Energy Bond Order Research Articles

New semi-empirical computational analysis of catalytic reactions for automobile

Reaction profiles of diatomic molecules, \(\hbox {O}_2, \hbox {N}_2\), and NO, on a transition \(d\)-metal surface were semi-empirically calculated using a new approach based on a bond-energy bond-order (BEBO) model. The BEBO model could be a useful relation for describing reaction configurations. In this work, we introduce a new semi-empirical model which combines density functional theory (DFT)-based interaction parameters with the empirical Miyazaki BEBO model and demonstrate that our model could also be used successfully in previous DFT calculation results. The predictions calculated using this model, such as adsorption energies and adsorption geometries of incoming gas molecules, are close to previous experimental and theoretical results. In particular, the most remarkable point is that previous DFT calculation results and experimental results are available to our procedure. In other words, our model could be extremely simple but powerful.

Excited-State Hydroxide Ion Transfer from a Model Xanthenol Photobase

This article reports a study of excited-state hydroxide ion release from a model xanthenol photobase, XanOH. The driving force for the reaction was tuned using solvent mixtures with varying water/acetonitrile ratios, and the kinetics of the reaction was monitored using ultrafast pump-probe spectroscopy. The intrinsic barrier for the heterolysis was evaluated using Marcus and bond-energy bond-order (BEBO) models. The obtained value (ΔG(o)(#) = 10.17-10.80 kcal/mol) is significantly higher than the intrinsic barriers found for the proton release from previously studied photoacids. These results were discussed in terms of the difference in structures of solvated H(+) and OH(-) ions.

The importance of molecular conformation to the properties: a DFT study of the polynitro heterocyclic compounds based on dodecahydrodiimidazo [4,5-b:4′,5′-e]pyrazine structure

Two series of polynitro heterocyclic compounds with three conformations are designed based on the obtained dodecahydrodiimidazo [4,5-b:4′,5′-e]pyrazine “565” structure. First, the conformations including boat, chair, and plane, are optimized at B3PW91/6-311+G(d,p) level and some important properties are calculated. Based on the bond order, bond dissociation enthalpies and molecular energy analysis, it is found that the boat conformation owns lower energy and better bond order than the other two, and thus is most stable. Then, a further study on the electrical potential surfaces (EPS) proves that the stability of boat conformation can be contributed to the better balance between the positive and negative EPS. Next, according to molecular energy gap and density of state, the effect of each group on molecule is investigated: electrons on nitro group, compared with those on the framework, are easier to be activated so as to cause decomposition, thus nitro groups will determine the stability of molecule. Finally, the explosive velocity, pressure, and impact sensitivity of designed compounds are calculated. Results show that their explosive performances are significantly better than current energetic materials, and it is extraordinary enough that some compounds among them also maintain very good sensitivity.

Exploring hydrogen bond in the excited state leading toward intramolecular proton transfer: detailed analysis of the structure and charge density topology along the reaction path using QTAIM

Excited state intramolecular proton transfer (ESIPT) reaction along the O-H[Symbol: see text][Symbol: see text][Symbol: see text][Symbol: see text]O hydrogen bond of o-hydroxy benzaldehyde (OHBA), methyl salicylate (MS) and salicylic acid (SA) was investigated by ab-initio quantum chemical calculation and theory of atoms and molecules (QTAIM) for the first time. Variation in several geometric as well as QTAIM parameters along the reaction coordinate was monitored in the fully relaxed excited state potential energy curve (PEC) obtained from intrinsic reaction coordinate (IRC) analysis. Although, the excited state barrier height for the forward reaction (∆E (0) (#) ) reduces substantially in all the systems, MS and SA do not show any obvious asymmetry for proton transfer. For MS and SA, the crossover of the bond index as well as the lengths of the participating bonds at the saddle point is assigned due to this symmetry in accordance with bond energy - bond order (BEBO) model, which does not hold true in OHBA both in the ground and excited states. Bond ellipticity, covalent and metallic character were examined for different structures along the reaction path within the QTAIM framework. The QTAIM analysis was found to be able to uniquely distinguish between the ground and excited states of the OHBA molecule as well as both determining the effects on the bonding character of adding different substituent groups and differentiating between the ESIPT reactions in the SA and MS molecules.

