Transition State Approximation Research Articles

Improved Elastic Image Pair Method for Finding Transition States.

The elastic image pair (EIP) method is a robust method for finding approximate transition states between two local minima. However, the original implementation of the method had some limitations. In this work, we present an improved EIP method, in which the moving procedure of the image pair and the convergence strategy are modified. In addition, this method is combined with the rational function optimization method to give exact transition states. Tests on a set of 45 different reactions show the reliability and efficiency in finding transition states.

Higher-order transition state approximation.

We generalize Slater's transition state concept by deriving systematic higher-order transition state approximations. Numerical validation is performed by the calculation of transition energies for various excitations, including core, valence, and charge-transfer excitations, at Hartree-Fock and Kohn-Sham density functional theory levels. All higher-order transition state approximations introduced in this study accurately reproduce the results from delta self-consistent-field calculations. In particular, we demonstrate that the third-order generalized transition state (GTS3) approximation is a promising alternative to the original, owing to a good balance between the accuracy and computational cost. We also demonstrate that accurate and reliable results can be obtained with a low computational cost by combining the GTS3 approximation with the transition potential scheme.

Enthalpies and Activation Energies of Several Gas Reactions by Intrinsic Reaction Coordinate (IRC) Calculations

In the present study, we have theoretically obtained the enthalpies and activation energies of several gas reactions by Intrinsic Reaction Coordinate (IRC) calculations. Being a first time, the approximate transition states used in the IRC calculations were obtained from the saddle points on the two dimensional Potential Energy Surface (PES) scans trucking the pathway of the reactions. In all the calculations, the Density Functional Theory (DFT/B3LYP) with 6-31 G (d, p) level was used. The saddle points on the PES graphs of the reactions were used one by one as an approximate transition state (TS) in the IRC calculations until the appropriate reaction path was obtained. The obtained TS’s from the IRC calculations were tested for having only one imaginary frequency. The energy diagram schemes showing the reactants, products and transition states of all the reactions were drawn, and their enthalpies and activation energies were determined. From the enthalpy values it was decided whether the reactions are endothermic or exothermic. The calculated activation energies were compared with the ones in the literature.

An improved Slater's transition state approximation.

We have extended Slater's transition state concept for the approximation of the difference in total energies of the initial and final states by three orbital energies of initial, final, and half-way Slater's transition states of the system. Numerical validation was performed with the ionization energies for H2O, CO, and pyrrole by calculation using Hartree-Fock (HF) and Kohn-Sham (KS) theories with the B3LYP and LCgau-core-BOP functionals. The present extended method reproduces full ΔSCF very accurately for all occupied orbitals obtained with HF and for valence orbitals obtained with KS. KS core orbitals have some errors due to the self-interaction errors, but the present method significantly improves the core electron binding energies. In its current form, the newly derived theory may not yet be practically useful, but it is simple and conceptually useful for gaining improved understanding of SCF-type orbital theories.

Catalytic Mechanism of Processive GlfT2: Transition Path Sampling Investigation of Substrate Translocation.

We applied the transition path sampling (TPS) method to study the translocation step of the catalytic mechanism of galactofuranosyl transferase 2 (GlfT2). Using TPS in the field of enzymatic reactions is still relatively rare, and we show its effectiveness on this enzymatic system. We decipher an unknown mechanism of the translocation step and, thus, provide a complete understanding of the catalytic mechanism of GlfT2 at the atomistic level. The GlfT2 enzyme is involved in the formation of the mycobacterial cell wall and transfers galactofuranose (Galf) from UDP-Galf onto a growing acceptor Galf chain. The biosynthesis of the galactan chain is accomplished in a processive manner, with the growing acceptor substrate remaining bound to GlfT2. The glycosidic bond formed by GlfT2 between the two Galf residues alternates between β-(1–6) and β-(1–5) linkages. The translocation of the growing galactan between individual additions of Galf residues is crucial for the function of GlfT2. Analysis of unbiased trajectory ensembles revealed that the translocation proceeds differently depending on the glycosidic linkage between the last two Galf residues. We also showed that the protonation state of the catalytic residue Asp372 significantly influences the translocation. Approximate transition state structures and potential energy reaction barriers of the translocation process were determined. The calculated potential reaction barriers in the range of 6–14 kcal/mol show that the translocation process is not the rate-limiting step in galactan biosynthesis.

