Bell-Evans-Polanyi Principle Research Articles

Sonofragmentation and sonocrystallization: How solids break and make in cavitating liquids

Mechanical action can produce dramatic physical and mechanochemical effects when the energy is spatially or temporally concentrated. The application of ultrasound to crystallization (i.e., sonocrystallization) can dramatically affect the properties of the crystalline products. Sonocrystallization induces rapid nucleation, generally yields smaller crystals of a more narrow size distribution compared to quiescent crystallizations, and has become increasingly important in the pharmaceutical industry for the preparation of APIs (active pharmaceutical ingredients). The control of morphology of the crystallization process is critical to reproducible dose response for APIs and is under increasing scrutiny in pharmaceutical manufacturing by the FDA. Ultrasound can induce significant improvement in the uniformity of crystallite size and rates of crystallization. We have developed a mechanistic understanding of the origin of these phenomena and begun to separate the details of the effects of ultrasound on nucleation, mass transport, shockwave fragmentation of crystallites, and inter-particulate collision. Decoupling experiments were performed to confirm that interactions between shockwaves and crystals are the main contributors to crystal breakage. We have discovered a mechanochemical extension the Bell–Evans–Polanyi principle: activation energies for solid fracture correlate with the binding energies of the solids.

Correlation between Kinetics and Thermodynamics for Excited-State Intramolecular Proton Transfer Reactions.

Finding the relation between thermodynamics and kinetics for a reaction is of fundamental importance. Here, the thermodynamics and kinetics correlation of excited-state intramolecular proton transfer (ESIPT) was investigated by the TD-DFT calculation under the CAM-B3LYP/6-311+G** level. We choose the family 2-(2'-aminophyenyl)benzothiazole and its amino derivatives as paradigms, which all possess the NH-type intramolecular hydrogen bond (H-bond), and investigate the corresponding ESIPT reaction. The H-bond strength can be systematically tuned, so both activation energy ΔG‡ and free energy difference between proton transfer tautomer (T*, product) and normal species (N*, reactant) ΔGT*-N* can be varied. To minimize the environmental interference such as solvent external H-bond and polarity perturbation, a nonpolar solvent such as cyclohexane is chosen as a bath with a polarizable continuum solvation model for the calculation. As a result, the comprehensive computational approach reveals a linear relationship between ΔGT*-N* and ΔG‡, which can be expressed as ΔG‡ = ΔG0 + αΔGT*-N*. The fundamental insight is reminiscent of the Bell-Evans-Polanyi (BEP) principle where α represents the character of the position of the transition state along the proton motion coordinate. In other words, the more exergonic the ESIPT reaction is, the faster the proton transfer rate can be observed. To verify that such a correlation is not a sporadic event, another ESIPT family with an -OH proton, 1-hydroxy-11H-benzo[b]fluoren-11-one and its derivatives, was also investigated and proved to follow the BEP principle as well. Unlike the quantum mechanics description of proton transfer where either proton tunneling is dominant or solute/solvent is coupled in ESIPT, this work demonstrates that reaction kinetics and thermodynamics are strongly correlated within the same class of ESIPT molecules with an intrinsic barrier free from solvent perturbation, being faster with the more exergonic reaction.

Broadening the Horizon of the Bell–Evans–Polanyi Principle towards Optically Triggered Structure Planarization

AbstractFinding a relationship between kinetics and thermodynamics may be difficult. However, semi‐empirical rules exist to compensate for this shortcoming, among which the Bell–Evans–Polanyi (B‐E‐P) principle is an example for reactions involving bond breakage and reformation. We expand the B‐E‐P principle to a new territory by probing photoinduced structure planarization (PISP) of a series of dibenz[b,f]azepine derivatives incorporating bent‐to‐planar and rotation motion. The latter involves twisting of the partial double bond character, thereby inducing a barrier that is substituent dependent at the para N‐phenyl position. The transition‐state structure and frequency data satisfy and broaden the B‐E‐P principle to PISP reactions without bond rearrangement. Together with dual emissions during PISP, this makes possible harnessing of the kinetics/thermodynamics relationship and hence ratiometric luminescence properties for excited‐state structural transformations.

1,3-Dipolar Cycloadditions by a Unified Perspective Based on Conceptual and Thermodynamics Models of Chemical Reactivity.

