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1. Introducing DDEC6 atomic population analysis: part 3. Comprehensive method to compute bond orders

   https://doi.org/10.1039/c7ra07400j  

   Manz, Thomas A. ( January 2017 , RSC Adv.)

   Developing a comprehensive method to compute bond orders is a problem that has eluded chemists since Lewis's pioneering work on chemical bonding a century ago. Here, a computationally efficient method solving this problem is introduced and demonstrated for diverse materials including elements from each chemical group and period. The method is applied to non-magnetic, collinear magnetic, and non-collinear magnetic materials with localized or delocalized bonding electrons. Examples studied include the stretched O 2 molecule, 26 diatomic molecules, 3d and 5d transition metal solids, periodic materials with 1 to 8748 atoms per unit cell, a biomolecule, a hypercoordinate molecule, an electron deficient molecule, hydrogen bound systems, transition states, Lewis acid–base complexes, aromatic compounds, magnetic systems, ionic materials, dispersion bound systems, nanostructures, and other materials. From near-zero to high-order bonds were studied. Both the bond orders and the sum of bond orders for each atom are accurate across various bonding types: metallic, covalent, polar-covalent, ionic, aromatic, dative, hypercoordinate, electron deficient multi-centered, agostic, and hydrogen bonding. The method yields similar results for correlated wavefunction and density functional theory inputs and for different S Z values of a spin multiplet. The method requires only the electron and spin magnetization density distributions as input and has a computational cost scaling linearly with increasing number of atoms in the unit cell. No prior approach is as general. The method does not apply to electrides, highly time-dependent states, some extremely high-energy excited states, and nuclear reactions. 

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2. The location of the chemical bond. Application of long covalent bond theory to the structure of silica

   https://doi.org/10.3389/fchem.2023.1123322  

   Miller, Stephen A. ( February 2023 , Frontiers in Chemistry)

   Oxygen is the most abundant terrestrial element and is found in a variety of materials, but still wanting is a universal theory for the stability and structural organization it confers. Herein, a computational molecular orbital analysis elucidates the structure, stability, and cooperative bonding of α-quartz silica (SiO 2 ). Despite geminal oxygen-oxygen distances of 2.61–2.64 Å, silica model complexes exhibit anomalously large O-O bond orders (Mulliken, Wiberg, Mayer) that increase with increasing cluster size—as the silicon-oxygen bond orders decrease. The average O-O bond order in bulk silica computes to 0.47 while that for Si-O computes to 0.64. Thereby, for each silicate tetrahedron, the six O-O bonds employ 52% (5.61 electrons) of the valence electrons, while the four Si-O bonds employ 48% (5.12 electrons), rendering the O-O bond the most abundant bond in the Earth’s crust. The isodesmic deconstruction of silica clusters reveals cooperative O-O bonding with an O-O bond dissociation energy of 4.4 kcal/mol. These unorthodox, long covalent bonds are rationalized by an excess of O 2 p –O 2 p bonding versus anti-bonding interactions within the valence molecular orbitals of the SiO 4 unit (48 vs. 24) and the Si 6 O 6 ring (90 vs. 18). Within quartz silica, oxygen 2 p orbitals contort and organize to avoid molecular orbital nodes, inducing the chirality of silica and resulting in Möbius aromatic Si 6 O 6 rings, the most prevalent form of aromaticity on Earth. This long covalent bond theory (LCBT) relocates one-third of Earth’s valence electrons and indicates that non-canonical O-O bonds play a subtle, but crucial role in the structure and stability of Earth’s most abundant material. 

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3. Stabilization of three-dimensional charge order through interplanar orbital hybridization in PrxY1−xBa2Cu3O6+δ

   https://doi.org/10.1038/s41467-022-33607-z  

   Ruiz, Alejandro ; Gunn, Brandon ; Lu, Yi ; Sasmal, Kalyan ; Moir, Camilla M. ; Basak, Rourav ; Huang, Hai ; Lee, Jun-Sik ; Rodolakis, Fanny ; Boyle, Timothy J. ; et al ( October 2022 , Nature Communications)

   The shape of 3d-orbitals often governs the electronic and magnetic properties of correlated transition metal oxides. In the superconducting cuprates, the planar confinement of the$${d}_{{x}^{2}-{y}^{2}}$$$d_{x^2-y^2}$orbital dictates the two-dimensional nature of the unconventional superconductivity and a competing charge order. Achieving orbital-specific control of the electronic structure to allow coupling pathways across adjacent planes would enable direct assessment of the role of dimensionality in the intertwined orders. Using CuL₃and PrM₅resonant x-ray scattering and first-principles calculations, we report a highly correlated three-dimensional charge order in Pr-substituted YBa₂Cu₃O₇, where the Prf-electrons create a direct orbital bridge between CuO₂planes. With this we demonstrate that interplanar orbital engineering can be used to surgically control electronic phases in correlated oxides and other layered materials.

