A theoretical study on excited state double proton transfer reaction of a 7-azaindole dimer: an ab initio potential energy surface and its empirical valence bond model

Double proton transfer (DPT) reaction of a 7-azaindole dimer in the first ππ* electronically excited state was studied theoretically. We investigated the reaction mechanism through constructing a full dimensional empirical valence bond potential energy function (PEF) based on potential energies evaluated by ab initio molecular orbital methods, and carrying out quantum dynamics calculations with the PEF. Potential energy surfaces of the DPT obtained at the multi-reference perturbation level of theory favors a concerted DPT mechanism, although a stepwise channel is suggested to open for an excited initial vibrational state. Reduced two dimensional quantum dynamics calculations for a reaction surface Hamiltonian of DPT coordinates were performed. Time constants of the reaction were evaluated to be on the order of picoseconds, which is consistent with experiments. On the other hand, the computed kinetic isotope effect deviates from experimental evidence, suggesting the importance of intermolecular stretching motion, which is not explicit in the present calculations for the quantum effect.     

Double proton transfer in the isolated and DNA-embedded guanine-cytosine base pair

The energetics and dynamics of double proton transfer (DPT) is investigated theoretically for the Watson-Crick conformation of the guanine-cytosine (GC) base pair. Using semiempirical density functional theory the isolated and DNA-embedded GC pair is considered. Differences in the energetics and dynamics of DPT thus addresses the question of how relevant studies of isolated base pairs are for the understanding of processes occurring in DNA. Two-dimensional potential energy surfaces involving the transferring hydrogen atoms and the proton donors and acceptors are presented for both systems. The DPT reaction is accompanied by a contraction of the distance between the two bases with virtually identical energetic barriers being 18.8 and 18.7 kcal/mol for the isolated and DNA-embedded system, respectively. However, the transition state for DPT in the DNA-embedded GC pair is offset by 0.1 A to larger N-H separation compared to the isolated GC pair. Using activated ab initio molecular dynamics, DPT is readily observed for the isolated base pair with a minimal amount of 21.4 kcal/mol of initial average kinetic energy along the DPT normal mode vector. On a time scale of approximately 100 fs DPT has occurred and the excess energy is redistributed. For the DNA-embedded GC pair considerably more kinetic energy is required (30.0 kcal/mol) for DPT and the process is completed within one hydrogen vibration. The relevance of studies of isolated base pairs and base pair analogs in regard of reactions or properties involving DNA is discussed.     

Hybrid quantum/classical path integral approach for simulation of hydrogen transfer reactions in enzymes

A hybrid quantum/classical path integral Monte Carlo (QC-PIMC) method for calculating the quantum free energy barrier for hydrogen transfer reactions in condensed phases is presented. In this approach, the classical potential of mean force along a collective reaction coordinate is calculated using umbrella sampling techniques in conjunction with molecular dynamics trajectories propagated according to a mapping potential. The quantum contribution is determined for each configuration along the classical trajectory with path integral Monte Carlo calculations in which the beads move according to an effective mapping potential. This type of path integral calculation does not utilize the centroid constraint and can lead to more efficient sampling of the relevant region of conformational space than free-particle path integral sampling. The QC-PIMC method is computationally practical for large systems because the path integral sampling for the quantum nuclei is performed separately from the classical molecular dynamics sampling of the entire system. The utility of the QC-PIMC method is illustrated by an application to hydride transfer in the enzyme dihydrofolate reductase. A comparison of this method to the quantized classical path and grid-based methods for this system is presented.     

Nuclear quantum effects on an enzyme-catalyzed reaction with reaction path potential: proton transfer in triosephosphate isomerase

Nuclear quantum mechanical effects have been examined for the proton transfer reaction catalyzed by triosephosphate isomerase, with the normal mode centroid path integral molecular dynamics based on the potential energy surface from the recently developed reaction path potential method. In the simulation, the primary and secondary hydrogens and the C and O atoms involving bond forming and bond breaking were treated quantum mechanically, while all other atoms were dealt classical mechanically. The quantum mechanical activation free energy and the primary kinetic isotope effects were examined. Because of the quantum mechanical effects in the proton transfer, the activation free energy was reduced by 2.3 kcal/mol in comparison with the classical one, which accelerates the rate of proton transfer by a factor of 47.5. The primary kinetic isotope effects of kH/kD and kH/kT were estimated to be 4.65 and 9.97, respectively, which are in agreement with the experimental value of 4+/-0.3 and 9. The corresponding Swain-Schadd exponent was predicted to be 3.01, less than the semiclassical limit value of 3.34, indicating that the quantum mechanical effects mainly arise from quantum vibrational motion rather than tunneling. The reaction path potential, in conjunction with the normal mode centroid molecular dynamics, is shown to be an efficient computational tool for investigating the quantum effects on enzymatic reactions involving proton transfer.     

