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

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.

Perspective on the reactions between F- and CH3CH2F: the free energy landscape of the E2 and SN2 reaction channels

Recently, we computed the 3D free energy surface of the base-induced elimination reaction between F(-) and CH(3)CH(2)F by using a powerful technique within Car-Parrinello molecular dynamics simulation. Here, the set of three order parameters is expanded to six, which allows the study of the competing elimination and substitution reactions simultaneously. The power of the method is exemplified by the exploration of the six-dimensional free energy landscape, sampling, and mapping out the eight stable states as well as the connecting bottlenecks. The free energy profile and barrier along the E2 and S(N)2 reaction channels are refined by using umbrella sampling. The two mechanisms do not share a common "E2C-like" transition state. Comparison with the zero temperature profiles shows a particularly significant entropy contribution to the S(N)2 channel.

Adsorption and diffusion of Mg, O, and O2 on the MgO(001) flat surface

A thorough investigation of the adsorption and diffusion of Mg, O, and O(2) on MgO(001) terraces is performed by first-principles calculations. The single Mg adatom weakly binds to surface oxygens, diffuses, and evaporates easily at room temperatures. Atomic O strongly binds to surface oxygens, forming peroxide groups. The diffusion of the O adatom is strongly influenced by the spin polarization, since energy barriers are significantly different for the singlet and triplet states. The crossing of the two Born-Oppenheimer surfaces corresponding to the distinct spin states is also analyzed. Although the O(2) molecule does not stick to the perfect surface, it chemisorbs on surface nonstoichiometric point defects such as O vacancies or Mg adatoms, forming in the latter case new chemical species on the surface. We show that the oxidation rate limiting factor in an O(2) atmosphere is the concentration of point defects (O vacancies and Mg adatoms) in the growing surface. The simulated O core-level shifts for the various adsorption configurations enable a meaningful comparison with the measured values, suggesting the presence of peroxide ions on growing surfaces. Finally, the computed energy barriers are used to estimate the Mg and O surface lifetimes and diffusion lengths, and some implications for the homoepitaxial growth of MgO are discussed.

Flexible docking in solution using metadynamics

We apply our recently developed metadynamics method to the docking of ligands on flexible receptors in water solution. This method mimics the real dynamics of a ligand exiting or entering an enzyme and in so doing reconstructs the free energy surface. We apply it to four docking cases: beta-trypsin/benzamidine, beta-trypsin/chlorobenzamidine, immunoglobulin McPC-603/phosphocholine, and cyclin-dependent kinase 2/staurosporine. In every case studied, the method is able to predict the docked geometry and the free energy of docking. Its added value with respect to many other available methods is that it reconstructs the complete free energy surface, including all the relevant minima and the barriers between them.

Topological Defects and Bulk Melting of Hexagonal Ice

We use classical molecular dynamics combined with the recently developed metadynamics method [Laio, A.; Parrinello, M. Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 20] to study the process of bulk melting in hexagonal ice. Our simulations show that bulk melting is mediated by the formation of topological defects which preserve the coordination of the tetrahedral network. Such defects cluster to form a defective region involving about 50 molecules with a surprisingly long lifetime. The subsequent formation of coordination defects triggers the transition to the liquid state.

A Recipe for the Computation of the Free Energy Barrier and the Lowest Free Energy Path of Concerted Reactions

The recently introduced hills method (Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 12562) is a powerful tool to compute the multidimensional free energy surface of intrinsically concerted reactions. We have extended this method by focusing our attention on localizing the lowest free energy path that connects the stable reactant and product states. This path represents the most probable reaction mechanism, similar to the zero temperature intrinsic reaction coordinate, but also includes finite temperature effects. The transformation of the multidimensional problem to a one-dimensional reaction coordinate allows for accurate convergence of the free energy profile along the lowest free energy path using standard free energy methods. Here we apply the hills method, our lowest free energy path search algorithm, and umbrella sampling to the prototype S(N)2 reaction. The hills method replaces the in many cases difficult problem of finding a good reaction coordinate with choosing relatively simple collective variables, such as the bond lengths of the broken and formed chemical bonds. The second part of the paper presents a guide to using the hills method, in which we test and fine-tune the method for optimal accuracy and efficiency using the umbrella sampling results as a reference.

Targeted Car–Parrinello molecular dynamics: Elucidating double proton transfer in formic acid dimer

The targeted molecular dynamics method, making possible the study of rare events, has been assessed in the framework of Car-Parrinello ab initio molecular dynamics. As a test case, we have studied the staggered-eclipsed rotation of ethane. The technique has subsequently been applied to investigate the nature of double proton transfer in formic acid dimer. The latter is found to follow a concerted transfer mechanism involving an essentially planar transition state. A "funnel-like region" of the potential energy surface is identified, where floppy intermolecular modes stiffen upon approaching the transition state.

