arXiv subjects

Koblar A. Jackson

Publications and source records attributed to Koblar A. Jackson.

13 recordsLinked to original sources

arXiv2026

A Wannier-first approach for extended chiral systems

We present a real-space formulation of DFT for extended systems in which localized Wannier-like functions are constructed directly from localized Gaussian basis functions without explicitly computing canonical Bloch-like states during the self-consistent cycle. Building on the formalism of Pederson and Lin [Phys. Rev. B \textbf{35}, 2273 (1987)], a variational set of Wannier-like functions is generated self-consistently within a finite Wannier domain and used to construct the charge density, electrostatic potential, and per cell total energy of the extended system. The occupied space can be determined entirely from the Wannier-like functions. Electronic band structures can be recovered in a post-processing step by solving the full Hamiltonian in a Bloch-like basis constructed from Gaussian orbitals. A key feature of the method is that it can incorporate combined translation--rotation, or screw, symmetries, enabling efficient simulations of chiral and helical systems with finite twist angles at essentially the same computational cost as systems described by pure translational symmetry. The approach is validated through calculations on linear and twisted $\mathrm{{-}C{\equiv}C{-}}$ and $\mathrm{{-}Li{-}F{-}}$ chains, as well as graphene, where total energies and band structures show excellent agreement with reference periodic calculations. To illustrate the ability of the method to treat three-dimensional systems, it is further applied to AA graphite, in which carbon atoms in adjacent graphene layers are aligned directly above one another, as well as helically stacked AA graphite structures. The Wannier-first framework provides a practical route for treating extended systems with nontrivial translational, rotational, and screw symmetries, and provides a natural foundation for the implementation of orbital-dependent functionals such as the Perdew--Zunger self-interaction correction.

cond-mat.mtrl-sci↗

arXiv2025

Universal Approach for Determining Multi-Dimensional Anharmonic Vibrations from Electronic Quantum Methods

We present a simple and efficient method to incorporate anharmonic effects in the vibrational \textcolor{black}{analyses} of molecules within density functional theory (DFT) calculations. This approach is closely related to the traditional vibrational \textcolor{black}{configuration} interaction (VCI) technique, which uses the harmonic oscillator wavefunctions as the basis. In our implementation, we employ Gaussian-type orbitals (GTOs), with polynomial prefactors, as the basis set to evaluate the anharmonic Hamiltonian. Although these basis functions are non-orthogonal, the matrix elements such as overlap, kinetic energy terms, and position moments can be evaluated analytically. The terms in the Hamiltonian due to the anharmonic potentials are numerically calculated on a Hermite-Quadrature grid. The potentials can be evaluated using any electronic structure method. This framework enables us to accurately calculate the anharmonicity-corrected vibrational frequencies, the fundamental frequencies, and the corrections to bond lengths in diatomic molecules. This method is also generalized to handle coupled anharmonic oscillators, which is essential to model more complex phenomena such as nitrogen tunneling in the umbrella mode of ammonia (NH$_3$) and Fermi resonances in carbon dioxide (CO$_2$).

physics.chem-ph↗

arXiv2025

Atomic Ionization: sd energy imbalance and Perdew-Zunger self-interaction correction energy penalty in 3d atoms

To accurately describe the energetics of transition metal systems, density functional approximations (DFAs) must provide a balanced description of s- and d- electrons. One measure of this is the sd transfer error, which has previously been defined as $E(\mathrm{3d}^{n-1}\mathrm{4s}^{1}) - E(\mathrm{3d}^{n-2}\mathrm{4s}^{2})$. Theoretical concerns have been raised about this definition due to its evaluation of excited-state energies using ground-state DFAs. A more serious concern appears to be strong correlation in the ${4s}^2$ configuration. Here we define a ground-state measure of the sd energy imbalance, based on the errors of s- and d-electron second ionization energies of the 3d atoms, that effectively circumvents the aforementioned problems. We find an improved performance as we move from LSDA to PBE to r$^2$SCAN for first-row transition metal atoms. However, we find large (~ 2 eV) ground-state sd energy imbalances when applying a Perdew-Zunger 1981 self-interaction correction. This is attributed to an "energy penalty" associated with the noded 3d orbitals. A local scaling of the self-interaction correction to LSDA results in a balance of s- and d-errors.

physics.chem-ph↗

arXiv2022

Study of self-interaction-errors in barrier heights using locally scaled and Perdew-Zunger self-interaction methods

