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.     

Efficient methods for finding transition states in chemical reactions: comparison of improved dimer method and partitioned rational function optimization method

A combination of interpolation methods and local saddle-point search algorithms is probably the most efficient way of finding transition states in chemical reactions. Interpolation methods such as the growing-string method and the nudged-elastic band are able to find an approximation to the minimum-energy pathway and thereby provide a good initial guess for a transition state and imaginary mode connecting both reactant and product states. Since interpolation methods employ usually just a small number of configurations and converge slowly close to the minimum-energy pathway, local methods such as partitioned rational function optimization methods using either exact or approximate Hessians or minimum-mode-following methods such as the dimer or the Lanczos method have to be used to converge to the transition state. A modification to the original dimer method proposed by [Henkelman and Jonnson J. Chem. Phys. 111, 7010 (1999)] is presented, reducing the number of gradient calculations per cycle from six to four gradients or three gradients and one energy, and significantly improves the overall performance of the algorithm on quantum-chemical potential-energy surfaces, where forces are subject to numerical noise. A comparison is made between the dimer methods and the well-established partitioned rational function optimization methods for finding transition states after the use of interpolation methods. Results for 24 different small- to medium-sized chemical reactions covering a wide range of structural types demonstrate that the improved dimer method is an efficient alternative saddle-point search algorithm on medium-sized to large systems and is often even able to find transition states when partitioned rational function optimization methods fail to converge.     

Multipath variational transition state theory: rate constant of the 1,4-hydrogen shift isomerization of the 2-cyclohexylethyl radical

We propose a new formulation of variational transition state theory called multipath variational transition state theory (MP-VTST). We employ this new formulation to calculate the forward and reverse thermal rate constant of the 1,4-hydrogen shift isomerization of the 2-cyclohexylethyl radical in the gas phase. First, we find and optimize all the local-minimum-energy structures of the reaction, product, and transition state. Then, for the lowest-energy transition state structures, we calculate the reaction path by using multiconfiguration Shepard interpolation (MSCI) method to represent the potential energy surface, and, from this representation, we also calculate the ground-state vibrationally adiabatic potential energy curve, the reaction-path curvature vector, and the generalized free energy of activation profile. With this information, the path-averaged generalized transmission coefficients <γ> are evaluated. Then, thermal rate constant containing the multiple-structure anharmonicity and torsional anharmonicity effects is calculated using multistructural transition state theory (MS-TST). The final MP-VTST thermal rate constant is obtained by multiplying k(MS-T)(MS-TST) by <γ>. In these calculations, the M06 density functional is utilized to compute the energy, gradient, and Hessian at the Shepard points, and the M06-2X density functional is used to obtain the structures (conformers) of the reactant, product, and the saddle point for computing the multistructural anharmonicity factors.     

基态氧(3^O2)氧化硅烯的密度泛函计算研究

采用密度泛函[B3LYP(full)/6-311+G^*]方法研究了基态氧(3^O2)氧化硅烯(Si2H4)的机理。计算了三重态初始中间体(IM(T1)到单重态中间体IM2(S0)反应交叉势能面,报道了各反应中间体、产物和过渡态的构型和能量,用频率分析方法对各过渡态进行了验证,进一步用IRC方法对主要的基元反应进行了考察,确定了历经生成1,2-二氧环氧硅烷中间体的氧化过程的主要反应通道。     

Communication: κ-dynamics--an exact method for accelerating rare event classical molecular dynamics

κ-dynamics is an accelerated molecular dynamics method for systems with slow transitions between stable states. Short trajectories are integrated from a transition state separating a reactant state from products. The first trajectory found that leads directly to a product without recrossing the transition state and starts in the reactant state is followed. The transition time is drawn from a distribution given by the transition state theory rate and the number of attempted trajectories. Repeating this procedure from each state visited gives a statistically exact state-to-state trajectory.     

CH自由基和NO~2反应研究: II.反应的动力学计算

采用MP2(FULL)/6-31G(d)方法从动力学计算上探讨了CH自由基与NO~2反应的可能途径,找到了反应物,中间体及产物之间的能量通道和过渡态,报道了它们的构型、电子态及能量。并通过频率分析和IRC方法对所有的过渡态进行了验证。在此基础上求出了各步反应的活化能。在以前热力学研究的基础上,对于可能的反应通道进一步作了动力学分析,找到了反应主产物通道的分支比,与实验得到的分支比基本吻合。     

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.     

