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1. Self-interaction error overbinds water clusters but cancels in structural energy differences

   https://doi.org/10.1073/pnas.1921258117  

   Sharkas, Kamal ; Wagle, Kamal ; Santra, Biswajit ; Akter, Sharmin ; Zope, Rajendra R. ; Baruah, Tunna ; Jackson, Koblar A. ; Perdew, John P. ; Peralta, Juan E. ( May 2020 , Proceedings of the National Academy of Sciences)

   We gauge the importance of self-interaction errors in density functional approximations (DFAs) for the case of water clusters. To this end, we used the Fermi–Löwdin orbital self-interaction correction method (FLOSIC) to calculate the binding energy of clusters of up to eight water molecules. Three representative DFAs of the local, generalized gradient, and metageneralized gradient families [i.e., local density approximation (LDA), Perdew–Burke–Ernzerhof (PBE), and strongly constrained and appropriately normed (SCAN)] were used. We find that the overbinding of the water clusters in these approximations is not a density-driven error. We show that, while removing self-interaction error does not alter the energetic ordering of the different water isomers with respect to the uncorrected DFAs, the resulting binding energies are corrected toward accurate reference values from higher-level calculations. In particular, self-interaction–corrected SCAN not only retains the correct energetic ordering for water hexamers but also reduces the mean error in the hexamer binding energies to less than 14 meV/${\mathrm{H}}_2\mathrm{O}$from about 42 meV/${\mathrm{H}}_2\mathrm{O}$for SCAN. By decomposing the total binding energy into many-body components, we find that large errors in the two-body interaction in SCAN are significantly reduced by self-interaction corrections. Higher-order many-body errors are small in both SCAN andmore »self-interaction–corrected SCAN. These results indicate that orbital-by-orbital removal of self-interaction combined with a proper DFA can lead to improved descriptions of water complexes.

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2. Embedded, graph‐theoretically defined many‐body approximations for wavefunction‐in‐DFT and DFT‐in‐DFT : Applications to gas‐ and condensed‐phase ab initio molecular dynamics, and potential surfaces for quantum nuclear effects

   https://doi.org/10.1002/qua.26244  

   Ricard, Timothy C. ; Kumar, Anup ; Iyengar, Srinivasan S. ( May 2020 , International Journal of Quantum Chemistry)

   We present a graph‐theoretic approach to adaptively compute many‐body approximations in an efficient manner to perform (a) accurate post‐Hartree–Fock (HF) ab initio molecular dynamics (AIMD) at density functional theory (DFT) cost for medium‐ to large‐sized molecular clusters, (b) hybrid DFT electronic structure calculations for condensed‐phase simulations at the cost of pure density functionals, (c) reduced‐cost on‐the‐fly basis extrapolation for gas‐phase AIMD and condensed phase studies, and (d) accurate post‐HF‐level potential energy surfaces at DFT cost for quantum nuclear effects. The salient features of our approach are ONIOM‐like in that (a) the full system (cluster or condensed phase) calculation is performed at a lower level of theory (pure DFT for condensed phase or hybrid DFT for molecular systems), and (b) this approximation is improved through a correction term that captures all many‐body interactions up to any given order within a higher level of theory (hybrid DFT for condensed phase; CCSD or MP2 for cluster), combined through graph‐theoretic methods. Specifically, a region of chemical interest is coarse‐grained into a set of nodes and these nodes are then connected to form edges based on a given definition of local envelope (or threshold) of interactions. The nodes and edges together define a graph,more »which forms the basis for developing the many‐body expansion. The methods are demonstrated through (a) ab initio dynamics studies on protonated water clusters and polypeptide fragments, (b) potential energy surface calculations on one‐dimensional water chains such as those found in ion channels, and (c) conformational stabilization and lattice energy studies on homogeneous and heterogeneous surfaces of water with organic adsorbates using two‐dimensional periodic boundary conditions.