Exploring potential energy surfaces for chemical reactions: an overview of some practical methods

Potential energy surfaces form a central concept in the application of electronic structure methods to the study of molecular structures, properties, and reactivities. Recent advances in tools for exploring potential energy surfaces are surveyed. Methods for geometry optimization of equilibrium structures, searching for transition states, following reaction paths and ab initio molecular dynamics are discussed. For geometry optimization, topics include methods for large molecules, QM/MM calculations, and simultaneous optimization of the wave function and the geometry. Path optimization methods and dynamics based techniques for transition state searching and reaction path following are outlined. Developments in the calculation of ab initio classical trajectories in the Born-Oppenheimer and Car-Parrinello approaches are described.     

Reaction path potential for complex systems derived from combined ab initio quantum mechanical and molecular mechanical calculations

Combined ab initio quantum mechanical and molecular mechanical calculations have been widely used for modeling chemical reactions in complex systems such as enzymes, with most applications being based on the determination of a minimum energy path connecting the reactant through the transition state to the product in the enzyme environment. However, statistical mechanics sampling and reaction dynamics calculations with a combined ab initio quantum mechanical (QM) and molecular mechanical (MM) potential are still not feasible because of the computational costs associated mainly with the ab initio quantum mechanical calculations for the QM subsystem. To address this issue, a reaction path potential energy surface is developed here for statistical mechanics and dynamics simulation of chemical reactions in enzymes and other complex systems. The reaction path potential follows the ideas from the reaction path Hamiltonian of Miller, Handy and Adams for gas phase chemical reactions but is designed specifically for large systems that are described with combined ab initio quantum mechanical and molecular mechanical methods. The reaction path potential is an analytical energy expression of the combined quantum mechanical and molecular mechanical potential energy along the minimum energy path. An expansion around the minimum energy path is made in both the nuclear and the electronic degrees of freedom for the QM subsystem internal energy, while the energy of the subsystem described with MM remains unchanged from that in the combined quantum mechanical and molecular mechanical expression and the electrostatic interaction between the QM and MM subsystems is described as the interaction of the MM charges with the QM charges. The QM charges are polarizable in response to the changes in both the MM and the QM degrees of freedom through a new response kernel developed in the present work. The input data for constructing the reaction path potential are energies, vibrational frequencies, and electron density response properties of the QM subsystem along the minimum energy path, all of which can be obtained from the combined quantum mechanical and molecular mechanical calculations. Once constructed, it costs much less for its evaluation. Thus, the reaction path potential provides a potential energy surface for rigorous statistical mechanics and reaction dynamics calculations of complex systems. As an example, the method is applied to the statistical mechanical calculations for the potential of mean force of the chemical reaction in triosephosphate isomerase.     

Six-dimensional quantum dynamics of H2 dissociative adsorption on the Pt(211) stepped surface

Results of experimental studies, and theoretical calculations utilizing classical trajectories, have shown that dissociation of H2 on the Pt(211) stepped surface is enhanced at low energies by a molecular trapping mechanism. Because quantum effects can play a large role at the low energies and long lifetimes that characterize molecular trapping, we have undertaken quantum dynamics calculations for this system, the first to treat all molecular degrees of freedom of a gas molecule reacting on a stepped metallic surface. The calculations show that molecular trapping persists in the quantum system, but only at much lower energies than experimentally seen, pointing to possible deficiencies in the potential energy surface. Classical and quasiclassical trajectory calculations on the same potential provide a reasonable picture of reaction overall, but many of the finer details are inaccurate, and certain classical reaction mechanisms are entirely invalid. We conclude that some skepticism should be shown toward any classical study for which long-lived trapping states play a role.     

Explanation of the unusual temperature dependence of the atmospherically important OH + H(2)S --> H(2)O + HS reaction and prediction of the rate constant at combustion temperatures

Rate constants for the OH + H2S --> H2O + HS reaction, which is important for both atmospheric chemistry and combustion, are calculated by direct dynamics with the M06-2X density functional using the MG3S basis set. Energetics are compared to high-level MCG3/3//MC-QCISD/3 wave function theory and to results obtained by other density functionals. We employ canonical variational transition-state theory with multidimensional tunneling contributions and scaled generalized normal-mode frequencies evaluated in redundant curvilinear coordinates with anharmonicity included in the torsion. The transition state has a quantum mechanically distinguishable, nonsuperimposable mirror image that corresponds to a separate classical reaction path; the effect of the multiple paths is examined through use of a symmetry number and by torsional methods. Calculations with the reference-potential Pitzer-Gwinn treatment of the torsional mode agree with experiment, within experimental scatter, and predict a striking temperature dependence of the activation energy, increasing from -0.1 kcal/mol at 200 K to 0.2, 1.0, 3.4, and 9.8 kcal/mol at 300, 500, 1000, and 2400 K. The unusual temperature dependence arises from a dynamical bottleneck at an energy below reactants, following an addition complex on the reaction path with a classical binding energy of 4.4 kcal/mol. As a way to check the mechanism, kinetic isotope effects of the OH + D2S and OD + D2S reactions have been predicted.     

