Force Constants and Bond Orders of Nitrogen Bonds

The force constants and the corresponding bond orders of nitrogen bonds have been calculated from the vibrational spectra (infrared and Raman spectra) of a great number of nitrogen compounds. Plotting the maximum bond order of stable nitrogen bonds against the sum of Pauling's electronegativities of the bonding partners (Σx) leads to one continuous curve for the N? X bonds where X represents elements of the first and the second short period of the periodic table. Furthermore, when the bonds formed between these elements are arranged in a coordinate system in such a way that the position of each bond is determined by the difference between the electronegativities of the bonding partners (Δx along the ordinate) and the sum of the electronegativities of the bonding partners (Σx along the abscissa), the bonding partners capable of forming multiple bonds all lie within a closed domain, where their position can be correlated with their polymerizability and other reactivities of the multiple bonds. Also discussed are the orders of bonds between nitrogen and some transition elements. In an appendix, the present methods used to calculate force constants and bond orders are surveyed.     

The calculation of matrix elements for valence bond functions

Pauling's formulas for the calculation of matrix elements for valence bond functions are derived using a simple substitutional process. The results generalize and simplify the formulas. In particular, the formulas do not depend upon orthogonality of atomic orbitals nor upon the nature of the choice of bond structures (canonical or not). The results are particularly adaptable to automatic computation.     

Introduction

According to the maximum overlap method and the concept that the overlap integral may be used as an indicator of bond strength, a further discussion of bond strength F, an universal formula of F, and the correlation between the bond strength discussed here and that defined by Pauling have been given in this paper. For the type of molecule ML_k, under the approximations of k = 2 and using the projection method of the angular part of bond orbitals, the same results as those derived by Pauling can be obtained from the universal formula. From the same formula, two more equations containing g and h atomic orbitals have been derived.     

分子轨道成键性质及原子间化学键强度的成键能判据

本文定义了成键能Eb并用作分子轨道成键性质和分子中原子间化学键强度的判据。与Mulliken重叠布居Pb不同, 在成键能Eb中同时包含了原子轨道间的重叠因素和原子轨道的能量因素。对一些分子所作计算结果表明, 成键能判据较Mulliken重叠布居判据所得结论与实验更相符。     

On a definition of bond energies based on localized molecular orbitals

A theoretical model is presented for defining bond energies based on localized molecular Orbitals. These bond energies are obtained by rearranging the total SCF energy including the nuclear repulsion term to a sum over orbital and orbital interaction terms and then to total orbital terms, which can be interpreted as the energies of localized orbitals in a molecule. A scaling procedure is used to obtain a direct connection with experimental bond dissociation energies. Two scale parameters are employed, the C-C and the C-H bond dissociation energy in C₂H₆ for A-B and C-H type bonds, respectively. The implications of this scaling procedure are discussed. Numerical applications to a number of organic molecules containing no conjugated bonds gives in general a very satisfactory agreement between experimental and theoretical bond energies.     

Maximum bond order hybrid orbitals

Summary Based on the simplified calculation scheme of the maximum bond order principle and the basic idea of the maximum overlap symmetry orbital method, a simple procedure is suggested for constructing systematically the bonding hybrid orbitals, called maximum bond order hybrid orbitals, for a given molecule from the first-order density matrix obtained from a molecular orbital calculation. As an example, the proposed procedure is performed for some typical small molecules by use of the density matrix obtained from CNDO/2 calculation. It is shown that the bonding hybrid orbitals constructed by using the procedure are extremely close to those by using the natural hybrid orbital procedure and in good agreement with chemical intuition, and that the proposed procedure can be performed more easily than the natural hybrid orbital procedure and can given simultaneously the values of the maximum bond order for all bonds in molecules.The project was supported by National Natural Science Foundation of China and also supported partly by Foundation of Hubei Education Commission     

Comparative analysis of blue‐shifted hydrogen bond versus conventional hydrogen bond in methyl radical complexes

Methyl radical complexes H₃C…HCN and H₃C…HNC have been investigated at the UMP2(full)/aug‐cc‐pVTZ level to elucidate the nature of hydrogen bonds. To better understand the intermolecular H‐bond interactions, topological analysis of electron density at bond critical points (BCP) is executed using Bader's atoms‐in‐molecules (AIM) theory. Natural bond orbital (NBO) analysis has also been performed to study the orbital interactions and change of hybridization. Theoretical calculations show that there is no essential difference between the blue‐shift H‐bond and the conventional one. In H₃C…HNC complex, rehybridization is responsible for shortening of the N? H bond. The hyperconjugative interaction between the single electron of the methyl radical and N? H antibonding orbital is up to 7.0 kcal/mol, exceeding 3.0 kcal/mol, the upper limit of hyperconjugative n(Y)→σ*(X–H) interaction to form the blue‐shifted H‐bond according to Alabugin's theory. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Computational study of structures and proton transfer in hydrogen‐bonded ammonia complexes using semiempirical valence‐bond approach

