Titus S. van Erp

A novel path sampling method for the calculation of rate constants

We derive a novel efficient scheme to measure the rate constant of transitions between stable states separated by high free energy barriers in a complex environment within the framework of transition path sampling. The method is based on directly and simultaneously measuring the fluxes through many phase space interfaces and increases the efficiency with at least a factor of 2 with respect to existing transition path sampling rate constant algorithms. The new algorithm is illustrated on the isomerization of a diatomic molecule immersed in a simple fluid.

Rate constants for diffusive processes by partial path sampling

We introduce a path sampling method for the computation of rate constants for complex systems with a highly diffusive character. Based on the recently developed transition interface sampling (TIS) algorithm this procedure increases the efficiency by sampling only parts of complete transition trajectories. The algorithm assumes the loss of memory for diffusive progression along the reaction coordinate. We compare the new partial path technique to the TIS method for a simple diatomic system and show that the computational effort of the new method scales linearly, instead of quadratically, with the width of the diffusive barrier. The validity of the memory loss assumption is also discussed.

Continuous Synthesis Process of Hexagonal Nanoplates of P6m Ordered Mesoporous Silica

Hexagonally ordered mesoporous silica coined COK-12 was synthesized in a continuous process by combining streams of sodium silicate and citric acid/sodium citrate buffered solution of (ethylene oxide)(20)-(propylene oxide)(70)-(ethylene oxide)(20) triblock copolymer (Pluronic P123) from separate reservoirs. COK-12 precipitated spontaneously upon combining both streams at nearly neutral pH and ambient temperature. Stable intermediates of the COK-12 formation process could be prepared by limiting sodium silicate addition. Investigation of these intermediates using small-angle X-ray scattering revealed COK-12 formed via an assembly process departing from spherical uncharged core-shell P123-silica micelles. The sterical stabilization of these micelles decreased upon accumulation of silicate oligomers in their shell. Aggregation of the spherical micelles led to cylindrical micelles, which aligned and adopted the final hexagonal organization. This unprecedentedly fast formation of P6m ordered mesoporous silica was caused by two factors in the synthesis medium: the neutral pH favoring uncharged silicate oligomers and the high salt concentration promoting hydrophobic interactions with surfactant micelles leading to silica accumulation in the PEO shell. The easy continuous synthesis process is convenient for large-scale production. The platelet particle morphology with short and identical internal channels will be advantageous for many applications such as pore replication, nanotube or fiber growth, catalytic functionalization, drug delivery, film and sensor development, and in nano dyes as well as for investigation of pore diffusion phenomena.

Ab Initio Molecular Dynamics Study of Aqueous Solvation of Ethanol and Ethylene

The structure and dynamics of aqueous solvation of ethanol and ethylene are studied by density functional theory based Car–Parrinello molecular dynamics. We did not find an enhancement of the structure of the hydrogen bonded network of hydrating water molecules. Both ethanol and ethylene can easily be accommodated in the hydrogen-bonded network of water molecules without altering its structure. This supports the conclusion from recent neutron diffraction experiments that there is no hydrophobic hydration around small hydrophobic groups. Analysis of the electronic charge distribution using Wannier functions shows that the dipole moment of ethanol increases from 1.8 D to 3.1 D upon solvation, while the apolar ethylene molecule attains an average dipole moment of 0.5 D. For ethylene, we identified configurations with π-H bonded water molecules, that have rare fourfold hydrogen-bonded water coordination, yielding instantaneous dipole moments of ethylene of up to 1 D. The results provide valuable information f...

Ab Initio Molecular Dynamics Study on the Interactions between Carboxylate Ions and Metal Ions in Water.

The interaction between a carboxylate anion (deprotonated propanoic acid) and the divalent Mg(2+), Ca(2+), Sr(2+), Ba(2+) metal ions is studied via ab initio molecular dynamics. The main focus of the study is the selectivity of the carboxylate-metal ion interaction in aqueous solution. The interaction is modeled by explicitly accounting for the solvent molecules on a DFT level. The hydration energies of the metal ions along with their diffusion and mobility coefficients are determined and a trend correlated with their ionic radius is found. Subsequently, a series of 16 constrained molecular dynamics simulations for every ion is performed, and the interaction free energy is obtained from thermodynamic integration of the forces between the metal ion and the carboxylate ion. The results indicate that the magnesium ion interacts most strongly with the carboxylate, followed by calcium, strontium, and barium. Because the interaction free energy is not enough to explain the selectivity of the reaction observed experimentally, more detailed analysis is performed on the simulation trajectories to understand the steric changes in the reaction complex during dissociation. The solvent dynamics appear to play an important role during the dissociation of the complex and also in the observed selectivity behavior of the divalent ions.

Density Functional Theory Study on the Interactions of Metal Ions with Long Chain Deprotonated Carboxylic Acids.