We study the effect of self-interaction errors on the barrier heights of chemical reactions. For this purpose we use the well-known Perdew-Zunger [J. P. Perdew and A. Zunger, Phys. Rev. B, {\bf 23}, 5048 (1981)] self-interaction-correction (PZSIC), as well as two variations of the recently developed, locally scaled self-interaction correction (LSIC) [R. R. Zope \textit{et al.}, J. Chem. Phys. {\bf 151}, 214108 (2019)] to study the barrier heights of the BH76 benchmark dataset. Our results show that both PZSIC and especially the LSIC methods improve the barrier heights relative to the local density approximation (LDA). The version of LSIC that uses the iso-orbital indicator $z$ as a scaling factor gives a more consistent improvement than an alternative version that uses an orbital-dependent factor $w$ based on the ratio of orbital densities to the total electron density. We show that LDA energies evaluated using the self-consistent and self-interaction-free PZSIC densities can be used to assess density-driven errors. The LDA reaction barrier errors for the BH76 set are found to contain significant density-driven errors for all types of reactions contained in the set, but the corrections due to adding SIC to the functional are much larger than those stemming from the density for the hydrogen transfer reactions and of roughly equal size for the non-hydrogen transfer reactions.

physics.chem-ph↗

arXiv2020

Self-Interaction Correction in Water-Ion Clusters

We study the importance of self-interaction errors in density functional approximations for various water-ion clusters. We have employed the Fermi-Löwdin orbital self-interaction correction (FLOSIC) method in conjunction with LSDA, PBE, and SCAN to describe binding energies of hydrogen-bonded water-ion clusters, \textit{i.e.}, water-hydronium, water-hydroxide, water-halide, as well as non-hydrogen-bonded water-alkali clusters. In the hydrogen-bonded water-ion clusters, the building blocks are linked by hydrogen atoms, although the links are much stronger and longer-ranged than the normal hydrogen bonds between water molecules, because the monopole on the ion interacts with both permanent and induced dipoles on the water molecules. We find that self-interaction errors overbind the hydrogen-bonded water-ion clusters and that FLOSIC reduces the error and brings the binding energies into closer agreement with higher-level calculations. The non-hydrogen-bonded water-alkali clusters are not significantly affected by self-interaction errors. Self-interaction corrected PBE predicts the lowest mean unsigned error in binding energies ($\leq$ 50 meV/\ce{H2O}) for hydrogen-bonded water-ion clusters. Self-interaction errors are also largely dependent on the cluster size, and FLOSIC does not accurately capture the subtle variation in all clusters, indicating the need for further refinement.

physics.chem-ph↗

arXiv2020

Study of self-interaction errors in density functional predictions of dipole polarizabilities and ionization energies of water clusters using Perdew-Zunger and locally scaled self-interaction corrected methods

We studied the effect of self-interaction error (SIE) on the static dipole polarizabilities of water clusters modelled with three increasingly sophisticated, non-empirical density functional approximations (DFAs), viz. the local spin density approximation (LDA), the Perdew-Burke-Ernzherof (PBE) generalized-gradient approximation (GGA), and the strongly constrained and appropriately normed (SCAN) meta-GGA, using the Perdew-Zunger self-interaction-correction (PZ-SIC) energy functional in the Fermi-Löwdin orbital SIC (FLO-SIC) framework. Our results show that while all three DFAs overestimate the cluster polarizabilities, the description systematically improves from LDA to PBE to SCAN. The self-correlation free SCAN predicts polarizabilities quite accurately with a mean absolute error (MAE) of 0.58 Bohr$^3$ with respect to coupled cluster singles and doubles (CCSD) values. Removing SIE using PZ-SIC correctly reduces the DFA polarizabilities, but over-corrects, resulting in underestimated polarizabilities in SIC-LDA, -PBE, and -SCAN. Finally, we applied a recently proposed local-scaling SIC (LSIC) method using a quasi self-consistent scheme and using the kinetic energy density ratio as an iso-orbital indicator. The results show that the LSIC polarizabilities are in excellent agreement with mean absolute error of 0.08 Bohr$^3$ for LSIC-LDA and 0.06 Bohr$^3$ for LSIC-PBE with most recent CCSD polarizabilities. Likewise, the ionization energy estimates as an absolute of highest occupied energy eigenvalue predicted by LSIC are also in excellent agreement with CCSD(T) ionization energies with MAE of 0.4 eV for LSIC-LDA and 0.04 eV for LSIC-PBE. The LSIC-LDA predictions of ionization energies are comparable to the reported GW ionization energies while the LSIC-PBE ionization energies are more accurate than reported GW results.

physics.chem-ph↗

arXiv2020

The Fermi-Löwdin self-interaction correction for ionization energies of organic molecules

