A new algorithm for inactive orbital optimization in valence bond theory

This paper presents an efficient algorithm for energy gradients in valence bond self-consistent field (VBSCF) method with non-orthogonal orbitals. The frozen core approximation method is extended to the case of non-orthogonal orbitals. The expressions for the total energy and its gradients are presented by introducing auxiliary orbitals, where inactive orbitals are orthogonal, while active orbitals are non-orthogonal themselves but orthogonal to inactive orbitals. It is shown that our new algorithm has a low scaling of (N _a + 1)m ⁴, where N _a and m are the numbers of the active orbitals and basis functions, respectively, and is more efficient than the existing VBSCF algorithms.     

Natural Bond Orbital Study on the Nature of Binding in the H2 Molecule

We use the natural bond orbital (NBO) method to decompose a MO wavefunction into the intuitive valence bond (VB) structures. At least two natural orbital type MO are required to describe the essential binding of the H₂ molecule at all inter nuclear distances. At first the MO wavefunction is transformed into an unrestricted Hartree-Fock wave-function consisted of non-orthogonal localized orbitals u' and v', and then the NBO method is used to decompose u' and v' into the physical meaningful orthogonal localized orbitals. Our results show that the orbitals u' and v' are decomposed into an atomic and an overlap parts. The latter part gives rise to the conventional ionic structure in the VB picture.     

An Orthogonal Dynamic Covalent Chemistry Tool for Ring-Opening Polymerization of Cyclic Oligochalcogenides on Detachable Helical Peptide Templates

A model system is introduced as a general tool to elaborate on orthogonal templation of dynamic covalent ring-opening polymerization (ODC-TROP). The tool consists of 3₁₀ helical peptides as unprecedented templates and semicarbazones as orthogonal dynamic covalent linkers. With difficult-to-control 1,2-dithiolanes, ODC-TROP on the level of short model oligomers occurs with high templation efficiency, increasing and diminishing upon helix stabilization and denaturation, respectively. Further, an anti-templated conjugate with mispositioned monomers gave reduced templation upon helix twisting. Even with the “unpolymerizable” 1,2-diselenolanes, initial studies already afford mild templation efficiency. These proof-of-principle results promise that the here introduced tool, recyclable and enabling late-stage side chain modification, will be useful to realize ODC-TROP of intractable or unknown cyclic dynamic covalent monomers for dynamer materials as well as cellular uptake and signaling applications.     

The factors influencing coordination numbers in solids

An empirical plot of average principal quantum number ($\text{n}$) versus average AX electronegativity difference (Δχ) for A_nX_m structures shows resolution of four-, six-, and eight-coordinate solid state structures (Pearson diagrams). A simple molecular orbital (and therefore covalent) analysis of the coordination number problem suggests that it is determined by the balance between X-X nonbonded repulsions and the number of stabilizing interactions (both of which increase with coordination number). A-A repulsions may also be important if A is significantly larger than X. The approach provides an alternative to the ionic model for structure rationalization but it is still not clear how relatively important covalent and ionic factors are in determining the structures of even “ionic” solids.     

Low-Barrier Hydrogen Bonds in Negative Thermal Expansion Material H3[Co(CN)6]

The covalent nature of the low-barrier N−H−N hydrogen bonds in the negative thermal expansion material H₃[Co(CN)₆] has been established by using a combination of X-ray and neutron diffraction electron density analysis and theoretical calculations. This finding explains why negative thermal expansion can occur in a material not commonly considered to be built from rigid linkers. The pertinent hydrogen atom is located symmetrically between two nitrogen atoms in a double-well potential with hydrogen above the barrier for proton transfer, thus forming a low-barrier hydrogen bond. Hydrogen is covalently bonded to the two nitrogen atoms, which is the first experimentally confirmed covalent hydrogen bond in a network structure. Source function calculations established that the present N−H−N hydrogen bond follows the trends observed for negatively charge-assisted hydrogen bonds and low-barrier hydrogen bonds previously established for O−H−O hydrogen bonds. The bonding between the cobalt and cyanide ligands was found to be a typical donor–acceptor bond involving a high-field ligand and a transition metal in a low-spin configuration.     

Ab initio valence-bond calculations of H2O

The first and second bond dissociation energies for H₂O have been calculated in anab initio manner using a multistructure valence-bond scheme. The basis set consisted of a minimal number of non-orthogonal atomic orbitals expressed in terms of gaussian-lobe functions. The valence-bond structures considered properly described the change in the molecular system as the hydrogen atoms were individually removed to infinity. The calculated equilibrium geometry for the H₂O molecule has an O-H bond length of 1.83 Bohrs and an HOH bond angle of 106.5°. With 49 valence-bond structures the energy of H₂O at this geometry was ?76.0202 Hartrees. The calculated equilibrium bond length for the OH radical was 1.86 Bohrs and the energy, using the same basis set, was ?75.3875 Hartrees. After correction for zero point energies the calculated bond dissociation energies are: H₂O → OH + H, D₁=75.38 kcal/mole and OH → O+H, D₂=54.79 kcal/mole.     

