Covalent Bond Orders Research Articles

Simultaneous identification of strong and weak interactions with Pauli energy, Pauli potential, Pauli force, and Pauli charge.

Strong and weak interatomic interactions in chemical and biological systems are ubiquitous, yet how to identify them on a unified theoretical foundation is still not well established. Recently, we proposed employing Pauli energy-based indexes, such as strong covalent interaction and bonding and noncovalent interaction indexes, in the framework of density functional theory for the purpose. In this work, we extend our previous theoretical work by directly employing Pauli energy, Pauli potential, Pauli force, and Pauli charge to simultaneously identify both strong covalent bonding and weak noncovalent interactions. Our results from this work elucidate that using their signature isosurfaces, we can identify different types of interactions, either strong or weak, including single, double, triple, and quadruple covalent bonds, ionic bond, metallic bond, hydrogen bonding, and van der Waals interaction. We also discovered strong linear correlations between Pauli energy derived quantities and different covalent bond orders. These qualitative and quantitative results from our present study solidify the viewpoint that a unified approach to simultaneously identify both strong and weak interactions is possible. In our view, this work signifies one step forward towards the goal of establishing a density-based theory of chemical reactivity in density functional theory.

Polarized Cu-Bi Site Pairs for Non-Covalent to Covalent Interaction Tuning toward N2 Photoreduction.

A universal atomic layer confined doping strategy is developed to prepare Bi24 O31 Br10 materials incorporating isolated Cu atoms. The local polarization can be created along the CuOBi atomic interface, which enables better electron delocalization for effective N2 activation. The optimized Cu-Bi24 O31 Br10 atomic layers show 5.3× and 88.2× improved photocatalytic nitrogen fixation activity than Bi24 O31 Br10 atomic layer and bulk Bi24 O31 Br10 , respectively, with the NH3 generation rate reaching 291.1µmol g-1 h-1 in pure water. The polarized Cu-Bi site pairs can increase the non-covalent interaction between the catalyst's surface and N2 molecules, then further weaken the covalent bond order in NN. As a result, the hydrogenation pathways can be altered from the associative distal pathway for Bi24 O31 Br10 to the alternating pathway for Cu-Bi24 O31 Br10 . This strategy provides an accessible pathway for designing polarized metal site pairs or tuning the non-covalent interaction and covalent bond order.

Bond Order Densities in Real Space.

In this contribution we introduce the concept of bond order density (BOD) on the basis of a previous work on natural adaptive orbitals. We show that BODs may be used to visualize both the global spatial distribution of the covalent bond order and its eigencomponents, which we call bond(ing) channels. BODs can be equally computed at correlated and noncorrelated levels of theory and in ground or excited states, thus offering an appealing description of bond-forming, bond-breaking, and bond-evolution processes. We show the power of the approach by examining a number of homo- and heterodiatomics, including the controversial existence of a fourth bonding component in dicarbon, by analyzing a few interesting bonding situations in polyatomics and chemical transformations, and by exemplifying exotic bonding behaviors in simple excited electronic states.

SCI: a robust and reliable density-based descriptor to determine multiple covalent bond orders

Very recently [J. Phys. Chem. A 2018, 122 (11), 3087-3095], we proposed to employ the Pauli energy to identify and determine strong covalent interactions (SCI), whose bond order are equal to or larger than two. This is done through the signature isosurface shape between the two bonding atoms. We discovered that the signature shape for a double, triple, and quadruple covalent bond is like a dumbbell, donut (torus), and four-beats, respectively. Systems with even higher bond orders were examined and confirmed. This work is a follow-up study of our previous work. The dependence of thesignature isosurface shape on the choice of methodologies and basis sets is systematically investigated. Its effectiveness and robustness in determining bond orders are highlighted again with more examples. In addition, using the molybdenum dimer in different environments, e.g., in vacuum, sandwiched between molecules, and encapsulated in the C80 cage, as illustrative examples, we show that, generally speaking, bond strength and bond order are two different chemical concepts. For systems containing transition metals, it is not always true that a short metal-metal bond length corresponds to a larger bond order. Put together, these results should provide additional pieces of convincing evidence showing that the SCI index is a robust and reliable density-based descriptor to accurately determine multiple covalent bond orders.

