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1. Weak covalent interactions and anionic charge-sharing polymerisation in cluster environments

   https://doi.org/10.1039/d1cp01213d  

   Dauletyarov, Yerbolat; Sanov, Andrei (May 2021, Physical Chemistry Chemical Physics)

   null (Ed.)

   We discuss the formation of weak covalent bonds leading to anionic charge-sharing dimerisation or polymerisation in microscopic cluster environments. The covalent bonding between cluster building blocks is described in terms of coherent charge sharing, conceptualised using a coupled-monomers molecular-orbital model. The model assumes first-order separability of the inter- and intra-monomer bonding structures. Combined with a Hückel-style formalism adapted to weak covalent and solvation interactions, it offers insight into the competition between the two types of forces and illuminates the properties of the inter-monomer orbitals responsible for charge-sharing dimerisation and polymerisation. Under typical conditions, the cumulative effect of solvation obstructs the polymerisation, limiting the size of covalently bound core anions. 

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2. 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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3. Solid state photodimerization of 9- tert -butyl anthracene ester produces an exceptionally metastable polymorph according to first-principles calculations

   https://doi.org/10.1039/C8CE01985A  

   Beran, Gregory J. (January 2019, CrystEngComm)

   Molecular crystal engineering seeks to tune the material properties by controlling the crystal packing. However, the range of achievable properties is constrained by the limited energy range of polymorphs which can be crystallized. Here, computational modeling highlights that a solid-state crystal-to-crystal chemical reaction in 9- tert -butyl anthracene ester (9TBAE) nanorods [Al-Kaysi et al. , J. Am. Chem. Soc. , 2006, 128 , 15938] imparts “synthetic memory” into the crystal structure that allows reproducible formation of a highly metastable, yet long-lived polymorph. Specifically, whereas the vast majority of known polymorphs exhibit lattice energy differences below 10 kJ mol −1 , the conformational polymorph formed via solid state reaction chemistry lies 14 kJ mol −1 higher in energy than the form grown from solution, according to calculations that combine a dispersion-corrected second-order Møller–Plesset perturbation theory (MP2D) treatment of the monomer and photodimer with a density functional theory treatment (B86bPBE-XDM) of the intermolecular interactions in the crystal. Moreover, the solid-state reaction environment traps a highly unstable intramolecular photodimer conformation which defies the conventional wisdom surrounding conformational polymorphs. These observations suggest that solid-state reaction chemistry represents an under-appreciated strategy for producing polymorphs that would likely be unobtainable otherwise. 

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4. Collisionless Relaxation from Near-equilibrium Configurations: Linear Theory and Application to Tidal Stripping

   https://doi.org/10.3847/1538-4357/ad4c6e  

   Rozier, Simon; Errani, Raphaël (August 2024, The Astrophysical Journal)

   Abstract Placed slightly out of dynamical equilibrium, an isolated stellar system quickly returns toward a steady virialized state. We study this process of collisionless relaxation using the matrix method of linear response theory. We show that the full phase-space distribution of the final virialized state can be recovered directly from the disequilibrium initial conditions, without the need to compute the time evolution of the system. This shortcut allows us to determine the final virialized configuration with minimal computational effort. Complementing this result, we develop tools to model the system's full time evolution in the linear approximation. In particular, we show that moments of the velocity distribution can be efficiently computed using a generalized moment matrix. We apply our linear methods to study the relaxation of energy-truncated Hernquist spheres, mimicking the tidal stripping of a cuspy dark matter subhalo. Comparison of our linear predictions against controlled, isolatedN-body simulations shows agreement at percent level for the parts of the system where a linear response to the perturbation is expected. We find that relaxation generates a tangential velocity anisotropy in the intermediate regions, despite the initial disequilibrium state having isotropic kinematics. Our results also strengthen the case for relaxation depleting the amplitude of the density cusp, without affecting its asymptotic slope. Finally, we compare the linear theory against anN-body simulation of tidal stripping on a radial orbit, confirming that the theory still accurately predicts density and velocity dispersion profiles for most of the system. 

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5. Natural determinant reference functional theory

   https://doi.org/10.1063/5.0180319  

   Yu, Jason M; Tsai, Jeffrey; Rajabi, Ahmadreza; Rappoport, Dmitrij; Furche, Filipp (January 2024, The Journal of Chemical Physics)

   The natural determinant reference (NDR) or principal natural determinant is the Slater determinant comprised of the N most strongly occupied natural orbitals of an N-electron state of interest. Unlike the Kohn–Sham (KS) determinant, which yields the exact ground-state density, the NDR only yields the best idempotent approximation to the interacting one-particle reduced density matrix, but it is well-defined in common atom-centered basis sets and is representation-invariant. We show that the under-determination problem of prior attempts to define a ground-state energy functional of the NDR is overcome in a grand-canonical ensemble framework at the zero-temperature limit. The resulting grand potential functional of the NDR ensemble affords the variational determination of the ground state energy, its NDR (ensemble), and select ionization potentials and electron affinities. The NDR functional theory can be viewed as an “exactification” of orbital optimization and empirical generalized KS methods. NDR functionals depending on the noninteracting Hamiltonian do not require troublesome KS-inversion or optimized effective potentials. 

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