A coupled kinetic Monte Carlo–finite element mesoscale model for thermoelastic martensitic phase transformations in shape memory alloys

A mesoscale modeling framework integrating thermodynamics, kinetic Monte Carlo (KMC) and finite element mechanics (FEM) is developed to simulate displacive thermoelastic transformations between austenite and martensite in shape memory alloys (SMAs). The model is based on a transition state approximation for the energy landscape of the two phases under loading or cooling, which leads to the activation energy and rate for transformation domains incorporating local stress states. The evolved stress state after each domain transformation event is calculated by FEM, and is subsequently used in the stochastic KMC algorithm to determine the next domain to transform. The model captures transformation stochasticity, and predicts internal phase and stress distributions and evolution throughout the entire incubation, nucleation and growth process. It also relates the critical transformation stresses or temperatures to internal activation energies. It therefore enables quantitative exploration of transformation dynamics and transformation–microstructure interactions. The model is used to simulate superelasticity (mechanically induced transformation) under both load control and strain control in single-crystal SMAs under uniaxial tension.

How to remove the spurious resonances from ring polymer molecular dynamics.

Two of the most successful methods that are presently available for simulating the quantum dynamics of condensed phase systems are centroid molecular dynamics (CMD) and ring polymer molecular dynamics (RPMD). Despite their conceptual differences, practical implementations of these methods differ in just two respects: the choice of the Parrinello-Rahman mass matrix and whether or not a thermostat is applied to the internal modes of the ring polymer during the dynamics. Here, we explore a method which is halfway between the two approximations: we keep the path integral bead masses equal to the physical particle masses but attach a Langevin thermostat to the internal modes of the ring polymer during the dynamics. We justify this by showing analytically that the inclusion of an internal mode thermostat does not affect any of the established features of RPMD: thermostatted RPMD is equally valid with respect to everything that has actually been proven about the method as RPMD itself. In particular, because of the choice of bead masses, the resulting method is still optimum in the short-time limit, and the transition state approximation to its reaction rate theory remains closely related to the semiclassical instanton approximation in the deep quantum tunneling regime. In effect, there is a continuous family of methods with these properties, parameterised by the strength of the Langevin friction. Here, we explore numerically how the approximation to quantum dynamics depends on this friction, with a particular emphasis on vibrational spectroscopy. We find that a broad range of frictions approaching optimal damping give similar results, and that these results are immune to both the resonance problem of RPMD and the curvature problem of CMD.

Theoretical study of the oxidation mechanisms of naphthalene initiated by hydroxyl radicals: the OH-addition pathway.

The oxidation mechanisms of naphthalene by OH radicals under inert (He) conditions have been studied using density functional theory along with various exchange-correlation functionals. Comparison has been made with benchmark CBS-QB3 theoretical results. Kinetic rate constants were correspondingly estimated by means of transition state theory and statistical Rice-Ramsperger-Kassel-Marcus (RRKM) theory. Comparison with experiment confirms that, on the OH-addition reaction pathway leading to 1-naphthol, the first bimolecular reaction step has an effective negative activation energy around -1.5 kcal mol(-1), whereas this step is characterized by an activation energy around 1 kcal mol(-1) on the OH-addition reaction pathway leading to 2-naphthol. Effective rate constants have been calculated according to a steady state analysis upon a two-step model reaction mechanism. In line with experiment, the correspondingly obtained branching ratios indicate that, at temperatures lower than 410 K, the most abundant product resulting from the oxidation of naphthalene by OH radicals must be 1-naphthol. The regioselectivity of the OH(•)-addition onto naphthalene decreases with increasing temperatures and decreasing pressures. Because of slightly positive or even negative activation energies, the RRKM calculations demonstrate that the transition state approximation breaks down at ambient pressure (1 bar) for the first bimolecular reaction steps. Overwhelmingly high pressures, larger than 10(5) bar, would be required for restoring to some extent (within ∼5% accuracy) the validity of this approximation for all the reaction channels that are involved in the OH-addition pathway. Analysis of the computed structures, bond orders, and free energy profiles demonstrate that all reaction steps involved in the oxidation of naphthalene by OH radicals satisfy Leffler-Hammond's principle. Nucleus independent chemical shift indices and natural bond orbital analysis also show that the computed activation and reaction energies are largely dictated by alterations of aromaticity, and, to a lesser extent, by anomeric and hyperconjugative effects.