(Semi)-local density functional approximations (DFAs) suffer from self-interaction error (SIE). When the first ionization energy (IE) is computed as the negative of the highest-occupied orbital (HO) eigenvalue, DFAs notoriously underestimate them compared to quasi-particle calculations. The inaccuracy for the HO is attributed to SIE inherent in DFAs. We assessed the IE based on Perdew-Zunger self-interaction corrections on 14 small to moderate-sized organic molecules relevant in organic electronics and polymer donor materials. Though self-interaction corrected DFAs were found to significantly improve the IE relative to the uncorrected DFAs, they overestimate. However, when the self-interaction correction is interiorly scaled using a function of the iso-orbital indicator zσ, only the regions where SIE is significant get a correction. We discuss these approaches and show how these methods significantly improve the description of the HO eigenvalue for the organic molecules.

physics.chem-ph↗

arXiv2020

A Step in the Direction of Resolving the Paradox of Perdew-Zunger Self-interaction Correction. II. Gauge Consistency of the Energy Density at Three Levels of Approximation

The Perdew-Zunger(PZ) self-interaction correction (SIC) was designed to correct the one-electron limit of any approximate density functional for the exchange-correlation (xc) energy, while yielding no correction to the exact functional. Unfortunately, it spoils the slowly-varying-in-space limits of the uncorrected approximate functionals, where those functionals are right by construction. The right limits can be restored by locally scaling down the energy density of the PZ SIC in many-electron regions, but then a spurious correction to the exact functional would be found unless the self-Hartree and exact self-xc terms of the PZ SIC energy density were expressed in the same gauge. Only the local density approximation satisfies the same-gauge condition for the energy density, which explains why the recent local-scaling SIC (LSIC) is found here to work excellently for atoms and molecules only with this basic approximation, and not with the more advanced generalized gradient approximations (GGAs) and meta-GGAs, which lose the Hartree gauge via simplifying integrations by parts. The transformation of energy density that achieves the Hartree gauge for the exact xc functional can also be applied to approximate functionals. Doing so leads to a simple scaled-down self-interaction (sdSIC) correction that is typically much more accurate than PZ SIC in tests for many molecular properties (including equilibrium bond lengths). The present work shows unambiguously that the largest errors of PZ SIC applied to standard functionals at three levels of approximation can be removed by restoring their correct slowly-varying-density limits. It also confirms the relevance of these limits to atoms and molecules.

physics.chem-ph↗

arXiv2020

Importance of self-interaction-error removal in density functional calculations on water cluster anions

Accurate description of the excess charge in water cluster anions is challenging for standard semi-local and (global) hybrid density functional approximations (DFAs). Using the recent unitary invariant implementation of the Perdew-Zunger self-interaction correction (SIC) method using Fermi-Löwdin orbitals, we assess the effect of self-interaction error on the vertical detachment energies of water clusters anions with the local spin density approximation (LSDA), Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation, and the strongly constrained and appropriately normed (SCAN) meta-GGA functionals. Our results show that for the relative energies of isomers with respect to reference CCSD(T) values, the uncorrected SCAN functional has the smallest deviation of 21 meV, better than that for the MP2 method. The performance of SIC-SCAN is comparable to that of MP2 and is better than SIC-LSDA and SIC-PBE, but it reverses the ordering of the two lowest isomers for water hexamer anions. Removing self interaction error (SIE) corrects the tendency of LSDA, PBE, and SCAN to over-bind the extra electron. The vertical detachment energies (VDEs) of water cluster anions, obtained from the total energy differences of corresponding anion and neutral clusters, are significantly improved by removing self-interaction and are better than the hybrid B3LYP functional, but fall short of MP2 accuracy. Removing SIE results in substantial improvement in the position of the eigenvalue of the extra electron. The negative of the highest occupied eigenvalue after SIC provides an excellent approximation to the VDE, especially for SIC-PBE where the mean absolute error with respect to CCSD(T) is only 17 meV, the best among all approximations compared in this work.

physics.chem-ph↗

arXiv2019

A step in the direction of resolving the paradox of Perdew-Zunger self-interaction correction

Self-interaction (SI) error, which results when exchange-correlation contributions to the total energy are approximated, limits the reliability of many density functional approximations. The Perdew-Zunger SI correction (PZSIC), when applied in conjunction with the local spin density approximation (LSDA), improves the description of many properties, but overall, this improvement is limited. Here we propose a modification to PZSIC that uses an iso-orbital indicator to identify regions where local SI corrections should be applied. Using this local-scaling SIC (LSIC) approach with LSDA, we analyze predictions for a wide range of properties including, for atoms, total energies, ionization potentials, and electron affinities, and for molecules, atomization energies, dissociation energy curves, reaction energies, and reaction barrier heights. LSIC preserves the results of PZSIC-LSDA for properties where it is successful and provides dramatic improvements for many of the other properties studied. Atomization energies calculated using LSIC are better than those of the Perdew, Burke, and Ernzerhof (PBE) generalized gradient approximation (GGA) and close to those obtained with the Strongly Constrained and Appropriately Normed (SCAN) meta-GGA. LSIC also restores the uniform gas limit for the exchange energy that is lost in PZSIC-LSDA. Further performance improvements may be obtained by an appropriate combination or modification of the local scaling factor and the particular density functional approximation.

