Single‐ended transition state finding with the growing string method

Reaction path finding and transition state (TS) searching are important tasks in computational chemistry. Methods that seek to optimize an evenly distributed set of structures to represent a chemical reaction path are known as double‐ended string methods. Such methods can be highly reliable because the endpoints of the string are fixed, which effectively lowers the dimensionality of the reaction path search. String methods, however, require that the reactant and product structures are known beforehand, which limits their ability for systematic exploration of reactive steps. In this article, a single‐ended growing string method (GSM) is introduced which allows for reaction path searches starting from a single structure. The method works by sequentially adding nodes along coordinates that drive bonds, angles, and/or torsions to a desired reactive outcome. After the string is grown and an approximate reaction path through the TS is found, string optimization commences and the exact TS is located along with the reaction path. Fast convergence of the string is achieved through use of internal coordinates and eigenvector optimization schemes combined with Hessian estimates. Comparison to the double‐ended GSM shows that single‐ended method can be even more computationally efficient than the already rapid double‐ended method. Examples, including transition metal reactivity and a systematic, automated search for unknown reactivity, demonstrate the efficacy of the new method. This automated reaction search is able to find 165 reaction paths from 333 searches for the reaction of NH₃BH₃ and (LiH)₄, all without guidance from user intuition. © 2015 Wiley Periodicals, Inc.     

Finding the transition state of quasi-barrierless reactions by a growing string method for newton trajectories: application to the dissociation of methylenecyclopropene and cyclopropane

A method for finding a transition state (TS) between a reactant minimum and a quasi-flat, high dissociation plateau on the potential energy surface is described. The method is based on the search of a growing string (GS) along reaction pathways defined by different Newton trajectories (NT). Searches with the GS-NT method always make it possible to identify the TS region because monotonically increasing NTs cross at the TS or, if not monotonically increasing, possess turning points that are located in the TS region. The GS-NT method is applied to quasi-barrierless and truly barrierless chemical reactions. Examples are the dissociation of methylenecyclopropene to acetylene and vinylidene, for which a small barrier far out in the exit channel is found, and the cycloaddition of singlet methylene and ethene, which is barrierless for a broad reaction channel with Cs-symmetry reminiscent of a mountain cirque formed by a glacier.     

A growing string method for the reaction pathway defined by a Newton trajectory

The reaction path is an important concept of theoretical chemistry. We use a projection operator for the following of the Newton trajectory (NT) along the reaction valley of the potential energy surface. We describe the numerical scheme for the string method, adapting the proposal of a growing string (GS) by [Peters et al.,J. Chem. Phys. 120, 7877 (2004)]. The combination of the Newton projector and the growing string idea is an improvement of both methods, and a great saving of the number of iterations needed to find the pathway over the saddle point. This combination GS-NT is at the best of our knowledge new. We employ two different corrector methods: first, the use of projected gradient steps, and second a conjugated gradient method, the CG+ method of Liu, Nocedal, and Waltz, generalized by projectors. The executed examples are Lennard-Jones clusters, LJ(7) and LJ(22), and an N-methyl-alanyl-acetamide (alanine dipeptide) rearrangement between the minima C7(ax) and C5. For the latter, the growing string calculation is interfaced with the GASSIAN03 quantum chemical software package.     

A growing string method for determining transition states: comparison to the nudged elastic band and string methods

Interpolation methods such as the nudged elastic band and string methods are widely used for calculating minimum energy pathways and transition states for chemical reactions. Both methods require an initial guess for the reaction pathway. A poorly chosen initial guess can cause slow convergence, convergence to an incorrect pathway, or even failed electronic structure force calculations along the guessed pathway. This paper presents a growing string method that can find minimum energy pathways and transition states without the requirement of an initial guess for the pathway. The growing string begins as two string fragments, one associated with the reactants and the other with the products. Each string fragment is grown separately until the fragments converge. Once the two fragments join, the full string moves toward the minimum energy pathway according to the algorithm for the string method. This paper compares the growing string method to the string method and to the nudged elastic band method using the alanine dipeptide rearrangement as an example. In this example, for which the linearly interpolated guess is far from the minimum energy pathway, the growing string method finds the saddle point with significantly fewer electronic structure force calculations than the string method or the nudged elastic band method.     

