Activation Free Energy Barrier Research Articles

Analysis of the pH-dependent stability and millisecond folding kinetics of horse cytochrome c

This paper analyzes the effect of pH on thermodynamic stability and folding kinetics of horse cytochrome c (cyt c). Analysis of equilibrium unfolding transitions of Ferricyt c and Ferrocyt c measured between pH 3.0 and pH 13.0 reveal that these proteins have maximum thermodynamic stability between pH 8.0 and pH 9.5. Theoretically predicted pH-dependent electrostatic unfolding energy of Ferricyt c also supports this result. Unfolded Ferrocyt c in refolding buffer at pH 7.0 and pH 12.7 refolds rapidly to native state. Between pH 7.0 and pH 12.7, the activation free energy barrier for folding of Ferrocyt c varies by <1.0 kcal mol−1 while the folding free energy, which is measured by two-state analysis of equilibrium unfolding transitions of Ferrocyt c varies by 8.0 kcal mol−1. This finding reveals that the large disparity in thermodynamic stability between pH 7.0 and pH 12.7 is not strongly reflected in the refolding rates. The Wyman Tanford linkage relation was used to calculate the βpH-value for folding of Ferrocyt c, which is <0.1 between pH 7.0 and pH 12.7, indicating that the electrostatic interactions are weakly formed in transition state and exhibit a very small effect on the folding kinetics.

The conformation effect of the diamine bridge on the stability of dinuclear platinum(II) complexes and their hydrolysis

In this paper, the hydrolysis process of a bisplatinum complex containing the flexible chain 1,6-hexanediamine between the two metal centers was investigated through the use of density functional theory (DFT) with the analysis of the role of the spacing group arrangement on the values of free energy activation barrier. All structures were fully optimized in aqueous solution using implicit model for solvent at DFT level. The energy profiles for the hydrolysis reaction were determined by using the supermolecule approach. Five transition states were proposed differing by the conformation of the bridge group, and the activation free energy calculated as a weighted average within the selected forms. The Gibbs population for reactant was used as a statistical weight leading to the predicted value of 23.1kcalmol−1, in good accordance with experiment, 23.8kcalmol−1. Our results suggests that for 1,6-hexanediamine bridge ligand, the extend forms with average torsional angle over the carbon chain larger than 130° have the greatest contribution to the hydrolysis kinetics. The results presented here point out that the hydrolysis mechanism might follow different paths for each conformation and each of these contributes to the observed energy barrier.

Investigation of the CH3Cl + CN(-) reaction in water: Multilevel quantum mechanics/molecular mechanics study.

The CH3Cl + CN(-) reaction in water was studied using a multilevel quantum mechanics/molecular mechanics (MM) method with the multilevels, electrostatic potential, density functional theory (DFT) and coupled-cluster single double triple (CCSD(T)), for the solute region. The detailed, back-side attack SN2 reaction mechanism was mapped along the reaction pathway. The potentials of mean force were calculated under both the DFT and CCSD(T) levels for the reaction region. The CCSD(T)/MM level of theory presents a free energy activation barrier height at 20.3 kcal/mol, which agrees very well with the experiment value at 21.6 kcal/mol. The results show that the aqueous solution has a dominant role in shaping the potential of mean force. The solvation effect and the polarization effect together increase the activation barrier height by ∼11.4 kcal/mol: the solvation effect plays a major role by providing about 75% of the contribution, while polarization effect only contributes 25% to the activation barrier height. Our calculated potential of mean force under the CCSD(T)/MM also has a good agreement with the one estimated using data from previous gas-phase studies.

Exploring the nature of silicon-noble gas bonds in H3SiNgNSi and HSiNgNSi compounds (Ng = Xe, Rn).

Ab initio and density functional theory-based computations are performed to investigate the structure and stability of H3SiNgNSi and HSiNgNSi compounds (Ng = Xe, Rn). They are thermochemically unstable with respect to the dissociation channel producing Ng and H3SiNSi or HSiNSi. However, they are kinetically stable with respect to this dissociation channel having activation free energy barriers of 19.3 and 23.3 kcal/mol for H3SiXeNSi and H3SiRnNSi, respectively, and 9.2 and 12.8 kcal/mol for HSiXeNSi and HSiRnNSi, respectively. The rest of the possible dissociation channels are endergonic in nature at room temperature for Rn analogues. However, one three-body dissociation channel for H3SiXeNSi and one two-body and one three-body dissociation channels for HSiXeNSi are slightly exergonic in nature at room temperature. They become endergonic at slightly lower temperature. The nature of bonding between Ng and Si/N is analyzed by natural bond order, electron density and energy decomposition analyses. Natural population analysis indicates that they could be best represented as (H3SiNg)+(NSi)− and (HSiNg)+(NSi)−. Energy decomposition analysis further reveals that the contribution from the orbital term (ΔEorb) is dominant (ca. 67%–75%) towards the total attraction energy associated with the Si-Ng bond, whereas the electrostatic term (ΔEelstat) contributes the maximum (ca. 66%–68%) for the same in the Ng–N bond, implying the covalent nature of the former bond and the ionic nature of the latter.