Further aspects of the roaming mechanism in formaldehyde dissociation

Recently we reported a novel “roaming” dissociation pathway of formaldehyde in which one of the H atoms strays far from the minimum energy reaction path, explores a broad region of the potential energy surface, then abstracts the remaining H atom to form molecular products, without going near the configuration of the conventional transition state saddle point. The detailed dynamics of the abstraction mechanism and its energy dependence have already been reported. Here, with a combination of experimental and theoretical results, we examine the roaming behavior at the energetic extremes. We show evidence of roaming below the threshold of the radical dissociation channel and consider the implications of this and the possible existence of a transition state for the roaming mechanism. We also show the occurrence of roaming up to 3200 cm⁻¹ above the threshold of the triplet dissociation channel. In addition, we present results affording deeper insight into the dynamics of the roaming mechanism: we show evidence of roaming leading to CO in v = 1, and examine the issue of nuclear spin conservation during dissociation via the roaming mechanism.     

Channeling on carbon nanotubes: a molecular dynamics approach

We have performed classical molecular dynamics on different kinds of carbon nanotubes in order to examine their response to self-irradiation nearly parallel to the tube axis. We have found that the critical angle for channeling decays as a power law. Following the energy loss along the projectile path, we have determined the maximum range as a function of energy at the critical angle. Narrower tubes seem to be more adequate for transporting particles to longer distances.     

Transmission coefficient calculation for proton transfer in triosephosphate isomerase based on the reaction path potential method

A global potential energy surface has been constructed through interpolation of our recently developed reaction path potential for chemical reactions in enzymes which is derived from combined ab initio quantum mechanical and molecular mechanical calculations. It has been implemented for the activated molecular dynamics simulations of the initial proton transfer reaction catalyzed by triosephosphate isomerase. To examine the dynamical effects on the rate constants of the enzymatic reaction, the classical transmission coefficient kappa(t) is evaluated to be 0.47 with the reactive flux approach, demonstrating considerable deviations from transition state theory. In addition, the fluctuations of protein environments have small effects on the barrier recrossing, and the transmission coefficient kappa(t) strongly depends on the fluctuations of atoms near the active site of the enzyme.     

Molecular dynamics of the hydrogeniodine reaction system

The molecular dynamics of the hydrogeniodine exchange reaction, H₂ + I₂ ? 2 HI, have been examined in a classical trajectory analysis with trajectories selected within the transition region. The results yield the overall mechanism, the rate and the energy distributions of reactants and products for reaction at 700°K.     

Vibrational deexcitation and rotational excitation of H(2) and D(2) scattered from Cu(111): Adiabatic versus non-adiabatic dynamics

We have studied survival and rotational excitation probabilities of H(2)(v(i) = 1, J(i) = 1) and D(2)(v(i) = 1, J(i) = 2) upon scattering from Cu(111) using six-dimensional (6D) adiabatic (quantum and quasi-classical) and non-adiabatic (quasi-classical) dynamics. Non-adiabatic dynamics, based on a friction model, has been used to analyze the role of electron-hole pair excitations. Comparison between adiabatic and non-adiabatic calculations reveals a smaller influence of non-adiabatic effects on the energy dependence of the vibrational deexcitation mechanism than previously suggested by low-dimensional dynamics calculations. Specifically, we show that 6D adiabatic dynamics can account for the increase of vibrational deexcitation as a function of the incidence energy, as well as for the isotope effect observed experimentally in the energy dependence for H(2)(D(2))/Cu(100). Furthermore, a detailed analysis, based on classical trajectories, reveals that in trajectories leading to vibrational deexcitation, the minimum classical turning point is close to the top site, reflecting the multidimensionally of this mechanism. On this site, the reaction path curvature favors vibrational inelastic scattering. Finally, we show that the probability for a molecule to get close to the top site is higher for H(2) than for D(2), which explains the isotope effect found experimentally.     