Optimizing the structures of minimum and transition state on the free energy surface

Presented here is the application of a scheme for optimizing the structures of minima and transition states on the free energy surface (FES) for a path along a fixed reaction coordinate with the aid of ab initio molecular dynamics (AIMD) simulation. In the direction of the reaction coordinate, the values corresponding to the stationary points were optimized using the quasi-Newton method, in which the gradient of the free energy along the reaction coordinate was obtained by a constraint AIMD method, and the Bofill Hessian update scheme was used. The equilibrium values for the other directions were taken as the corresponding averages in the dynamic simulation. This scheme was applied to several elementary bimolecular addition reactions: (A) BH(3) + H(2)O --> H(2)O.BH(3); (B) BF(3) + NH(3) --> FB(3).NH(3); (C) SO(3) + NH(3) --> O(3)S.NH(3); (D) C(2)H(4) + CCl(2) --> H(4)C(2).CCl(2); (E) Ni(NH(2))(2) + PH(3) --> (NH(2))(2)Ni.PH(3); (F) W(CO)(5) + CO --> W(CO)(6). For reactions A, B, C, and F, no transition state (TS) exists on the potential energy surface (PES). However there is a TS on the FES. This stems from the curvature difference of the PES and -TDeltaS as a function of the reaction coordinate. For all reactions, it is found that the TS shifts toward the complexation product with increasing temperature because of the curvature increase of -TDeltaS. The equilibrium bond distances for the inactive coordinates perpendicular to the reaction coordinate always increase with temperature, which is due to the thermal excitation and anharmonicity of the PES.     

CH3CH2+O(3P)反应机理的理论研究

The reaction for CH3CH2+O(3P) was studied by ab initio method. The geometries of the reactants, intermediates, transition states and products were optimized at MP2/6-311+G(d,p) level. The corresponding vibration frequencies were calculated at the same level. The single-point calculations for all the stationary points were carried out at the QCISD(T)/6-311+G(d,p) level using the MP2/6-311+G(d,p) optimized geometries. The results of the theoretical study indicate that the major products are the CH2O＋CH3, CH3CHO+H and CH2CH2+OH in the reaction. For the products CH2O＋CH3 and CH3CHO+H, the major production channels are A1: (R)→IM1→TS3→(A) and B1: (R)→IM1→TS4→(B), respectively. The majority of the products CH2CH2+OH are formed via the direct abstraction channels C1 and C2: (R)→TS1(TS2)→(C). In addition, the results suggest that the barrier heights to form the CO reaction channels are very high, so the CO is not a major product in the reaction.     

Transition pathways in complex systems: Application of the finite-temperature string method to the alanine dipeptide

The finite-temperature string method proposed by E, et al. [W. E, W. Ren, and E. Vanden-Eijnden, Phys. Rev. B 66, 052301 (2002)] is a very effective way of identifying transition mechanisms and transition rates between metastable states in systems with complex energy landscapes. In this paper, we discuss the theoretical background and algorithmic details of the finite-temperature string method, as well as the application to the study of isomerization reaction of the alanine dipeptide, both in vacuum and in explicit solvent. We demonstrate that the method allows us to identify directly the isocommittor surfaces, which are approximated by hyperplanes, in the region of configuration space where the most probable transition trajectories are concentrated. These results are verified subsequently by computing directly the committor distribution on the hyperplanes that define the transition state region.     

