Development of a new molecular dynamics method for tribochemical reaction and its application to formation dynamics of MoS2 tribofilm

Recently we have developed a novel molecular dynamics program NEW-RYUDO-CR, which can deal with chemical reactions. The developed method has been applied to the study of tribochemical reaction dynamics of MoS₂ tribofilm on iron surface. The initially amorphous MoS₂ layer self-organized its structure as result of the tribochemical reactions and formed layered MoS₂ tribofilm. The friction coefficient significantly decreased as the MoS₂ tribofilm was formed. Besides, sliding was observed between sulfur layers of MoS₂ tribofilms which occurred due to repulsive Coulombic interaction forces between sulfur atoms. This indicates that the formation of the layered MoS₂ tribofilm is important to achieve better lubrication properties.     

Exploration of pulse timing for multiple laser hits within a combined heat transfer, phase change, and gas dynamics model for laser ablation

Laser ablation involves heat transfer, phase changes and/or chemical reactions, and gas dynamics. All three of these processes are tightly coupled with each other. A model has previously been developed to simulate the nanosecond scale laser ablation of carbon. This model has been extended to accommodate longer term simulations and multiple laser pulses. The effects of varying the timing of a second laser pulse by tens of nanoseconds are explored. It is shown that by changing this interval one can control the total mass ablated and the mass transfer rate.     

Efficient exploration of reactive potential energy surfaces using Car-Parrinello molecular dynamics

The possibility of observing chemical reactions in ab initio molecular dynamics runs is severely hindered by the short simulation time accessible. We propose a new method for accelerating the reaction process, based on the ideas of the extended Lagrangian and coarse-grained non-Markovian metadynamics. We demonstrate that by this method it is possible to simulate reactions involving complex atomic rearrangements and very large energy barriers in runs of a few picoseconds.     

Adsorption and catalysis: The effect of confinement on chemical reactions

Confinement within porous materials can affect chemical reactions through a host of different effects, including changes in the thermodynamic state of the system due to interactions with the pore walls, selective adsorption, geometrical constraints that affect the reaction mechanism, electronic perturbation due to the substrate, etc. In this work, we present an overview of some of our recent research on some of these effects, on chemical equilibrium, kinetic rates and reaction mechanisms. We also discuss our current and future directions for research in this area.     

A new method to study the crystallization or chemical reaction kinetics using thermal analysis technique

In this work, a new method to study the transformation kinetics is introduced. With this method, the activation energy, E_c, for crystallization (phase transition or chemical reaction), the pre-exponential coefficient of effective overall reaction rate, k_o, and the reaction order, n, can be determined. No approximation has been used in this method. This method can be used for isothermal and non-isothermal study. It is deduced from Avrami's equation without any approximation. This new method has been tested to study the amorphous-crystalline transformation kinetics under isothermal and non-isothermal conditions in the context of glassy selenium. The source of error is discussed. The calculated values of E_c, under isothermal and non-isothermal conditions are 75.3±2.5 and 79.4±2.3 kJ/mol, respectively. The predominant crystallization mechanism of the amorphous phase of glassy selenium in isothermal or non-isothermal conditions is one-dimensional growth. The deduced values of k_o were found to be 19.4±0.9 and 20.8±0.7 s⁻¹ for isothermal and non-isothermal conditions, respectively. Resulting values of the parameter, n, are compared with values obtained from other known methods used to study the reaction kinetics in thermal analyses. The difference in the results obtained with this method and the results obtained with other known methods is acceptable or lie within the experimental error range.     

Quantum hydrodynamics with trajectories: The nonlinear conservation form mixed/discontinuous Galerkin method with applications in chemistry

We present a solution to the conservation form (Eulerian form) of the quantum hydrodynamic equations which arise in chemical dynamics by implementing a mixed/discontinuous Galerkin (MDG) finite element numerical scheme. We show that this methodology is stable, showing good accuracy and a remarkable scale invariance in its solution space. In addition the MDG method is robust, adapting well to various initial-boundary value problems of particular significance in a range of physical and chemical applications. We further show explicitly how to recover the Lagrangian frame (or pathline) solutions.     

