Mechanism of pyridine protonation in water clusters of increasing size

This work presents a theoretical mechanistic study of the protonation of pyridine in water clusters, at the B3LYP/cc-pVDZ theory level. Clusters from one to five water molecules were used. Starting from previously determined structures, the reaction paths for the protonation process were identified. For complexes of pyridine with water clusters of up to three water molecules just one transition state (TS) links the solvated and protonated forms. It is found that the activation energy decreases with the number of water molecules. For complexes of four and five water molecules two transition states are found. For four water molecules, the first TS links the starting solvated structure with a new, less stable, solvated form through a concerted proton transfer between a ring of water molecules. The second TS links the new solvated structure to the protonated form. Thus, protonation is a two-step process. For the five water molecules cluster, the new solvated structure is more stable than the starting one. This structure exhibits two double hydrogen bonds involving the pyridinic nitrogen and several water molecules. The second TS links the new structure with the protonated form. Now the process occurs in one step. In all cases considered, the proton transfers involve an interconversion between covalent and hydrogen bonds. For four and five water molecules, the second TS is structurally and energetically very close to the protonated form. As evidenced by the vibration frequencies, this is due to a flat potential energy hypersurface in the direction of the reaction coordinate. Determination of DeltaG at 298.15 K and 1 atm shows that the protonation of pyridine needs at least four water molecules to be spontaneous. The complex with five water molecules exhibits a large DeltaG. This value yields a pKa of 2.35, relatively close to the reported 5.21 for pyridine in water.     

Mechanisms of nucleophilic reactions of carbonyl compounds in the gas phase and in a solution

The effect of substituents on nucleophilic addition at the C=O bond, which occurs by the mechanism of intramolecular proton transfer, has been studied by the quantum-chemical MNDO/H method. The effect of nucleophiles and substituents at the carbonyl C atom in the gas phase is opposite to that in solution. Strengthening of the bond between the nucleophile and the carbonyl compound as the result of the transfer of electron density to the carbonyl C atom results in the stabilization of the tetrahedral bipolar adduct. In the formation of an adduct with a strong nucleophile the geometry of the transition state (TS) is closer to that of the reaction product, whereas in the case of a weak nucleophile it is similar to that of the initial reagents. Attack by a weak nucleophile and electron-donating groups at the carbonyl C atom favor the situation in which the reaction system achieves a TS earlier and proton transfer occurs with a low activation barrier.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 227–230, February, 1994.     

FMO-MD simulations on the hydration of formaldehyde in water solution with constraint dynamics

Full-quantum mechanical fragment molecular orbital-based molecular dynamics (FMO-MD) simulations were applied to the hydration reaction of formaldehyde in water solution under neutral conditions. Two mechanisms, a concerted and a stepwise one, were considered with respect to the nucleophilic addition and the proton transfer. Preliminary molecular orbital calculations by means of polarized continuum model reaction field predicted that the hydration prefers a concerted mechanism. Because the calculated activation barriers were too high for free FMO-MD simulations to give reactive trajectories spontaneously, a More O'Ferrall-Jencks-type diagram was constructed from the statistical analysis of the FMO-MD simulations with constraint dynamics. The diagram showed that the hydration proceeds through a zwitterionic-like (ZW-like) structure. The free energy changes along the reaction coordinate calculated by means of the blue moon ensemble for the hydration and the amination of formaldehyde indicated that the hydration proceeds through a concerted process through the ZW-like structure, whereas the amination goes through a stepwise mechanism with a ZW intermediate. In inspection of the FMO-MD trajectories, water-mediated cyclic proton transfers were observed in both reactions on the way from the ZW-like structure to the product. These proton transfers also have an asynchronous character, in which deprotonation from the nucleophilic oxygen atom (or nitrogen atom for amination) precedes the protonation of the carbonyl oxygen atom. The results showed the strong advantage of the FMO-MD simulations to obtain detailed information at a molecular level for solution reactions.     