Quantum mechanical and molecular mechanics approach with a multilayered-quantum representation study of solvent effects and potentials of mean force for the CH3CH2Cl + ClO− SN2 reaction in aqueous solution

The bimolecular nucleophilic substitution reaction of CH3CH2Cl + ClO− in aqueous solution was investigated using a multilayered-quantum representation, quantum mechanical and molecular mechanics approach with an explicit water model. Ten configurations along the reaction pathway including reactant complex, transition state and product complex were analyzed in the presence of the aqueous solution. The obtained free energy activation barrier under the CCSD(T)/MM representation is 13.2 kcal/mol, while it is 11.7 kcal/mol under the DFT/MM representation which agrees very well with the DFT calculation, at 11.0 kcal/mol, with a polarizable continuum solvent model. The solvent effects including the solvation free energy contribution and the polarization effect raise the free activation barrier by 9.8 kcal/mol. The rate constant, at 298 K, is 5.27 × 10−17 cm3/molecule/s which is about seven orders of magnitude smaller than that in the gas phase (1.10 × 10−10 cm3/molecule/s). All in all, the aqueous solution plays an essential role in shaping the reaction pathway for this reaction in water.

Solvation dynamics and energetics of intramolecular hydride transfer reactions in biomass conversion.

Hydride transfer changes the charge structure of the reactant and thus, may induce reorientation/reorganization of solvent molecules. This solvent reorganization may in turn alter the energetics of the reaction. In the present work, we investigate the intramolecular hydride transfer by taking Lewis acid catalyzed glucose to fructose isomerization as an example. The C2-C1 hydride transfer is the rate limiting step in this reaction. Water and methanol are used as solvents and hydride transfer is simulated in the presence of explicit solvent molecules, treated quantum mechanically and at a finite temperature, using Car-Parrinello molecular dynamics (CPMD) and metadynamics. Activation free energy barrier for hydride transfer in methanol is found to be 50 kJ mol(-1) higher than that in water. In contrast, in density functional theory calculations, using an implicit solvent environment, the barriers are almost identical. Analysis of solvent dynamics and electronic polarization along the molecular dynamics trajectory and the results of CPMD-metadynamics simulation of the hydride transfer process in the absence of any solvent suggest that higher barrier in methanol is a result of non-equilibrium solvation. Methanol undergoes electronic polarization during the hydride transfer step. However, its molecular orientational relaxation is a much slower process that takes place after the hydride transfer, over an extended timescale. This results in non-equilibrium solvation. Water, on the other hand, does not undergo significant electronic polarization and thus, has to undergo minimal molecular reorientation to provide near equilibrium solvation to the transition state and an improved equilibrium solvation to the post hydride shift product state. Hence, the hydride transfer step is also observed to be exergonic in water and endergonic in methanol. The aforementioned explanation is juxtaposed to enzyme catalyzed charge transfer reactions, where the enhanced solvation of the transition and product states by enzymes, due to electrostatic interactions, reduces the activation free energy barrier and the free energy change of the reaction. Similarly, we suggest that, in the intramolecular hydride shift, improved solvation of the transition state and of the product state by water is achieved due to minimal polarization and reorientation, and (near) equilibrium solvation.

ChemInform Abstract: Asymmetric Garratt—Braverman Cyclization: A Route to Axially Chiral Aryl Naphthalene—Amino Acid Hybrids.

We report the first example of a highly diastereoselective Garratt–Braverman cyclization leading to the synthesis of chiral aryl naphthalene–amino acid hybrids in excellent yields. The stereogenecity in the amino acid has induced high diastereoselectivity for the reaction. Computations based on density functional theory indicated a lower activation free energy barrier for the M isomer as compared to that for the P diastereomer (ΔΔG = 3.48 kcal/mol). Comparison of the recorded CD spectrum of the product with the calculated one also supported the preferential formation of the M diastereomer.

Activation barriers in the growth of molecular clusters derived from sulfuric acid and ammonia.