In this study, the seGVB method was implemented for the N H bonding system, specifically for hydrogen‐bonded ammonia complexes, and the model well reproduces the MP2 geometries and energetics. A comparison between the ammonia dimer and water dimer is given from the viewpoint of valance‐bond structures in terms of the calculated bond energies and pair–pair interactions. The linear hydrogen bond is found to be stronger than the bent bonds in both cases, with the difference in energy between the linear and cyclic structures being comparable in both cases although the NH bonds are generally weaker. The energy decomposition clearly demonstrates that the changes in electronic energy are quite different in the two cases due to the presence of an additional lone pair on the water molecule, and it is this effect which leads to the net stabilization of the cyclic structure for the ammonia dimer. Proton‐transfer profiles for hydrogen‐bonded ammonia complexes [NH₂ H NH₂]⁻ and [NH₃ H NH₃]⁺ were calculated. The barrier for proton transfer in [NH₃ H NH₃]⁺ is larger than that in [NH₂ H NH₂]⁻, but smaller than that in the protonated water dimer. The different bonding structures substantially affect the barrier to proton transfer, even though they are isoelectronic systems. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 73: 357–367, 1999     

Ab initio Valence Bond Study on AB-type Molecules,A Description for XH(X=L,Be,B,C,N,O,F) and XF(X=Li,Be,B)

Ab initio valence bond method is employed to quantitatively study the concepts of ionic resonance energy and ionicity of a chemical bond in the cases of hydrides XH(X=Li,Be,B,C,N,O,F) and fluorides XF(X=Li,Be,B),By establishing the relationship between resonance and stability,and comparing the calculated ionicities with Pauling‘s earlier estimations in the above diatomic molecules,the merits of Pauling‘s classical resonance theory were demonstrated at the ab initio level.     

Research on the correlation between the optical gap and chemical bond in sulphur and selenium co-doped chalco-halide glasses

The Ge–Ga–Se–S–CsCl glasses were prepared by the melting-quenching method. The absorption and transmission spectrum were measured under room temperature. It is found that these glasses have high broad spectral range of transparency from visible to far-infrared region (0.4–12 μm). The relationship between the optical gap and chemical composition in terms of novel chalco-halide glasses is discussed based on the Pauling's theory model, which is using the modified heats of atomization and the coordination number of the elements, to explain this phenomena for the first time.     

Maximum overlap symmetry orbitals

Based on the principle of maximum overlap, a new simple method is suggested for constructing the symmetry orbitals of arbitrary molecules and the delocalized molecular orbitals of molecules that do not involve the rings with an odd number of atoms. All these orbitals, called “maximum overlap symmetry orbitals,” are determined by an extended maximum overlap criterion and form the bases for the irreducible representations of the molecular point symmetry group. The theoretical analysis and the numerical results show that the obtained molecular orbitals are close to those obtained from the customary LCAO method, and calculation by the proposed method requires less computing time than does the LCAO method, thus illustrating a fact that the method is not only a reasonable approximation of the LCAO method, but simpler and feasible in large molecular systems.     

Hydrogen bond lifetime for water in classic and quantum molecular dynamics

The lifetime of hydrogen bonds in water at T = 298 K and p = 0.1 MPa is computed by means of classic molecular dynamics with eight different potentials of pair lifetime interaction and Car-Parinello molecular dynamics. The results obtained using various computational techniques for hydrogen bond life-times are compared. It is shown that they can differ from one another by several times. The dependence for the hydrogen bond lifetime computed in our numerical experiment upon the method of its determination is found.     

Effect of hydrogen bridge geometry on the vibrational spectra of water: Three-parameter potential of H bond

The ability of water molecules to form a three-dimensional network of hydrogen bonds basically determines both the intrinsic structure and unique properties of this liquid and also a character of interactions with other molecules. However, the dependence of the H bond energy on the geometry of its hydrogen bridge, namely on the R_O…_O length and non-linearity, is unknown, i.e. the deviations of O—H group directions and the lone pair forming this bond from optimum ones (angles (φ = H—_O…_O and χ = —_O…_O correspondingly). Even in computer simulation methods, the contribution of H bonds to the total interaction potential is not separated; that does not allow one to define unequivocally these bonds in a model and to analyze quantitatively the features of their networks. The purpose of this work is to fill in this gap by expressing the energy E through geometric parameters (R, φ, χ). The obtained solution quality is proved by an agreement between the distributions of OH vibrational frequencies (which are very sensitive to the H bond strength) calculated with its help and the shape of experimental spectra in a wide temperature range. Based on this, the distributions of H bond energies P(E, T) and of their bend angles P(φ, T) and P(χ, T) are also calculated. It is shown that the main contribution to spectra is made by the shortest bonds with their lengths close to a minimum of the potential E(R). Thus, the low-frequency slope of a band corresponds to slightly bent H bonds, while the central part relates to also short but sufficiently nonlinear H bonds. LongH bonds are responsible for only well known high-frequency Walrafens’s wing near 3620 cm^-1. Moreover, these weak bonds are very strongly bent.     