Study of behaviour of Ni(III) macrocyclic complexes in acidic aqueous medium through kinetic measurement involving hydrogen peroxide oxidation and DFT calculations

The Cu(II) ion-catalysed kinetics of oxidation of H2O2 by [Ni IIIL] [where L = L1 (cyclam) and L2 (1,8-bis(2-hydroxyethyl)-1,3,6,8,10,13-hexaazacyclotetradecane)] was studied in the pH range of 3.6–5.6 in acetic acid-acetate buffer medium at 25°C in the presence of sulphate ion. The ionic strength (I) was maintained at 0.5 M (NaClO4). The rate constants showed an inverse acid dependence and [Ni III L 2] was observed to be more stable than [Ni III L 1]. The rate of the reaction of both complexes with hydrogen peroxide shows contrasting behaviour at pH > 2.5 when compared to the same reaction in perchloric acid medium. DFT calculations performed on the complexes [Ni III L 1(SO4)(OAc)] and [Ni III L 2(SO4)(OAc)] reveal that both the acetate and sulphate ligands are axially coordinated to the metal centre. In addition, there is strong hydrogen bonding between the axial ligand and NH hydrogen of the macrocyclic ligand. The computed covalent bond orders in the aqueous medium predict that the acetate forms stronger coordinate bond with Ni ion than the sulphate ligand. The hydroxyl group present in one of the pendant groups of L2 forms a strong hydrogen bond with the sulphate ligand which leads to additional stability in [Ni III L 2(SO4)(OAc)]. The Cu(II) ion-catalysed kinetics of oxidation of H2O2 by [NiIIIL] [where L = L1 (cyclam) and L2 (1,8-bis(2-hydroxyethyl)-1,3,6,8,10,13-hexaazacyclotetradecane)] was studied in the pH range of 3.6-5.6. The structure and bonding patterns of the [NiIIIL1(SO4)(OAc)] and [NiIIIL2(SO4)(OAc)] were studied using DFT calculations.

Biological and spectral studies of O-Tolyl Biguanide: Experimental and theoretical approach

Antibiotic and antimicrobial compound O-Tolyl Biguanide (OTB) structure was calculated at the B3LYP using 6-311++G(d,p) basis set level of theory. Optimized geometric bond lengths, bond angles and dihedral angles of the molecule were calculated and analyzed. FT-IR and FT-Raman spectra of OTB were recorded and vibrational assignments of the observed fundamental bands had been proposed on the basis of peak positions and relative intensities. Molecular geometry, vibrational spectra, covalent bond orders and atomic charges of OTB had been used to investigate the effects of charge delocalization leading to Y-aromaticity.

New insights from domain-averaged Fermi holes and bond order analysis into the bonding conundrum in C2

ABSTRACTThe bonding in the ground state of C2 is examined using a combined approach based on the analysis of domain-averaged Fermi holes and of the contributions to covalent bond orders that can be associated with individual localised natural orbitals. The σ system in this molecule turns out to be particularly sensitive, evolving from a description that includes a fairly traditional shared electron pair σ bond, for a range of intermediate nuclear separations, to a somewhat different situation near equilibrium geometry, where non-classical repulsive interactions are particularly important. The various results provide further support for the view that the electronic structure of this molecule sufficiently exceeds the scope of traditional bonding paradigms that attempts to classify the bonding in terms of a classical bond multiplicity are highly questionable.

Electric field effects on the intermolecular interactions in water whiskers: insight from structures, energetics, and properties.