The main aim in the present report is to gain a deeper understanding of typical 1,3-dipolar cycloadditions by means of three chemical reactivity models in a unified perspective: conceptual density functional theory, distortion/interaction, and reaction force analysis. The focus is to explore the information provided by each reactivity model and how they complement or reinforce each other. Our results showed that the Bell-Evans-Polanyi (BEP) relationship is fulfilled, which is consistent with the Hammond-Leffler postulate. The electronic chemical potential based analysis classifies the reactions as HOMO-, HOMO/LUMO-, and LUMO-controlled reactions as the activation energy increases. It seems likely that HOMO-controlled reaction shifts into LUMO-controlled one as the transition state (TS) position does from early into late. Therefore, the transition from HOMO- (and early TS) into LUMO-controlled (and late TS) is paid by shifting the overall energy change into an endothermic direction, thus supporting the fulfillment of the BEP principle. While thermodynamic models unveil that the distortion or structural rearrangements mainly drive the activation barriers rather than interaction or electronic rearrangements in accord with the distortion/interaction and reaction force analysis, respectively. It is also found that both models are consistent when energy associated with structural and electronic reordering from reaction force analysis is respectively confronted with destabilizing (distortion and Pauli repulsion) and stabilizing (electrostatic and orbital interactions) contributions from the distortion/interaction model, which, on the other hand, increases as low activation barrier and high exothermicity are converted into the high barrier and low exothermicity along with the BEP relation. Finally, the reaction force constant reveals that all 1,3-dipolar cycloaddition reactions proceed by a synchronous single-step mechanism, unveiling that the degree of synchronicity is quite the same in all reactions, confirming the statement that BEP is fulfilled for similar reactions proceeding by a quite alike degree of synchronicity.

When is the Bell–Evans–Polanyi principle fulfilled in Diels–Alder reactions of fullerenes?

We present a theoretical study on the thermodynamic and kinetic reactivity of Diels-Alder cycloadditions to several empty fullerenes in order to investigate the relationship between reaction energies and energy barriers. The results show that fullerenes with large HOMO-LUMO gaps present good correlation coefficients. In all other cases, two factors are responsible for the lack of correlation. First, the formation of unexpected adducts which are not the ones resulting from a [4+2] addition and second the change in the electronic structure of some adducts due to the mixing of the ground state with excited states close in energy.

Tuning the Dissociative Action of Cationic Rh Clusters Toward NO by Substituting a Single Ta Atom

Modification of Rh chemical activity for decomposition of NO by alloying with Ta was studied by vibrational spectroscopy of gas-phase clusters, where one single Rh atom was substituted by Ta, with NO adsorbed. While NO adsorbs molecularly on pure Rh clusters, it was found to adsorb dissociatively on RhnTa+ (n = 2–8) with the O bound to the Ta on-top site. A reaction path for NO decomposition obtained by density functional theory calculations for octahedral Rh5Ta+ and Rh6+ suggests that the Ta oxygen affinity strongly reduces the energy barrier right before bond cleavage, facilitating NO dissociation. The trend is consistent with the Bell–Evans–Polanyi principle. The addition of other less oxophilic dopant atoms could plausibly enhance catalytic reactivity of Rh.

Theoretical Study of the Reactivity and Selectivity of Various Free Radicals with Cysteine Residues.

Radicals in biochemical environments can lead to protein damage. Theoretical studies can help us to understand the observed radical selectivity. In this work, the kinetics and thermodynamics of the hydrogen-transfer (HT) and single-electron transfer (SET) reactions between a cysteine derivative and 17 free radicals of biological significance have been theoretically investigated in aqueous and lipid media. With the exception of the reaction with •OCCl3, all SET reactions in aqueous medium have rate constants in the diffusion-limited regime. The γ site of cysteine was found to be the most reactive for the HT reactions with all the radicals, with rate constants in the diffusion limit for •OH, •OCHCl2, and •OCCl3. The HT reactions from the α and γ positions have very similar ΔG° values and even though the β position is the least thermodynamically favored, when the HT from β is exergonic it is a more reactive site than α. The results obtained confirm that the Bell–Evans–Polanyi principle does not apply to the reactions between amino acid residues and free radicals and that reactivity comparisons demand proper kinetic calculations.

Precise Design of Phosphorescent Molecular Butterflies with Tunable Photoinduced Structural Change and Dual Emission

Photoinduced structural change (PSC) is a fundamental excited-state dynamic process in chemical and biological systems. However, precise control of PSC processes is very challenging, owing to the lack of guidelines for designing excited-state potential energy surfaces (PESs). A series of rationally designed butterfly-like phosphorescent binuclear platinum complexes that undergo controlled PSC by Pt–Pt distance shortening and exhibit tunable dual (greenish-blue and red) emission are herein reported. Based on the Bell–Evans–Polanyi principle, it is demonstrated how the energy barrier of the PSC, which can be described as a chemical-reaction-like process between the two energy minima on the first triplet excited-state PES, can be controlled by synthetic means. These results reveal a simple method to engineer the dual emission of molecular systems by manipulating PES to control PSC.

Probing Potential Energy Surface Exploration Strategies for Complex Systems.

