Analytic atomic gradients in the fermi-löwdin orbital self-interaction correction

The rise and fall of stretched bond errors: Extending the analysis of Perdew-Zunger self-interaction corrections of reaction barrier heights beyond the LSDA

Incorporating self-interaction corrections (SIC) significantly improves chemical reaction barrier height predictions made using density functional theory methods. We present a detailed orbital-by-orbital analysis of these corrections for three semi-local density functional approximations (DFAs) situated on the three lowest rungs of Jacob's ladder of approximations. The analysis is based on Fermi-Löwdin Orbital Self-Interaction Correction (FLOSIC) calculations performed at several steps along the reaction pathway from the reactants (R) to the transition state (TS) to the products (P) for four representative reactions selected from the BH76 benchmark set. For all three functionals, the major contribution to self-interaction corrections of the barrier heights can be traced to stretched bond orbitals that develop near the TS configuration. The magnitude of the ratio of the self-exchange-correlation energy to the self-Hartree energy (XC/H) for a given orbital is introduced as an indicator of one-electron self-interaction error. XC/H = 1.0 implies that an orbital's self-exchange-correlation energy exactly cancels its self-Hartree energy and that the orbital, therefore, makes no contribution to the SIC in the FLOSIC scheme. For the practical DFAs studied here, XC/H spans a range of values. The largest values are obtained for stretched or strongly lobed orbitals. We show that significant differences in XC/H for corresponding orbitals in the R, TS, and P configurations can be used to identify the major contributors to the SIC of barrier heights and reaction energies. Based on such comparisons, we suggest that barrier height predictions made using the strongly constrained and appropriately normed meta-generalized gradient approximation may have attained the best accuracy possible for a semi-local functional using the Perdew-Zunger SIC approach.

Bond length alternation of π-conjugated polymers predicted by the Fermi-Löwdin orbital self-interaction correction method

π-conjugated polymers have been used in a wide range of practical applications, partly due to their unique properties that originate in the delocalization of electrons through the polymer backbone. The level of delocalization can be characterized by the induced bond length alternation (BLA), with shorter BLA connected with strong delocalization and vice versa. The accurate description of this structural parameter can be considered a benchmark for testing the capability of different electronic structure methods for self-interaction error (SIE) removal and electron correlation inclusion. Density functional theory (DFT), in its local or semi-local flavors, suffers from SIE and, thus, underestimates the BLA compared to self-interaction-free methods. In this work, we utilize the Fermi-Löwdin orbital self-interaction correction (FLOSIC) method for one-electron self-interaction removal to characterize the BLA of five oligomers with increasing length extrapolated to the polymeric limit. We compare the self-interaction-free BLA to several DFT approximations, Møller-Plesset second-order perturbation theory (MP2), and the BLA obtained with the domain based local pair natural orbital CCSD(T) [DLPNO-CCSD(T)] approximation. Our findings show that FLOSIC corrects for the small BLA given by (semi-)local DFT approximations, but it tends to overcorrect with respect to CAM-B3LYP, MP2, and DLPNO-CCSD(T).

Self-consistent implementation of locally scaled self-interaction-correction method

Recently proposed local self-interaction correction (LSIC) method [Zope et al., J. Chem. Phys. 151, 214108 (2019)] is a one-electron self-interaction-correction (SIC) method that uses an iso-orbital indicator to apply the SIC at each point in space by scaling the exchange-correlation and Coulomb energy densities. The LSIC method is exact for the one-electron densities, also recovers the uniform electron gas limit of the uncorrected density functional approximation, and reduces to the well-known Perdew-Zunger SIC (PZSIC) method as a special case. This article presents the self-consistent implementation of the LSIC method using the ratio of Weizsäcker and Kohn-Sham kinetic energy densities as an iso-orbital indicator. The atomic forces as well as the forces on the Fermi-Löwdin orbitals are also implemented for the LSIC energy functional. Results show that LSIC with the simplest local spin density functional predicts atomization energies of the AE6 dataset better than some of the most widely used generalized-gradient-approximation (GGA) functional [e.g., Perdew-Burke-Ernzerhof (PBE)] and barrier heights of the BH6 database better than some of the most widely used hybrid functionals (e.g., PBE0 and B3LYP). The LSIC method [a mean absolute error (MAE) of 0.008 Å] predicts bond lengths of a small set of molecules better than the PZSIC-LSDA (MAE 0.042 Å) and LSDA (0.011 Å). This work shows that accurate results can be obtained from the simplest density functional by removing the self-interaction-errors using an appropriately designed SIC method.