Theoretical analysis of reaction kinetics with singlet oxygen molecules

A comparative analysis of predictive ability of three approaches to estimate the rate constants of reactions of H(2), H, H(2)O and CH(4) with electronically excited O(2)(a(1)Δ(g)) and O(2)(b(1)Σ(g)(+)) molecules is conducted. The first approach is based on a detailed ab initio study of potential energy surfaces. The second one is known as the "bond energy-bond order" method, and the third approach is a modification of the updated method of vibronic terms that makes it possible to evaluate the activation energy of reactions involving electronically excited species. The comparison showed that the estimates of the energy barrier by the updated method of vibronic terms for some reactions can be in good agreement with ab initio calculations and available experimental data. It was revealed that reactions of O(2)(b(1)Σ(g)(+)) molecules with H(2), H(2)O and CH(4) molecules and with the H atom result in the formation of electronically excited species. The reactivity of O(2)(b(1)Σ(g)(+)) molecules is smaller than that of O(2)(a(1)Δ(g)) ones, but much higher as compared to the reactivity of ground state O(2) molecules. For each reaction under study involving oxygen molecules in the excited electronic states O(2)(a(1)Δ(g)) and O(2)(b(1)Σ(g)(+)) the recommended temperature-dependent rate constants are presented.

Normalized kinetic field potentials for the atom-diatom reactions. Testing the collinear surfaces

The method of constructing the potential energy surface (WW) for the collinear atom-diatom chemical reactions, via the virial theorem from the normalized rotating Morse function (rotated around the united atom) representation (T-RMF) of the electronic kinetic energy, T, is tested by generating various WW surfaces for the H + H—H H—H + H and F + H—H F—H + H collinear reactions, and comparing them with the corresponding ab initio (H3) and LEPS (FHH) surfaces. To obtain the T-RMF parameters, only a knowledge of the coordinates and energy along the zero-virial path (zvp) is required, WW = WW[ZVP]. Two approximations of the ZVP have been used: an analytical fit of the ab initio steepest descent minimum energy path (MEP), and the bond energy/bond order (BEBO) path. Tests of both the WT[MEP] and WW[BEBO] surfaces suggest considerable utility of the T-RMF approach in which the virial theorem and the so called T-normalization condition are employed to a priori control the valleys curvature variations during reaction. A notable feature of the H3WW model surfaces is a relatively good representation of the repulsive wall of the surface.

The BEBO calculation of resonance energies of fullerene cages

A bond energy–bond order (BEBO) relationship for fullerene molecules was obtained by combining density functional theory (DFT) calculations with the Morse potential. The BEBO relationship provides a simple method to calculate the individual binding energies of all the C–C bonds of fullerenes. Consequently, one can easily calculate the resonance energies of the fullerenes using hypothetical compounds with non-resonant double bonds as reference states. This approach was applied to C 60 and C 70, both of which have about 3.9 kcal/mol of resonance energy per carbon.

Rate coefficients for the reactions of hydrogen atoms with 1-bromopropane, 2-bromopropane, 1-bromobutane, and 2-bromobutane

The rate coefficients for the reactions of hydrogen atoms with n-C3H7Br, s-C3H7Br, n-C4H9Br, and s-C4H9Br were determined in a discharge flow-reactor at 298 K and a pressure of 4 mbar. Molecular-beam sampling and subsequent mass-spectrometric detection with electron-impact ionisation was used for the measurement of the bromo-hydrocarbon concentration. The rate coefficients obtained are (in 1010 cm3 mol−1 s−1): 2.3±1.2 for n-C3H7Br, 2.3±1.2 for s-C3H7Br, 2.4±1.2 for n-C4H9Br, and 2.8±1.4 for s-C4H9Br. The results are compared with predictions from bond-energy bond-order (BEBO) calculations, where a reasonable agreement is found. Furthermore, also by BEBO calculations, the relative importance of bromine abstraction as compared to hydrogen abstraction is estimated. © 1998 John Wiley & Sons, Inc. Int J Chem Kinet: 30: 721–727, 1998