Modulation of intermolecular interactions in response to external electric fields could be fundamental to the formation of unusual forms of water, such as water whiskers. However, a detailed understanding of the nature of intermolecular interactions in such systems is lacking. In this paper, we present novel theoretical results based on electron correlation calculations regarding the nature of H-bonds in water whiskers, which is revealed by studying their evolution under external electric fields with various field strengths. We find that the water whiskers consisting of 2-7 water molecules all have a chain-length dependent critical electric field. Under the critical electric field, the most compact chain structures are obtained, featuring very strong H-bonds, herein referred to as covalent H-bonds. In the case of a water dimer whisker, the bond length of the novel covalent H-bond shortens by 25%, the covalent bond order increases by 9 times, and accordingly the H-bond energy is strengthened by 5 times compared to the normal H-bond in a (H2O)2 cluster. Below the critical electric field, it is observed that, with increasing field strength, H-bonding orbitals display gradual evolutions in the orbital energy, orbital ordering, and orbital nature (i.e., from typical π-style orbital to unusual σ-style double H-bonding orbital). We also show that, beyond the critical electric field, a single water whisker may disintegrate to form a loosely bound zwitterionic chain due to a relay-style proton transfer, whereas two water whiskers may undergo intermolecular cross-linking to form a quasi-two-dimensional water network. Overall, these results help shed new insight on the effects of electric fields on water whisker formation.

Are orbital-resolved shared-electron distribution indices and Cioslowski covalent bond orders useful for molecules?

Values of a delocalisation index that is also known as the shared-electron distribution index can be resolved into contributions from individual domain-averaged Fermi hole functions. In order to assess the utility of this approach, as well as of the partitioning of Cioslowski covalent bond orders into contributions associated with individual localised natural orbitals, results are examined for three molecular test cases: HeH and Be2 are considered for short nuclear separations, for which these systems are demonstrably not bound, and the σ framework of N2 near its equilibrium geometry is examined.

A General Quantum Mechanically Derived Force Field (QMDFF) for Molecules and Condensed Phase Simulations.

A black-box type procedure is presented for the generation of molecule-specific, classical potential energy functions (force-field, FF) solely from quantum mechanically (QM) computed input data. The approach can treat covalently bound molecules and noncovalent complexes with almost arbitrary structure. The necessary QM information consists of the equilibrium structure and the corresponding Hessian matrix, atomic partial charges, and covalent bond orders. The FF fit is performed automatically without any further input and yields a specific (nontransferable) potential which very closely resembles the QM reference potential near the equilibrium. The resulting atomistic, fully flexible FF is anharmonic and allows smooth dissociation of covalent bonds into atoms. A newly proposed force-constant-bond-energy relation with little empiricism provides reasonably accurate (about 5-10% error) atomization energies for almost arbitrary diatomic and polyatomic molecules. Intra- and intermolecular noncovalent interactions are treated by using well established and accurate D3 dispersion coefficients, CM5 charges from small basis set QM calculations, and a new interatomic repulsion potential. Particular attention has been paid to the construction of the torsion potentials which are partially obtained from automatic QM-tight-binding calculations for model systems. Detailed benchmarks are presented for conformational energies, atomization energies, vibrational frequencies, gas phase structures of organic molecules, and transition metal complexes. Comparisons to results from standard FF or semiempirical methods reveal very good accuracy of the new potential. While further studies are necessary to validate the approach, the initial results suggest QMDFF as a routine tool for the computation of a wide range of properties and systems (e.g., for molecular dynamics of isolated molecules, explicit solvation, self-solvation (melting) or even for molecular crystals) in particular when standard parametrizations are unavailable.

Stockholder projector analysis: A Hilbert-space partitioning of the molecular one-electron density matrix with orthogonal projectors

A previously introduced partitioning of the molecular one-electron density matrix over atoms and bonds [D. Vanfleteren et al., J. Chem. Phys. 133, 231103 (2010)] is investigated in detail. Orthogonal projection operators are used to define atomic subspaces, as in Natural Population Analysis. The orthogonal projection operators are constructed with a recursive scheme. These operators are chemically relevant and obey a stockholder principle, familiar from the Hirshfeld-I partitioning of the electron density. The stockholder principle is extended to density matrices, where the orthogonal projectors are considered to be atomic fractions of the summed contributions. All calculations are performed as matrix manipulations in one-electron Hilbert space. Mathematical proofs and numerical evidence concerning this recursive scheme are provided in the present paper. The advantages associated with the use of these stockholder projection operators are examined with respect to covalent bond orders, bond polarization, and transferability.

