On the ion‐pair dissociation mechanisms in the small NaCl·(H2O)6 cluster: A perspective from reaction path search calculations

We performed reaction path search calculations for the NaCl·(H₂O)₆ cluster using the global reaction route mapping (GRRM) code to understand the atomic‐level mechanisms of the NaCl → Na⁺ + Cl⁻ ionic dissociation induced by water solvents. Low‐lying minima, transition states connecting two local minima and corresponding intrinsic reaction coordinates on the potential energy surface are explored. We found that the Na Cl distances at the transitions states for the dissociation pathways were distributed in a relatively wide range of 2.7–3.7 Å and that the Na Cl distance at the transition state did not correlate with the commonly used solvation coordinates. This suggests that the definition of the transition states with specific structures as well as good reaction coordinate is very difficult for the ionic dissociation process even in a small water cluster. © 2018 Wiley Periodicals, Inc.     

Pathways for conformational change in nitrogen regulatory protein C from discrete path sampling

Pathways corresponding to the conformational change in nitrogen regulatory protein C are calculated using the CHARMM19 force field with an implicit solvation model. Our analysis employs the discrete path sampling approach to grow a database of local minima and transition states from the potential energy surface that contains kinetically relevant pathways. The pathways with the largest contribution to the phenomenological two-state rate constants are found to exhibit a number of structural features that agree with experimental observations. Further details of the calculated pathways for conformational change may therefore provide useful predictions of how this large-scale motion is achieved.     

PathOpt—A global transition state search approach: Outline of algorithm

We propose a new algorithm to determine reaction paths and test its capability for Ar₁₂ and Ar₁₃ clusters. Its main ingredient is a search for the local minima on a (n?1) dimensional hyperplane (n = dimension of the complete system in Cartesian coordinates) lying perpendicular to the straight line connection between initial and final states. These minima are part of possible reaction paths and are, hence, used as starting points for an uphill search to the next transition state. First, path fragments are obtained from subsequent relaxations starting from these transition states. They can be combined with information from the straight line connection procedure to obtain complete paths. Our test computations for Ar₁₂ and Ar₁₃ clusters prove that PathOpt delivers several reaction paths in one round. © 2013 Wiley Periodicals, Inc.     

Potential energy and free energy landscapes

Familiar concepts for small molecules may require reinterpretation for larger systems. For example, rearrangements between geometrical isomers are usually considered in terms of transitions between the corresponding local minima on the underlying potential energy surface, V. However, transitions between bulk phases such as solid and liquid, or between the denatured and native states of a protein, are normally addressed in terms of free energy minima. To reestablish a connection with the potential energy surface we must think in terms of representative samples of local minima of V, from which a free energy surface is projected by averaging over most of the coordinates. The present contribution outlines how this connection can be developed into a tool for quantitative calculations. In particular, stepping between the local minima of V provides powerful methods for locating the global potential energy minimum, and for calculating global thermodynamic properties. When the transition states that link local minima are also sampled we can exploit statistical rate theory to obtain insight into global dynamics and rare events. Visualizing the potential energy landscape helps to explain how the network of local minima and transition states determines properties such as heat capacity features, which signify transitions between free energy minima. The organization of the landscape also reveals how certain systems can reliably locate particular structures on the experimental time scale from among an exponentially large number of local minima. Such directed searches not only enable proteins to overcome Levinthal's paradox but may also underlie the formation of "magic numbers" in molecular beams, the self-assembly of macromolecular structures, and crystallization.     

Comparison of double-ended transition state search methods

While a variety of double-ended transition state search methods have been developed, their relative performance in characterizing complex multistep pathways between structurally disparate molecular conformations remains unclear. Three such methods (doubly-nudged elastic band, a string method, and a growing string method) are compared for a series of benchmarks ranging from permutational isomerizations of the seven-atom Lennard-Jones cluster (LJ(7)) to highly cooperative LJ(38) and LJ(75) rearrangements, and the folding pathways of two peptides. A database of short paths between LJ(13) local minima is used to explore the effects of parameters and suggest reasonable default values. Each double-ended method was employed within the framework of a missing connection network flow algorithm to construct more complicated multistep pathways. We find that in our implementation none of the three methods definitively outperforms the others, and that their relative effectiveness is strongly system and parameter dependent.     