Further examination of the BEBO model with the results of ab initio calculations of a reaction series

The BEBO (bond energy-bond order) model of Johnston and Parr is examined with the results of ab initio MO calculations on a series of metathetic reactions which involve hydrogen transfer. Energies are calculated at the 6-31G**/PMP2 = full//6-31G** level while the bond orders are estimated using the 6-31G** basis set with the geometry optimisation at the single configuration unrestricted Hartree-Fock frame. Our analysis reveals that the bond-order exponent in the BEBO theory is greater than unity for the reaction series and the entropy term becomes implicitly present in the BEBO model.

Quantum chemical bond order as a local descriptor for modelling reaction paths

The feasibility of studying chemical reactions by focusing attention only on the bonds actively involved in the reaction process is explored. Active bond order (BO) profiles are shown frequently to be characterized by the occurrence of sharp inflexions at a point close to the saddle point on the reaction path. The sum of the active BOs is shown to remain approximately conserved. Active BOs may therefore be used as a local descriptor of the reaction path. This leads to extended bond-energy bond-order (EBEBO) postulates which are proposed to transcribe an essentially local picture of a reaction as a superposition of elementary chemical events into a semi-global description. A local Hammond postulate and its ramifications are explored along with a local measure of the asynchronicity of the bond-breaking and bond-making processes in a chemical reaction. The origin of BO inflexions is theoretically sought to be connected with Fermi correlation.

Quantum mechanical valence study of a bond‐breaking–bond‐forming process in triatomic systems

AbstractThe recently introduced set of the quadratic, two‐electron covalent and ionic valence indices is used to investigate the bond‐breaking–bond‐forming (BB‐BF) process in an atom exchange reaction between H2 and X (X = H, F—I) as well as in the O2—H system. Valence changes accompanying selected charge reorganizations are examined within the three‐orbital model and valence diagrams for symmetric transition states (TSs) are given. The UHF valence data for Li2O and CO2 and the H—H—X, O—O—H, and O—H—O (ABC) TSs (collinear and angular) are reported and compared to valence data in the separated fragments limits (SFL), AB and BC. The overall valence, ν(ABC), and the total (ionic plus covalent) diatomic valences, νAB and νBC, are used as measures of the overall bond‐order in a concerted BB–BF reaction, to test the postulate of the bond‐energy–bond‐order (BEBO) model. In collinear TSs of H2X, ν ≊ −1, i.e., one bonding electron pari, is found to be roughly preserved, whereas in the angular H2X and in collinear O—H—O TSs, the effect of increased valence at the saddle‐point is observed, relative to that of diatomic fragments (reactiants or products). For the angular O—O—H TS, a similar increase in | ν (ABC)| relative to both O2 and OH SFLs is detected; smaller changes relative to the O2 data are found in the collinear TS. This observation is in agreement with earlier predictions from the intersecting‐state model. The relative diatomic valences, ν/ν and ν/ν, are shown to conserve the overall relative bond multiplicity around 1 in both collinear and angular TSs of the H2—X systems. © 1994 John Wiley & Sons, Inc.

An examination of the BEBO model with the results of ab initio calculations of a reaction series

The BEBO (bond energy-bond order) model of Johnston and Parr is examined with the results of ab initio MO calculations on a series of metathetic reactions which involve hydrogen transfer. Energies are calculated at the 6-31G**/PMP2=full//6-31G** level while the bond orders are estimated using the 6-31G** basis set with the geometry optimisation at the single configuration unrestricted Hartree-Fock frame. Our analysis reveals that the bond-order exponent in the BEBO theory is greater than unity for the reaction series and the entropy term becomes implicity present in the BEBO model.