FMO‐MD Simulations on the Hydration of Formaldehyde in Water Solution with Constraint Dynamics

Full‐quantum mechanical fragment molecular orbital‐based molecular dynamics (FMO‐MD) simulations were applied to the hydration reaction of formaldehyde in water solution under neutral conditions. Two mechanisms, a concerted and a stepwise one, were considered with respect to the nucleophilic addition and the proton transfer. Preliminary molecular orbital calculations by means of polarized continuum model reaction field predicted that the hydration prefers a concerted mechanism. Because the calculated activation barriers were too high for free FMO‐MD simulations to give reactive trajectories spontaneously, a More O’Ferrall–Jencks‐type diagram was constructed from the statistical analysis of the FMO‐MD simulations with constraint dynamics. The diagram showed that the hydration proceeds through a zwitterionic‐like (ZW‐like) structure. The free energy changes along the reaction coordinate calculated by means of the blue moon ensemble for the hydration and the amination of formaldehyde indicated that the hydration proceeds through a concerted process through the ZW‐like structure, whereas the amination goes through a stepwise mechanism with a ZW intermediate. In inspection of the FMO‐MD trajectories, water‐mediated cyclic proton transfers were observed in both reactions on the way from the ZW‐like structure to the product. These proton transfers also have an asynchronous character, in which deprotonation from the nucleophilic oxygen atom (or nitrogen atom for amination) precedes the protonation of the carbonyl oxygen atom. The results showed the strong advantage of the FMO‐MD simulations to obtain detailed information at a molecular level for solution reactions.     

A theoretical investigation of the plausibility of reactions between ammonia and carbonyl species (formaldehyde, acetaldehyde, and acetone) in interstellar ice analogs at ultracold temperatures

We have reexamined the reaction between formaldehyde and ammonia, which was previously studied by us and other workers in modestly sized cluster calculations. Larger model systems with up to 12H(2)O were employed, and reactions of two more carbonyl species, acetaldehyde and acetone, were also carried out. Calculations were performed at the B3LYP/6-31+G** level with bulk solvent effects treated with a polarizable continuum model; limited MP2/6-31+G** calculations were also performed. We found that while the barrier for the concerted proton relay mechanism described in previous work remains modest, it is still prohibitively high for the reaction to occur under the ultracold conditions that prevail in dense interstellar clouds. However, a new pathway emerged in more realistic clusters that involves at least one barrierless step for two of the carbonyl species considered here: ammonia reacts with formaldehyde and acetaldehyde to form a partial charge transfer species in small clusters (4H(2)O) and a protonated hydroxyamino intermediate species in large clusters (9H(2)O, 12H(2)O); modest barriers that decrease sharply with cluster size are found for the analogous processes for the acetone-NH(3) reaction. Furthermore, if a second ammonia replaces one of the water molecules in calculations in the 9H(2)O clusters, deprotonation can occur to yield the same neutral hydroxyamino species that is formed via the original concerted proton relay mechanism. In at least one position, deprotonation is barrierless when zero-point energy is included. In addition to describing the structures and energetics of the reactions between formaldehyde, acetaldehyde, and acetone with ammonia, we report spectroscopic predictions of the observable vibrational features that are expected to be present in ice mixtures of different composition.     

Addition Mechanisms of Phenol toward Formaldehyde under Acidic Condition： a Theoretical Investigation

The reaction mechanisms of phenol with formaldehyde in the first and second addition at the ortho- and para-position in acid solution were theoretically investigated at the PW91/DNP level with solvent effects included. The reaction of phenol with protonated methanediol firstly forms an adduct intermediate, via a SN2 mechanism with a water molecule as the leaving group. From the adduct intermediate, there are two reaction channels involving a proton transfer to form the addition products. One is that a proton directly transfers via a four-membered ring transition state with a notable energy barrier (Four-member mechanism). Another mechanism involving a water molecule as catalyst to mediate the proton transfer (WCP mechanism), is a barrierless process, indicating that the formation of the adduct intermediate, the first reaction step, is rate-limiting. The reaction products are free hydroxymethyl phenols and/or hydroxybenzy carbocation (HOC6H4CH2+) which plays an important role in the following formation of methylene and methylene ether linkages. The second addition reactions between formaldehyde and hydroxymethyl phenol at all possible reaction sites of the phenol ring in acid solution were also investigated and discussed.     

