Abstract Within density-functional theory (DFT), Moreau–Yosida regularization enables both a reformulation of the theory and a mathematically well-defined definition of the Kohn–Sham approach. It is further employed in density–potential inversion schemes and, through the choice of topology for the density and potential space, can be directly linked to classical field theories. This perspective collects various appearances of the regularization technique within DFT alongside possibilities for their future development.

Abstract Carbon clusters are fundamental building blocks of nanostructured carbon materials with applications
in materials science, biomaterials, and energy technologies. In this work, the structural
stability, electronic properties, and vibrational characteristics of small carbon clusters Cn (n=3–8)
were investigated using ab initio methods, including Hartree–Fock (HF), density functional theory
(DFT) with the B3LYP functional with and without Grimme’s dispersion correction (GD3), and
coupled-cluster singles and doubles (CCSD). Calculations employed the 6-31+G(d), 6-311+G(d,p),
and cc-pVTZ basis sets. Linear isomers were identified as the most stable structures for all cluster
sizes, indicating that linear geometries can already be captured at the HF level. Binding energies
increase with cluster size, while DFT and CCSD accurately reproduce stability trends and identify
C3 and C5 as magic-number clusters. Vibrational analyses reveal dominant asymmetric stretching
modes in the mid-infrared region and bending modes in the far-infrared region, consistent with
available experimental data.

Abstract Density Functional Theory (DFT) is widely used for electronic structure calculations, primarily utilizing the Kohn-Sham scheme. However, this approach reintroduces orbitals, resulting in a high computational cost. In contrast, the original orbital-free Hohenberg-Kohn DFT (OF-DFT) offers the potential for linear-scaling computations suitable for large systems. The advancement of OF-DFT relies on the development of an accurate and universal kinetic energy density functional (KEDF). This review surveys the progress, challenges, and prospects in KEDF development. It presents the essential physical and mathematical constraints that any KEDF must comply with, tracing the evolution from early models like Thomas-Fermi and von Weizs"acker to contemporary semi-local, nonlocal, and machine-learned approaches. While the developed KEDFs have improved the treatment of metals and some semiconductors, achieving transferable accuracy for molecules and systems with considerable density inhomogeneities remains a critical challenge. We highlight two emerging paradigms; the use of physics-guided machine learning to identify accurate KEDFs and information-theoretic approaches that provide deep insights. The path forward requires a renewed focus on fundamental physical constraints, steering the field away from purely empirical fitting toward a universal, computationally efficient KEDF that maximizes the advantages of OF-DFT. The main KEDFs are listed, including gradient expansions, enhancement-factor strategies, density-decomposition methods, and nonlocal KEDFs guided by linear-response theory.

Abstract First-principles calculations of the structural, electronic and mechanical properties of the Ag7PS6 crystal have been performed. A detailed analysis of the influence of various functionals on the structural parameters of the unit cell after full optimization was performed. The investigation of its physical characteristics using the DFT-D approach, which accounts for dispersion interactions, has been carried out for the first time. The phonon spectra and partial phonon density of states of Ag7PS6 were obtained and analyzed. Experimental studies of the vibrational properties of bulk Ag7PS6 samples were conducted, and the calculated vibrational characteristics were compared with available Raman scattering data, showing good agreement. In addition, the elastic properties of the Ag7PS6 crystal were modeled and analyzed for the first time.

Abstract We present the modification of electronic structure properties due to the presence of oxygen vacancies in monoclinic-Zirconia (m-ZrO 2 ). Using a combined density functional theory (DFT) and GW formalism, we study the electronic structure and charge transition levels (CTLs) of oxygen vacancy defects in m-ZrO 2 . The CTLs are calculated using two paths and employing electrostatic corrections due to localized charge at the defect site. We find +1/0 CTL is at 3.48 eV (2.50 eV) and +2/+1 CTL is at 1.92 eV (0.98 eV) for 3-fold (4-fold) oxygen vacancy in m-ZrO 2 . We also describe a relaxation mechanism of atoms near an oxygen vacancy site. Finally, we compare the calculated CTLs using only density functional theory and the combined approach of both density functional theory and GW method with appropriate electrostatic corrections. Our results agree well with the experimental findings of electronic trap level in m-ZrO 2 [1][2][3].

Abstract This study presents a comprehensive density functional theory (DFT) analysis of the structural and electronic modifications induced by point defects and spin-orbit coupling (SOC) in monolayer 1H-WSe2 . Among intrinsic point defects, the selenium vacancy is identified as the most energetically favorable and is shown to generate well-localized in-gap states predominantly originating from the d orbitals of neighboring W atoms. Spin-orbit coupling lifts the spin degeneracy of these defect states, giving rise to pronounced spin splitting with a dominant out-of-plane spin component as a consequence of broken local in-plane mirror symmetry and the strong atomic spin-orbit interaction of tungsten. Spin-resolved band structure calculations further reveal valley-dependent spin polarization with a dominant out-of-plane spin component at the K and K ′ points, indicating a nontrivial coupling between defect states and the spin and valley degrees of freedom. The essential features of the defect-induced spin splitting and spin texture are captured by a minimal k • p Hamiltonian, providing analytical insight into the underlying symmetry and spin-orbit mechanisms. Our results establish defect engineering as an effective route to realize localized spin-polarized states in two-dimensional transition metal dichalcogenides, offering promising prospects for spintronic and valleytronic quantum device applications.