An Explicit Consideration of Desolvation is Critical to Binding Free Energy Calculations of Charged Molecules at Ionic Surfaces.

Identifying factors that control the strength and specificity of interactions between peptides and nanoparticles is essential for understanding the potential beneficial and deleterious effects of nanoparticles on biological systems. Computer simulations are valuable in this context, although the reliability of such calculations depends on the force field and sampling algorithm, as well as how the binding constant and binding free energy are defined; the latter must be carefully defined with a clear connection to microscopic models based on statistical mechanics. Using the example of formate binding to the rutile titanium dioxide (TiO2) (110) surface, we demonstrate that a reliable description of the binding process requires an explicit consideration of changes in the solvation state of the binding site. Specifically, we carry out metadynamics simulations in which the solvent coordination number of the binding site, s, is introduced as a collective variable in addition to the vertical distance of the adsorbate to the surface (z). The resulting two-dimensional potential of mean force (2D-PMF) clearly shows that explicitly including the local desolvation of the binding site on the TiO2 surface strongly impacts the convergence and result of the binding free energy calculations. Projecting the 2D-PMF into a one-dimensional PMF along either z or s leads to large errors in the free energy barriers. Results from metadynamics simulations are quantitatively supported by independent alchemical free energy simulations, in which the solvation state of the binding site is also carefully considered by explicitly introducing water molecules to the binding site as the adsorbate is decoupled from the system. On the other hand, preliminary committor analysis for the approximate transition state ensemble constructed based on the 2D-PMF suggests that to properly describe the binding/unbinding kinetics, variables beyond s and z, such as those describing the hydrogen bonding pattern of the adsorbate and surface water, need to be included. We expect that the insights and computational methodologies established in this work will be generally applicable to the analysis of binding interactions between highly charged adsorbates and ionic surfaces in solution, such as those implicated in peptide/nanoparticle binding and biomineralization processes.

Quantum Chemical Challenges for the Binding of Simple Alkanes to Supramolecular Hosts

Binding of hydrocarbon guests to supramolecular hosts can lead to unusual geometric changes such as bending or coiling of guests upon encapsulation. Cucurbiturils (CBs) are classic cation binders that were recently used for the selective binding of small-membered hydrocarbons with a very high association constant (Ka ≈ 10(6) M(-1)). In this study, we have systematically investigated the binding of some alkanes to CB-[6] using a series of quantum chemical methods. The calculated binding free energies are very strong and are largely influenced by guest orientations inside the host and reorganization of host and guests. The computed (1)H NMR chemical shifts of the encapsulated alkanes agree with the experimental estimates thus confirming guest encapsulation. Further, we have shown that although binding of both cyclopentane and neopentane have very strong binding affinities (>20 kcal mol(-1)), the selectivity of cyclopentane to neopentane at CB-[6] is a kinetically driven process through the computation of approximate transition state structures of both alkanes to CB-[6]. The calculated binding affinities with dispersion corrected density functionals (DFs) are very close to the experimental estimates, whereas DFs that lack dispersion correction predict that alkane binding to CB-[6] is largely unfavorable. Finally, we have investigated the binding of some long chain alkanes to several supramolecular hosts using dispersion corrected semiempirical methods which cannot be routinely studied through density functional theory methods due to the larger size of the system.

The Mechanism of Hydrolysis of Aryldiazonium Ions Revisited: Marcus Theory vs. Canonical Variational Transition State Theory

AbstractSeveral models, theoretical levels and computational methods, all based on the canonical variational transition state approximation, have been used to predict both the experimental activation energies (ΔEexp≠) and the experimental activation free energies (ΔGexp≠) for the hydrolysis of aryldiazonium ions. It is demonstrated that the computation of activation energies (ΔE≠), instead of activation free energies (ΔG≠), agrees better with the corresponding experimental data, showing that the employed computational methods do not afford reliable entropic contributions to the free energy barriers in the case of the studied reaction. However, the most fitted computations of ΔE≠ were not able to clearly differentiate between the mechanisms proposed for this interesting reaction (SN1, SN2 and water cluster). In contrast, the use of the Marcus theory (hyperbolic‐cosine equation) instead of the canonical variational transition state theory leads to excellent agreement between the in‐water‐computed activation energies (ΔEwM≠) and the corresponding ΔEexp≠ values for the SN2 mechanism, but far beyond the limit of error for the SN1 process. The validity of the Marcus theory for the studied SN1 and SN2 reactions is ensured by the fact that both reactions can be described as SET processes. On the other hand, apparently compelling evidence against the SN2 mechanism, such as 13C KIEs and experimental observation of N2 scrambling, are also discussed and alternative explanations are proposed.

