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We study the transition pathways of a Lennard-Jones cluster of seven particles in three dimensions. Low lying saddle points of the LJ cluster, which can be reached directly from a minimum without passing through another minimum, are identified without any presumption of their characteristics, nor of the product states they lead to. The probabilities are computed for paths going from a given minimum to the surrounding saddle points. These probabilities are directly related to prefactors in the rate formula. This determination of the rate prefactors includes all anharmonicities, near or far from saddle points, which are pertinent in the very sophisticated energy landscape of LJ clusters and in many other complex systems.

In this paper, the structural and dynamical properties of the 19-atom double icosahedral silver cluster are studied by using the classical molecular dynamics. It is found that the melting of the 19-atom cluster starts with the migrations of the surface atoms. The surface atoms can interchange positions with each other atoms through three ways. The first and second ways involve with only part of the surface atoms. The third way can involve the surface atoms at all symmetrical positions. With the increase of temperature, the inner atoms can hop onto the surface of the cluster and the position interchange between the surface atoms and the inner atoms can be realized. With further increase of temperature, the isomerization of the cluster becomes frequent and the motion of the atoms of the cluster becomes more and more disordered. When the temperature reaches the value corresponding to the second peak of the heat capacity, the solid cluster turns into the fully melted state.

The occurrence of high-T_c superconductivity in the iron pnictides shares a similar amorphous characteristic with that of high-T_c superconducting cuprates. Here we show that nearly frictionless (electric-field-driven) transport of condensed electrons in amorphous superconductors could happen after using the Eyring's transition-rate approach which has been successfully adopted to study the critical transport of other superconductors as well as supersolid helium in very low temperature environment. The critical temperatures related to the nearly frictionless transport of electrons were found to be directly relevant to the superconducting temperature of high-temperature superconductors (like La[O_1-xF_x]FeAs(x = 0.11-0.12)) after selecting specific activation energies and activation volumes.

Rydberg atom is highly excited with one valence electron being in a high quantum state, which is very far away from the nucleus. The energy level is similar to that of the hydrogen atom. Introducing externally perpendicular electric and magnetic fields breaks the rotation symmetry and the traditional view is that the ionized electron crosses from the bound into the unbound region and will never return. However, we find that when the field is strong enough, the electron does not move off to infinity and there is a certain possibility of return. Three new periodic orbits are found by the variational method and the physical significance of the phenomenon is also discussed.

The reaction mechanisms and kinetics for DMS + O₃ ⇒ DMSO + O₂ in water vapor are studied using density functional theory. A series of reaction pathways are determined with molecular clusters containing the reacting species and up to three water molecules. The results show that the energy barrier, defined as the energy difference between the reactant complex and the transition state, decreases progressively as each water molecule is added to the reacting system. A decreasing energy barrier is attributed to favorable electrostatic interactions between the reacting species and water at the transition state and at the more polar product. Rate constants for the second-order reactions, involving different combinations of hydrated reactants up to three water molecules, are calculated using transition state theory with Eckart tunneling corrections. Effective rate constants for DMS + O₃ ⇒ DMSO + O₂ are obtained using the calculated second-order rate constants and the concentrations of hydrated reactants present in saturated water vapor. The results show that the rate of reaction for DMS + O₃ ⇒ DMSO + O₂ increases dramatically in the presence of water vapor, by up to seven orders of magnitude for reactions involving three water molecules. The study implies that the gas-phase reaction of DMS with ozone is significant in the troposphere and can greatly influence the global climate.

Direct dynamics within the framework of DFT has been used to study the reaction between Boron trichloride and H radical. Two sets of trajectories amounting to a total of 40 were simulated for different collision sites and initial velocities. Two reactive channels have been found. One is a Cl atom abstraction channel and the other is a Cl atom elimination channel. The detailed mechanisms of both reactive channels were depicted by sampling trajectories. For the first channel, the reaction mechanism proposed by ab initio calculations was represented. For the second channel, transition state was mapped out after the dynamics simulation.