Study of Self-Interaction Errors in Density Functional Calculations of Magnetic Exchange Coupling Constants Using Three Self-Interaction Correction Methods

We examine the role of self-interaction error (SIE) removal on the evaluation of magnetic exchange coupling constants. In particular, we analyze the effect of scaling down the self-interaction correction (SIC) for three nonempirical density functional approximations (DFAs) namely, the local spin density approximation, the Perdew-Burke-Ernzerhof generalized gradient approximation, and the recent SCAN family of meta-GGA functionals. To this end, we employ three one-electron SIC methods: Perdew-Zunger SIC [Perdew, J. P.; Zunger, A. Phys. Rev. B, 1981, 23, 5048.], the orbitalwise scaled SIC method [Vydrov, O. A. et al. J. Chem. Phys. 2006, 124, 094108.], and the recent local scaling method [Zope, R. R. et al. J. Chem. Phys. 2019, 151, 214108.]. We compute the magnetic exchange coupling constants using the spin projection and nonprojection approaches for sets of molecules composed of dinuclear and polynuclear H···He models, organic radical molecules, and chlorocuprate and compare these results against accurate theories and experiment. Our results show that for the systems that mainly consist of single-electron regions, PZSIC performs well, but for more complex organic systems and the chlorocuprates, an overcorrecting tendency of PZSIC combined with the DFAs utilized in this work is more pronounced, and in such cases, LSIC with kinetic energy density ratio performs better than PZSIC. Analysis of the results in terms of SIC corrections to the density and to the total energy shows that both density and energy correction are required to obtain an improved prediction of magnetic exchange couplings.

How well do self-interaction corrections repair the overestimation of static polarizabilities in density functional calculations?

We examine the effect of removing self-interaction error (SIE) on the calculation of molecular polarizabilities in the local spin density (LSDA) and generalized gradient approximations (GGA). To this end, we utilize a database of 132 molecules taken from a recent benchmark study [Hait and Head-Gordon, Phys. Chem. Chem. Phys., 2018, 20, 19800] to assess the influence of SIE on polarizabilities by comparing results with accurate reference data. Our results confirm that the general overestimation of molecular polarizabilities by these density functional approximations can be attributed to SIE. However, removing SIE using the Perdew-Zunger self-interaction-correction (PZ-SIC) method, implemented using the Fermi-Löwdin Orbital SIC approach, leads to an underestimation of molecular polarizabilities, showing that PZ-SIC overcorrects when combined with LSDA or GGA. Application of a recently proposed locally scaled SIC [Zope, et al., J. Chem. Phys., 2019, 151, 214108] is found to provide more accurate polarizabilities. We attribute this to the ability of the local scaling scheme to selectively correct for SIE in the regions of space where the correction is needed most.

Replacing hybrid density functional theory: motivation and recent advances

Density functional theory (DFT) is the most widely-used electronic structure approximation across chemistry, physics, and materials science. Every year, thousands of papers report hybrid DFT simulations of chemical structures, mechanisms, and spectra. Unfortunately, hybrid DFT's accuracy is ultimately limited by tradeoffs between over-delocalization and under-binding. This review summarizes these tradeoffs, and introduces six modern attempts to go beyond them while maintaining hybrid DFT's relatively low computational cost: DFT+U, self-interaction corrections, localized orbital scaling corrections, local hybrid functionals, real-space nondynamical correlation, and our rung-3.5 approach. The review concludes with practical suggestions for DFT users to identify and mitigate these tradeoffs' impact on their simulations.

Local self-interaction correction method with a simple scaling factor

The local self-interaction correction method with a simple scaling factor performs better than the Perdew-Zunger self-interaction correction method and also provides a good description of the binding energies of weakly bonded water clusters. 

Assessing the effect of regularization on the molecular properties predicted by SCAN and self-interaction corrected SCAN meta-GGA

Recent regularization of the SCAN meta-GGA functional (rSCAN) has simplified the numerical complexities of the SCAN functional, alleviating SCAN's stringent demand on the numerical integration grids to some extent. The regularization of rSCAN, however, results in the breaking of some constraints such as the uniform electron gas limit, the slowly varying density limit, and coordinate scaling of the iso-orbital indicator. Here, we assess the effects of regularization on the electronic, structural, vibrational, and magnetic properties of molecules by comparing the SCAN and rSCAN predictions. The properties studied include atomic energies, atomization energies, ionization potentials, electron affinities, barrier heights, infrared intensities, dissociation and reaction energies, spin moments of molecular magnets, and isomer ordering of water clusters. Our results show that rSCAN requires less dense numerical grids and gives very similar results to those of SCAN for all properties examined with the exception of atomization energies, which are worsened in rSCAN. We also examine the performance of self-interaction-corrected (SIC) rSCAN with respect to SIC-SCAN using the Perdew-Zunger (PZ) SIC method. The PZSIC method uses orbital densities to compute one-electron self-interaction errors and places an even more stringent demand on numerical grids. Our results show that SIC-rSCAN gives marginally better performance than SIC-SCAN for almost all properties studied in this work with numerical grids that are on average half or less as dense as that needed for SIC-SCAN.