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3. Machine learning the Hohenberg-Kohn map for molecular excited states

   https://doi.org/10.1038/s41467-022-34436-w  

   Bai, Yuanming ; Vogt-Maranto, Leslie ; Tuckerman, Mark E. ; Glover, William J. ( November 2022 , Nature Communications)

   The Hohenberg-Kohn theorem of density-functional theory establishes the existence of a bijection between the ground-state electron density and the external potential of a many-body system. This guarantees a one-to-one map from the electron density to all observables of interest including electronic excited-state energies. Time-Dependent Density-Functional Theory (TDDFT) provides one framework to resolve this map; however, the approximations inherent in practical TDDFT calculations, together with their computational expense, motivate finding a cheaper, more direct map for electronic excitations. Here, we show that determining density and energy functionals via machine learning allows the equations of TDDFT to be bypassed. The framework we introduce is used to perform the first excited-state molecular dynamics simulations with a machine-learned functional on malonaldehyde and correctly capture the kinetics of its excited-state intramolecular proton transfer, allowing insight into how mechanical constraints can be used to control the proton transfer reaction in this molecule. This development opens the door to using machine-learned functionals for highly efficient excited-state dynamics simulations.
4. The Lieb-Oxford Lower Bounds on the Coulomb Energy, Their Importance to Electron Density Functional Theory, and a Conjectured Tight Bound on Exchange

   John P. Perdew ; Jianwei Sun ( July 2022 , The Elliott Lieb Anniversary Volume)

   M. Lewin, Rupert L. (Ed.)

   Abstract: Lieb and Oxford (1981) derived rigorous lower bounds, in the form of local functionals of the electron density, on the indirect part of the Coulomb repulsion energy. The greatest lower bound for a given electron number N depends monotonically upon N, and the N→∞ limit is a bound for all N. These bounds have been shown to apply to the exact density functionals for the exchange- and exchange-correlation energies that must be approximated for an accurate and computationally efficient description of atoms, molecules, and solids. A tight bound on the exact exchange energy has been derived therefrom for two-electron ground states, and is conjectured to apply to all spin-unpolarized electronic ground states. Some of these and other exact constraints have been used to construct two generations of non-empirical density functionals beyond the local density approximation: the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA), and the strongly constrained and appropriately normed (SCAN) meta-GGA.
5. Embedding short-range correlations in relativistic density functionals through quasi-deuterons

   https://doi.org/10.1140/epja/s10050-022-00765-z  

   Burrello, S. ; Typel, S. ( July 2022 , The European Physical Journal A)

   Abstract The formation of clusters at sub-saturation densities, as a result of many-body correlations, constitutes an essential feature for a reliable modelization of the nuclear matter equation of state (EoS). Phenomenological models that make use of energy density functionals (EDFs) offer a convenient approach to account for the presence of these bound states of nucleons when introduced as additional degrees of freedom. However, in these models clusters dissolve, by construction, when the nuclear saturation density is approached from below, revealing inconsistencies with recent findings that evidence the existence of short-range correlations (SRCs) even at larger densities. The idea of this work is to incorporate SRCs in established models for the EoS, in light of the importance of these features for the description of heavy-ion collisions, nuclear structure and in the astrophysical context. Our aim is to describe SRCs at supra-saturation densities by using effective quasi-clusters immersed in dense matter as a surrogate for correlations, in a regime where cluster dissolution is usually predicted in phenomenological models. Within the EDF framework, we explore a novel approach to embed SRCs within a relativistic mean-field model with density dependent couplings through the introduction of suitable in-medium modifications of the cluster properties, in particularmore »their binding energy shifts, which are responsible for describing the cluster dissolution. As a first exploratory step, the example of a quasi-deuteron within the generalized relativistic density functional approach is investigated. The zero temperature case is examined, where the deuteron fraction is given by the density of a boson condensate. For the first time, suitable parameterizations of the cluster mass shift at zero temperature are derived for all baryon densities. They are constrained by experimental results for the effective deuteron fraction in nuclear matter near saturation and by microscopic many-body calculations in the low-density limit. A proper description of well-constrained nuclear matter quantities at saturation is kept through a refit of the nucleon meson coupling strengths. The proposed parameterizations allow to also determine the density dependence of the quasi-deuteron mass fraction at arbitrary isospin asymmetries. The strength of the deuteron-meson couplings is assessed to be of crucial importance. Novel effects on some thermodynamic quantities, such as the matter incompressibility, the symmetry energy and its slope, are finally discerned and discussed. The findings of the present study represent a first step to improve the description of nuclear matter and its EoS at supra-saturation densities in EDFs by considering correlations in an effective way. In a next step, the single-particle momentum distributions in nuclear matter can be explored using proper wave functions of the quasi-deuteron in the medium. The momentum distributions are expected to exhibit a high-momentum tail, as observed in the experimental study of SRCs by nucleon knockout with high-energy electrons. This will be studied in a forthcoming publication with an extensive presentation of the theoretical method and the results.« less