Computational study on the reaction pathway of α-bromoacetophenones with hydroxide ion: possible path bifurcation in the addition/substitution mechanism

The reaction of an α-haloketone with a nucleophile has three reaction channels: carbonyl addition, direct substitution, and proton abstraction. DFT calculations for the reaction of PhCOCH(2)Br with OH(-) showed that there exists an addition/substitution TS on the potential energy surface, in which OH(-) interacts with both the α- and carbonyl carbons. The intrinsic reaction coordinate calculations revealed that the TS serves as the TS for direct substitution for XC(6)H(4)COCH(2)Br with an electron-donating X or a X less electron-withdrawing than m-Cl, whereas the TS serves as the TS for carbonyl addition for derivatives with a X more electron-withdrawing than m-CF(3). Trajectory calculations starting at respective TS indicated that the single TS can serve for the two mechanisms, substitution and addition, through path bifurcation after the TS for borderline substrates. The reaction is the first example of dynamic path bifurcation for fundamental reaction types of carbonyl addition and substitution.     

Urea-formaldehyde resins. III. Constitutional characterization by 13C fourier transform NMR spectroscopy

¹³C Fourier transform NMR has been used to characterize a random chemical structure of ureaformaldehyde resins. By comparison of ¹³C chemical shifts with synthesized standard derivatives from urea and formaldehyde the analysis of reacted formaldehyde was completed. In a ¹³C spectrum of resin each signal due to reacted formaldehyde (e.g., methylol group, methylene group, and dimethylene ether group) was isolated. Measurement of a ¹³C spectrum of resin by the gated decoupling of proton without nuclear Overhauser effect made a quantitative analysis of reacted formaldehyde possible. In this quantitative analysis a ¹³C quantity of carbonyl groups in urea residue can be directly compared with that of each combined formaldehyde.     

Novel quantum mechanical/molecular mechanical method combined with the theory of energy representation: free energy calculation for the Beckmann rearrangement promoted by proton transfers in the supercritical water

The Beckmann rearrangement of acetone oxime promoted by proton transfers in the supercritical water has been investigated by means of the hybrid quantum mechanical/molecular mechanical approach combined with the theory of energy representation (QM/MM-ER) recently developed. The transition state (TS) structures have been explored by ab initio calculations for the reaction of hydrated acetone oxime on the assumption that the reaction is catalyzed by proton transfers along the hydrogen bonds connecting the solute and the solvent water molecules. Up to two water molecules have been considered as reactants that take part in the proton transfers. As a result of the density functional theory calculations with B3LYP functional and aug-cc-pVDZ basis set, it has been found that participation of two water molecules in the reaction reduces the activation free energy by -12.3 kcal/mol. Furthermore, the QM/MM-ER simulations have revealed that the TS is more stabilized than the reactant state in the supercritical water by 2.7 kcal/mol when two water molecules are involved in the reaction. Solvation free energies of the reactant and the TS have been decomposed into terms due to the electronic polarization of the solute, electron density fluctuation, and others to elucidate the origin of the stabilization of the TS as compared with the reactant. It has been revealed that the promotion of the chemical reaction due to the hydration mainly originates from the interaction between the nonpolarized solute and the solvent water molecules at the supercritical state.     