Finding transition pathways using the string method with swarms of trajectories

An approach to find transition pathways in complex systems is presented. The method, which is related to the string method in collective variables of Maragliano et al. (J. Chem. Phys. 2006, 125, 024106), is conceptually simple and straightforward to implement. It consists of refining a putative transition path in the multidimensional space supported by a set of collective variables using the average dynamic drift of those variables. This drift is estimated on-the-fly via swarms of short unbiased trajectories started at different points along the path. Successive iterations of this algorithm, which can be naturally distributed over many computer nodes with negligible interprocessor communication, refine an initial trial path toward the most probable transition path (MPTP) between two stable basins. The method is first tested by determining the pathway for the C7eq to C7ax transition in an all-atom model of the alanine dipeptide in vacuum, which has been studied previously with the string method in collective variables. A transition path is found with a committor distribution peaked at 1/2 near the free energy maximum, in accord with previous results. Last, the method is applied to the allosteric conformational change in the nitrogen regulatory protein C (NtrC), represented here with a two-state elastic network model. Even though more than 550 collective variables are used to describe the conformational change, the path converges rapidly. Again, the committor distribution is found to be peaked around 1/2 near the free energy maximum between the two stable states, confirming that a genuine transition state has been localized in this complex multidimensional system.     

Computational study of the Stone-Wales transformation in C36

The transition of the D6h neutral and charged isomers to D2d isomers of C36 via Stone-Wales transformation has been studied by means of the hybrid density functional method (B3LYP). The results show that the transition state (TS) and reaction pathway could be identified for the rearrangement from C36-D6h to C36-D2d on the potential energy surface. We found that the neutral and charged transition states all have C2 molecular point group symmetry with the two migrating carbon atoms remaining close to the fullerene surface. The other kind of possible TS with a carbene-like structure along the stepwise reaction path does not exist as a stationary point with the density functionals utilized here. The classical barriers are 6.23 eV through the neutral TS, 6.37 eV through the anionic TS, and 6.29 eV through the cationic TS at the B3LYP/6-31G level of theory.     

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.     

A string model for the chemical reaction coordinate in static external fields

A theoretical method for estimating the effects of a static external field upon a reaction path is proposed. The reaction path is defined as the intrinsic reaction coordinate (IRC) which is treated as a string. The string is deformed by the external static force field. We project the external force onto the normal modes orthogonal and parallel to the string. The string is dragged along each direction of the normal mode. The cell structure [10b] attached to the string is also deformed; the transition state (TS) is shifted, and the internal structure of the reaction system is expanded or compressed in configuration space. A min-max relationship of the external effect on the string is found: the smaller the magnitude of the force constant of the normal mode orthogonal to the string, the larger the deformation of the string in the direction of the normal mode. As an example, the effects of one water molecule for hydrogen-migrating isomerization of formaldehyde and fluoroformaldehyde are considered.     

C(3P)与H2S反应的反应机理

The mechanisms of the C(3P)+H 2S→HCS+H and C(3P)+H 2S → HSC+H reactions have been studied at the UMP2/6-31G(d,p),UMP2/6-311G(d,p),and G2 levels, and six transition states and three intermediates have been located along the reaction paths. The predicted path for the C(3P)+H2S→HCS+H reaction is: C(3P)+H2S→IM1→TS1→IM2→TS4→HCS+H, in line with the reaction process suggested by Lee et al. [1] in which only the intermediates were given. Our energetic results indicate that the C(3P)+H2S→HCS+H reaction is more favorable than the C(3P)+H 2S→HSC+H reaction, in agreement with experiment.     

烯酮或乙烯与甲醛环加成协同反应机理的对比研究

本文研究了烯酮与甲醛, 乙烯与甲醛两个环加成反应的协同过程的过渡态(TS),用能量分解方法对两个过渡态中反应物间的相互作用能的本质做了剖析。通过对比,发现在乙烯与甲的过渡态中反应物的占有轨道间电子的交换排斥作用能比较大, 从而可以说明此反应比乙烯与烯酮间的协同过程难于进行。     

Reaction Ergodography and Transition State Analyses of the Addition of AIH_3 to Acetylene

The present paper covers the reaction ergodography for the addition of AlH3 to acetylene investigated by ab initio calculation with RHF/3-21G basis set. The changes in some physical properties along the reaction path (IRC) are presented. The formations of FMOs of the transition state have been analyzed according to the Fukui' s method. On the basis of the perturbation theory and Wolfsborg Helmholtz formula, we calculated the FMO' s energy orders of TS and its formation that shows the HOMO of TS consists of LUMO, HOMO of AlH3 and HOMO of HCCH.     