Microscopic Mechanism of Antibiotics Translocation through a Porin

OmpF from the outer membrane of Escherichia coli is a general porin considered to be the main pathway for beta-lactam antibiotics. The availability of a high-resolution crystal structure of OmpF and new experimental techniques at the single-molecule level have opened the way to the investigation of the microscopic mechanisms that allow the passage of antibiotics through bacterial pores. We applied molecular dynamics simulations to investigate the translocation process of ampicillin (Amp) through OmpF. Using a recent algorithm capable of accelerating molecular dynamics simulations we have been able to obtain a reaction path for the translocation of Amp through OmpF. The mechanism of passage depends both on the internal degrees of freedom of Amp and on interactions of Amp with OmpF. Understanding this mechanism would help us design more efficient antibiotics and shed light on nature's way of devising channels able to enhance the transport of molecules through membranes.

Molecular dynamics investigation of oxygen vacancy diffusion in rutile

Oxygen vacancy diffusion in rutile was studied by Born-Oppenheimer molecular dynamics techniques in the framework of the semiempirical molecular orbital method MSINDO. Migration of an oxygen vacancy from the rutile (110) surface towards the bulk was simulated. The metadynamics technique was employed to accelerate the diffusion processes. In this way, transition state structures and activation energies for the diffusion processes were obtained. Rate constants and the time scale of diffusion processes were estimated for different temperatures using the calculated activation energy. It was found that the vacancies in the bulk are less stable than on the surface. The feasibility of oxygen vacancy diffusion under experimental conditions is discussed.

Azulene-to-Naphthalene Rearrangement: The Car-Parrinello Metadynamics Method Explores Various Reaction Mechanisms

We studied the thermal intramolecular and radical rearrangement of azulene to naphthalene by employing a novel metadynamics method based on Car-Parrinello molecular dynamics. We demonstrate that relatively short simulations can provide us with several possible reaction mechanisms for the rearrangement. We show that different choices of the collective coordinates can steer the reaction along different pathways, thus offering the possibility of choosing the most probable mechanism. We consider herein three intramolecular mechanisms and two radical pathways. We found the norcaradiene pathway to be the preferable intramolecular mechanism, whereas the spiran mechanism is the favored radical route. We obtained high activation energies for all the intramolecular pathways (81.5-98.6 kcal mol(-1)), whereas the radical routes have activation energies of 24-39 kcal mol(-1). The calculations have also resulted in elementary steps and intermediates not yet considered. A few attractive features of the metadynamics method in studying chemical reactions are pointed out.

A Minimum Free Energy Reaction Path for the E2 Reaction between Fluoro Ethane and a Fluoride Ion

The prototype binuclear elimination (E2) reaction illustrates the mechanism of a large number of biochemical and industrial applied processes but has received surprisingly little attention in theoretical studies compared to, for example, the substitution (SN2) reaction. This is due to its concerted mechanism, which requires an independent description of the three bonds that are being formed or broken. In this work, we have taken the advantage of a new and promising methodology to efficiently sample intrinsically multidimensional free-energy surfaces. We locate the lowest free-energy reaction path in the 3D configurational space and use this finite-temperature intrinsic reaction coordinate in an umbrella sampling scheme to access the temperature contributions to high accuracy. The small increase of the barrier and the decrease of the overall endothermicity for the E2 reaction due to entropic contributions is non-trivial. Moreover, our strategy to efficiently handle multiple reaction coordinates could be a great benefit to many chemistry-related fields, such as enzyme catalysis, reactions in solution, and nucleation processes.

Proton transfer in heterocycle crystals

We study the proton diffusion process in imidazole-based molecular crystals, which are new candidate materials for fuel cell membranes. These materials are characterized by hydrogen bonded networks of molecules, which provide viable routes for the long-range diffusion of protons. By the application of a recently developed, powerful technique to determine reaction pathways in complex systems, we are able to reproduce the diffusion process in the imidazole crystal and in the more complicated and rigid structure of imidazole 2-ethyleneoxide. Our results cast new light on the atomistic details of the molecular rearrangements sustaining the ionic diffusion.

Reconstructing the density of states by history-dependent metadynamics

We present a novel method for the calculation of the energy density of states D(E) for systems described by classical statistical mechanics. The method builds on an extension of a recently proposed strategy that allows the free-energy profile of a canonical system to be recovered within a preassigned accuracy [Proc. Natl. Acad. Sci. U.S.A. 99, 12562 (2002)]]. The method allows a good control over the error on the recovered system entropy. This fact is exploited to obtain D(E) more efficiently by combining measurements at different temperatures. The accuracy and efficiency of the method are tested for the two-dimensional Ising model (up to size 50 x 50) by comparison with both exact results and previous studies. This method is a general one and should be applicable to more realistic model systems.

Hydrogen Bond Driven Chemical Reactions: Beckmann Rearrangement of Cyclohexanone Oxime into ε-Caprolactam in Supercritical Water

Recent experiments have shown that supercritical water (SCW) has the ability to accelerate and make selective synthetic organic reactions, thus replacing the common but environmentally harmful acid and basic catalysts. In an attempt to understand the intimate mechanism behind this observation, we analyze, via first-principles molecular dynamics, the Beckmann rearrangement of cyclohexanone oxime into epsilon-caprolactam in supercritical water, for which accurate experimental evidence has been reported. Differences in the wetting of the hydrophilic parts of the solute, enhanced by SCW, and the disrupted hydrogen bond network are shown to be crucial in triggering the reaction and in making it selective. Furthermore, the enhanced concentrations of H(+) in SCW play an important role in starting the reaction.