In-situ growth of V2O5 flower-like structures on ceramic tubes and their trimethylamine sensing properties

V₂O₅ flower-like structures assembled by thin nanosheets were in-situ growth on ceramic tubes by hydrothermal process. The structural characterization indicates that V₂O₅ flower-like structures is orthogonal diamond phase, which entirely covered on the surface of ceramic tubes. TMA sensing measured results revealed that the sensor based on V₂O₅ flower-like structures exhibited fast reversible and response, good selectivity to TMA and good stability at 200 °C. The good sensing performance may be ascribed to flower-like structures and directly growth sensing film on the ceramic tube without structure damage. Our works give a simple in-situ growth flower-like structures route on sensing device, which exhibits potential application for detecting trace amounts of TMA gas.     

First-principles study of ternary metal borocarbide compounds containing finite linear BC2 units

Electronic structures of the ternary metal borocarbide compounds Sc₂BC₂, Al₃BC₃ and Lu₃BC₃ containing linear BC₂ units are compared using density functional calculations. Results reveal a covalent bonding between the metallic matrix and the formally BC₂⁵⁻ nonmetal anions which is stronger for the aluminum compound than for the two others.     

The use of population localised orbitals to interpret molecular orbital calculations

An efficient and general method is derived to calculate population localised molecular orbitals (LMO's) from a given SCF eigenvector matrix, by reduction to an eigenvalue problem. Applications to both localised molecules (NH₃ and C₂H₂) and delocalised ones (B₂H₆, C₆H₆ and butadiene) are discussed in some detail. It is shown that unequal occupation of atomic energy levels leads to non-orthogonal LMO's. The consequences of non-orthogonal atomic hybrid orbitals are discussed, formulas for their overlap in terms of atomic occupation numbers are derived and it is shown that the occupation numbers are connected to LMO atomic orbital coefficients by various sum rules.     

Application of modified Neumann expansion for analytical evaluation of two-center,two-electron integrals over slater-type orbitals

A modified form of the Neumann expansion in terms of products of orthogonal polynomials for the inverse interelectronic distance r¹₁₂ is proposed. This expansion has been applied in order to derive a unified analytical formula for two-center and two-electron integrals over Slater-type orbitals. The results are equivalent to those given recently by Yasui and Saika, but the expansion itself can be used for building up a realistic algorithm for evaluation of three- and four-electron integrals determined by using correlated variational wave functions.     

Valence-bond studies of AH2 molecules

Minimal Slater basis set calculations are reported for H₂S. The calculations used both natural and hybrid atomic orbitals. The calculations were performed at H-S-H bond angles of 90 °, 92.2 ° and 95 °. The results are compared with similar calculations on H₂O and with calculations using the molecular orbital approximation. The only definite trend found in going from H₂O to H₂S is that the importance of the SH⁺H^– structure decreases. Changes in the relative importance of covalent and ionic structures depend upon which measure of importance is used. Calculations using a set of orthogonal hybrid orbitals again find the hybrid orbitals exhibiting non-perfect following behaviour with the hybrids remaining at about the equilibrium bond angle. Localized molecular orbitals were found to move in the opposite direction to the change in the H-S-H bond angle.     

Chemi-Inspired Silicon Allotropes—Experimentally Accessible Si9 Cages as Proposed Building Block for 1D Polymers, 2D Sheets,Single-Walled Nanotubes,and Nanoparticles

Numerous studies on silicon allotropes with three-dimensional networks or as materials of lower dimensionality have been carried out in the past. Herein, allotropes of silicon, which are based on structures of experimentally accessible [Si₉]⁴⁻ clusters known as stable anionic molecular species in neat solids and in solution, are predicted. Hypothetical oxidative coupling under the formation of covalent Si–Si bonds between the clusters leads to uncharged two-, one- and zero-dimensional silicon nanomaterials not suffering from dangling bonds. A large variety of structures are derived and investigated by quantum chemical calculations. Their relative energies are in the same range as experimentally known silicene, and some structures are even energetically more favorable than silicene. Significantly smaller relative energies are reached by the insertion of linkers in form of tetrahedrally connected Si atoms. A chessboard pattern built of Si₉ clusters bridged by tetrahedrally connected Si atoms represents a two-dimensional silicon species with remarkably lower relative energy in comparison with silicene. We discuss the structural and electronic properties of the predicted silicon materials and their building block nido-[Si₉]^4– based on density functional calculations. All considered structures are semiconductors. The band structures exclusively show bands of low dispersion, as is typical for covalent polymers.     

