-limited, which illustrates why even stable materials may be kinetically challenging to grow. Our techniques here broadly open the door to first-principles investigations into the structure-bonding-stability relationships of aperiodic materials.

This work introduces Extent of Violation Indices (EVIs), a novel metric for quantifying how well exchange-correlation functionals adhere to local conditions. Applying EVIs to a diverse set of molecules for GGA functionals reveals widespread violations, particularly for semi-empirical functionals. We leverage EVIs to explore potential connections between these violations and errors in chemical properties. While no correlation is observed for atomization energies, a link emerges between EVIs and total energies. Similarly, the analysis of reaction energies suggests weak positive correlations for specific conditions, but definitive conclusions about error cancellation require advancements in both functional accuracy and our understanding of cancellation mechanisms. Overall, this study highlights EVIs as a powerful tool for analyzing functional behavior and adherence to local conditions, paving the way for future research to fully elucidate the impact of violations on energy errors.

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 3-dimensional convolutional integrals into a tensor product of 1-dimensional convolution integrals. Our numerical implementation uses a parallelization strategy that balances the memory and communication bottlenecks, alongside overalapping compute and communication operations to enhance computational efficiency and parallel scalability. The accuracy and computational efficiency is demonstrated on various systems, including Pt clusters of various sizes and a $\text{TiO}_{\text{2}}$ cluster with 3,684 electrons.

Energy barriers, which control the rates of chemical reactions, are seriously underestimated by computationally efficient semilocal approximations for the exchange-correlation energy. The accuracy of a semilocal density functional approximation is strongly boosted for reaction barrier heights by evaluating that approximation non-self-consistently on Hartree–Fock electron densities, which has been known for ∼30 years. The conventional explanation is that the Hartree–Fock theory yields the more accurate density. This work presents a benchmark Kohn–Sham inversion of accurate coupled-cluster densities for the reaction H 2 + F → HHF → H + HF and finds a strong, understandable cancellation between positive (excessively overcorrected) density-driven and large negative functional-driven errors (expected from stretched radical bonds in the transition state) within this Hartree–Fock density functional theory. This confirms earlier conclusions ( Kaplan, A. D., et al. J. Chem. Theory Comput. 2023, 19, 532−543) based on 76 barrier heights and three less reliable, but less expensive, fully nonlocal density functional proxies for the exact density.

Ab initio electronic-structure has remained dichotomous between achievable accuracy and length-scale. Quantum many-body (QMB) methods realize quantum accuracy but fail to scale. Density functional theory (DFT) scales favorably but remains far from quantum accuracy. We present a framework that breaks this dichotomy by use of three interconnected modules: (i) invDFT: a methodological advance in inverse DFT linking QMB methods to DFT; (ii) MLXC: a machine-learned density functional trained with invDFT data, commensurate with quantum accuracy; (iii) DFT-FE-MLXC: an adaptive higher-order spectral finite-element (FE) based DFT implementation that integrates MLXC with efficient solver strategies and HPC innovations in FE-specific dense linear algebra, mixed-precision algorithms, and asynchronous compute-communication. We demonstrate a paradigm shift in DFT that not only provides an accuracy commensurate with QMB methods in ground-state energies, but also attains an unprecedented performance of 659.7 PFLOPS (43.1% peak FP64 performance) on 619,124 electrons using 8,000 GPU nodes of Frontier supercomputer.

The conventional approaches to the inverse density functional theory problem typically assume nondegeneracy of the Kohn–Sham (KS) eigenvalues, greatly hindering their use in open-shell systems. We present a generalization of the inverse density functional theory problem that can seamlessly admit degenerate KS eigenvalues. Additionally, we allow for fractional occupancy of the Kohn–Sham orbitals to also handle noninteracting ensemble-v-representable densities, as opposed to just noninteracting pure-v-representable densities. We present the exact exchange-correlation (XC) potentials for six open-shell systems─four atoms (Li, C, N, and O) and two molecules (CN and CH 2 )─using accurate ground-state densities from configuration interaction calculations. We compare these exact XC potentials with model XC potentials obtained using nonlocal (B3LYP, SCAN0) and local/semilocal (SCAN, PBE, PW92) XC functionals. Although the relative errors in the densities obtained from these DFT functionals are of O (10 –3 to 10 –2 ), the relative errors in the model XC potentials remain substantially large─ O (10 –1 to 10 0 ).

Abstract Electronic structure calculations have been instrumental in providing many important insights into a range of physical and chemical properties of various molecular and solid-state systems. Their importance to various fields, including materials science, chemical sciences, computational chemistry, and device physics, is underscored by the large fraction of available public supercomputing resources devoted to these calculations. As we enter the exascale era, exciting new opportunities to increase simulation numbers, sizes, and accuracies present themselves. In order to realize these promises, the community of electronic structure software developers will however first have to tackle a number of challenges pertaining to the efficient use of new architectures that will rely heavily on massive parallelism and hardware accelerators. This roadmap provides a broad overview of the state-of-the-art in electronic structure calculations and of the various new directions being pursued by the community. It covers 14 electronic structure codes, presenting their current status, their development priorities over the next five years, and their plans towards tackling the challenges and leveraging the opportunities presented by the advent of exascale computing.