Unraveling the chemical mechanism of atmospheric new particle formation (NPF) has important implications for the broader understanding of the role of aerosols in global climate. We present computational results of the transition states and activation barriers for growth of atmospherically relevant positively charged molecular clusters containing ammonia and sulfuric acid. Sulfuric acid uptake onto the investigated clusters has a small activation free-energy barrier, consistent with nearly collision-limited uptake. Ammonia uptake requires significant reorganization of ions in the preexisting cluster, which yields an activation barrier on the order of 29-53 kJ/mol for the investigated clusters. For this reason, ammonia uptake onto positively charged clusters may be too slow for cluster growth to proceed by the currently accepted mechanism of stepwise addition of sulfuric acid followed by ammonia. The results presented here may have important implications for modeling atmospheric NPF and nanoparticle growth, which typically does not consider an activation barrier along the growth pathway and usually assumes collision-limited molecular uptake.

Rhodium bis(quinolinyl)benzene complexes for methane activation and functionalization.

A series of rhodium(III) bis(quinolinyl)benzene (bisq(x)) complexes was studied as candidates for the homogeneous partial oxidation of methane. Density functional theory (DFT) (M06 with Poisson continuum solvation) was used to investigate a variety of (bisq(x)) ligand candidates involving different functional groups to determine the impact on Rh(III)(bisq(x))-catalyzed methane functionalization. The free energy activation barriers for methane C-H activation and Rh-methyl functionalization at 298 K and 498 K were determined. DFT studies predict that the best candidate for catalytic methane functionalization is Rh(III) coordinated to unsubstituted bis(quinolinyl)benzene (bisq). Support is also found for the prediction that the η(2)-benzene coordination mode of (bisq(x)) ligands on Rh encourages methyl group functionalization by serving as an effective leaving group for SN2 and SR2 attack.

Kinetic and computational studies on Pd(I) dimer-mediated halogen exchange of aryl iodides.

Building on our previous discovery and reactivity explorations of the Pd(I) dimer [(PtBu3)PdBr]2-mediated halogen exchange of aryl iodides [Chem. Sci. 2013, 4, 4434], this report presents kinetic studies of this process, giving first-order kinetic dependence in the Pd(I) dimer and aryl iodide. An activation free energy barrier of ΔG(‡) = 24.9 ± 3.3 kcal/mol was experimentally determined. Extensive computational studies on the likely reaction pathway were subsequently carried out. A variety of DFT methods were assessed, ranging from dispersion-free methods to those that better account for dispersion (M06L, ωB97XD, D3-DFT). While significant discrepancies in the quantitative prediction of activation barriers were observed, all computational methods consistently predicted the analogous qualitative reactivity that is in agreement with all spectroscopic and reactivity data collected. Overall, these data provide compelling additional support of the direct reactivity of Pd(I)-Pd(I) with aryl iodides.

Catalytic NO activation and NO–H2 reaction pathways

Kinetic and isotopic data on Pt clusters and activation free energy barriers from density functional theory (DFT) on Pt(111) are used to assess the elementary steps involved in NO–H2 reactions. Pt clusters 1–10nm in diameter gave similar turnover rates, indicating that these elementary steps are insensitive to surface-atom coordination. N–O cleavage occurs after sequential addition of two chemisorbed H-atoms (H*) to NO* which are quasi-equilibrated with H2 and NO co-reactants. The first step is equilibrated and forms HNO*, while the second addition is irreversible and forms *HNOH*; this latter step limits NO–H2 rates and forms OH* and NH* intermediates that undergo fast reactions to give H2O, N2O, NH3, and N2. These conclusions are consistent with (i) measured normal H/D kinetic isotope effects; (ii) rates proportional to H2 pressure, but reaching constant values at higher pressures; (iii) fast H2–D2 equilibration during catalysis; and (iv) DFT-derived activation barriers. These data and calculations, taken together, rule out N–O cleavage via NO* reactions with another NO* (forming O* and N2O) or with vicinal vacancies (forming N* and O*), which have much higher barriers than H*-assisted routes. The cleavage of N–O bonds via *HNOH* intermediates is reminiscent of C–O cleavage in CO–H2 reactions (via *HCOH*) and of O–O cleavage in O2–H2 reactions (via OOH* or *HOOH*). H*-addition weakens the multiple bonds in NO, CO, and O2 and allows coordination of each atom to metal surfaces; as a result, dissociation occurs via such assisted routes at all surface coverages relevant in the practice of catalysis.

