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1. Static polarizabilities within the generalized Kohn–Sham semicanonical projected random phase approximation (GKS-spRPA)

   https://doi.org/10.1063/5.0103664  

   Balasubramani, Sree Ganesh; Voora, Vamsee K.; Furche, Filipp (October 2022, The Journal of Chemical Physics)

   An analytical implementation of static dipole polarizabilities within the generalized Kohn–Sham semicanonical projected random phase approximation (GKS-spRPA) method for spin-restricted closed-shell and spin-unrestricted open-shell references is presented. General second-order analytical derivatives of the GKS-spRPA energy functional are derived using a Lagrangian approach. By resolution-of-the-identity and complex frequency integration methods, an asymptotic [Formula: see text] scaling of operation count and [Formula: see text] scaling of storage is realized, i.e., the computational requirements are comparable to those for GKS-spRPA ground state energies. GKS-spRPA polarizabilities are assessed for small molecules, conjugated long-chain hydrocarbons, metallocenes, and metal clusters, by comparison against Hartree–Fock (HF), semilocal density functional approximations (DFAs), second-order Møller–Plesset perturbation theory, range-separated hybrids, and experimental data. For conjugated polydiacetylene and polybutatriene oligomers, GKS-spRPA effectively addresses the “overpolarization” problem of semilocal DFAs and the somewhat erratic behavior of post-PBE RPA polarizabilities without empirical adjustments. The ensemble averaged GKS-spRPA polarizabilities of sodium clusters (Na n for n = 2, 3, …, 10) exhibit a mean absolute deviation comparable to PBE with significantly fewer outliers than HF. In conclusion, analytical second-order derivatives of GKS-spRPA energies provide a computationally viable and consistent approach to molecular polarizabilities, including systems prohibitive for other methods due to their size and/or electronic structure. 

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2. Introductory lecture: when the density of the noninteracting reference system is not the density of the physical system in density functional theory

   https://doi.org/10.1039/D0FD00102C  

   Jin, Ye; Su, Neil Qiang; Chen, Zehua; Yang, Weitao (December 2020, Faraday Discussions)

   null (Ed.)

   A major challenge in density functional theory (DFT) is the development of density functional approximations (DFAs) to overcome errors in existing DFAs, leading to more complex functionals. For such functionals, we consider roles of the noninteracting reference systems. The electron density of the Kohn–Sham (KS) reference with a local potential has been traditionally defined as being equal to the electron density of the physical system. This key idea has been applied in two ways: the inverse calculation of such a local KS potential for the reference from a given density and the direct calculation of density and energy based on given DFAs. By construction, the inverse calculation can yield a KS reference with the density equal to the input density of the physical system. In application of DFT, however, it is the direct calculation of density and energy from a DFA that plays a central role. For direct calculations, we find that the self-consistent density of the KS reference defined by the optimized effective potential (OEP), is not the density of the physical system, when the DFA is dependent on the external potential. This inequality holds also for the density of generalized KS (GKS) or generalized OEP reference, which allows a nonlocal potential, when the DFA is dependent on the external potential. Instead, the density of the physical system, consistent with a given DFA, is given by the linear response of the total energy with respect to the variation of the external potential. This is a paradigm shift in DFT on the use of noninteracting references: the noninteracting KS or GKS references represent the explicit computational variables for energy minimization, but not the density of the physical system for external potential-dependent DFAs. We develop the expressions for the electron density so defined through the linear response for general DFAs, demonstrate the results for orbital functionals and for many-body perturbation theory within the second-order and the random-phase approximation, and explore the connections to developments in DFT. 

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3. Multireference Calculations on Bond Dissociation and Biradical Polycyclic Aromatic Hydrocarbons as Guidance for Fractional Occupation Number Weighted Density Analysis in DFT Calculations

   Carvalho, Jhonatas R; Nieman, Reed; Kertesz, Miklos; Aquino, Adelia_J_A; Hansen, Andreas; Lischka, Hans (August 2024, Theoretical Chemistry accounts)