cond-mat.mtrl-sci↗

arXiv2019

Fermi-Löwdin orbital self-interaction correction using the strongly constrained and appropriately normed meta-GGA functional

Despite the success of density functional approximations (DFAs) in describing the electronic properties of many-electron systems, the most widely used approximations suffer from self-interaction errors (SIE) that limit their predictive power. Here we describe the effects of removing SIE from the strongly constrained and appropriately normed (SCAN) meta-generalized gradient approximation (GGA) using the Fermi-Lowdin Orbital Self-Interaction Correction (FLOSIC) method. FLOSIC is a size-extensive implementation of the Perdew-Zunger self-interaction correction (PZ-SIC) formalism. We find that FLOSIC-SCAN calculations require careful treatment of numerical details and describe an integration grid that yields reliable accuracy with this approach. We investigate the performance of FLOSIC-SCAN for predicting a wide array of properties and find that it provides better results than FLOSIC-LDA and FLOSIC-PBE in nearly all cases. It also gives better predictions than SCAN for orbital energies and dissociation energies where self-interaction effects are known to be important, but total energies and atomization energies are made worse. For these properties, we also investigate the use of the self-consistent FLOSIC-SCAN density in the SCAN functional and find that this DFA@FLOSIC-DFA approach yields improved results compared to pure, self-consistent SCAN calculations. Thus FLOSIC-SCAN provides improved results over the parent SCAN functional in cases where SIEs are dominant, and even when they are not, if the SCAN@FLOSIC-SCAN method is used.

physics.chem-ph↗

arXiv2019

Impacts of Quantum Chemistry Calculations on Exoplanetary Science, Planetary Astronomy, and Astrophysics

Several of NASA missions (TESS, JWST, WFIRST, etc.) and mission concepts (LUVOIR, HabEx, and OST) emphasize the exploration and characterization of exoplanets, and the study of the interstellar medium. We anticipate that a much broader set of chemical environments exists on exoplanets, necessitating data from a correspondingly broader set of chemical reactions. Similarly, the conditions that exist in astrophysical environments are very different from those traditionally probed in laboratory chemical kinetics studies. These are areas where quantum mechanical theory, applied to important reactions via well-validated chemical kinetics models, can fill a critical knowledge gap. Quantum chemical calculations are also introduced to study interior of planets, photochemical escape, and many critical chemical pathways (e.g. prebiotic environments, contaminations, etc.) After years of development of the relevant quantum chemical theories and significant advances in computational power, quantum chemical simulations have currently matured enough to describe real systems with an accuracy that competes with experiments. These approaches, therefore, have become the best possible alternative in many circumstances where performing experiments is too difficult, too expensive, or too dangerous, or simply not possible. In this white paper, several existing quantum chemical studies supporting exoplanetary science, planetary astronomy, and astrophysics are described, and the potential positive impacts of improved models associated with scientific goals of missions are addressed. In the end, a few recommendations from the scientific community to strengthen related research efforts at NASA are provided.

astro-ph.EP↗

arXiv2019

Stretched or noded orbital densities and self-interaction correction in density functional theory

Semi-local approximations to the density functional for the exchange-correlation energy of a many-electron system necessarily fail for lobed one-electron densities, including not only the familiar stretched densities but also the less familiar but closely-related noded ones. The Perdew-Zunger (PZ) self-interaction correction (SIC) to a semi-local approximation makes that approximation exact for all one-electron ground- or excited-state densities and accurate for stretched bonds. When the minimization of the PZ total energy is made over real localized orbitals, the orbital densities can be noded, leading to energy errors in many-electron systems. Minimization over complex localized orbitals yields nodeless orbital densities, which reduce but typically do not eliminate the SIC errors of atomization energies. Other errors of PZ SIC remain, attributable to the loss of the exact constraints and appropriate norms that the semi-local approximations satisfy, and suggesting the need for a generalized SIC. These conclusions are supported by calculations for one-electron densities, and for many-electron molecules. While PZ SIC raises and improves the energy barriers of standard generalized gradient approximations (GGA's) and meta-GGA's, it reduces and often worsens the atomization energies of molecules. Thus PZ SIC raises the energy more as the nodality of the valence localized orbitals increases from atoms to molecules to transition states. PZ SIC is applied here in particular to the SCAN meta-GGA, for which the correlation part is already self-interaction-free. That property makes SCAN a natural first candidate for a generalized SIC.

physics.chem-ph↗