Theoretical Study on Photoisomerization of 2-Methylfuran to 3-Methylfuran

1 INTRODUCTION 2-Methylfuran belongs to the basic heteroaromatic compounds relevant to many fields of modern che- mistry, ranging from the study of natural products and biologically active substances to the develop- ment of building blocks for organic synthesis and conducting polymers[1]. Since the photochemistry ofR-furan was gradually recognized in 1960s[2～7], lots of interest has been aroused. Herein we only study one branch of photoche- mistry of R-furan: the isomerization of 2-methy…     

Improved transition path sampling methods for simulation of rare events

The free energy surfaces of a wide variety of systems encountered in physics, chemistry, and biology are characterized by the existence of deep minima separated by numerous barriers. One of the central aims of recent research in computational chemistry and physics has been to determine how transitions occur between deep local minima on rugged free energy landscapes, and transition path sampling (TPS) Monte-Carlo methods have emerged as an effective means for numerical investigation of such transitions. Many of the shortcomings of TPS-like approaches generally stem from their high computational demands. Two new algorithms are presented in this work that improve the efficiency of TPS simulations. The first algorithm uses biased shooting moves to render the sampling of reactive trajectories more efficient. The second algorithm is shown to substantially improve the accuracy of the transition state ensemble by introducing a subset of local transition path simulations in the transition state. The system considered in this work consists of a two-dimensional rough energy surface that is representative of numerous systems encountered in applications. When taken together, these algorithms provide gains in efficiency of over two orders of magnitude when compared to traditional TPS simulations.     

Using swarm intelligence for finding transition states and reaction paths

We describe an algorithm that explores potential energy surfaces (PES) and finds approximate reaction paths and transition states. A few (≈6) evolving atomic configurations ("climbers") start near a local minimum M1 of the PES. The climbers seek a shallow ascent, low energy, path toward a saddle point S12, cross over to another valley of the PES, and climb down to a new minimum M2 that was not known beforehand. Climbers use both energy and energy derivatives to make individual decisions, and they use relative fitness to make team-based decisions. In sufficiently long runs, they keep exploring and may go through a sequence M1-S12-M2-S23-M3 ... of minima and saddle points without revisiting any of the critical points. We report results on eight small test systems that highlight advantages and disadvantages of the method. We also investigated the PES of Li(8), Al(7)(+), Ag(7), and Ag(2)NH(3) to illustrate potential applications of this new method.     

Inherent structures for soft long-range interactions in two-dimensional many-particle systems

We generate inherent structures, local potential-energy minima, of the "k-space overlap potential" in two-dimensional many-particle systems using a cooling and quenching simulation technique. The ground states associated with the k-space overlap potential are stealthy (i.e., completely suppress single scattering of radiation for a range of wavelengths) and hyperuniform (i.e., infinite wavelength density fluctuations vanish). However, we show via quantitative metrics that the inherent structures exhibit a range of stealthiness and hyperuniformity depending on the fraction of degrees of freedom χ that are constrained. Inherent structures in two dimensions typically contain five-particle rings, wavy grain boundaries, and vacancy-interstitial defects. The structural and thermodynamic properties of the inherent structures are relatively insensitive to the temperature from which they are sampled, signifying that the energy landscape is relatively flat along the directions sampled, with wide shallow local minima and devoid of deep wells. Using the nudged-elastic-band algorithm, we construct paths from ground-state configurations to inherent structures and identify the transition points between them. In addition, we use point patterns generated from a random sequential addition (RSA) of hard disks, which are nearly stealthy, and examine the particle rearrangements necessary to make the configurations absolutely stealthy. We introduce a configurational proximity metric to show that only small local, but collective, particle rearrangements are needed to drive initial RSA configurations to stealthy disordered ground states. These results lead to a more complete understanding of the unusual behaviors exhibited by the family of "collective-coordinate" potentials to which the k-space overlap potential belongs.     

Comparison of proton conduction in KTaO3 and SrZrO3

In the present paper, the authors focus on proton conduction pathways in a cubic perovskite KTaO(3) and an orthorhombic perovskite SrZrO(3). Density functional theory with a generalized gradient approximation is used to find proton binding sites. The nudged elastic band method is used to find transition states between minima. With this potential energy map of binding and transition states, adjacency matrices and their analogs identify four types of conduction paths in KTaO(3). Distortions from these paths are seen in SrZrO(3). In both cases, the lowest energy path has an intraoctahedral transfer rate-limiting barrier. A Fourier analysis of the OH stretch in ab initio molecular dynamics simulations revealed a strongly redshifted OH stretch in SrZrO(3) relative to KTaO(3). Hence, an orthorhombic system with a lowest energy conduction path limited by an intraoctahedral barrier can exhibit a redshifted OH stretch.     