Covalent bond orders and atomic anisotropies from iterated stockholder atoms

Iterated stockholder atoms are produced by dividing molecular electron densities into sums of overlapping, near-spherical atomic densities. It is shown that there exists a good correlation between the overlap of the densities of two atoms and the order of the covalent bond between the atoms (as given by simple valence rules). Furthermore, iterated stockholder atoms minimise a functional of the charge density, and this functional can be expressed as a sum of atomic contributions, which are related to the deviation of the atomic densities from spherical symmetry. Since iterated stockholder atoms can be obtained uniquely from the electron density, this work gives an orbital-free method for predicting bond orders and atomic anisotropies from experimental or theoretical charge density data.

Weakening Hydrogen Bond of Thick Oil of Petroleum by Several Catalysts

The process of use catalyst or functional material that contains iron ion to weaken -O-H-X- (X=O, N and S) bond of the thick oil to reduce viscidity or crack, in aspects of the ion charge, covalent bond order, total energy and the average distance of Fe-X, is studied with density function theory and discrete variational method (DFT-DVM), one of the first principle methods. Sulfur is with positive charge, and the hydrogen bond of -O-H-S- does not form. The strength of -O-H-N- hydrogen bond is a bit larger than that of -O-H-O-. With the decrease of the distance of Fe-X (X=O, N), the charge of Fe ion increases, the charge of hydrogen ion decreases, and hydrogen bond is weakened.

On the stability of metal–aminoacid complexes in water based on water–ligand exchange reactions and electronic properties: Detailed study on iron–glycine hexacoordinated complexes

Thermodynamic stability of metal-aminoacid complexes in water is discussed in terms of the Gibbs free energy of water-ligand exchange processes, and the electronic stabilizing factors thoroughly investigated by means of 1-electron and 2-electron density properties. Hexacoordinated complexes formed between iron cations and glycine molecules acting as monodentate or bidentate ligands have been chosen as targets for the current study. Results agree with experimental findings, and complexes formed with bidentate ligands are found to be more stable than those formed with monodentate ones. The larger the number of the coordinated glycine molecules the more stable is the complex. Fe(III) complexes are more stable than Fe(II) ones, but differences are small and the Fe(3+)/Fe(2+) exchange process appears to be energetically feasible for these complexes. Formation of the second glycine-iron interaction involving the amino nitrogen in the bidentate ligands is enthalpycally unfavorable but takes place due to the large entropy rise of the process. The larger stability of Fe(III) complexes is due however to the balance between energetic and solvation terms, which is favorable to these complexes. Electron density properties account satisfactorily for the electronic energy changes along the complex formation in terms of ligand-metal electron transfer and covalent bond orders.

Towards Spontaneous Heterolysis of the Homonuclear PP Bond in Diphosphines: The Case of Diazaphospholeniumtriphospholides

Computational studies on a series of polyphospholyl-substituted N-heterocyclic phosphines (CH)(2)(NR)(2) P-P(n)(CH)(5-n) (R=Me, n=1-5) disclosed that increasing formal replacement of CH units in the phosphole ring by phosphorus atoms is associated with an increase in P-P distances and charge separation, and a decrease in covalent bond orders. Altogether, these trends imply that the CH versus P substitution enhances ionic P-P bond polarization in these compounds. Experimental verification of this hypothesis was obtained for the triphospholyl diazaphospholenes (CR)(2)(NR')(2)P-P(3)(CtBu)(2) (8a: R=H, R'=tBu; 8b: R=Me, R'=Mesityl [Mes]), which were prepared through metathesis reactions from suitable precursors and identified by solution and solid-state NMR data and a single-crystal X-ray diffraction study of 8a. Analysis of J(PP) coupling patterns suggested that both species are characterized by the absence of a strong covalent P-P bond connecting both rings. This interpretation was confirmed by the finding of a unique P-P distance of 2.79 A for crystalline 8 a, and further supported by computational studies, which led to the conclusion that both species are better described as diazaphospholenium-triphospholide contact ion pairs rather than covalent molecules. Variable-temperature (VT) NMR spectra of 8b showed a collapse of J(PP) couplings between atoms in different rings, which indicates scrambling of the diazaphospholenium and triphospholide units between different molecules in solution, and further substantiates the proposed view on the molecular structure.