PCN and PNC are possible interstellar species that have not been experimentally characterized. With various ab initio methods, including multireference and restricted open-shell single-reference electronic structure theory, the PCN/PNC species and the transition state for the isomerization reaction PCN ↔ PNC have been studied. The Dunning series of correlation-consistent basis sets, cc-pVXZ and aug-cc-pVXZ (X = T and Q), have been used. Geometries, total energies, dipole moments, harmonic vibrational frequencies, infrared intensities, and zero-point vibrational energies are reported for the PCN/PNC isomers and the transition state. Both PCN and PNC are linear with ³Σ^- ground states, and linear is predicted to lie 13.7 kcal mol^-1 (13.5 kcal mol^-1 with ZPVE correction) above linear at the aug-cc-pVQZ CCSD(T) level of theory. The CN bond distance in is predicted to be 1.174 Å, only 0.002 Å longer than the experimental value of 1.172 Å for diatomic CN (X²Σ⁺, suggesting that CN has triple bond character in . The isomerization transition state is found to be cyclic , with angles θ_e (PCN) = 82.2°, θ_e (CNP) = 63.1°, and θ_e (NPC) = 34.7°. The isomerization barrier is predicted to be 35.7 kcal mol^-1 (34.5 kcal mol^-1 with ZPVE correction) relative to linear . The predicted dipole moments are substantial, 2.79 debye (polarity ⁺PCN^-) and 2.51 debye (polarity ⁺PNC^-).

Hydrolysis of trans-dichloro(ammine)(quinoline)platinum, a novel potential anticancer drug, is believed to be the key activation step before the drug reaches its intracellular target DNA. To obtain an accurate hydrolysis mechanism for this nonclassical class of square-planar Pt(II) complex, five different models were used at the experimental temperature with the solvent effect B3LYP/PCM using hybrid density functional theory. The stationary points on the potential energy surfaces for the first and second hydrolysis steps, proceeding via a five-coordinate trigonal-bipyramidal (TBP)-like structure of transition state, were fully optimized and characterized. The most remarkable structural variations in the hydrolysis process were found to occur in the equatorial plane of the TBP-like structures of the intermediates and transition states. It was found that the explicit solvent effect originating from the inclusion of extra water molecules into the system is significantly stronger than those arising from the bulk aqueous medium, especially for the first aquation step, which emphasizes the use of appropriate models for these types of problems. The results give detailed energy profiles for the mechanism of hydrolysis of trans-dichloro(ammine)(quinoline)platinum, which may assist in understanding the reaction mechanism of the drug with DNA target and in the design of novel platinum-based anticancer drugs with trans geometries.

The reaction mechanism of CuI-catalyzed formation of ethyl 2-phenylacetoacetate by arylation of ethyl acetoacetate has been investigated by density functional theory (DFT) using Becke's three-parameter nonlocal exchange functional and the Lee, Yang, and Parr nonlocal correlation functional (B3LYP). The geometries of the reactants, intermediates, transition states, and products have been optimized and verified by means of vibration frequency calculations. According to our assumption, this reaction can be divided into two stages. The rate-determining step is found to be the 3 → 4-TS procedure, which is the first procedure of stage 1. The low energy barrier of 39.85 kcal/mol indicates that this reaction can be carried out, which is in accordance with the experimental facts. For comparison, we have investigated the reaction mechanism of the same chemical reaction without CuI catalyst, whose energy barrier of rate-determining step is 212.76 kcal/mol higher than that with CuI catalyst. This fact suggests that CuI catalyst accelerates the reaction by remarkably lowering the energy barrier. The solvation effects on the barriers of the reaction are important. But the energetic order in DMSO solvent seems to be almost the same as that in gas-phase, which indicates that our conclusion achieved in gas-phase is believable. Our findings reveal the microscopic catalytic mechanism of CuI and are in agreement with the experimental facts.

The proton assisted isomerization reactions of 1H-imidazo(4,5-b)pyridine (IMP) derivatives have been studied by using B3LYP/6-31G + (d,p) calculations, and the transition states of the reactions are analyzed with B3LYP/6-31+G(d,p) opt=qst3 route. It has been found that the prototropic transformation could be the feasible pathway of isomerization, since the energy gaps between the various protonated isomers are found closer compared to free molecules. The conversion of IMP-a1 to IMP-b1 may pass through several protrotopic isomerization, since the activation energy as well as the relative energy levels of these isomers are not small compared to other pathways. However, the results suggest that some of the reactions may take place simultaneously through protrotopic transformation. The relative variations of energy gaps in the excited states are smaller than the ground states. The protrotropic transformation in the excited states may be more feasible than the ground state.