Growing string method with interpolation and optimization in internal coordinates: Method and examples

The growing string method (GSM) has proven especially useful for locating chemical reaction paths at low computational cost. While many string methods use Cartesian coordinates, these methods can be substantially improved by changes in the coordinate system used for interpolation and optimization steps. The quality of the interpolation scheme is especially important because it determines how close the initial path is to the optimized reaction path, and this strongly affects the rate of convergence. In this article, a detailed description of the generation of internal coordinates (ICs) suitable for use in GSM as reactive tangents and in string optimization is given. Convergence of reaction paths is smooth because the IC tangent and orthogonal directions are better representations of chemical bonding compared to Cartesian coordinates. This is not only important quantitatively for reducing computational cost but also allows reaction paths to be described with smoothly varying chemically relevant coordinates. Benchmark computations with challenging reactions are compared to previous versions of GSM and show significant speedups. Finally, a climbing image scheme is included to improve the quality of the transition state approximation, ensuring high reliability of the method.

Reaction Mechanism of Photoinduced Decarboxylation of the Photoactivatable Green Fluorescent Protein: An ONIOM(QM:MM) Study

Photoactivatable (PA) fluorescent proteins are a new class of fluorescent proteins in which the intensity of fluorescence is dramatically enhanced through photoinduced decarboxylation process. In the present study, the reaction mechanism of the photoinduced decarboxylation in PA-GFP was investigated by the ONIOM(QM:MM) method. The decarboxylation process starts from the first excited state (IntraCT state) and then proceeds along an InterCT state after the first crossing (or an approximate transition state). Relative to an equilibrium structure in S(0), a barrier of ~94 kcal/mol to reach this approximate transition state is the rate-determining step for the entire decarboxylation process. The InterCT state becomes the open-shell ground state in the product, after the subsequent crossing with a closed-shell state that holds an extra electron on the dissociated CO(2). The present study elucidated for the first time the mechanism of the photoinduced decarboxylation of PA-GFP and supports the widely accepted Kolbe pathway, which could be a common mechanism for the irreversible photoinduced decarboxylation in different fluorescent proteins.

Harmonic transition-state theory of thermal spin transitions

A rate theory for thermally activated transitions in spin systems is presented. It is based on a transition-state approximation derived from Landau-Lifshitz equations of motion and quadratic expansion of the energy surface at minima and first order saddle points. While the flux out of the initial state vanishes at first order saddle points, the integrated flux over the hyperplanar transition state is nonzero and gives a rate estimate in good agreement with direct dynamical simulations of test systems over a range in damping constant. The preexponential factor obtained for transitions in model systems representing nanoclusters with 3 to 139 transition metal adatoms is on the order of ${10}^{11}$ to ${10}^{13}\phantom{\rule{0.28em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$, similar to that of atomic rearrangements.

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.

Finding Reaction Pathways of Type A + B → X: Toward Systematic Prediction of Reaction Mechanisms

In these five decades, many useful tools have been developed for exploring quantum chemical potential energy surfaces. The success in theoretical studies of chemical reaction mechanisms has been greatly supported by these tools. However, systematic prediction of reaction mechanisms starting only from given reactants and catalysts is still very difficult. Toward this goal, we describe the artificial force induced reaction (AFIR) method for automatically finding reaction paths of type A + B → X (+ Y). By imposing an artificial force to given reactants and catalysts, the method can find the reactive sites very efficiently. Further pressing by the artificial force provides approximate transition states and product structures, which can be easily reoptimized to the corresponding true ones. This procedure can be executed very efficiently just by minimizing a single function called the AFIR function. All important reaction paths can be found by repeating this cycle starting from many initial orientations. We also discuss perspectives of automated reaction path search methods toward the above goal.