Divergence-free WKB theory

We present a divergence-free WKB theory, which is a new semiclassical theory modified by nonperturbative quantum corrections. Conventionally, the WKB theory is constructed upon a trajectory that obeys the bare classical dynamics expressed by a quadratic equation in momentum space. Contrary to this, the divergence-free WKB theory is based on a higher-order algebraic equation in momentum space, which represents a dressed classical dynamics. More precisely, this higher-order algebraic equation is obtained by including quantum corrections to the quadratic equation, which is the bare classical limit. An additional solution of the higher-order algebraic equation enables us to construct a uniformly converging perturbative expansion of the wavefunction. Namely, our theory removes the notorious divergence of wavefunction at a turning point from the WKB theory. Moreover, our theory is able to produce wavefunctions and eigenenergies more accurate than those given by the traditional WKB method. In addition, the divergence-free WKB theory that is based on the cubic equation allows us to construct a uniformly valid wavefunction for the nonlinear Schrödinger equation (NLSE). A recent short letter [T. Hyouguchi, S. Adachi, M. Ueda, Phys. Rev. Lett. 88 (2002) 170404] is the opening of the divergence-free WKB theory. This paper presents full formalism of this theory and its several applications concerning wavefunction and eigenenergy to show that our theory is a natural extension of the traditional WKB theory that incorporates nonperturbative quantum corrections.     

Theoretical investigation of ethylene/1-butene copolymerization process using constrained geometry catalyst (CpSiH2NH)-Ti-Cl2

The ethylene/1-butene copolymerization using constrained geometry catalyst CpSiH₂-NH-TiCl₂ (CGC) was investigated by the density functional theory and molecular dynamics. Structures and energetics of reactants, π-complexes, transition states, and products during insertion of ethylene and 1-butene monomers into the catalytic reactive site of the CGC were investigated by the density functional theory (DFT) using the software Dmol³, while dynamics of atoms during copolymerization process was investigated by classical molecular dynamics (MD) using the New-Ryudo-CR program. The calculated results were compared with the available experimental and theoretical ones. It was found that the ethylene insertion into Ti-Me active species is energetically more favorable than the butene one and the 2,1-butene insertion is more favorable than 1,2-butene one. Once the initial ethylene insertion has taken place, the further ethylene insertion occurring with a less energy barrier, in good agreement with experimental findings.     

Quantum mechanical free energy barrier for an enzymatic reaction

We discuss problems related to in silico studies of enzymes and show that accurate and converged free energy changes for complex chemical reactions can be computed if a method based on a thermodynamic cycle is employed. The method combines the sampling speed of molecular mechanics with the accuracy of a high-level quantum mechanics method. We use the method to compute the free energy barrier for a methyl transfer reaction catalyzed by the enzyme catechol O-methyltransferase at the level of density functional theory. The surrounding protein and solvent are found to have a profound effect on the reaction, and we show that energies can be extrapolated easily from one basis set and exchange-correlation functional to another. Using this procedure we calculate a barrier of 69 kJ/mol, in excellent agreement with the experimental value of 75 kJ/mol.     

Non-perturbative approach to high-index-contrast variations in electromagnetic systems

We present a method that formally calculates exact frequency shifts of an electromagnetic field for arbitrary changes in the refractive index. The possible refractive index changes include both anisotropic changes and boundary shifts. Degenerate eigenmode frequencies pose no problems in the presented method. The approach relies on operator algebra to derive an equation for the frequency shifts, which eventually turn out in a simple and physically sound form. Numerically the equations are well-behaved, easy implementable, and can be solved very fast. Like in perturbation theory a reference system is first considered, which then subsequently is used to solve another related, but different system. For our method precision is only limited by the reference system basis functions and the error induced in frequency is of second order for first-order basis set error. As an example we apply our method to the problem of variations in the air-hole diameter in a photonic crystal fiber.     