Structural dissimilarity sampling with dynamically self‐guiding selection

Structural dissimilarity sampling (SDS) has been proposed as an enhanced conformational sampling method for reproducing the structural transitions of a given protein. SDS consists of cycles of two steps: (1) Selections of initial structures with structural dissimilarities by referring to a measure. (2) Conformational resampling by restarting short‐time molecular dynamics (MD) simulations from the initial structures. In the present study, an efficient measure is proposed as a dynamically self‐guiding selection to accelerate the structural transitions from a reactant state to a product state as an extension to the original SDS. In the extended SDS, the inner product (IP ) between the reactant and the snapshots generated by short‐time MD simulations are evaluated and ranked according to the IP s at every cycle. Then, the snapshots with low IP s are selected as initial structures for the short‐time MD simulations. This scheme enables one to choose dissimilar and distant initial structures from the reactant, and thus the initial structures dynamically head towards the product, promoting structural transitions from the reactant. To confirm the conformational sampling efficiency, the extended SDS was applied to maltodextrin binding protein (MBP), and we successfully reproduced the structural transition from the open to closed states with submicrosecond‐order simulation times. However, a conventional long‐time MD simulation failed to reproduce the same structural transition. We also compared the performance with that obtained by the ordinary SDS and other sampling techniques that have been developed by us to characterize the possible utility of the extended SDS for actual applications. © 2017 Wiley Periodicals, Inc.     

Characterization of the Structure and Dynamics of the HDV Ribozyme at Different Stages Along the Reaction Path

The structure and dynamics of the hepatitis delta virus ribozyme (HDVr) are studies using molecular dynamics simulations at several stages along its catalytic reaction path, including reactant, activated precursor, transition state mimic and product states, departing from an initial structure based on the C75U mutant crystal structure (PDB: 1VC7). Results of five 350 ns molecular dynamics simulations reveal a spontaneous rotation of U-1 that leads to an in-line conformation and support the role of protonated C75 as the general acid in the transition state. Our results provide rationale for the interpretation of several important experimental results, and make experimentally testable predictions regarding the roles of key active site residues that are not obvious from any available crystal structures.     

Transition state theory with Tsallis statistics

We discuss the rate of an elementary chemical reaction. We use the reaction path and especially its saddle point on the potential energy surface. The reaction path connects reactant and product of a reaction over the transition state (TS). Usually, the TS is assumed near or at the single saddle point of the reaction path. By means of comparison of the statistics of states at the reactant and at the TS, one can estimate the reaction rate by the Eyring theory. We propose to use the Tsallis statistics at the TS, a statistics of seldom accidents. Thus, we propose to generalize the well‐known Boltzmann–Gibbs statistics, which is the limiting case of the Tsallis statistics. We use features of this nonextensive thermostatistics. The basic properties of the statistics are used to derive (approximated) partition functions, and they are applied on reaction rates. The approximation includes a factorization of the partition functions. The theory is applied to HCN isomerization to HNC, and to the reaction H₂ + CN → H + HCN. It allows an accordance with experimental estimations of the reaction rates. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Finding the transition state without initial guess: the growing string method for Newton trajectory to isomerization and enantiomerization reaction of alanine dipeptide and poly(15)alanine

We report a new, high-dimensional application of a method for finding a transition state (TS) between a reactant and a product on the potential energy surface: the search of a growing string along a reaction path defined by any Newton trajectory in combination with the Berny method (Quapp, J Chem Phys (2005), 122, 174106; we have provided this algorithm on a web page). Two given minima are connected by a one-dimensional, but usually curvilinear reaction coordinate. It leads to the TS region. The application of the method to alanine dipeptide finds the TS of the isomerisation C(7 ax) --> C(5), some TSs of the enantiomerisation of C(7 ax) from L-form to quasi-D-form, and it finds the TS region of a transition of a partly unfolded, bent structure which turns back into a mainly alpha-helix in the Ac(Ala)(15)NHMe polyalanine (all at the quantum mechanical level B3LYP/6-31G: the growing string calculation is interfaced with the Gaussian03 package). The formation or dissolvation of some alpha- or 3(10)-hydrogen bonds of the helix are discussed along the TS pathway, as well as the case of an enantiomer at the central residue of the helix.     

Cleavage and recovery of molecular water in silica

The network response associated with the incorporation and reactivity of water molecules in bulk phases of amorphous and crystalline silica are investigated using density functional theory. The extent of network relaxation is found to change the relative stabilities of the reactant and product states. A highly reactive site, with a low activation barrier, is associated with a highly strained site in which network relaxation significantly stabilizes the silanol state by effectively annealing the local structure. Diffusion and exchange reaction paths are found to likely be associated with minimum energy paths in which the stability of the product and reactant states are equal. These latter paths are associated with minimal network response, although the ability of the silanol groups to take on several conformations has an overall effect of changing the stability along a given reaction path.     