A harmonic transition state approximation for the duration of reactive events in complex molecular rearrangements

Motivated by recent experimental efforts to measure the time a molecular system spends in transit between the reactants and the products of a chemical reaction, here we study the properties of the distribution of such transit times for the case of conservative dynamics on a multidimensional energy landscape. Unlike reaction rates, transit times are not invariant with respect to the order parameter (a.k.a. the experimental signal) used to monitor the progress of a chemical reaction. Nevertheless, such order parameter dependence turns out to be relatively weak. Moreover, for several model systems we find that the probability distribution of transit times can be estimated analytically, with reasonable accuracy, by assuming that the order parameter coincides with the direction of the unstable normal mode at the transition state. Although this approximation tends to overestimate the actual mean transit time measured using other order parameters, it yields asymptotically correct long-time behavior of the transit time distribution, which is independent of the order parameter.

Electron correlation beyond the local density approximation: self-interaction correction ingadolinium

We report on detailed first-principles calculations which focus on the magnetic andstructural properties of the (0001) surface of gadolinium. The electronic correlation withinthe localized 4f states is treated within the self-interaction correction (SIC), thus goingbeyond the local spin-density approximation. The ferromagnetic ground state is predictedcorrectly if the SIC is applied; the effect of surface relaxations on Heisenberg exchangeparameters and on the Curie temperature are addressed by Monte Carlo calculations. TheSIC also has a profound effect on the dispersion of the d surface states, due tohybridization of the 4f states with the 5d valence states. The best agreement withphotoemission experiments is obtained within the transition state approximation, whichtakes into account the orbital relaxation. The Rashba spin–orbit coupling in the dsurface states is fully captured by our relativistic multiple scattering approach.

Acid dissociation mechanisms of Si(OH)4 and Al(H2O)63+ in aqueous solution

Abstract Silicic acid and the hexa-aqua of Al3+ are fundamental model aqueous species of chemical importance in nature. In order to investigate their hydroxyl dissociation mechanisms, Car–Parrinello molecular dynamics (CPMD) simulations were carried out, which allow treating the solutes and solvents on the same footing. The method of constraint was employed to trigger the reactions by taking coordination number as the reaction coordinate and the thermodynamic integration was used to obtain the free-energy profiles. The approximate transition states were located and the reactant and product states were also characterized. The free-energy changes of dissociation are found about 15.0 kcal/mol and 7.7 kcal/mol for silicic acid and Al-aqua, respectively. From the simulation results, the first pKas were calculated by using two approaches, which are based on the pristine thermodynamic relation and the RDF (radial distribution function)-free energy relation, respectively. Because of more uncertainties involved in the RDF way, it is suggested that the pristine way should be favored, which shows an error margin of 1 pKa unit. This study provides an encouraging basis for applying the present methodology to predict acidity constants of those groups that are difficult to measure experimentally.

Identification of the Transition States in the Inversion of 1,4-Benzodiazepines with the Ab Initio Replica Path Method

The inversion of four 1,4-benzodiazepines was investigated with the ab initio "replica path method" with density functional theory at the B3LYP/6-31G* level. The reaction path constructed with this method for the inversion provides an approximate transition state (TS) geometry, which, upon further TS optimization, leads to the TS geometry characterized by a single vibrational frequency. 1,4-Benzodiazepines lacking a 5-phenyl ring have a single reaction path for the inversion with Cs symmetry at the TS. In contrast, the inversion of benzodiazepines with a 5-phenyl ring, such as the peripheral benzodiazepine receptor ligand 4'-chlorodiazepam (Ro5-4864) and its N1-desmethyl analog (Ro5-2752), can proceed through multiple reaction paths having a TS with or without Cs symmetry. Notably, the replica path method found a path connecting two asymmetric TSs of 4'-chlorodiazepam via a symmetrical TS, suggesting that these inversion paths can be readily crossed from one to another. The stabilization energies gained by 4'-chlorodiazepam and its N1-desmethyl analog from the breaking of Cs symmetry at the TS were calculated to be 0.10 and 0.07 kcal/mol, respectively. The origin of the broken symmetry of Cs was traced to the coupling of the puckering of the diazepine ring with the rotation of the chlorophenyl ring. These results show the advantages of the replica path method for locating the TSs as well as for constructing the reaction paths for the inversion of 1,4-benzodiazepines.