Dynamic high performance liquid chromatography on chiral stationary phases. Low temperature separation of the interconverting enantiomers of diazepam, flunitrazepam, prazepam and tetrazepam

Diazepam and the structurally related 1,4-benzodiazepin-2-ones tetrazepam, prazepam and flunitrazepam are chiral molecules because they adopt a ground state conformation featuring a non-planar seven membered ring devoid of any reflection-symmetry element. The two conformational enantiomers of this class of benzodiazepines interconvert rapidly at room temperature by a simple ring flipping process. Low temperature HPLC on the Whelk-O1 chiral stationary phase allowed us to separate the conformational enantiomers of diazepam and of the related 1,4-benzodiazepin-2-ones, under conditions where the interconversion rate is sufficiently low, compared to the chromatographic separation rate. Diazepam, tetrazepam and prazepam showed temperature dependent dynamic HPLC profiles with interconversion plateaus indicative of on-column enantiomer interconversion (enantiomerization) in the temperature range between −10°C and −35°C, whereas for flunitrazepam on-column interconversion was observed at temperatures between −40°C and −66°C. Simulation of exchange-deformed HPLC profiles using a computer program based on the stochastic model yielded the apparent rate constants for the on-column enantiomerization and the corresponding free energy activation barriers. At −20°C the enantiomerization barriers, ΔG≠, for diazepam, prazepam and tetrazepam were determined to be in the range 17.6–18.7kcal/mol. At −55°C ΔG≠ for flunitrazepam was determined to be in the 15.6–15.7kcal/mol range. The experimental dynamic chromatograms and the corresponding interconversion barriers reported in this paper call for a reinterpretation of previously published results on the HPLC behavior of diazepam on chiral stationary phases.

A metal-free strategy to release chemisorbed H2 from hydrogenated boron nitride nanotubes.

Chemisorbed hydrogen on boron nitride nanotubes (BNNT) can only be released thermally at very high temperatures above 350 °C. However, no catalyst has been identified that could liberate H2 from hydrogenated BN nanotubes under moderate conditions. Using different density functional methods we predict that the desorption of chemisorbed hydrogen from hydrogenated BN nanotubes can be facilitated catalytically by triflic acid at low free-energy activation barriers and appreciable rates under metal free conditions and mildly elevated temperatures (40-50 °C). Our proposed mechanism shows that the acid is regenerated in the process and can further facilitate similar catalytic release of H2 , thus suggesting all the chemisorbed hydrogen on the surface of the hydrogenated nanotube can be released in the form of H2 . These findings essentially raise hope for the development of a sustainable chemical hydrogen storage strategy in BN nanomaterials.

Protein folding dynamics in the cell.

Protein folding is a remarkably fast unimolecular reaction, spanning microseconds to hours at room temperature. Thus, free energy differences and activation barriers on the free energy landscape of proteins are rather small. This opens up the possibility of living cells modulating their protein's landscapes, providing cells another way to control the function of their proteomes after transcriptional control, translational control, and post-translational modification. In this Feature Article, we discuss advances in physicochemical studies of protein stability and folding inside living cells. We focus in particular on our studies using fast relaxation imaging (FREI). Although the effect of the cell on protein free energy landscapes is only a few kT, the strong cooperativity of many folding and binding processes allows small modulation of the energy and entropy to produce a large population modulation. Lastly, we discuss some biomolecular processes that are particularly likely to be affected by in-cell modulation of the proteome, and thus of interest for quantitative physical chemistry studies.

Asymmetric Garratt-Braverman cyclization: a route to axially chiral aryl naphthalene-amino acid hybrids.

We report the first example of a highly diastereoselective Garratt-Braverman cyclization leading to the synthesis of chiral aryl naphthalene-amino acid hybrids in excellent yields. The stereogenecity in the amino acid has induced high diastereoselectivity for the reaction. Computations based on density functional theory indicated a lower activation free energy barrier for the M isomer as compared to that for the P diastereomer (ΔΔG = 3.48 kcal/mol). Comparison of the recorded CD spectrum of the product with the calculated one also supported the preferential formation of the M diastereomer.

Mechanism of AuCl₃-catalyzed cyclization of 1-(indol-2-yl)-3-alkyn-1-ols: a DFT study.

A computational study with the B3LYP functional was carried out to elucidate the mechanisms of AuCl₃- and AgOTf-catalyzed cyclization of 1-(indol-2-yl)-3-alkyn-1-ols. The theoretical studies suggested that the two main processes, cycloaddition and hydrogen-transfer, are included in all possible reaction pathways. Calculations revealed that AuCl₃ is more effective in catalytic ability than AgOTf to catalyze the cyclization of 1-(indol-2-yl)-3-alkyn-1-ols into carbazole derivatives. More importantly, we found that the ligands of catalysts, Cl⁻ and OTf⁻, are critical in a stepwise proton-transport process involved in intramolecular nucleophilic addition because they act as a proton shuttle to lower the activation free energy barrier of the rate-determining step. The theoretical discovery of the role of ligands of catalysts in hydrogen shift process suggests that AuCl₃- and AgOTf-catalyzed cyclization of 1-(indol-2-yl)-3-alkyn-1-ols can be accelerated when ligands with the property of nucleophile are used. Our theoretical calculations reproduced the experimental results very well. The present study is expected to help understand other transition metal-catalyzed reactions and to give guidance for future design of new catalysts.