An algorithm to find minimum free-energy paths using umbrella integration

The calculation of free-energy barriers by umbrella sampling and many other methods is hampered by the necessity for an a priori choice of the reaction coordinate along which to sample. We avoid this problem by providing a method to search for saddle points on the free-energy surface in many coordinates. The necessary gradients and Hessians of the free energy are obtained by multidimensional umbrella integration. We construct the minimum free-energy path by following the gradient down to minima on the free-energy surface. The change of free energy along the path is obtained by integrating out all coordinates orthogonal to the path. While we expect the method to be applicable to large systems, we test it on the alanine dipeptide in vacuum. The minima, transition states, and free-energy barriers agree well with those obtained previously with other methods.     

Competitive Diels-Alder reactions: cyclopentadiene and phospholes with butadiene

Diene-dienophile competing Diels-Alder reaction pathways of cyclopentadiene, 1H-, 2H- and 3H-phospholes with butadiene were explored at the B3LYP level using 6-31G(d) and 6-311+G(d,p) basis sets, and at the CCSD(T)/6-31G(d)//B3LYP/6-31G(d) level. Activation barriers show that cyclopentadiene favors a diene rather than a dienophile conformation. Pathways 1 and 2 (A and B) corresponding to butadiene as the diene and dienophile are predicted to be highly competitive in the case of 1H-phosphole. Secondary orbital interactions and the preferable bispericyclic nature of transition states are responsible for the stability of endo transition states. The study indicates that some of the transition states are bispericyclic and most of them are highly asynchronous. The reactions require a lower activation energy when the conversion of weak C=P to C-P occurs in the case of 2H- and 3H-phospholes. The high stability of the products resulting via path 1 can be attributed to the less strain in the bicyclo[4.3.0]nonadiene skeleton compared to the norbornene derivatives obtained from path 2. Activation and reaction energy values for these Diels-Alder reaction pathways are compared with the values reported for the [4+2] cyclodimerizations of each of the reactants to examine the likelihood of cyclodimerizations along these pathways.     

Quantum-chemical study of the photoisomerization and photocyclization reactions of styrylquinolines: Potential energy surfaces

The cross sections of potential energy surfaces (PES) for the S₀ and S₁ states were calculated by the semiempirical PM3 and PM3-CI (8 × 8) methods, respectively, along the reaction coordinate of the isomerization and cyclization of 2- and 4-styrylquinolines (SQ). The PES of the S₀ state exhibits three minima separated by the transition-state barriers of isomerization and cyclization corresponding to three isomeric SQ forms, the E- and Z-isomers and the dihydrogenated cyclic product. On the PES of the S₁ state, the “perpendicular minimum” at dihedral angle values of ～ 90° corresponds to the transition state of the isomerization reaction and the pericyclic minimum with a distance of 1.7–2.0 Å between the atoms involved in cyclization corresponds to the transition state of the cyclization reaction. With simultaneous scanning of the PES of the S₁ state along the isomerization and cyclization reaction coordinates, the minimal-energy path was found for 4SQ, which makes it possible to explain the formation of the photocyclization product in the single-photon process upon irradiation of the E-isomer. It was found that the PM3 method overestimates the stability of the structures in which the aromatic ring is oriented perpendicular to the plane of the molecule, resulting in virtual minima on the PES of the S₁ states.     

Racemization barriers of 1,1'-binaphthyl and 1,1'-binaphthalene-2,2'-diol: a DFT study

Density functional theory has been applied to the study of various pathways and transition states for the configurational inversion of 1,1'-binaphthyl (1) and 1,1'-binaphthalene-2,2'-diol (2). The preferred pathway is found to be anti with centrosymmetric transition state. Whereas the reaction path of 1 goes downhill from transition to ground state, in the case of 2 it contains one unexpected local minimum. Very satisfactory agreement with available experimental values of activation Gibbs energies is achieved.     