    

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4. Visualizing atomic sizes and molecular shapes with the classical turning surface of the Kohn–Sham potential

   https://doi.org/10.1073/pnas.1814300115  

   Ospadov, Egor ; Tao, Jianmin ; Staroverov, Viktor N. ; Perdew, John P. ( November 2018 , Proceedings of the National Academy of Sciences)

   The Kohn–Sham potential$v_{\text{eff}}\left(\mathbf{r}\right)$is the effective multiplicative operator in a noninteracting Schrödinger equation that reproduces the ground-state density of a real (interacting) system. The sizes and shapes of atoms, molecules, and solids can be defined in terms of Kohn–Sham potentials in a nonarbitrary way that accords with chemical intuition and can be implemented efficiently, permitting a natural pictorial representation for chemistry and condensed-matter physics. Let${ϵ}_{\text{max}}$be the maximum occupied orbital energy of the noninteracting electrons. Then the equation$v_{\text{eff}}\left(\mathbf{r}\right)={ϵ}_{\text{max}}$defines the surface at which classical electrons with energy$ϵ\le {ϵ}_{\text{max}}$would be turned back and thus determines the surface of any electronic object. Atomic and ionic radii defined in this manner agree well with empirical estimates, show regular chemical trends, and allow one to identify the type of chemical bonding between two given atoms by comparing the actual internuclear distance to the sum of atomic radii. The molecular surfaces can be fused (for a covalent bond), seamed (ionic bond), necked (hydrogen bond), or divided (van der Waals bond). This contribution extends the pioneering work of Z.-Z. Yang et al. [Yang ZZ, Davidson ER (1997)Int J Quantum Chem62:47–53; Zhao DX, et al. (2018)Mol Phys116:969–977] by our consideration of the Kohn–Sham potential, protomolecules, doubly negative atomic ions, a bond-type parameter, seamed and necked molecular surfaces, and a more extensive table of atomic and ionic radii that are fully consistent with expected periodic trends.

    

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5. Introducing DDEC6 atomic population analysis: part 4. Efficient parallel computation of net atomic charges, atomic spin moments, bond orders, and more

   https://doi.org/10.1039/c7ra11829e  

   Limas, Nidia Gabaldon ; Manz, Thomas A. ( January 2018 , RSC Advances)

   The DDEC6 method is one of the most accurate and broadly applicable atomic population analysis methods. It works for a broad range of periodic and non-periodic materials with no magnetism, collinear magnetism, and non-collinear magnetism irrespective of the basis set type. First, we show DDEC6 charge partitioning to assign net atomic charges corresponds to solving a series of 14 Lagrangians in order. Then, we provide flow diagrams for overall DDEC6 analysis, spin partitioning, and bond order calculations. We wrote an OpenMP parallelized Fortran code to provide efficient computations. We show that by storing large arrays as shared variables in cache line friendly order, memory requirements are independent of the number of parallel computing cores and false sharing is minimized. We show that both total memory required and the computational time scale linearly with increasing numbers of atoms in the unit cell. Using the presently chosen uniform grids, computational times of ∼9 to 94 seconds per atom were required to perform DDEC6 analysis on a single computing core in an Intel Xeon E5 multi-processor unit. Parallelization efficiencies were usually >50% for computations performed on 2 to 16 cores of a cache coherent node. As examples we study a B-DNA decamer, nickel metal, supercells of hexagonal ice crystals, six X@C 60 endohedral fullerene complexes, a water dimer, a Mn 12 -acetate single molecule magnet exhibiting collinear magnetism, a Fe 4 O 12 N 4 C 40 H 52 single molecule magnet exhibiting non-collinear magnetism, and several spin states of an ozone molecule. Efficient parallel computation was achieved for systems containing as few as one and as many as >8000 atoms in a unit cell. We varied many calculation factors ( e.g. , grid spacing, code design, thread arrangement, etc. ) and report their effects on calculation speed and precision. We make recommendations for excellent performance. 

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