Theory of the Trojan-Horse method

The Trojan-Horse method is an indirect approach to determine the energy dependence of S factors of astrophysically relevant two-body reactions. This is accomplished by studying closely related three-body reactions under quasi-free scattering conditions. The basic theory of the Trojan-Horse method is developed starting from a post-form distorted wave Born approximation of the T-matrix element. In the surface approximation the cross-section of the three-body reaction can be related to the S-matrix elements of the two-body reaction. The essential feature of the Trojan-Horse method is the effective suppression of the Coulomb barrier at low energies for the astrophysical reaction leading to finite cross-sections at the threshold of the two-body reaction. In a modified plane wave approximation the relation between the two- and three-body cross-sections becomes very transparent. The appearing Trojan-Horse integrals are studied in detail.     

Modeling the coupling of reaction kinetics and hydrodynamics in a collapsing cavity

We introduce a model of cavitation based on the multiphase Lattice Boltzmann method (LBM) that allows for coupling between the hydrodynamics of a collapsing cavity and supported solute chemical species. We demonstrate that this model can also be coupled to deterministic or stochastic chemical reactions. In a two-species model of chemical reactions (with a major and a minor species), the major difference observed between the deterministic and stochastic reactions takes the form of random fluctuations in concentration of the minor species. We demonstrate that advection associated with the hydrodynamics of a collapsing cavity leads to highly inhomogeneous concentration of solutes. In turn these inhomogeneities in concentration may lead to significant increase in concentration-dependent reaction rates and can result in a local enhancement in the production of minor species.     

Quantum ergodicity and energy flow in molecules

We review a theory for coupled many-nonlinear oscillator systems that describes quantum ergodicity and energy flow in molecules. The theory exploits the isomorphism between quantum energy flow in Fock space, that is, vibrational state space, and single-particle quantum transport in disordered solid-state systems. The quantum ergodicity transition in molecules is thereby analogous to the Anderson transition in disordered solids. The theory reviewed here, local random matrix theory (LRMT), describes the nature of the quantum ergodicity transition, statistical properties of vibrational eigenstates, and quantum energy flow through the vibrational states of molecules. Predictions of LRMT have been observed in computational studies of coupled nonlinear oscillator systems, which are summarized here. We also review applications of LRMT to molecular spectroscopy and chemical reaction rate theory, including adoption of LRMT in theories that predict rates of conformational change of molecules taking place at energies corresponding to those below and above the quantum ergodicity transition. A number of specific examples are reviewed, including the application of LRMT to predict (1) dilution factors of IR spectra of organic molecules, (2) rates of conformational change in chemical and photochemical reactions, (3) conformational dynamics of biological molecules in molecular beams, (4) rates of hydrogen bond breaking and rearrangement in clusters of biological molecules and water, and (5) excited state proton transfer reactions in proteins.     

Ab initio path-integral molecular dynamics

A path-integral molecular dynamics technique for strongly interacting atoms using ab initio potentials derived from density functional theory is implemented. This allows the efficient inclusion of nuclear quantum dispersion in ab initio simulations at finite temperatures. We present an application to the quantum cluster H ₅ ⁺ .     

On analytic potential functions and molecular dynamics for reactions on metal surfaces

We present a method that allows one to obtain reaction energy profiles for dissociation/recombination reactions on metal surfaces. Our method is related to the bond order conservation-Morse potential method of Shustorovich but with the differences that we employ dynamic Morse potentials and our modified bond order conservation law. Our method approximates the energy curves along the reaction coordinates and is applicable to all manner of dissociations (not just symmetric dissociations). We compare the results of our method with ab initio energy curves in the literature, experimental results and the results of the BOC-MP model of Shustorovich. Our model is able to produce reasonable representations of the reaction energy profiles for the decomposition of methane thiol and SH on gold, and, it produces energy profiles that agree with ab initio calculations and the model of Shustorovich. We also present a molecular dynamics simulation of the dissociation of H₂ on Ni(111), employing this method for obtaining reactive potential energy functions, and, demonstrate that the reciprocals of the computed reaction times obey Arrhenius kinetics.     