Multiple pathways in conformational transitions of the alanine dipeptide: an application of dynamic importance sampling

We present multiple dynamic transition pathways on the two-dimensional dihedral plane between conformational states of the alanine dipeptide. The method used in this study is dynamic importance sampling (DIMS). To perform DIMS, unbiased molecular dynamic simulations are used to generate equilibrium ensembles for the alanine dipeptide within different states. Free energy surfaces on the dihedral plane are calculated from the equilibrium simulations, and four energy minima defined from the surface are used as the starting and ending points for DIMS dynamics. The DIMS method represents an important step towards finding multiple transition pathways within complex biomolecular systems.     

Transiting the molecular potential energy surface along low energy pathways: The TRREAT algorithm

The Transition Rapidly exploring Random Eigenvector Assisted Tree (TRREAT) algorithm is introduced to perform searches along low curvature pathways on a potential energy surface (PES). The method combines local curvature information about the PES with an iterative Rapidly exploring Random Tree algorithm (LaValle, Computer Science Department, Iowa State University, 1998, TR98–11) that quickly searches high‐dimensional spaces for feasible pathways between local minima. Herein, the method is applied to identifying conformational changes of molecular systems using Cartesian coordinates while avoiding a priori definition of collective variables. We analyze the pathway identification problem for alanine dipeptide, cyclohexane and glycine using nonreactive and reactive forcefields. We show how TRREAT‐identified pathways can be used as valuable input guesses for double‐ended methods such as the Nudged Elastic Band when ascertaining transition state energies. This method can be utilized to improve/extend the reaction databases that lie at the core of automatic chemical reaction mechanism generator software currently developed to build kinetic models of chemical reactions. © 2013 Wiley Periodicals, Inc.     

Multicoordinate driven method for approximating enzymatic reaction paths: automatic definition of the reaction coordinate using a subset of chemical coordinates

We present a generalization of the reaction coordinate driven method to find reaction paths and transition states for complicated chemical processes, especially enzymatic reactions. The method is based on the definition of a subset of chemical coordinates; it is simple, robust, and suitable to calculate one or more alternative pathways, intermediate minima, and transition-state geometries. Though the results are approximate and the computational cost is relatively high, the method works for large systems, where others often fail. It also works when a certain reaction path competes with others having a lower energy barrier. Accordingly, the procedure is appropriate to test hypothetical reaction mechanisms for complicated systems and provides good initial guesses for more accurate methods. We present tests on a number of simple reactions and on several complicated chemical transformations and compare the results with those obtained by other methods. Calculation of the reaction path for the enzymatic hydrolysis of the substrate by dUTPase for an active-site model with 85 atoms, including several loosely bound water molecules, indicates that the method is feasible for the study of enzyme mechanisms.     

Transition path sampling for discrete master equations with absorbing states

Transition path sampling (TPS) algorithms have been implemented with deterministic dynamics, with thermostatted dynamics, with Brownian dynamics, and with simple spin flip dynamics. Missing from the TPS repertoire is an implementation with kinetic Monte Carlo (kMC), i.e., with the underlying dynamics coming from a discrete master equation. We present a new hybrid kMC-TPS algorithm and prove that it satisfies detailed balance in the transition path ensemble. The new algorithm is illustrated for a simplified Markov State Model of trp-cage folding. The transition path ensemble from kMC-TPS is consistent with that obtained from brute force kMC simulations. The committor probabilities and local fluxes for the simple model are consistent with those obtained from exact methods for simple master equations. The new kMC-TPS method should be useful for analysis of rare transitions in complex master equations where the individual states cannot be enumerated and therefore where exact solutions cannot be obtained.     

Energy Landscape Exploration of Sub‐Nanometre Copper–Silver Clusters

The energy landscapes of sub‐nanometre bimetallic coinage metal clusters are explored with the Threshold Algorithm coupled with the Birmingham Cluster Genetic Algorithm. Global and energetically low‐lying minima along with their permutational isomers are located for the Cu${_4 }$ Ag${_4 }$ cluster with the Gupta potential and density functional theory (DFT). Statistical tools are employed to map the connectivity of the energy landscape and the growth of structural basins, while the thermodynamics of interconversion are probed, based on probability flows between minima. Asymmetric statistical weights are found for pathways across dividing states between stable geometries, while basin volumes are observed to grow independently of the depth of the minimum. The DFT landscape is found to exhibit significantly more frustration than that of the Gupta potential, including several open, pseudo‐planar geometries which are energetically competitive with the global minimum. The differences in local minima and their transition barriers between the two levels of theory indicate the importance of explicit electronic structure for even simple, closed shell clusters.