Melamine–formaldehyde resins: Constitutional characterization by fourier transform 13C-NMR spectroscopy

The random chemical structures of melamine–formaldehyde resins, including methylated melamine–formaldehyde resins and urea–melamine formaldehyde resins, were investigated by ¹³C-NMR spectroscopy (Fourier transform). All the combined formaldehydes, methylol and methyl ether groups, methylene structures, and dimethylene ether structures were assigned. A ¹³C chemical shift of methylene carbon occurred by substitution of other constituents of the methylene group for a proton of the adjacent monosubstituted nitrogen atom, as shown in a ¹³C-NMR spectrum of urea–formaldehyde resins. It was found that the chemical shift of each corresponding carbon of both melamine resins and urea–melamine resins was almost superimposed with that of urea resins.     

Hydration effects on the reaction with an open-shell transition state: QM/MM-ER study for the dehydration reaction of alcohol in hot water

The reaction mechanism for the dehydration of 1,4-butanediol in hot water has been investigated by means of the hybrid quantum mechanical/molecular mechanical approach combined with the theory of energy representation (QM/MM-ER). We have assumed that the proton transfers along the hydrogen bonds of the water molecules catalyze the reaction, where the transition state (TS) forms a singlet biradical electronic structure. It has been revealed by the simulation that the biradical electronic state at the TS changes to zwitterionic structure in solution due to the hydration of the polar solvent. Such the electronic structure change gives rise to the substantial stabilization of the TS in hot water. As a result, the water-catalytic path becomes more favorable in aqueous solution than another possible path that proceeds without proton transfers as opposed to the reaction mechanism in the gas phase. Furthermore, the activation free energy computed by the present method is in excellent agreement with the experimental result.     

1,6-六亚甲基二异氰酸酯自聚产物的结构表征

用IR与NMR表征了用醋酸钾为催化剂时 1,6 六亚甲基二异氰酸酯 (HDI)自聚产物的结构 .结果表明 ,自聚主产物是三聚体异氰脲酸酯 ,主要含有三聚体异氰脲基、异氰酸根 ,同时含有由杂质带来的微量氨基甲酸酯、脲基甲酸酯基、取代脲基、缩二脲基 .一维核磁谱及二维化学位移相关谱分辨出 7种羰基 ,一种NCO基 ,确定了氮上 8种不同取代结构的分子链连接情况 .通过建立理论模型 ,定量地描述了自聚产物的结构 .     

A new specific mechanism for the acid catalysis of the addition step in the Baeyer-Villiger rearrangement

[structure: see text] A new transition state of the addition step in the Baeyer-Villiger reaction was found. The role of proton acceptor is played by the carbonyl oxygen atom, and the free energy barrier is 12.7 kcal/mol lower than that previously reported. This finding changes the mechanism for the acid catalysis and could be of interest for similar reactions in which it is known that such catalysis occurs, especially in nonpolar solvents.     

The intramolecular mechanism for the second proton transfer in triosephosphate isomerase (TIM): a QM/FE approach

The intramolecular mechanism we earlier proposed [Alagona, G.; Desmeules, P.; Ghio, C.; Kollman, P. A. J Am Chem Soc 1984, 106, 3623] for the second proton transfer of the reaction catalyzed by triosephosphate isomerase (TIM) is examined ab initio at the HF and MP2/6-31+G** levels in vacuo for two conformers of the enediolate phosphate (ENEP), with the ethereal oxygen of the phosphate group either syn (X), as in the crystal structure, or anti (Y) with respect to the enediolate carbonyl O. The barrier height for the intramolecular proton transfer occurring in enediolate is very sensitive to electron correlation corrections. The MP2 internal energy barrier is much lower than the HF one, while the free energy (FE) barrier is even more favorable, indicating that the enzyme presence is not requested to speed up that step. An investigation of the dynamical aspects of the mechanism, along the pathway from ENEP A (with H on O(1)) to TS and from TS to ENEP B (with H on O(2)), was, however, carried out in the presence of the enzyme field while using a neutral His-95 with its proton on Ndelta. To perform the FE simulations, it was necessary to parametrize in the AMBER force-field the ENEP A, TS and B species, whose partial charges have been determined with the RESP procedure, with the X and Y arrangements of the phosphate head. Actually, the FE/QM approach produced a low barrier and a substantial balance between A and B, especially at the MP2 level. The trajectories, analyzed paying a particular attention to the positions assumed by His-95 and by the other active site residues, put forward somewhat different H-bond patterns around the X or Y enediolate phosphate.     