The asymmetric Michael reaction of aldehydes and nitrostyrene catalyzed by a new (S)-tertbutyl-diphenyl-silyl-pyrrolidine catalyst has been investigated by using density functional theory calculations. The Re face of the enamine is effectively shielded, because of the bulky 2-substituent group on the pyrrolidine ring. For acetaldehyde, there are two different conformers of enamines. Based on the two conformers of enamines, four different reaction pathways have been considered. The calculated enantiomeric excess value is 80.27% in favor of the (R)-configuration product. For propanal, eight different reaction pathways have been considered and the eight corresponding transition states have been located. The calculated enantiomeric excess value is 98.96% in favor of the (2S, 3R)-configuration product. These calculated results are in good agreement with the experimental observations. In addition, the calculations also show that both the used solvent and the enamines play important roles in determining the stereochemical outcome of the product.

A MP2/6-31++G(d,p)//B3LYP/6-31++G(d,p) method was used to investigate the mechanisms of α-H and proton transfers of glycine induced by Mg²⁺. Eight complexes were obtained, six of which were neutral and the other two were zwitterionic. Among them, the zwitterion with a binding energy of 159.4 kcal/mol was the most stable structure. Conformation transformations of the complexes caused by the rotation of single bond and the transfers of α-H and proton were completed via seven transition states. The inductive effect of Mg²⁺ made the electron cloud of glycine deviate to Mg²⁺, which activated the covalent bond involving the transferred proton. The neutral complex can be turned into the zwitterionic one by the transfers of both carboxyl hydrogen and α-H, and the energy barrier of each reaction was less than 9.2 kcal/mol. After the transfer of α-H, a delocalized π bond was formed in glycine skeleton and the α-C atom took 0.19 positive charges. So the chemical activity of the glycine enhanced, and glycine was readily available for addition and nucleophilic substitution reactions. The path from the most stable glycine conformer G1 to the zwitterionic conformation I is G1 → G1–G3 → G3 → G3–G4 → G4 → G2–G4 → G2 → VI → I–VI → I, and the highest energy barrier of this path is 9.2 kcal/mol.

To understand the reaction mechanism involving hydrogen transfers through hydrogen-bond bridge, we carried out both Self-Consistent Charge Density Functional Tight-Binding (SCC-DFTB) calculations of bulk nitromethane and Density Functional Theory (DFT) calculations of singlet ground state/triplet excited state molecular nitromethane using B3LYP functional. Firstly, we tuned the repulsive parameters of the SCC-DFTB method for nitromethane with dataset calculated from DFT at B3LYP/6-311g level. The molecular dynamics simulations are carried out with tuned parameters to get the dynamical properties of the bulk nitromethane, and the static calculations are intended to give energy profile of the reaction process. These calculations indicate the excitation of nitromethane molecule making the proton transfer reactions possible, and lowering the reaction barrier.

Multistep dissociative chemisorption reactions of water with Pd₄ and Pd₇ clusters were studied using density functional theory. The adsorption energies and referred adsorption sites from water molecule (H₂O) to partially dissociative (H₂+O and OH+H), then to fully dissociative (O+H+H) configurations are carefully determined. It is found that the adsorption energies of three dissociative reactions are 5–6 times larger than that of water molecule. Atop sites of Pd₄ and Pd₇ clusters are found to be the most stable sites for the adsorbed H₂O molecule. For the coadsorption cases of partially and fully dissociated products, H₂ and OH molecules preferably tend to bind at the low coordination (atop or bridge) sites, and O and H atoms prefer to adsorb on the high coordination (hollow) sites. It is also found that the most favorable adsorption sites for the molecular adsorbates (H₂O, H₂ and OH) are adjacent to the Pd atoms with the largest site-specific polarizabilities. Therefore, site-specific polarizability is a good predictor of the favorable adsorption sites for the weakly bound molecules. The different directions of charge transfer between the Pd clusters and the adsorbate(s) is observed. Furthermore, the processes of the adsorption, dissociation, and the dissociative products diffusion of H₂O are analyzed.

The geometry structure, vibrational frequency, and the isomerization of neutral and cation copper cyanide systems (CuCN and CuCN⁺) were investigated by employing three DFT methods (B3LYP, B3P86 and B3PW91) and MP2 functional with 6-311+G* basis set. The cyanides CuCN(¹Σ⁺) is the most stable one among the isomers of CuCN, and CuNC⁺(²Σ⁺) isocyanides is the global minimum on its potential energy surface (PES). The vibrational modes of these isomers were assigned. Two dissociation mechanisms were designed for each species. The complex (CuCN and CuCN⁺) tends to dissociate through neutral mechanism into CN cluster. The useful information is brought forward about the synthesis of material and biological macromolecule. The state–state isomerization pathways were established using the intrinsic reaction coordinate (IRC).