On the van der Waals interactions and the stability of polypeptide chains in helical conformations

In this work, we aim to investigate the contribution of van der Waals (vdW) interactions to the stability of polypeptides in helical conformations studying infinitely long chains of alanine and glycine with density functional theory. To account for vdW interactions, we have used the interatomic pairwise dispersion approach proposed by Tkatchenko–Scheffler (TS), the TS approach with self‐consistent screening (SCS) that self‐consistently includes long‐range electrostatic effects (TS + SCS), the D2 and D3 methods of Grimme et al., and the Langreth–Lundqvist procedure that treats nonlocally the correlation part of the approximation to the exchange‐correlation (xc) functional (called DF). First, we have tested the performance of these strategies studying a set of representative hydrogen bonded dimers. Next, we have studied polyalanine and polyglicine in π‐helix, α‐helix, ‐helix, 2₇, and polyproline‐II conformations and in a fully extended structure. We have found that the DF methodology in combination with a modified version for the Becke approximation to the exchange (optB86b), the D2, D3, TS, and TS + SCS strategies in combination with the Perdew–Burke–Ernzerhof approximation to the xc functional, describe fairly well dimer association energies. Furthermore, the DF method and the D2, D3, TS, and TS + SCS strategies predict very similar helical stabilities even though the approximation used in DF for describing the long‐range dispersion interactions is different that the one used in D2/D3 and TS/TS + SCS. We found that the stability doubles for π and α helices if vdW interactions are taken into account. © 2015 Wiley Periodicals, Inc.     

Reliable and efficient reaction path and transition state finding for surface reactions with the growing string method

The computational challenge of fast and reliable transition state and reaction path optimization requires new methodological strategies to maintain low cost, high accuracy, and systematic searching capabilities. The growing string method using internal coordinates has proven to be highly effective for the study of molecular, gas phase reactions, but difficulties in choosing a suitable coordinate system for periodic systems has prevented its use for surface chemistry. New developments are therefore needed, and presented herein, to handle surface reactions which include atoms with large coordination numbers that cannot be treated using standard internal coordinates. The double‐ended and single‐ended growing string methods are implemented using a hybrid coordinate system, then benchmarked for a test set of 43 elementary reactions occurring on surfaces. These results show that the growing string method is at least 45% faster than the widely used climbing image‐nudged elastic band method, which also fails to converge in several of the test cases. Additionally, the surface growing string method has a unique single‐ended search method which can move outward from an initial structure to find the intermediates, transition states, and reaction paths simultaneously. This powerful explorative feature of single ended‐growing string method is demonstrated to uncover, for the first time, the mechanism for atomic layer deposition of TiN on Cu(111) surface. This reaction is found to proceed through multiple hydrogen‐transfer and ligand‐exchange events, while formation of H‐bonds stabilizes intermediates of the reaction. Purging gaseous products out of the reaction environment is the driving force for these reactions. © 2017 Wiley Periodicals, Inc.     

G2(+) investigation on the alpha-effect in the SN2 reactions at saturated carbon

As a continuing theoretical study on the alpha-effect in the S(N)2 reactions at saturated carbon centers, 28 gas-phase reactions have been examined computationally by using the high-level G2(+) method. The reactions include: Nu(-)+CH(3)X-->CH(3)Nu+X(-) (X=F and Cl; Nu(-)=HO(-), HS(-), CH(3)O(-), Cl(-), Br(-), HOO(-), HSO(-), FO(-), ClO(-), BrO(-), NH(2)O(-), and HC(==O)OO(-)). It was found that all alpha-nucleophiles examined exhibit downward deviations from the correlation line between the overall barriers and proton affinities for normal nucleophiles, indicating the existence of the alpha-effect in the gas phase. The transition states (TS) for the alpha-nucleophiles are characterized by less advanced C--X bond cleavages than the normal nucleophiles, leading to smaller deformation energies and overall barriers. The size of the alpha-effect is related to the electron density on the alpha-atom, and increases when the position of alpha-atom is changed from left to right and from bottom to top in the periodic table. The reaction with CH(3)F exhibits a larger alpha-effect than that with CH(3)Cl, which can be explained by a later TS and a more positively charged methyl group at the TS for CH(3)F, [NuCH(3)F](- not equal). Thus, a higher electron density on the alpha-atom and a more positive methyl moiety at the TS result in a larger alpha-effect.     