   This study explores open shell biradical and polyradical molecular compounds based on extended multireference (MR) methods (MR-configuration interaction with singles and doubles (CISD) and MR-averaged quadratic coupled cluster (AQCC) approach) using the numbers of unpaired densities NU. These results were used to guide the analysis of the fractional occupation number weighted density (FOD) calculated within the finite temperature (FT) density functional theory (DFT) approach. As critical test examples, the dissociation of carbon-carbon (CC) single, double and triple bonds, and a benchmark set of polycyclic aromatic hydrocarbons (PAHs) has been chosen. By examining single, double, and triple bond dissociations, we demonstrate the utility and accuracy but also limitations of the FOD analysis for describing these dissociation processes. In significant extension of previous work (Phys Chem Chem Phys 25: 27380-27393) the assessment of FOD applications for different classes of DFT functionals was performed examining the range-separated functionals ωB97XD, ωB97M-V, CAM-B3LYP, LC-ωPBE, and MN12-SX, the hybrid (M06-2X) functional and the double hybrid (B2P-LYP) functional. In all cases, strong correlations between NFOD and NU values are found. The major task was to develop a new linear regression formula for range-separated functionals allowing a convenient determination of the optimal electronic temperature Tel for the FT-DFT calculation. We also established an optimal temperature for the semi-empirical extended tight-binding GFN2-xTB method. These findings significantly broaden the applicability of FOD analysis across various DFT functionals and semi-empirical methods. 

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4. Towards understanding the electronic structure of the simpler members of two-dimensional halide-perovskites

   https://doi.org/10.1103/PhysRevB.108.045130  

   Manousakis, Efstratios (July 2023, Physical Review B)

   In this paper, we analyze the band structure of two-dimensional (2D) halide perovskites by considering structures related to the simpler case of the series, (BA)2⁢PbI4, in which PbI4 layers are intercalated with butylammonium [BA=CH3(CH2)3⁢NH3] organic ligands. We use density-functional-theory (DFT) based calculations and tight-binding (TB) models aiming to discover a simple description of the bands within 1 eV below the valence-band maximum and 2 eV above the conduction-band minimum, which, including the energy gap, is about a Δ⁢𝐸=5 eV energy range. The bands in this Δ⁢𝐸 range are those expected to contribute to the transport phenomena, photoconductivity, and light emission in the visible spectrum, at room and low temperature. We find that the atomic orbitals of the butylammonium chains have negligible contribution to the Bloch states which form the conduction and valence bands in the above defined Δ⁢𝐸 range. Our calculations reveal a rather universal, i.e., independent of the intercalating BA, rigid-band picture inside the above Δ⁢𝐸 range characteristic of the layered perovskite “matrix” (i.e., PbI4 in our example). Besides demonstrating the above conclusion, the main goal of this paper is to find accurate TB models which capture the essential features of the DFT bands in this Δ⁢𝐸 range. First, we ignore electron hopping along the 𝑐 axis and the octahedral distortions and this increased symmetry (from C2 to C4) halves the Bravais lattice unit cell size and the Brillouin zone unfolds to a 45∘ rotated square and this allows some analytical handling of the 2D TB Hamiltonian. The Pb 6⁢𝑠 and I 5⁢𝑠 orbitals are far away from the above Δ⁢𝐸 range and, thus, we integrate them out to obtain an effective model which only includes hybridized Pb 6⁢𝑝 and I 5⁢𝑝 states. Our TB-based treatment (a) provides a good quantitative description of the DFT band structure, (b) helps us conceptualize the complex electronic structure in the family of these materials in a simple way, and (c) yields the one-body part to be combined with appropriately screened electron interaction to describe many-body effects, such as excitonic bound states. 

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5. Energy-specific Bethe–Salpeter equation implementation for efficient optical spectrum calculations

   https://doi.org/10.1063/5.0260895  

   Hillenbrand, Christopher; Li, Jiachen; Zhu, Tianyu (May 2025, The Journal of Chemical Physics)

   We present an energy-specific Bethe–Salpeter equation (BSE) implementation for efficient core and valence optical spectrum calculations. In the energy-specific BSE, high-lying excitation energies are obtained by constructing trial vectors and expanding the subspace targeting excitation energies above the predefined energy threshold in the Davidson algorithm. To calculate optical spectra over a wide energy range, energy-specific BSE can be applied to multiple consecutive small energy windows, where trial vectors for each subsequent energy window are made orthogonal to the subspace of preceding windows to accelerate the convergence of the Davidson algorithm. For seven small molecules, energy-specific BSE combined with G0W0 provides small errors around 0.8 eV for absolute and relative K-edge excitation energies when starting from a hybrid PBEh solution with 45% exact exchange. We further showcase the computational efficiency of this approach by simulating the N 1s K-edge excitation spectrum of the porphine molecule and the valence optical spectrum of silicon nanoclusters involving 6000 excited states using G0W0-BSE. This work expands the applicability of the GW-BSE formalism for investigating high-energy excited states of large systems. 

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