$N$-tert-butylmethanimine $N$-oxide is a potent spin-trapping probe for biologically important radicals, and this nitrone undergoes complete regioselective cycloadditions to less electron-deficient monosubstituted olefins. In the present study, solvent effects on the cycloaddition of this nitrone to styrene have been theoretically studied in terms of the global properties of the reactants, electrophilic and nucleophilic Parr function analysis and the activation and reaction energies of located transition states and products. Formation energies of optimized radical adducts were computed to determine their stabilities in different solvents. The cycloaddition is predicted to be completely ortho regioselective which is in complete agreement with experiments and involved earlier C–C bond formation owing to the insufficient depopulation of $\beta$-conjugated carbon atom in styrene and shows varying asymmetry indices in different solvents. Decrease in activation parameters and increase in stability of cycloadducts are predicted with decreasing solvent polarity. Aqueous media destabilize the radical adducts as predicted from the calculated formation energy, enthalpy and free energy of reaction. Hydroxyl as well as methyl radical adducts are predicted to be more stable than superoxide anion radical adducts. These predictions are in complete agreement with the experiments.

A crucial event in protein folding is the formation of a folding nucleus, which is a structured part of the protein chain in the transition state. We demonstrate a correlation between locations of residues involved in the folding nuclei and locations of predicted amyloidogenic regions. The average Φ-values are significantly greater inside amyloidogenic regions than outside them. We have found that fibril formation and normal folding involve many of the same key residues, giving an opportunity to outline the folding initiation site in protein chains. The search for folding initiation sites for apomyoglobin and ribonuclease. A coincides with the predictions made by other approaches.

We adopted the verified quantum chemistry approach to demonstrate the possible frictionless transport of solid He-4 with high shear viscosity in a confined 3 nm (diameter) nanopore. Both the sharp decrease of flow resistance and sudden increase of shear viscosity of solid ⁴He in nanodomains near the onset of possible supersolidity are illustrated.

In this chapter, we recount a recent success story in the quest for a molecular-level view of a large-scale catalytic process, namely ethylene (C₂H₄) partial oxidation to ethylene epoxide (C₂H₄O). This selective oxidation reaction, which is catalyzed uniquely by silver, is more than sixty years old and one of the most widely studied in heterogeneous catalysis. What the microscopic mechanism of this reaction is, however, remains unclear, and why the noble metal Ag is the only metal that catalyses this process is also unknown. Traditionally, studies (and hence debates!) have centered on identifying the nature of the ‘active’ oxygen species, i.e. the one that actuates the catalysis and leads to the desired partial oxidation product. Here, we begin by describing density functional theory (DFT), scanning tunneling microscopy (STM) and STM simulation studies which have characterized the atomic level structures of O on the {111} surface of Ag. These studies have identified two types of stable phase of O on Ag: (i) Low coverage O adatom phases (θ ∼ 0.05 monolayers); and (ii) ultra-thin Ag_xO(x ≠ 2) surface oxides. Following this, the relative stabilities of these overlayers are assessed at finite temperatures and pressures in order to link these ‘surface science’ ultrahigh- vacuum conclusions with the high pressure and high temperature realm of industrial catalysis. This is done through the application of thermodynamics (with a strategy now commonly referred to as “ab initio thermodynamics”) and leads to an ab initio surface phase diagram for O on Ag{111}. Next the reactivity of the phases predicted to be stable at, or close to, industrial epoxidation conditions is examined. This involves (i) a combined STM and DFT study of ethylene adsorption on one of the ultra-thin Ag_xO surface oxides; and (ii) a DFT study in which reaction pathways and transition states for the conversion of ethylene to ethylene epoxide have been determined. One of the key findings of the latter study is that whether on a surface oxide overlayer or on a surface with a low coverage of O adatoms, ethylene epoxidation is not a direct reaction. Instead it is a two-step non-concerted process, which proceeds via an oxametallacycle intermediate.

The stability of an organic compound depends on its nature and the environment in which it is placed. It depends on the presence or absence of reagents (acid, base, oxidizing agent, reducing agent, light, etc.) and catalysts. The stability may not be the same in the solid, liquid or gaseous state. In a homogenous solution, the stability might be affected by the polarity of the solvent and its concentration. For instance a polar solvent favors ionization. In a non-polar solvent ionization is difficult. In the gas phase ionization never occurs. In the gas phase and in solution stability depends on pressure and the presence of impurities. We are interested here in the thermal stability of pure compounds in the gas phase or in non-polar solvents under one atmosphere…