Computing the chemical reaction path with a ray-based fast marching technique for solving the Hamilton-Jacobi equation in a general coordinate system

This article presents a ray-based fast marching approach for solving the static Hamilton-Jacobi equation. The approach is very general and can be used for both orthogonal and non-orthogonal coordinate system. The method is unconditionally stable, algorithmatically simple and highly accurate. As an application, we use the method to compute different types of reaction path. Specifically, we consider the path for which the change in action or time is less than that of all other conceivable paths connecting two states. Such reaction paths are efficiently evaluated by back-tracing on the least-action or least-time surfaces. The method is illustrated by applying it to the collinear reactions, F + H₂ →HF + H and HF + H→H + FH.     

Segregation of tetracarbon units in low-energy tetracarbindane structures: Major differences from their aluminum and gallium analogs

The structures and energetics of the tetracarbindanes C₄In_n−4Me_n (n = 6-14) have been determined by density functional theory. In contrast to their aluminum and gallium analogs, the lowest energy tetracarbindanes typically have all four carbon atoms segregated into a single C₄ unit. Thus, linear C₄ units resembling butadiene are found in the lowest energy C₄In_n−4Me_n structures. In addition, some higher energy tetracarbindane structures have a structural feature not found in any of the corresponding tetracarbalanes and tetracarbagallanes, namely closed trapezoidal C₄ units resembling cyclobutene. Such trapezoidal C₄ units bind to the In_n−4 subcluster with the CC edge bonding to a single indium atoms as an olefin-metal or 3-center 2-electron bond. These differences may be attributed to the larger size of indium atoms (1.42 Å covalent radius) relative to gallium atoms (1.22 Å covalent radius).     

Covalent Structures of Phosphorus: A Comprehensive Theoretical Study

Starting from earlier work by Baudler we introduce a chemical heuristic for the systematic deduction and classification of covalent partial structures of phosphorus in polycyclic phosphanes, phosphorus-rich polycyclic phosphides, and allotropes of phosphorus except the black forms. This approach is used to direct ab initio techniques (which also confirm the rules) in the quest for as yet unknown forms of molecular or macromolecular phosphorus. Based on calculated stabilities of systematically generated structural alternatives we rationalize the stabilities of Hittorf's phosphorus and of molecular P₄, confirm the possible existence of at least one other crystalline allotropic form of phosphorus, and provide insight into the probable structure of amorphous red phosphorus. In total, the combined approach of chemical heuristics and large scale ab initio calculations presented in this work supplies a coherent chemical understanding of covalent polyphosphorus structures.     

Facile and efficient synthesis of C3-symmetric benzoxazine: a novel tri-arm molecular scaffold

Six novel C₃-symmetric benzoxazines (1a–f) were synthesized via a one-pot condensation, in which twelve covalent bonds were formed up to 96% yield. Two X-ray crystal structures confirmed their proposed conformations and showed their potential as a novel tri-arm molecular scaffold.     

Controlled polymerization of cyclic esters. structure of initiators and of active species related to the selectivity of initiation and propagation

This paper reviews mostly the already published work of our own, complemented with some new data and related to the control (i.e. selectivity) in the anionic and covalent (pseudoanionic) polymerization of cyclic esters. Ionic and covalent growing species are briefly compared in terms of their susceptibility to undergo side reactions. Then, structures of covalent initiators (mostly multivalent metal alkoxides) are discussed from the view point of their behavior in initiation and formation of active species. R₂AlOR', (RO)₃Al, and other metal alkoxides are discussed.     

A steepest-descent method for the calculation of localized orbitals and pseudoorbitals

A method for direct calculation of localized non-orthogonal orbitals, which has been proposed by the authors recently, is extended to cases where the overlap between different subsystems is very large. This is achieved by using a steepest-descent procedure. In addition, a computationally simple treatment of correlation effects is introduced into the method by means of the density functional formalism. Results of the method are given for e.g. LiH, CH₄, Ne₂, CO,(FH)₂.     

Covalent Cross-Linking of 2H-MoS2 Nanosheets

The combination of 2D materials opens a wide range of possibilities to create new-generation structures with multiple applications. Covalently cross-linked approaches are a ground-breaking strategy for the formation of homo or heterostructures made by design. However, the covalent assembly of transition metal dichalcogenides flakes is relatively underexplored. Here, a simple covalent cross-linking method to build 2H-MoS₂–MoS₂ homostructures is described, using commercially available bismaleimides. These assemblies are mainly connected vertically, basal plane to basal plane, creating specific molecular sized spaces between MoS₂ sheets. Therefore, this straightforward approach gives access to the controlled connection of sulfide-based 2D materials.