The efficiency of minimum-energy configuration searching algorithms is closely linked to the energy landscape structure of complex systems, yet these algorithms often include a number of steps of which the effect is not always clear. Decoupling these steps and their impacts can allow us to better understand both their role and the nature of complex energy landscape. Here, we consider a family of minimum-energy algorithms based, directly or indirectly, on the well-known Bell-Evans-Polanyi (BEP) principle. Comparing trajectories generated with BEP-based algorithms to kinetically correct off-lattice kinetic Monte Carlo schemes allow us to confirm that the BEP principle does not hold for complex systems since forward and reverse energy barriers are completely uncorrelated. As would be expected, following the lowest available energy barrier leads to rapid trapping. This is why BEP-based methods require also a direct handling of visited basins or barriers. Comparing the efficiency of these methods with a thermodynamical handling of low-energy barriers, we show that most of the efficiency of the BEP-like methods lie first and foremost in the basin management rather than in the BEP-like step.

The Bell–Evans–Polanyi Principle and the regioselectivity of electrophilic aromatic substitution reactions

Relative activation energies of competing electrophilic aromatic substitution transition states are shown to correlate precisely with computed relative enthalpy changes leading to the corresponding σ complexes. The correlations manifest the Bell–Evans–Polanyi Principle, which may be summarized by the relationship, Ea=m(ΔH)+I. Close correlation occurs for a variety of reactions and reactivities, but correlation does not occur for nitration of toluene, a case known to be exceptional. The correlations imply that activation energies control regioselectivity, and that the properties of the competing transition states resemble those of the σ complexes.

Use of the Bell–Evans–Polanyi Principle to predict regioselectivity of nucleophilic aromatic photosubstitution reactions

Regioselectivity of nucleophilic aromatic photosubstitution has been shown experimentally to depend upon activation energies of the competing transition states. Computational means of determining relative activation energies were sought, therefore, in order to predict regioselectivity. Optimization of the three triplet transition states of 2-chloro-4-nitroanisole with hydroxide ion gave energies of insufficient accuracy to predict regioselectivity. Computed enthalpy changes from the first triplet transition state to the triplet σ-complexes correlated precisely with the experimental activation energies. This exemplifies the Bell–Evans–Polanyi Principle, and it provides an accurate means of assessing regioselectivity.

Computational scheme for ab-initio predictions of chemical compositions interfaces realized by deposition growth

We present a novel computational scheme to predict chemical compositions at interfaces as they emerge in a growth process. The scheme uses the Gibbs free energy of reaction associated with the formation of interfaces with a specific composition as predictor for their prevalence. It explicitly accounts for the growth conditions by rate-equation modeling of the deposition environment. The Bell–Evans–Polanyi principle motivates our emphasis on an effective nonequilibrium thermodynamic description inspired by chemical reaction theory. We illustrate the scheme by characterizing the interface between TiC and alumina. Equilibrium thermodynamics favors a nonbinding interface, being in conflict with the wear-resistant nature of TiC/alumina multilayer coatings. Our novel scheme predicts that deposition of a strongly adhering interface is favored under realistic conditions.

ChemInform Abstract: Kinetics and Mechanism of the Aminolysis of Cycloalkyl Arenesulfonates

Nucleophilic substitution reactions of cycloalkyl arenesulfonates (CnH2n–1OSO2C6H4Z) with anilines in acetonitrile at 65.0 °C are studied. The reactivity decreases in the order n= 5 > 7 > 4 > 6, which is influenced by angular deformation energies in the transition state (TS), steric effect and exoergicity of the reaction. The cross-interaction constants, ρxz, between substituents in the nucleophile (X) and nucleofuge (Z) for all the cycloalkyl compounds, irrespective of the ring size, are uniformly the same (0.11) as those observed for isopropyl arenesulfonates. This indicates that the TS for SN2 processes at a secondary carbon atom is substantially looser than that at a primary carbon for which a greater ρxz value (0.33) has been reported, regardless of the size of the group attached to the reaction centre. The TS shifts toward an earlier position along the reaction coordinate, and becomes more asymmetric, as the ring size decreases, n= 7→4, in accordance with the Bell–Evans–Polanyi principle.

ChemInform Abstract: Synthesis, Structure, and Theoretical Study of Lower Trifluoromethyl Derivatives of [60]Fullerene.

AbstractChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 200 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a “Full Text” option. The original article is trackable via the “References” option.