Evaluation of the phase stability of modified IN738LC alloys with New Phacomp

At the present time, single-crystal superalloys have the highest temperature capability and the best combination of elevated temperature properties of any structural materials and have been successfully applied as turbine airofoils. Although several special alloys suitable for single-crystal processing have been developed in recent years, only few efforts have been put into the development of so-called "hot corrosion-resistant single-crystal superalloys" which will be suitable for long-term and high-performance marine and industrial gas turbine applications. The purpose of this study is to search for the proper alloy compositions for such alloys with the guide of New Phacomp (PHAse COMPutation). This method is a newly developed alloy design concept based on DV-Xo: cluster calculations of the electronic structure of transition metals [1-3], in which Md and Bo (d-orbital energy level and bond order, respectively, of alloying transition metals) are employed as the parameters controlling the phase stability. In the alloy design process, the average values of Md and Bo are defined by taking the compositional average as

Kinetic study of the collisional behaviour of Mg(3 3P J ) with alkanes at elevated temperatures following pulsed dye-laser excitation

The collisional behaviour of electronically excited magnesium atoms in the Mg(3s3p(3PJ)) state, 2.712 eV above the 3s2(1S0) ground state, is investigated by time-resolved atomic fluorescence at λ= 457.1 nm [Mg(3 3P1)→ Mg(3 1S0)+hν] following pulsed dye-laser excitation of magnesium vapour at the resonance wavelength. Decay profiles for Mg(3 3P1), which demonstrate clear exponential behaviour, are recorded on time-scales within which a Boltzmann equilibrium has been established in the 3PJ spin–orbit manifold using signal averaging and computerised analysis. The kinetic behaviour of Mg(3 3PJ) is investigated as a function of temperature in the range 680–905 K in He and Xe alone and in the presence of CH4, C2H6, C3H8 and C4H10 using He as the excess buffer gas both in a static system and in a flow system, kinetically equivalent to a static system. The mean radiative lifetime, τe[Mg(3 3P1)] has been re-investigated with particular care to eliminate impurity quenching and employing low densities of Mg(3 1S0) and low laser pulse energies to minimise effects arising from both collisional quenching by the ground state and by energy pooling. This yields τe= 3.9 ± 0.2 ms, in accord with more recent theoretical calculations. The diffusion of Mg(3 3PJ) is also investigated in some detail as a function of temperature and considered quantitatively in terms of the first-approximation Chapman–Enskog equation. Absolute second-order rate constants for the collisional removal of Mg(3 3PJ) by the alkanes (RH) are measured as a function of temperature, yielding the following Arrhenius forms [kR=A exp(–E/RT)]: [graphic omitted]. These data are considered in terms of the bond-energy, bond-order (BEBO) approach, yielding estimates of activation energies consistent with the experimental observations and with H-atom abstraction to yield MgH. The results are also compared with analogous kinetic data for the removal of Mg(3 3PJ) by H2 and D2 investigated hitherto by a similar method.

Reactions of hydroxyl and hydroxyl-d with hydrogen peroxide and hydrogen peroxide-d2

The reactions OH + H{sub 2}O{sub 2} {yields} products (k{sub 1}) and OD + D{sub 2}O{sub 2} {yields} products (k{sub 3}) were studied in the temperature range 273-410 K. The obtained Arrhenius expressions are as follows: k{sub 1} = (2.76 {plus minus} 0.80) {times} 10{sup {minus}12} exp((-110 {plus minus} 60)/T) and k{sub 3} = (1.75 {plus minus} 0.30) {times} 10{sup {minus}12} exp((-320 {plus minus} 20)/T) cm{sup 3} molecule{sup {minus}1} s{sup {minus}1}. The indicated errors are 2{sigma}, including estimated systematic errors. The rate coefficients were independent of the buffer gas (He, N{sub 2}, or SF{sub 6}) used and the pressure (50-500 Torr) employed. The measured kinetic isotope effect, k{sub 1}/k{sub 3}, ranges from 2.7 at 410 K to 3.5 at 273 K. The values of the rate coefficients for OH + D{sub 2}O{sub 2} {yields} products (k{sub 2}) at 273 K and OD + H{sub 2}O{sub 2} {yields} products (k{sub 4}) at 298 K were the same as those of k{sub 3} at 273 K and k{sub 1} at 298 K, respectively. The possible exchange reaction such as OD + H{sub 2}O{sub 2} {yields} OH + HOOD is unimportant, with an upper limit of 2 {times} 10{sup {minus}15} cm{sup 3} molecule{supmore » {minus}1} s{sup {minus}1} for the rate coefficient at 273 K. Bond energy-bond order (BEBO) calculations using a linear five-particle transition state for a H-abstraction reaction do not yield results that agree with experiments. Transition-state theory calculations using a five-particle nonlinear transition state, (HO)-O-H-O-H, yield results in reasonable agreement with the data.« less