Ab initio evaluation of primary cyclo-hexane oxidation reaction rates

Naphthenes are chemical species that are always present in liquid hydrocarbon fuels and their pyrolysis and oxidation can play an important role in real liquid fuel combustion. In spite of its practical relevance, the chemical kinetics of naphthene pyrolysis and oxidation is not yet thoroughly investigated and there is not a general agreement on the role and rate of several elementary reactions involved. In this paper, the kinetics of the pyrolysis and oxidation of a simple naphthene, namely cyclo-hexane, has been investigated through detailed kinetic modeling. Ab initio calculations were performed to estimate the kinetic parameters of some primary reactions following the oxygen attack to the cyclo-hexane radical. In fact, due to the complex behavior induced by the ring structure of cyclo-hexane, such data were difficult to determine through thermo-chemical methods. Density functional theory (B3LYP/6-31g(d, p)) was adopted to determine structure and vibrational frequencies of transition states and reaction intermediates, while energies were evaluated using the G2MP2 approach. The kinetic parameters of the investigated primary reactions were then introduced in a general detailed kinetic model consisting of elementary reactions whose kinetic constants were taken from the literature. The so obtained kinetic model was used to simulate ignition delay times and species concentrations measured in various experiments reported in the literature. The agreement between experimental data and theoretical predictions shows the validity of the chosen approach and supports the correctness of the proposed kinetic model.     

Quantum field theoretical analysis on unstable behavior of Bose-Einstein condensates in optical lattices

We study the dynamics of Bose-Einstein condensates flowing in optical lattices on the basis of quantum field theory. For such a system, a Bose-Einstein condensate shows an unstable behavior which is called the dynamical instability. The unstable system is characterized by the appearance of modes with complex eigenvalues. Expanding the field operator in terms of excitation modes including complex ones, we attempt to diagonalize the unperturbative Hamiltonian and to find its eigenstates. It turns out that although the unperturbed Hamiltonian is not diagonalizable in the conventional bosonic representation the appropriate choice of physical states leads to a consistent formulation. Then we analyze the dynamics of the system in the regime of the linear response theory. Its numerical results are consistent with those given by the discrete nonlinear Schrödinger equation.     

Experimental motivation and empirical consistency in minimal no-collapse quantum mechanics

We analyze three important experimental domains (SQUIDs, molecular interferometry, and Bose-Einstein condensation) as well as quantum-biophysical studies of the neuronal apparatus to argue that (i) the universal validity of unitary dynamics and the superposition principle has been confirmed far into the mesoscopic and macroscopic realm in all experiments conducted thus far; (ii) all observed “restrictions” can be correctly and completely accounted for by taking into account environmental decoherence effects; (iii) no positive experimental evidence exists for physical state-vector collapse; (iv) the perception of single “outcomes” is likely to be explainable through decoherence effects in the neuronal apparatus. We also discuss recent progress in the understanding of the emergence of quantum probabilities and the objectification of observables. We conclude that it is not only viable, but moreover compelling to regard a minimal no-collapse quantum theory as a leading candidate for a physically motivated and empirically consistent interpretation of quantum mechanics.     

Optical absorption of 1,3-diphenyl-1H-Pyrazolo[3,4-b]quinoline and its derivatives

Paper deals with the experimental investigations and quantum chemical calculations of the absorption spectra of newly synthesized 1,3-diphenyl-1H-Pyrazolo[3,4-b]quinoline and its 6-Vinyl, 6-N,N-Diphenyl, 6-Methyl, 6-Fluoro, 6-Bromo, and 6-Chloro derivatives. The calculations are performed by means of the semiempirical quantum chemical methods AM1 or PM3 combined with: (a) equilibrium molecular conformation (EMC) in vacuo; (b) the molecular conformation model considering a dynamical rotation of phenyl rings only (T = 300 K); and (c) the most general model of the conformational molecular dynamics (MD) at T = 300 K. It is shown that the phenyl dynamics appears to be not important in the spectral position of absorption thresholds as well as in a broadening of most absorbtion bands. On the other hand, the MD simulations reproduce a broadening of the absorbtion spectra as well as the electron-vibronic coupling leading to a red-shift of absorption bands with increasing of temperature. The conformational MD model in combination with the quantum chemical AM1 method gives in most cases the best agreement with the experimental data, namely in the sense of spectral positions and width of the absorption bands including first oscillators (absorption thresholds).