Trigger bond analysis of nitroaromatic energetic materials using wiberg bond indices

The identification of trigger bonds, bonds that break to initiate explosive decomposition, using computational methods could help direct the development of novel, “green” and efficient high energy density materials (HEDMs). Comparing bond densities in energetic materials to reference molecules using Wiberg bond indices (WBIs) provides a relative scale for bond activation (%ΔWBIs) to assign trigger bonds in a set of 63 nitroaromatic conventional energetic molecules. Intramolecular hydrogen bonding interactions enhance contributions of resonance structures that strengthen, or deactivate, the C NO₂ trigger bonds and reduce the sensitivity of nitroaniline‐based HEDMs. In contrast, unidirectional hydrogen bonding in nitrophenols strengthens the bond to the hydrogen bond acceptor, but the phenol lone pairs repel and activate an adjacent nitro group. Steric effects, electron withdrawing groups and greater nitro dihedral angles also activate the C NO₂ trigger bonds. %ΔWBIs indicate that nitro groups within an energetic molecule are not all necessarily equally activated to contribute to initiation. %ΔWBIs generally correlate well with impact sensitivity, especially for HEDMs with intramolecular hydrogen bonding, and are a better measure of trigger bond strength than bond dissociation energies (BDEs). However, the method is less effective for HEDMs with significant secondary effects in the solid state. Assignment of trigger bonds using %ΔWBIs could contribute to understanding the effect of intramolecular interactions on energetic properties. © 2018 Wiley Periodicals, Inc.     

Hybridization in methylenecyclopropane and related molecules having exocyclic double bonds

The hybridization in methylenecyolopropane, dimethylenecyclopropane, bisethanoallene, and related molecules containing double bonds externally attached to a cyclopropane ring is considered by applying the method of maximum overlap. The results show that the bond overlap of an exocyclic double bond is larger than the bond overlap of a normal C=C bond, and double bonds in allenes have even larger overlap than an exocyclic C=C bond. The results of the calculations are correlated with some available experimental data.     

Calculation of carbon-carbon bond deformation curves for fluorinated ethylenes and the corresponding carbocations

Carbon-carbon bond deformation curves for fluorinated ethylene molecules and the corresponding carbocations were calculated by the ab initio self-consistent field method in the 5-31G basis set. The maximum force required for bond cleavage was taken as a criterion for bond strength. It has been found that for ethylene, replacement of hydrogen by fluorine insignificantly strengthens the C=C bonds in symmetric molecules. However, in molecules with an asymmetric arrangement of fluorine atoms, the bond is slightly weakened due to different charges on the carbon atoms. The configuration of the corresponding carbocations also depends on the bond polarity: an assymmetric distribution of electron density in the C=C bond region leads to the formation of σ-complexes, while a symmetric distribution of electron density (pure covalent bonding) gives π-complexes. Since the carbon-carbon bond in the σ-complexes is essentially weaker, one should expect significant weakening of the bond in high-acidity media if the bond exhibits any kind of asymmetry (chain branching, defects, etc.). For the considered molecules, an antibatic correlation has been established between the strength criterion F_max (unlike the dissociation energy) and the bond length. Institute of Physical Chemistry, Russian Academy of Sciences, Moscow. Translated fromZhurnal Strukturnoi Khimii, Vol. 36, No. 1, pp. 34–41, January–February, 1995. Translated by I. Izvekova     

The value of the π-bond order–bond length relationship in geometry prediction and chemical bonding interpretation

The π-bond order–bond length relationship is reintroduced to the literature and extended to heteronuclear bonds by presenting graphs derived solely by theoretical methods. π-bond order and overlap population results for carbon–carbon, carbon–nitrogen, and carbon–oxygen bonds obtained from ab initio STO -3G calculations using theoretically-optimized geometries are reported for a series of pteridines and for a wide range of small organic molecules. The order–length correlation graphs are used in predicting the “intrinsic” single bond lengths for sp² – sp² and sp – sp hybridized C? C, C? N, and C? O bonds, and in evaluating the relative importance of hybridization, π-electron delocalization and bond polarization effects in causing bond shortening in conjugated and hyperconjugated molecules. The calculated value of the π-bond order for a given bond in a molecule is shown to be relatively insensitive to moderate geometry changes: Hence, a use for the correlation graphs in geometry prediction is suggested. Some results for the extended 4-21G basis set are also presented.     

Detailed comparison of the pnicogen bond with chalcogen,halogen, and hydrogen bonds

The characteristics of the pnicogen bond are explored using a variety of quantum chemical techniques. In particular, this interaction is compared with its halogen and chalcogen bond cousins, as well as with the more common H‐bond. In general, these bonds are all of comparable strength. More specifically, they are strengthened by the presence of an electronegative substituent on the electron‐acceptor atom, and each gains strength as one moves down the appropriate column of the periodic table, for example, from N to P to As. These noncovalent bonds owe their stability to a mixture in nearly equal parts of electrostatic attraction and charge transfer, along with a smaller dispersion component. The charge transfer arises from the overlap between the lone pair of the electron donor and a σ* antibond of the acceptor. The angular characteristics of the equilibrium geometry result primarily from a compromise between electrostatic and induction forces. Angular distortions of the H‐bond are typically less energetically demanding than comparable bends of the other noncovalent bonds. © 2012 Wiley Periodicals, Inc.