Bond orders from ab initio calculations and a test of the principle of bond order conservation

Bond orders and valence indexes of atoms were calculated from ab initio wave functions using the definition suggested by Mayer. Changes of these quantities were investigated under conditions occurring in chemical reactions. Calculations were performed to reveal the dependence of bond orders on bond length. The results are compared with Pauling's bond order-bond length relation. Bond orders were also calculated in triatomic metathesis reactions. Bond orders are able to describe the similarity of the transition state of reactants or products. Along the minimum-energy path the principle of conservation of bond order is valid a good approximation. The obtained correlations are applied to a bond energy-bond order type model to estimate trends in reaction series.

Theoretical investigations of reactions of some radicals with hydroperoxo. 1. Hydrogen abstractions by direct mechanisms

Ab initio quantum mechanical methods are used to calculate saddle-point geometries and energies for hydrogen abstractions from HO{sub 2} by N, ClO, O, Cl, H, OH, and F assuming direct attack at the hydrogen atom. Results are consistent with bond energy-bond order principles and indicate that activation energies for these reactions should decrease with increasing exothermicity of reaction. In addition, the large rate constant for OH + HO{sub 2} {yields} H{sub 2}O + O{sub 2} is interpreted to be due to long-range dipole-dipole attraction, leading ultimately to formation of a hydrogen bond and to stabilization of an early transition state. Results for the ClO + HO{sub 2} {yields} HOCl + O{sub 2} reaction suggest a dual mechanism dominated by direct abstraction at high temperatures and by elimination from a stable intermediate at lower temperatures, perhaps the only reaction in this series which does so. These results are in good agreement with current experimental rate data.

The role of reaction energy and transition state bond order on the reactivity of ambifunctional compounds in solution

The ambident behaviour of some reagents, NO2–, SCN– and ambident bases, in liquid solutions can be accounted for, quantitatively, in terms of the intersecting-state model. For many reactions changes in reactivity are dominated by the reaction energy, ΔG°, and the transition state bond order, n‡. A gain in polarity of the reactive bonds during the course of reaction leads to more negative ΔG° and to a decrease in n‡. This reveals that for the reaction energy barrier, ΔG° and n‡ can work in opposite directions as a function of the electronegativity of the reaction sites and be responsible for ambident behaviour in ‘charge control’ reactions (ΔG°) and ‘frontier-orbital control’ reactions (n‡). These concepts are employed to interpret the role of reagent, solvent, cation, and reaction mechanism on ambident reactivity.

Extension of the bebo method for the calculation of activation energies of intraradical 1,3-, 1,4- and 1,5-hydrogen shift reactions

The bond-energy—bond-order (BEBO) method has been extended for the calculation of activation energies of the radical isomerization reactions occurring via 1,3-, 1,4- and 1,5-hydrogen atom shifts. The energy of the cyclic activated complexes comprises four contributions, i.e. the energy change in formation of the transition state due to the occurrence of fractional and strained bonds, the triplet repulsion, the deformation energy and the non-bonding interaction. The method has been applied to a set of 11 reactions. The agreement between the calculated and the experimental activation energies is satisfactory.

The effects of friction on the electron transfer of 9,10-dicyanoanthracene

We have used the the bond energybond order (BEBO) method to approximate the shape of the barrier to electron transfer and combined it with the Kramers relation and with the Grote-Hynes relation to demonstrate a possible role of friction in electron transfer reactions. Using our own data and that of Abdullah and Kemp we have shown that not only can friction be considered in electron transfer reactions, but that this friction might be the non-markovian frequency-dependent friction derivable from the generalized Langevin equation. From these results we have estimated possible limits of the frequency-dependent friction for the electron transfer from 9,10-dicyanoanthracene to electron acceptors.