In this work, interactions between carboxylate ions and calcium or sodium ions are investigated via density functional theory (DFT). Despite the ubiquitous presence of these interactions in natural and industrial chemical processes, few DFT studies on these systems exist in the literature. Special focus has been placed on determining the influence of the multibody interactions (with up to 4 carboxylates and one metal ion) on an effective pair-interaction potential, such as those used in molecular mechanics (MM). Specifically, DFT calculations are employed to quantify an effective pair-potential that implicitly includes multibody interactions to construct potential energy curves for carboxylate-metal ion pairs. The DFT calculated potential curves are compared to a widely used molecular mechanics force field (OPLS-AA). The calculations indicate that multibody effects do influence the energetic behavior of these ionic pairs and the extent of this influence is determined by a balance between (a) charge transfer from the carboxylate to the metal ions which stabilizes the complex and (b) repulsion between carboxylates, which destabilizes the complex. Additionally, the potential curves of the complexes with 1 and 2 carboxylates and one counterion have been examined to higher separation distance (20 Å) by the use of relaxed scan optimization and constrained density functional theory (CDFT). The results from the relaxed scan optimization indicate that near the equilibrium distance, the charge transfer between the metal ion and the deprotonated carboxylic acid group is significant and leads to non-negligible differences between the DFT and MM potential curves, especially for calcium. However, at longer separation distances the MM calculated interaction potential functions converge to those calculated with CDFT, effectively indicating the approximate domain of the separation distance coordinate where charge transfer between the ions is occurring.

Molecular dynamics in principal component space.

A molecular dynamics algorithm in principal component space is presented. It is demonstrated that sampling can be improved without changing the ensemble by assigning masses to the principal components proportional to the inverse square root of the eigenvalues. The setup of the simulation requires no prior knowledge of the system; a short initial MD simulation to extract the eigenvectors and eigenvalues suffices. Independent measures indicated a 6-7 times faster sampling compared to a regular molecular dynamics simulation.

A test on reactive force fields for the study of silica dimerization reactions.

We studied silica dimerization reactions in the gas and aqueous phase by density functional theory (DFT) and reactive force fields based on two parameterizations of ReaxFF. For each method (both ReaxFF force fields and DFT), we performed constrained geometry optimizations, which were subsequently evaluated in single point energy calculations using the other two methods. Standard fitting procedures typically compare the force field energies and geometries with those from quantum mechanical data after a geometry optimization. The initial configurations for the force field optimization are usually the minimum energy structures of the ab initio database. Hence, the ab initio method dictates which structures are being examined and force field parameters are being adjusted in order to minimize the differences with the ab initio data. As a result, this approach will not exclude the possibility that the force field predicts stable geometries or low transition states which are realistically very high in energy and, therefore, never considered by the ab initio method. Our analysis reveals the existence of such unphysical geometries even at unreactive conditions where the distance between the reactants is large. To test the effect of these discrepancies, we launched molecular dynamics simulations using DFT and ReaxFF and observed spurious reactions for both ReaxFF force fields. Our results suggest that the standard procedures for parameter fitting need to be improved by a mutual comparative method.

Foundations and latest advances in replica exchange transition interface sampling

Nearly 20 years ago, transition path sampling (TPS) emerged as an alternative method to free energy based approaches for the study of rare events such as nucleation, protein folding, chemical reactions, and phase transitions. TPS effectively performs Monte Carlo simulations with relatively short molecular dynamics trajectories, with the advantage of not having to alter the actual potential energy surface nor the underlying physical dynamics. Although the TPS approach also introduced a methodology to compute reaction rates, this approach was for a long time considered theoretically attractive, providing the exact same results as extensively long molecular dynamics simulations, but still expensive for most relevant applications. With the increase of computer power and improvements in the algorithmic methodology, quantitative path sampling is finding applications in more and more areas of research. In particular, the transition interface sampling (TIS) and the replica exchange TIS (RETIS) algorithms have, in turn, improved the efficiency of quantitative path sampling significantly, while maintaining the exact nature of the approach. Also, open-source software packages are making these methods, for which implementation is not straightforward, now available for a wider group of users. In addition, a blooming development takes place regarding both applications and algorithmic refinements. Therefore, it is timely to explore the wide panorama of the new developments in this field. This is the aim of this article, which focuses on the most efficient exact path sampling approach, RETIS, as well as its recent applications, extensions, and variations.

Gluing Potential Energy Surfaces with Rare Event Simulations

We develop a new method combining replica exchange transition interface sampling with two distinct potential energy surfaces. The method can be used to combine different levels of theory in a simulation of a molecular process (e.g., a chemical reaction), and it can serve as a dynamical version of QM-MM, connecting classical dynamics with Ab Initio dynamics in the time domain. This new method, which we coin QuanTIS, could be applied to use accurate but expensive density functional theory based molecular dynamics for the breaking and making of chemical bonds, while the diffusion of reactants in the solvent are treated with classical force fields. We exemplify the method by applying it to two simple model systems (an ion dissociation reaction and a classical hydrogen model), and we discuss a possible extension of the method in which classical force field parameters for chemical reactions can be optimized on the fly.