Synthesis, Structure, and Theoretical Study of Lower Trifluoromethyl Derivatives of [60]Fullerene

AbstractA number of C60(CF3)n compounds with n = 2–10 have been synthesized by the reaction of C60 with silver trifluoroacetate and successfully isolated by means of HPLC. This resulted in the first crystal structure determination of six lower trifluoromethyl derivatives with n = 2 (single isomer), 4 (two isomers), and 6 (three isomers). A kinetic model of sequential trifluoromethylation based on the Bell–Evans–Polanyi principle has been used to explain the experimentally observed isomeric distribution in the mixtures of C60(CF3)n compounds up ton = 6. (© Wiley‐VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2007)

Ultrasound-assisted hydrogenation of cinnamaldehyde

The hydrogenation, employing hydrogen gas, of cinnamaldehyde was performed using Pd-black and Raney Ni catalysts at 298 ± 3 K in a water-cooled (jacketed) reaction vessel. Sampling at pre-determined time intervals and GC/MS analysis yielded time-dependent product state distribution information. A kinetic modeling of the data revealed that cinnamaldehyde was both hydrogenated directly to the final product benzenepropanol, as well as a fraction being converted to the intermediate benzenepropanal, where the latter was subsequently hydrogenated to benzenepropanol. Comparing the ultrasound-assisted and blank (stirred) experiments revealed that a higher maximum relative concentration of the intermediate benzenepropanal was formed in the ultrasound experiments compared to the stirred experiment. The activity of the ultrasound experiments compared to blank were 9-fold and 20-fold greater for the Pd-black and Raney Ni catalysts, respectively. Finally, an application of the Bell–Evans–Polanyi principle to yield an estimate of the ratio of rate coefficients for benzenepropanal and benzenepropanol formation was performed by considering chemical group energy differences and surface adsorption energy differences in the first mechanistic step of hydrogenation.

Prediction of approximate transition states by Bell-Evans-Polanyi principle: I

We propose a specific mathematical model of the Bell–Evans–Polanyi principle (BEP) to locate approximate transition structures of elementary reactions. The BEP adiabatic energy surface is built as a combination of three quadratic energy surfaces. Two of these quadratic energy surfaces are associated with the reactants and products, whereas the third one is associated with the crossing point energy minimum resulting from the intersection of the reactant and product quadratic energy surfaces. In this way, the resonance energy terms are taken into account. The resulting approximate transition structure and the corresponding Hessian matrix can be used as an initial geometry and a Hessian matrix to locate and optimize the true transition state on the real potential energy surface. In addition, the method provides a simple way to analyze the transition in terms of the contribution weights of the reactants and products. This model is illustrated by different numerical examples, such as the analytical Muller–Brown potential energy surface, the ring opening of cyclopropyl radical, the rearrangement of trans-hydroxycarbene to formaldehyde, and the rearrangement of bicyclo[3.1.0]hex-3-en-2-il radical to cyclohexadienyl radical. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1112–1129, 1999

Ab initio studies of three-membered ring formation through intramolecular nucleophilic substitution

Three-membered ring (3MR) forming processes of −X(SINGLE BOND)CH2(SINGLE BOND)CH2(SINGLE BOND)F and −CH2(SINGLE BOND)C((SINGLE BOND)Y)(SINGLE BOND)CH2(SINGLE BOND)F (X(DOUBLE BOND)CH2, O, or S and Y(DOUBLE BOND)0 or S) through a gas phase neighboring group mechanism (SNi) are studied theoretically using the ab initio molecular orbital method with the 6–31+G* basis set. When electron correlation effects are considered, the activation (ΔG≠) and reaction energies (ΔG0) are lowered by ca. 10 kcal mol−1, indicating the importance of the electron correlation effect in these reactions. The contribution of entropy of activation (−TΔS≠) at 298 K to ΔG≠ is very small, and the reactions are enthalpy controlled. The ΔG≠ and ΔG0 values for these ring closure processes largely depend on the stabilities of the reactants and the heteroatom acting as a nucleophilic center. The Bell–Evans–Polanyi principle applies well to all these reaction series. © 1997 John Wiley & Sons, Inc. J Comput Chem18: 1773–1784, 1997

Kinetics and mechanism of the aminolysis of cycloalkyl arenesulfonates

Nucleophilic substitution reactions of cycloalkyl arenesulfonates (CnH2n–1OSO2C6H4Z) with anilines in acetonitrile at 65.0 °C are studied. The reactivity decreases in the order n= 5 > 7 > 4 > 6, which is influenced by angular deformation energies in the transition state (TS), steric effect and exoergicity of the reaction. The cross-interaction constants, ρxz, between substituents in the nucleophile (X) and nucleofuge (Z) for all the cycloalkyl compounds, irrespective of the ring size, are uniformly the same (0.11) as those observed for isopropyl arenesulfonates. This indicates that the TS for SN2 processes at a secondary carbon atom is substantially looser than that at a primary carbon for which a greater ρxz value (0.33) has been reported, regardless of the size of the group attached to the reaction centre. The TS shifts toward an earlier position along the reaction coordinate, and becomes more asymmetric, as the ring size decreases, n= 7→4, in accordance with the Bell–Evans–Polanyi principle.