The mechanism of cis-trans isomerization of prolyl peptides by cyclophilin

The mechanism of cis-trans isomerization of prolyl peptides catalyzed by cyclophilin (CyP) was studied computationally via molecular dynamics (MD) simulations of the transition state (TS) and the cis and trans forms of the ground state (GS), when bound to CyP and when free in aqueous solution. The MD simulations include four enzyme-bound species of tetrapeptide (Suc-Ala-XC([double bond]O)-NPro-Phe-pNA; X = Gly, Trp, Ala, and Leu). In water, the prolyl amide bond is favorably planar with the presence of conformers exhibiting +/-20 degrees twist of the C-N dihedral. In the active site a hydrogen bond between the cis-prolyl amide carbonyl O and the backbone amide N-H of Asn102 retains the 20 degrees twist of the C-N dihedral. The TS structure is characterized by a 90 degrees twist of the amide C-N bond and a more favorable interaction with Asn102 due to the shorter distance between Asn102(HN) and the amide carbonyl O. The conformational change of cis --> TS also involves pyramidalization of the amide N, which results in the formation of a hydrogen bond between the amide N and the guanidino group of Arg55. Both Asn102 and Arg55 are held in the same position in CyP.cis-isomer as in CyP.TS. In the ligand-free CyP the Arg55 guanidino group is highly disorganized and Asn102 is displaced 1 A from the position in the ligand-bound CyP. Thus, the organization of Arg55 and Asn102 occurs upon substrate binding. The geometrical complimentarity of the organized enzyme structure to the TS structure is a result of preferential binding of the proline N and the amide carbonyl of the TS compared to that of GS. However, the N-terminal part (Suc-Ala) becomes repositioned in the TS such that two hydrogen bonds disappear, one hydrogen bond appears and two other hydrogen bonds becomes weaker on the conversion of CyP.cis to CyP.TS. During this conversion, total hydrophobic contact between enzyme and the peptide is preserved. Thus, the interaction energies of GS and TS with enzyme are, as a whole, much alike. This does not support the contention that TS is bound more tightly than GS by K(m)/K(TS) = 10(6) in the cis --> trans reaction. Repositioning of the N-terminal part of the peptide on CyP.TS formation becomes more pronounced when the substrate X residue is changed from Gly < Trp < Ala < Leu. We propose that the larger turning of the N-terminus is responsible for the larger value of the experimentally observed Delta S(++) and Delta H(++), which sum up to little change in Delta G(++). The positioning of the Arg55 and the degree of 20 degrees twist of the amide C-N bond are considered as criteria for Near Attack Conformers (NACs) in cis-trans isomerization. NACs account for approximately 30% of the total GS populations of the cis-isomer. Similar NAC populations were observed with four different substrates. This is consistent with the insensitivity of enzymatic activity to the nature of the X residue. Also, the NAC population in CyP.trans-AAPF was comparable to that in CyP.cis-AAPF, in accord with similar experimentally measured rates of the cis --> trans and trans --> cis reaction in CyP. These NACs, found in CyP.cis and CyP.trans, resemble only one of the four possible TS configurations in the water reaction. The identity of this TS structure (syn/exo) is in accord with experimentally determined KIE values in the enzymatic reaction. However, the geometry of the active site was also complementary to another TS structure (anti/exo) that was not detected in the active site by the same KIE measurements, implying that the geometrical fitness of the TS cannot be a single determining factor for enzymatic reactions.     