Abstract Ga 2 O 3 has garnered substantial interest owing to its promising applications in power electronics and optoelectronics. Herein, the electronic properties of N-doped κ -Ga 2 O 3 are explored through density functional theory calculations. A variety of N-doped complex defects are examined, including <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mtext>N</mml:mtext> </mml:mrow> <mml:mrow> <mml:mtext>O</mml:mtext> </mml:mrow> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> (N-doped κ -Ga 2 O 3 ), N O V O (N-doped κ -Ga 2 O 3 with O vacancy), N O V Ga (N-doped κ -Ga 2 O 3 with Ga vacancy), N O O i (N-doped κ -Ga 2 O 3 with O interstitial), N O Ga i (N-doped κ -Ga 2 O 3 with Ga interstitial), alongside nitrogen substituting gallium at tetrahedral ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mtext>N</mml:mtext> </mml:mrow> <mml:mrow> <mml:mrow> <mml:mtext>Ga</mml:mtext> </mml:mrow> <mml:mo>,</mml:mo> <mml:mrow> <mml:mtext>tetra</mml:mtext> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> ) and octahedral ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mtext>N</mml:mtext> </mml:mrow> <mml:mrow> <mml:mrow> <mml:mtext>Ga</mml:mtext> </mml:mrow> <mml:mo>,</mml:mo> <mml:mrow> <mml:mtext>octa</mml:mtext> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> ) sites. Analysis of their formation energies reveals that N O predominates under both Ga-rich and O-rich environments, functioning as a shallow acceptor. Intriguingly, under Ga-rich conditions, there exists a pronounced preference for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mtext>N</mml:mtext> </mml:mrow> <mml:mrow> <mml:mtext>O</mml:mtext> </mml:mrow> </mml:msub> </mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mtext>V</mml:mtext> </mml:mrow> <mml:mrow> <mml:mtext>O</mml:mtext> </mml:mrow> </mml:msub> </mml:mrow> <mml:mrow> <mml:mtext> </mml:mtext> </mml:mrow> </mml:mrow> </mml:math> defects over other acceptor-like deep defects, implying that such complexes may obstruct the attainment of p-type conductivity in κ -Ga 2 O 3 due to extensive compensation by oxygen vacancies. Moreover, it is demonstrated that <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mtext>N</mml:mtext> </mml:mrow> <mml:mrow> <mml:mtext>O</mml:mtext> </mml:mrow> </mml:msub> </mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mtext>V</mml:mtext> </mml:mrow> <mml:mrow> <mml:mtext>O</mml:mtext> </mml:mrow> </mml:msub> </mml:mrow> <mml:mrow> <mml:mtext> </mml:mtext> </mml:mrow> </mml:mrow> </mml:math> complexes can elicit red luminescence, arising from oxygen vacancies coupled with holes localized at acceptor sites introduced by N doping. The intricate electronic structure of κ -Ga 2 O 3 with these complex defects is elucidated through comprehensive analyses of the density of states and electronic band structures. Complementary examinations of electron localization and real-space wavefunctions further illuminate the influence of these defects on the κ -Ga 2 O

Abstract In this work, we introduce a selective and scalable extension of&amp;#xD;the multi-step Rayleigh–Schrödinger and Brillouin–Wigner (RSBW) perturbative&amp;#xD;scheme (see Ref. [5]) , designed to efficiently access the low-energy spectrum&amp;#xD;of molecular systems. The method proceeds by combining successive effective&amp;#xD;Hamiltonian diagonalizations inspired by second-order Rayleigh–Schrödinger&amp;#xD;perturbation theory, with a Brillouin–Wigner correction applied to individually&amp;#xD;optimized states using an updated partitioning of the Hamiltonian. At each&amp;#xD;step, a candidate zeroth-order state is identified and progressively decoupled&amp;#xD;from the remaining higher-lying states, thereby enabling a well-conditioned&amp;#xD;Brillouin–Wigner expansion for the energy correction. In contrast to previous&amp;#xD;approaches, the method selectively targets a small number of low-lying&amp;#xD;states, significantly reducing the numerical overhead while maintaining chemical&amp;#xD;accuracy. The robustness of the method is demonstrated on the LiH and&amp;#xD;H4 molecules, where accurate excitation energies are obtained for the lowest&amp;#xD;singlet states using compact model spaces, confirming its potential for realistic&amp;#xD;applications.