Mixed quantum-classical reaction path dynamics of C2H5F --> C2H4 + HF

A mixed quantum-classical method for calculating product energy partitioning based on a reaction path Hamiltonian is presented and applied to HF elimination from fluoroethane. The goal is to describe the effect of the potential energy release on the product energies using a simple model of quantized transverse vibrational modes coupled to a classical reaction path via the path curvature. Calculations of the minimum energy path were done at the B3LYP/6-311++G(2d,2p) and MP2/6-311++G** levels of theory, followed by energy-partitioning dynamics calculations. The results for the final HF vibrational state distribution were found to be in good qualitative agreement with both experimental studies and quasiclassical trajectory simulations.     

Realistic modeling of ruthenium-catalyzed transfer hydrogenation

We report the first computational study of a fully atomistic model of the ruthenium-catalyzed transfer hydrogenation of formaldehyde and the reverse reaction in an explicit methanol solution. Using ab initio molecular dynamics techniques, we determined the thermodynamics, mechanism, and electronic structure along the reaction path. To assess the effect of the solvent quantitatively, we make a direct comparison with the gas-phase reaction. We find that the energy profile in solution bears little resemblance to the profile in the gas phase and a distinct solvation barrier is found: the activation barriers in both directions are lowered and the concerted hydride and proton transfer in the gas phase are converted into a sequential mechanism in solution with the substrate appearing as methoxide-like intermediate. Our results indicate that besides the metal-ligand bifunctional mechanism, as proposed by Noyori, also a concerted solvent-mediated mechanism is feasible. Our study gives a new perspective of the active role a solvent can have in transition-metal-catalyzed reactions.     

Accelerating the convergence of path integral dynamics with a generalized Langevin equation

The quantum nature of nuclei plays an important role in the accurate modelling of light atoms such as hydrogen, but it is often neglected in simulations due to the high computational overhead involved. It has recently been shown that zero-point energy effects can be included comparatively cheaply in simulations of harmonic and quasiharmonic systems by augmenting classical molecular dynamics with a generalized Langevin equation (GLE). Here we describe how a similar approach can be used to accelerate the convergence of path integral (PI) molecular dynamics to the exact quantum mechanical result in more strongly anharmonic systems exhibiting both zero point energy and tunnelling effects. The resulting PI-GLE method is illustrated with applications to a double-well tunnelling problem and to liquid water.     

Improving the convergence of closed and open path integral molecular dynamics via higher order Trotter factorization schemes

Higher order factorization schemes are developed for path integral molecular dynamics in order to improve the convergence of estimators for physical observables as a function of the Trotter number. The methods are based on the Takahashi-Imada and Susuki decompositions of the Boltzmann operator. The methods introduced improve the averages of the estimators by using the classical forces needed to carry out the dynamics to construct a posteriori weighting factors for standard path integral molecular dynamics. The new approaches are straightforward to implement in existing path integral codes and carry no significant overhead. The Suzuki higher order factorization was also used to improve the end-to-end distance estimator in open path integral molecular dynamics. The new schemes are tested in various model systems, including an ab initio path integral molecular dynamics calculation on the hydrogen molecule and a quantum water model. The proposed algorithms have potential utility for reducing the cost of path integral molecular dynamics calculations of bulk systems.     

Uptake of phenol on aerosol particles

We present a study of the interaction between a phenol molecule and an aerosol particle. The aerosol particle is represented by a cluster of 128 water molecules. Using a classical approach, we present interaction energy surfaces for different relative distances and for three orientations of phenol relative to the particle. From the energy surfaces we find the reaction pathways with the largest interaction between the molecule and the particle. We use a quantum mechanics/molecular mechanics (QM/MM) method to calculate a potential energy curve for each reaction path. Coupled cluster methods are used for the part of the system described by quantum mechanics, while the part described by molecular mechanics is represented by a polarizable force field. We compare results obtained from the classical approach with the QM/MM results. Furthermore, we use the QM/MM results to calculate mass accommodation coefficients using a quantum-statistical (QM-ST) model and show how the mass accommodation coefficient depends on the relative orientation of phenol with respect to the aerosol particle.     

Dissociative and non-dissociative adsorption dynamics of N2 on Fe(110)

We study the adsorption dynamics of N(2) on the Fe(110) surface. Classical molecular dynamics calculations are performed on top of a six-dimensional potential energy surface calculated within density functional theory. Our results show that N(2) dissociation on this surface is a highly activated process that takes place along a very narrow reaction path with an energy barrier of around 1.1 eV, which explains the measured low reactivity of this system. By incorporating energy exchange with the lattice in the dynamics, we also study the non-dissociative molecular adsorption process. From the analysis of the potential energy surface, we observe the presence of two distinct N(2) adsorption wells. Our dynamics calculations show that the relative population of these adsorption sites varies with the incident energy of the molecule and the surface temperature. We find an activation energy of around 150 meV that prevents molecular adsorption under thermal and hypothermal N(2) gas exposure of the surface. This finding is also consistent with the available experimental information.