Aerobic damage to [FeFe]-hydrogenases: activation barriers for the chemical attachment of O2.

[FeFe]-hydrogenases are the best natural hydrogen-producing enzymes but their biotechnological exploitation is hampered by their extreme oxygen sensitivity. The free energy profile for the chemical attachment of O2 to the enzyme active site was investigated by using a range-separated density functional re-parametrized to reproduce high-level ab initio data. An activation free-energy barrier of 13 kcal mol−1 was obtained for chemical bond formation between the di-iron active site and O2, a value in good agreement with experimental inactivation rates. The oxygen binding can be viewed as an inner-sphere electron-transfer process that is strongly influenced by Coulombic interactions with the proximal cubane cluster and the protein environment. The implications of these results for future mutation studies with the aim of increasing the oxygen tolerance of this enzyme are discussed.

DFT calculations on kinetic data for some [4+2] reactions in solution.

The reaction mechanisms of [4+2] cycloaddition reactions between dienes and dienophiles have been investigated with several density functional theory (DFT) methods, such as CAM-B3LYP, BMK, M062x wB97x and wB97xd, and the obtained results show that most of the reactions are synchronous or asynchronous. The stability of the transition state is moderated by the interaction of frontier molecular orbitals (FMOs), in which a diene acts as an electron-donating partner and a dienophile acts as an electron-acceptor from the charge transfer direction in the transition state. The activation free energy barriers have been calculated with both gas-phase translational entropy and solution translational entropy, in which those from gas-phase translational entropy (output of the Gaussian job) are far away from the experimental estimations. It has been found that free-energy barriers generated from solution translational entropies with CAM-B3LYP+IDSCRF/6-31G(d), BMK+IDSCRF/6-31G(d) and wB97x+IDSCRF/6-31G(d) are very close to the experimental measurements, but both M062x and wB97xd methods predict too low free-energy barriers for most of the studied reactions. The substituent and solvent effects on reaction dynamic data have also been addressed.

Comprehensive Comparative Study Using Ab Initio Computational Approaches on the Structures of Cisplatin, Oxaliplatin and BNP3029 (A Novel Substituted Cyano Ligand-based Platinum Analogue) and Activation Energy Barriers for the Attack of Nucleophiles on Cisplatin and BNP3029 and their Monoaquated Derivatives

Cisplatin is an important anti-cancer agent widely used in the clinic; however, it has several notable limitations. To develop novel platinum analogues, key characteristics were considered that may result in more effective platinum analogues. Herein results based on ab initio geometry optimizations (gas- and solution-phase) on cisplatin (1), oxaliplatin_1R_2R (2) and BNP3029 (3, a novel substituted cyano ligand-based platinum analogue, PtCl2[N≡C(CH2)3(C6H5)]2) using the recently published potentials and basis sets for platinum are presented. Optimized quantum mechanical derived geometries of the 3 platinum agents were in good agreement with available experimental geometries. The reactivity of BNP3029 was compared to cisplatin by computing the activation free energy barriers for the attack of various nucleophiles on both 1 and 3 and their monoaquated derivatives. Based on the activation energy barriers, it was determined that: (i) the reaction rate may be similar for the attack of water on cisplatin and BNP3029; (ii) the reaction rate for the attack of DNA bases was slower for monoaquated BNP3029 compared to monoaquated cisplatin; and (iii) the reaction rates for a thiol/thiolate attack on monoaquated cisplatin or monoaquated BN3029 were similar. BNP3029 demonstrated potent cytotoxic activity in a variety of human cancer cell lines in comparison to cisplatin and oxaliplatin and also had potent cytotoxic activity in several platinum resistant cell lines.

Dramatic reduction in the activation barrier for dinitrogen splitting using amine–borane as a hydrogen carrier: insights from the DFT study

DFT based mechanistic investigations on a silica surface supported Tantalum system reveal that there is a significant reduction in the free energy activation barrier for N≡N bond dissociation upon using a suitable amine-borane as a hydrogenating agent as compared to that of using molecular H2 for the same purpose, which suggests that dinitrogen dissociation can be achieved in surface chemistry at much lower temperatures than those in the presently used systems.