Covalent bond orders for non-bonded atoms: The case for carbon–carbon interactions

The Cioslowski–Mixon (CM) covalent bond order and the atoms-in-molecules (AIM) delocalization index can be used to study bonding characteristics between atoms not bonded in the conventional chemical sense. In particular, the bond orders between atoms (AIM basins) with one intervening atom evolve in a predictable manner and are related to the bond orders of conventionally bonded species. The CM approach shows that it is the tails of the incompletely localized orbitals that provide for such interactions. Single, multiple, and resonant bond effects are seen which are physically meaningful and useful as an additional characterization of molecular bonding. The important case of carbon–carbon interactions is studied here.

Covalent bond orders revisited: the open-shell case

This article states the concept of covalent bond order for open-shell systems from the invariance properties of the first- and second-order reduced density matrices for all the components of a multiplet state. A general bond order definition is formulated in the framework of the electronic population analyses in the Hilbert space of atomic orbitals.

Determination of covalent bond orders and atomic valence indices using topological features of the experimental electron density

We present an approach for the determination of covalent bond orders from the experimental electron density and its derivatives at the bond critical points. An application of this method to a series of organic compounds has shown that it provides a bonding quantification that is in reasonable agreement with that obtained by orbital theory. The 'experimental' atomic valence indices are also defined and their significance for the characterization of chemical problems is discussed.

Electron population uncertainty and atomic covalency

The atoms-in-molecules (AIM) index of atomic covalency is directly related to the AIM atomic population uncertainty. The covalent bond order, delocalization index, and, therefore, the atomic covalency are maximal when electron pairs are equally shared by the atoms involved. When polarization effects are present, these measures of covalent bond character decrease. We present atomic covalences for the single- and double-heavy atom hydrides of elements of the first and second low rows of the periodic table to illustrate these effects. Some usual behavior is seen in hydrogen-bridged species due in some cases to stronger than expected multicenter bonds and in other cases to many atoms contributing to the covalency index.

Computational Study of Solvent Effects and the Vibrational Spectra of Anderson Polyoxometalates

The structures and vibrational frequencies of the type II Anderson heteropolyanions [TeMo6O24]6- and [IMo6O24]5- have been calculated by using density functional theory using a number of common functionals and basis sets. For the first time, Raman intensities have been calculated and the effect of solvent on the modeling has been investigated. The calculated IR and Raman spectral traces are in good agreement with experiment allowing the characteristic group frequencies for this class of polyoxometalate to be identified. The stretching vibrations of the molybdenum-oxygen bonds are predicted to occur at somewhat lower frequencies than in the type I polyoxometalates. Stretching of the heteroatom-oxygen bonds occurs at significantly lower frequencies than in the Keggin anions as a simple consequence of the higher coordination number of the central heteroatom in the Anderson systems. For the [Mo2O7]2- and [Mo6O19]2- ions, the relatively low negative charge leads to small structural changes when solvent is included. In these systems, solvent leads to an increase in the bond polarity and a decrease in the covalent bond orders, resulting in decreases in the calculated frequencies. For the Anderson anions, the higher negative charges leads to greater solvent effects with contraction of the clusters and increases in the frequencies of bands due to stretching of the two, cis-related molybdenum-oxygen bonds.