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1. 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. 

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2. Accurate and efficient prediction of double excitation energies using the particle–particle random phase approximation

   https://doi.org/10.1063/5.0251418  

   Yu, Jincheng; Li, Jiachen; Zhu, Tianyu; Yang, Weitao (March 2025, The Journal of Chemical Physics)

   Double excitations are crucial to understanding numerous chemical, physical, and biological processes, but accurately predicting them remains a challenge. In this work, we explore the particle–particle random phase approximation (ppRPA) as an efficient and accurate approach for computing double excitation energies. We benchmark ppRPA using various exchange-correlation functionals for 21 molecular systems and two point defect systems. Our results show that ppRPA with functionals containing appropriate amounts of exact exchange provides accuracy comparable to high-level wave function methods such as CCSDT and CASPT2, with significantly reduced computational cost. Furthermore, we demonstrate the use of ppRPA starting from an excited (N − 2)-electron state calculated by ΔSCF for the first time, as well as its application to double excitations in bulk periodic systems. These findings suggest that ppRPA is a promising tool for the efficient calculation of double and partial double excitation energies in both molecular and bulk systems. 

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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)

   Abstract 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. 

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4. The interplay of intra- and intermolecular errors in modeling conformational polymorphs

   https://doi.org/10.1063/5.0088027  

   Beran, Gregory J. O.; Wright, Sarah E.; Greenwell, Chandler; Cruz-Cabeza, Aurora J. (March 2022, The Journal of Chemical Physics)

   Conformational polymorphs of organic molecular crystals represent a challenging test for quantum chemistry because they require careful balancing of the intra- and intermolecular interactions. This study examines 54 molecular conformations from 20 sets of conformational polymorphs, along with the relative lattice energies and 173 dimer interactions taken from six of the polymorph sets. These systems are studied with a variety of van der Waals-inclusive density functionals theory models; dispersion-corrected spin-component-scaled second-order Møller–Plesset perturbation theory (SCS-MP2D); and domain local pair natural orbital coupled cluster singles, doubles, and perturbative triples [DLPNO-CCSD(T)]. We investigate how delocalization error in conventional density functionals impacts monomer conformational energies, systematic errors in the intermolecular interactions, and the nature of error cancellation that occurs in the overall crystal. The density functionals B86bPBE-XDM, PBE-D4, PBE-MBD, PBE0-D4, and PBE0-MBD are found to exhibit sizable one-body and two-body errors vs DLPNO-CCSD(T) benchmarks, and the level of success in predicting the relative polymorph energies relies heavily on error cancellation between different types of intermolecular interactions or between intra- and intermolecular interactions. The SCS-MP2D and, to a lesser extent, ωB97M-V models exhibit smaller errors and rely less on error cancellation. Implications for crystal structure prediction of flexible compounds are discussed. Finally, the one-body and two-body DLPNO-CCSD(T) energies taken from these conformational polymorphs establish the CP1b and CP2b benchmark datasets that could be useful for testing quantum chemistry models in challenging real-world systems with complex interplay between intra- and intermolecular interactions, a number of which are significantly impacted by delocalization error. 

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5. Performance of density functional theory for describing hetero‐metallic active‐site motifs for methane‐to‐methanol conversion in metal‐exchanged zeolites

   https://doi.org/10.1002/jcc.25714  

   Dandu, Naveen K.; Adeyiga, Olajumoke; Panthi, Dipak; Bird, Shaina A.; Odoh, Samuel O. (October 2018, Journal of Computational Chemistry)

   Methane‐to‐methanol conversion (MMC) can be facilitated with high methanol selectivities by copper‐exchanged zeolites. There are however two open questions regarding the use of these zeolites to facilitate the MMC process. The first concerns the possibility of operating the three cycles in the stepwise MMC process by these zeolites in an isothermal fashion. The second concerns the possibility of improving the methanol yields by systematic substitution of some copper centers in these active sites with other earth‐abundant transition metals. Quantum‐mechanical computations can be used to compare methane activation by copper oxide species and analogous mixed‐metal systems. To carry out such screening, it is important that we use theoretical methods that are accurate and computationally affordable for describing the properties of the hetero‐metallic catalytic species. We have examined the performance of 47 exchange‐correlation density functionals for predicting the relative spin‐state energies and chemical reactivities of six hetero‐metallic [M‐O‐Cu]²⁺and [M‐O₂‐Cu]²⁺, (where MCo, Fe, and Ni), species by comparison with coupled cluster theory including iterative single, double excitations as well as perturbative treatment of triple excitations, CCSD(T). We also performed multireference calculations on some of these systems. We considered two types of reactions (hydrogen addition and oxygen addition) that are relevant to MMC. We recommend the use of τ‐HCTH and OLYP to determine the spin‐state energy splittings in the hetero‐metallic motifs. ωB97, ωB97X, ωB97X‐D3, and MN15 performed best for predicting the energies of the hydrogen and oxygen addition reactions. In contrast, local, and semilocal functionals do poorly for chemical reactivity. Using [Fe‐O‐Cu]²⁺as a test, we see that the nonlocal functionals perform well for the methane CH activation barrier. In contrast, the semilocal functionals perform rather poorly. © 2018 Wiley Periodicals, Inc. 

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