Investigation of the mechanism of the cell wall DD-carboxypeptidase reaction of penicillin-binding protein 5 of Escherichia coli by quantum mechanics/molecular mechanics calculations

Penicillin-binding protein 5 (PBP 5) of Escherichia coli hydrolyzes the terminal D-Ala-D-Ala peptide bond of the stem peptides of the cell wall peptidoglycan. The mechanism of PBP 5 catalysis of amide bond hydrolysis is initial acylation of an active site serine by the peptide substrate, followed by hydrolytic deacylation of this acyl-enzyme intermediate to complete the turnover. The microscopic events of both the acylation and deacylation half-reactions have not been studied. This absence is addressed here by the use of explicit-solvent molecular dynamics simulations and ONIOM quantum mechanics/molecular mechanics (QM/MM) calculations. The potential-energy surface for the acylation reaction, based on MP2/6-31+G(d) calculations, reveals that Lys47 acts as the general base for proton abstraction from Ser44 in the serine acylation step. A discrete potential-energy minimum for the tetrahedral species is not found. The absence of such a minimum implies a conformational change in the transition state, concomitant with serine addition to the amide carbonyl, so as to enable the nitrogen atom of the scissile bond to accept the proton that is necessary for progression to the acyl-enzyme intermediate. Molecular dynamics simulations indicate that transiently protonated Lys47 is the proton donor in tetrahedral intermediate collapse to the acyl-enzyme species. Two pathways for this proton transfer are observed. One is the direct migration of a proton from Lys47. The second pathway is proton transfer via an intermediary water molecule. Although the energy barriers for the two pathways are similar, more conformers sample the latter pathway. The same water molecule that mediates the Lys47 proton transfer to the nitrogen of the departing D-Ala is well positioned, with respect to the Lys47 amine, to act as the hydrolytic water in the deacylation step. Deacylation occurs with the formation of a tetrahedral intermediate over a 24 kcal x mol(-1) barrier. This barrier is approximately 2 kcal x mol(-1) greater than the barrier (22 kcal x mol(-1)) for the formation of the tetrahedral species in acylation. The potential-energy surface for the collapse of the deacylation tetrahedral species gives a 24 kcal x mol(-1) higher energy species for the product, signifying that the complex would readily reorganize and pave the way for the expulsion of the product of the reaction from the active site and the regeneration of the catalyst. These computational data dovetail with the knowledge on the reaction from experimental approaches.     

A new mechanism for the Favorskii rearrangement

The title reaction was investigated by the use of ONIOM-RB3LYP calculations. A reaction system composed of alpha-chlorocyclohexanone, a methoxide ion and 8 MeOH solvent molecules was adopted. Two reaction channels, the semibenzilic acid mechanism (A) and cyclopropanone mechanism (B), were compared. B is found to be more favorable than A. The rate-determining step of B is the (MeOH)(3) addition transition state (TS3B) to the cyclopropanone intermediate. While TS3B involves a concerted function of MeO(-) addition and proton relays, it has a large activation energy. A new route was found, where the chloride ion evolved at the cyclopropane formation step (TS2B) works as a nucleophile to the cyclopropanone intermediate. Thus, a cyclopentane-carbonyl chloride intermediate is formed with a small activation energy. A new cyclopropanone mechanism is proposed.     

Theoretical study of the acid-promoted hydrolysis of oxazolin-5-one: a microhydration model

