Ensemble Generalization of the Perdew-Zunger Self-Interaction Correction: A Way Out of Multiple Minima and Symmetry Breaking

The Perdew-Zunger (PZ) self-interaction correction (SIC) is an established tool to correct unphysical behavior in density functional approximations. Yet, the PZ-SIC is well-known to sometimes break molecular symmetries. An example of this is the benzene molecule, for which the PZ-SIC predicts a symmetry-broken electron density and molecular geometry, since the method does not describe the two possible Kekulé structures on an even footing, leading to local minima [Lehtola et al. J. Chem. Theory Comput. 2016, 12, 3195]. The PZ-SIC is often implemented with Fermi-Löwdin orbitals (FLOs), yielding the FLO-SIC method, which likewise has issues with symmetry breaking and local minima [Trepte et al. J. Chem. Phys. 2021, 155, 224109]. In this work, we propose a generalization of the PZ-SIC─the ensemble PZ-SIC (E-PZ-SIC) method─which shares the asymptotic computational scaling of the PZ-SIC (albeit with an additional prefactor). The E-PZ-SIC is straightforwardly applicable to various molecules, merely requiring one to average the self-interaction correction over all possible Kekulé structures, in line with chemical intuition. We showcase the implementation of the E-PZ-SIC with FLOs, as the resulting E-FLO-SIC method is easy to realize on top of an existing implementation of the FLO-SIC. We show that the E-FLO-SIC indeed eliminates symmetry breaking, reproducing a symmetric electron density and molecular geometry for benzene. The ensemble approach suggested herein could also be employed within approximate or locally scaled variants of the PZ-SIC and its FLO-SIC versions.

Stretching Bonds without Breaking Symmetries in Density Functional Theory

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

Assessing r2SCAN meta-GGA functional for structural parameters, cohesive energy, mechanical modulus, and thermophysical properties of 3d, 4d, and 5d transition metals

The recent development of accurate and efficient semilocal density functionals on the third rung of Jacob's ladder of density functional theory, such as the revised regularized strongly constrained and appropriately normed (r2SCAN) density functional, could enable rapid and highly reliable prediction of the elasticity and temperature dependence of thermophysical parameters of refractory elements and their intermetallic compounds using the quasi-harmonic approximation (QHA). Here, we present a comparative evaluation of equilibrium cell volumes, cohesive energy, mechanical moduli, and thermophysical properties (Debye temperature and thermal expansion coefficient) for 22 transition metals using semilocal density functionals, including the local density approximation (LDA), Perdew-Burke-Ernzerhof (PBE) and PBEsol generalized gradient approximations (GGAs), and the r2SCAN meta-GGA. PBEsol and r2SCAN deliver the same level of accuracies for structural, mechanical, and thermophysical properties. PBE and r2SCAN perform better than LDA and PBEsol for calculating cohesive energies of transition metals. Among the tested density functionals, r2SCAN provides an overall well-balanced performance for reliably computing cell volumes, cohesive energies, mechanical properties, and thermophysical properties of various 3d, 4d, and 5d transition metals using QHA. Therefore, we recommend that r2SCAN could be employed as a workhorse method to evaluate thermophysical properties of transition metal compounds and alloys in high throughput workflows.

Scalable Molecular GW Calculations: Valence and Core Spectra

We present a scalable implementation of the GW approximation using Gaussian atomic orbitals to study the valence and core ionization spectroscopies of molecules. The implementation of the standard spectral decomposition approach to the screened-Coulomb interaction, as well as a contour-deformation method, is described. We have implemented both of these approaches using the robust variational fitting approximation to the four-center electron repulsion integrals. We have utilized the MINRES solver with the contour-deformation approach to reduce the computational scaling by 1 order of magnitude. A complex heuristic in the quasiparticle equation solver further allows a speed-up of the computation of core and semicore ionization energies. Benchmark tests using the GW100 and CORE65 data sets and the carbon 1s binding energy of the well-studied ethyl trifluoroacetate, or ESCA molecule, were performed to validate the accuracy of our implementation. We also demonstrate and discuss the parallel performance and computational scaling of our implementation using a range of water clusters of increasing size.

Accurate density functional made more versatile

We propose a one-electron self-interaction-free correlation energy functional compatible with the order-of-limit problem-free Tao-Mo (TM) semilocal functional (regTM) [J. Tao and Y. Mo, Phys. Rev. Lett. 117, 073001 (2016) and Patra et al., J. Chem. Phys. 153, 184112 (2020)] to be used for general purpose condensed matter physics and quantum chemistry. The assessment of the proposed functional for large classes of condensed matter and chemical systems shows its improvement in most cases compared to the TM functional, e.g., when applied to the relative energy difference of MnO₂ polymorphs. In this respect, the present exchange-correction functional, which incorporates the TM technique of the exchange hole model combined with the slowly varying density correction, can achieve broad applicability, being able to solve difficult solid-state problems.