Structure Elucidation and Theoretical Investigation of Key Steps in the Biogenetic Pathway of Schisanartane Nortriterpenoids by Using DFT Methods

Rubrifloradilactone C ( 4 ), a novel bioactive nortriterpenoid, along with four other nortriterpenoids ( 1 – 3 , 5 ) were isolated from Schisandra rubriflora. The structure of 4 was determined by extensive NMR spectral analysis, computational evidence by using the GIAO method at the B3LYP/6–311++G(2d,p)//B3LYP/6–31G(d) levels, and X‐ray analysis. DFT at the B3LYP/6–311+G(d,p) level was selected to clarify the key mechanistic steps in the formation of 1 and 4 through transition‐state (TS) investigations. The effect of enzymes on the TS barriers was considered by using the polarized continuum model. Other possible products based on the new mechanism were predicted.     

Application of QM simulations and multivariate analysis in the study of alkene reactivity in the zeolite H‐ZSM5

Reported herein are the results of an investigation into the effect of the extended framework of the zeolite ZSM‐5 on the reaction energetics and structures of (a) the physisorbed complex formed between the zeolite and six alkenes, (b) the corresponding chemisorbed alkoxide intermediate and (c) the transition states (TS) connecting the two. For this, quantum mechanical (QM) simulations of ZSM‐5 in the presence and absence of the zeolite framework have been employed. A 46T density functional theory (DFT) cluster model and a 3T:46T DFT:UFF ONIOM model are used to represent the former scenario and a simple 3T DFT cluster model for the latter. The structural implications of neglecting the zeolite framework have been rigorously compared using the multivariate statistical method principal components analysis (PCA). This method allows one to assess the correlated nature of the changes in structure along the reaction coordinate, for multiple different alkenes, in a facile, reliable way. Copyright © 2008 John Wiley & Sons, Ltd.     

The fate of branched and linear isomers in the rhodium-catalyzed hydroformylation of 3,4,4-trimethylpent-1-ene

In nonreversible hydroformylations, the computational evaluation of regio- and stereoselectivities from the relative energy barriers of the transition states (TS) for the alkyl-Rh intermediate formation step is possible, provided all low energy conformers are considered. In contrast, in reversible hydroformylations, also the subsequent reaction steps need to be taken into account to shed some light on mechanistic details. Thus, an extensive comparison of branched (B) and linear (L) reaction pathways for the Rh-catalyzed hydroformylation of 3,4,4-trimethylpent-1-ene (a bulky chiral substrate), going from a number of reactant complexes to products, has been carried out to rationalize the experimental result that pointed to reaction reversibility, although the value of the regioselectivity ratio (B:L = 15:85), based on alkyl-Rh TS free energies, computed under the hypothesis of nonreversibility, was in satisfactory agreement with the experimental one (5:95). A density functional theory approach at the B3P86/6-31G* level coupled to effective core potentials for Rh in the LanL2DZ valence basis set has been employed. By comparing the activation free energies involved in the various steps for the different reactant adducts, interestingly a similar behavior along all the linear pathways is found: the alkyl-Rh formation TS presents the highest barrier; thus, the reaction is nonreversible for all the linear isomers that invariably proceed to yield the linear aldehyde. Conversely, the behavior is quite different along the branched pathways. While some branched isomers eventually produce the corresponding aldehydes, two of the others follow distinct competing pathways, because β-hydride elimination occurs (a) to the terminal olefin-Rh complex (the starting material) that reacts again with the original regioselectivity, increasing the linear fraction, when the CO addition and insertion TS are higher than the alkyl-Rh TS and (b) to the internal olefin-Rh complex when the CO addition and insertion TS are higher than the relevant β-hydride elimination TS, but not than the alkyl-Rh TS. The solvent effect on the reversible profile, evaluated either in the supermolecule approach by adding a benzene molecule to the calculations or in the IEF-PCM framework (ε = 2.247), does not bring about any substantial change in the profile, leaving unaltered the conclusions reached.