The acid-promoted hydrolysis of 2,4,4-trimethyloxazolin-5-one (TMO) is studied employing the density functional theory (B3LYP) method in conjunction with the 6-31++G(d,p) basis set. Two types of reaction mechanism, N-protonated and O-protonated, are considered, involving protonation at the nitrogen and carbonyl oxygen of TMO to activate the C2 and C5 atoms, respectively, in favor of attack by water molecules. In the N-protonated pathway, the nucleophilic water molecule attacks the activated C2 atom, with a proton transfer from the water molecule to the oxygen atom attached to C2 and the fission of the C2-O bond, leading to a cis ring-opening product (N-acyl-alpha-amino isobutyric acid). While, in the O-protonated pathway, the nucleophilic water molecule attacks the activated carbonyl C5 atom, accompanied by a proton transfer from the water molecule toward the nitrogen atom of oxazole ring and the cleavage of C5-O bond; as a result, a corresponding trans product is generated. The water-assisted hydrolysis reactions are also examined together. A local microhydration model, in which an extra water molecule was added to obtain a continuous H-bond network around the reaction centers, was adopted to mimic the system for the two types of reaction processes. In addition, bulk solvent effect is introduced by use of the conductor-like polarizable continuum model (CPCM). Our computational results in kinetics and thermodynamics clearly manifest that the O-protonated pathway with the nucleophilic attack at the carbonyl C5 atom is more favorable than the N-protonated one, in nice agreement with the available experimental conclusion.     

Fundamental reaction pathway and free energy profile for inhibition of proteasome by Epoxomicin

First-principles quantum mechanical/molecular mechanical free energy calculations have been performed to provide the first detailed computational study on the possible mechanisms for reaction of proteasome with a representative peptide inhibitor, Epoxomicin (EPX). The calculated results reveal that the most favorable reaction pathway consists of five steps. The first is a proton transfer process, activating Thr1-O(γ) directly by Thr1-N(z) to form a zwitterionic intermediate. The next step is nucleophilic attack on the carbonyl carbon of EPX by the negatively charged Thr1-O(γ) atom, followed by a proton transfer from Thr1-N(z) to the carbonyl oxygen of EPX (third step). Then, Thr1-N(z) attacks on the carbon of the epoxide group of EPX, accompanied by the epoxide ring-opening (S(N)2 nucleophilic substitution) such that a zwitterionic morpholino ring is formed between residue Thr1 and EPX. Finally, the product of morpholino ring is generated via another proton transfer. Noteworthy, Thr1-O(γ) can be activated directly by Thr1-N(z) to form the zwitterionic intermediate (with a free energy barrier of only 9.9 kcal/mol), and water cannot assist the rate-determining step, which is remarkably different from the previous perception that a water molecule should mediate the activation process. The fourth reaction step has the highest free energy barrier (23.6 kcal/mol) which is reasonably close to the activation free energy (～21-22 kcal/mol) derived from experimental kinetic data. The obtained novel mechanistic insights should be valuable for not only future rational design of more efficient proteasome inhibitors but also understanding the general reaction mechanism of proteasome with a peptide or protein.     

Global mapping of equilibrium and transition structures on potential energy surfaces by the scaled hypersphere search method: applications to ab initio surfaces of formaldehyde and propyne molecules

Technical details of a new global mapping technique for finding equilibrium (EQ) and transition structures (TS) on potential energy surfaces (PES), the scaled hypersphere search (SHS) method (Ohno, K.; Maeda, S. Chem. Phys. Lett. 2004, 384, 277), are presented. On the basis of a simple principle that reaction pathways are found as anharmonic downward distortions of PES around an EQ point, the reaction pathways can be obtained as energy minima on the scaled hypersphere surface, which would have a constant energy when the potentials are harmonic. Connections of SHS paths between each EQ are very similar to corresponding intrinsic reaction coordinate (IRC) connections. The energy maximum along the SHS path reaches a region in close proximity to the TS of the reaction pathway, and the subsequent geometry optimization from the SHS maximum structure easily converges to the TS. The SHS method, using the one-after-another algorithm connecting EQ and TS, considerably reduces the multidimensional space to be searched to certain limited regions around the pathways connecting each EQ with the neighboring TS. Applications of the SHS method have been made to ab initio surfaces of formaldehyde and propyne molecules to obtain systematically five EQ and nine TS for formaldehyde and seven EQ and 32 TS for propyne.