(4-溴甲基双环[4.4.1]-1,3,5,7,9-十一碳五烯基-3-)甲醇环氧化反应机理的理论研究

A reaction mechanism of epoxidation reaction of the 4-(bromomethyl)bicyclo4.4.1undeca-1,3,5,7,9-pentaen-3-ylmethanol has been studied by using the density functional theory(DFT) method at B3LYP level with 6 31G* basis set. The geometric structures of reactant, product and transition state have been optimized. The transition state is found by the QST2 method and characterized by the vibration frequency analysis. The intrinsic reaction coordinate(IRC) for this reaction is traced and confirms the reaction mechanism. The changes and the nature of related chemical bonds along the IRC path have been analyzed by the theory of electronic charge density. The result shows that the elimination reaction and ring closing reaction are synergistic, and the hydrogen in the elimination reaction derives from hydroxyl. In addition, the activation energy of the reaction is 139.2 kJ/mol.     

1, 2-丙二醇酸性条件下反应机理的量子化学研究

用MNDO方法研究了1, 2-丙二醇在酸性条件下反应机理, 寻找到了反应过渡态, 并从理论上确证了它最可行的反应过程和最终产物。     

环丙基卡宾重排为环丁烯机理的密度泛函研究

采用 B3LYP 方法,用 6-311G(d)基组计算了环丙基卡宾重排为环丁烯的反应物、过渡态和产物的能量和振动频率,并用 IRC 计算验证了过渡态。结果表明环丙基卡宾的重排机理不同于通常碳正离子重排采用的亲核重排机理,而是一个亲电重排机理。     

一个方酸内鎓盐衍生物合成机理的理论研究

用ＰＭ３方法对新近合成的一个方酸内Ｗｅｎｇ盐衍生物：２－（Ｎ,Ｎ－二羟乙基）胺基－４－二甲胺苯基方酸内Ｗｅｎｇ盐的微观反应机理进行了研究,计算结果表明：以（Ｎ,Ｎ－二羟乙基）胺基负离子,二甲胺一方酸制备该方酸内Ｗｅｎｇ盐有邻位和对位两种产物,且对位更易生成,同时,还探讨了提高光致材料产率的可能方法。     

Evaluation of the rate coefficients and arrhenius parameters of hydrogen atom transfer reactions. I. The method

A method is presented for the prediction of rate coefficients and Arrhenius parameters for bimolecular hydrogen atom transfer reactions A + BC → AB + C. The treatment sets out from structural considerations of the complex A ? B ? C and calculates the energy of the complex along the reaction path from empirical functions for a bonding energy term and an endgroup contribution. The treatment proceeds by assuming ultrasimple transition state models and assigning the force constants and vibrational frequencies. Finally the rate coefficient and Arrhenius parameters are obtained on the basis of separable activated complex theory. Application of the method requires known properties of reactant and product molecules and does not demand the use of adjustable parameters. The relation and differences between this method and the BEBO treatment as well as Zavitsas' method are dealt with.     

Oxidation and Reduction Pathways in the Knowles Hydroamination via a Photoredox-Catalyzed Radical Reaction**

Systematic reaction path exploration revealed the entire mechanism of Knowles's light-promoted catalytic intramolecular hydroamination. Bond formation/cleavage competes with single electron transfer (SET) between the catalyst and substrate. These processes are described by adiabatic processes through transition states in an electronic state and non-radiative transitions through the seam of crossings (SX) between different electronic states. This study determined the energetically favorable SET path by introducing a practical computational model representing SET as non-adiabatic transitions via SXs between substrate's potential energy surfaces for different charge states adjusted based on the catalyst's redox potential. Calculations showed that the reduction and proton shuttle process proceeded concertedly. Also, the relative importance of SET paths (giving the product and leading back to the reactant) varies depending on the catalyst's redox potential, affecting the yield.     

Finding transition states using reduced potential-energy surfaces

 We propose a method to locate saddle points that is based on the interplay between the driving coordinate and the restricted quasi-Newton algorithm. The method locates the transition state using a reduced potential-energy surface. The reduced potential-energy surface is characterized by the set of driving coordinates. The proposed algorithm starts at a point on the surface that is slightly perturbed from either reactant or product and, in principle, converges to the transition state. Finally we give a special type of update Hessian matrix formula that should be applied in optimizations carried out on reduced potential-energy surfaces. Received: 29 September 2000 / Accepted: 3 January 2001 / Published online: 3 April 2001