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Quapp W, Bofill JM. Theory and Examples of Catch Bonds. J Phys Chem B 2024; 128:4097-4110. [PMID: 38634732 DOI: 10.1021/acs.jpcb.4c00468] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/19/2024]
Abstract
We discuss slip bonds, catch bonds, and the tug-of-war mechanism using mathematical arguments. The aim is to explain the theoretical tool of molecular potential energy surfaces (PESs). For this, we propose simple 2-dimensional surface models to demonstrate how a molecule under an external force behaves. Examples are selectins. Catch bonds, in particular, are explained in more detail, and they are contrasted to slip bonds. We can support special two-dimensional molecular PESs for E- and L-selectin which allow the catch bond property. We demonstrate that Newton trajectories (NT) are powerful tools to describe these phenomena. NTs form the theoretical background of mechanochemistry.
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Affiliation(s)
- Wolfgang Quapp
- Mathematisches Institut, Universität Leipzig, PF 100920, Leipzig D-04009, Germany
| | - Josep Maria Bofill
- Departament de Química Inorgànica i Orgànica, Secció de Química Orgànica, Universitat de Barcelona, Martí i Franquès 1, Barcelona 08028, Spain
- Institut de Química Teòrica i Computacional, (IQTCUB), Universitat de Barcelona, Martí i Franquès 1, Barcelona 08028, Spain
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2
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Georgiou A, Vandecasteele H, Bello-Rivas JM, Kevrekidis I. Locating saddle points using gradient extremals on manifolds adaptively revealed as point clouds. CHAOS (WOODBURY, N.Y.) 2023; 33:123108. [PMID: 38048255 PMCID: PMC10697725 DOI: 10.1063/5.0178947] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2023] [Accepted: 11/01/2023] [Indexed: 12/06/2023]
Abstract
Steady states are invaluable in the study of dynamical systems. High-dimensional dynamical systems, due to separation of time scales, often evolve toward a lower dimensional manifold M. We introduce an approach to locate saddle points (and other fixed points) that utilizes gradient extremals on such a priori unknown (Riemannian) manifolds, defined by adaptively sampled point clouds, with local coordinates discovered on-the-fly through manifold learning. The technique, which efficiently biases the dynamical system along a curve (as opposed to exhaustively exploring the state space), requires knowledge of a single minimum and the ability to sample around an arbitrary point. We demonstrate the effectiveness of the technique on the Müller-Brown potential mapped onto an unknown surface (namely, a sphere). Previous work employed a similar algorithmic framework to find saddle points using Newton trajectories and gentlest ascent dynamics; we, therefore, also offer a brief comparison with these methods.
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Affiliation(s)
- A. Georgiou
- Department of Chemical and Biomolecular Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA
| | | | - J. M. Bello-Rivas
- Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, Maryland 21218, USA
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Bofill JM, Severi M, Quapp W, Ribas-Ariño J, Moreira IDPR, Albareda G. An algorithm to find the optimal oriented external electrostatic field for annihilating a reaction barrier in a polarizable molecular system. J Chem Phys 2023; 159:114112. [PMID: 37724726 DOI: 10.1063/5.0167749] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2023] [Accepted: 08/23/2023] [Indexed: 09/21/2023] Open
Abstract
The use of oriented external electric fields (OEEFs) to promote and control chemical reactivity has motivated many theoretical and computational studies in the last decade to model the action of OEEFs on a molecular system and its effects on chemical processes. Given a reaction, a central goal in this research area is to predict the optimal OEEF (oOEEF) required to annihilate the reaction energy barrier with the smallest possible field strength. Here, we present a model rooted in catastrophe and optimum control theories that allows us to find the oOEEF for a given reaction valley in the potential energy surface (PES). In this model, the effective (or perturbed) PES of a polarizable molecular system is constructed by adding to the original, non-perturbed, PES a term accounting for the interaction of the OEEF with the intrinsic electric dipole and polarizability of the molecular system, so called the polarizable molecular electric dipole (PMED) model. We demonstrate that the oOEEF can be established by locating a point in the original PES with unique topological properties: the optimal barrier breakdown or bond-breaking point (oBBP). The essential feature of the oBBP structure is the fact that this point maintains its topological properties for all the applied OEEFs, also for the unperturbed PES, thus becoming much more relevant than the commonly used minima and transition state structures. The PMED model proposed here has been implemented in an open access package and is shown to successfully predict the oOEEF for two processes: an isomerization reaction of a cumulene derivative and the Huisgen cycloaddition reaction.
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Affiliation(s)
- Josep Maria Bofill
- Departament de Química Inorgànica i Orgànica, Secció de Química Orgànica, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain
- Institut de Química Teòrica i Computacional, (IQTCUB), Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain
| | - Marco Severi
- Department of Chemistry G. Ciamician, University of Bologna, Via F. Selmi 2, 40126 Bologna, Italy
| | - Wolfgang Quapp
- Mathematisches Institut, Universität Leipzig, PF 100920, D-04009 Leipzig, Germany
| | - Jordi Ribas-Ariño
- Institut de Química Teòrica i Computacional, (IQTCUB), Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain
- Departament de Ciència de Materials i Química Física, Secció de Química Física, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain
| | - Ibério de P R Moreira
- Institut de Química Teòrica i Computacional, (IQTCUB), Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain
- Departament de Ciència de Materials i Química Física, Secció de Química Física, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain
| | - Guillermo Albareda
- Ideaded, Carrer de la Tecnologia, 35, 08840 Viladecans, Barcelona, Spain
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A catastrophe theory-based model for optimal control of chemical reactions by means of oriented electric fields. Theor Chem Acc 2023. [DOI: 10.1007/s00214-023-02959-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/10/2023]
Abstract
AbstractThe effect of oriented external electric fields (OEEF) on chemical reactivity has been studied theoretically and computationally in the last decades. A central goal in this research area is to predict the orientation and the smallest amplitude electric field that renders a barrierless chemical process with the smallest possible strength. Recently, a model to find the optimal electric field has been proposed and described (Bofill JM et al., J. Chem. Theory Comput. 18:935, 2022). We here proof that this model is based on catastrophe and optimum control theories. Based on both theories a technical treatment of the model is given and applied to a two-dimensional generic example that provides insight into its nature and capability. Finally, the model is applied to determine the optimal OEEF for the trans-to-cis isomerization of a [3]cumulene derivative.
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Bofill JM, Quapp W, Albareda G, Moreira IDPR, Ribas-Ariño J. Controlling Chemical Reactivity with Optimally Oriented Electric Fields: A Generalization of the Newton Trajectory Method. J Chem Theory Comput 2022; 18:935-952. [PMID: 35044173 DOI: 10.1021/acs.jctc.1c00943] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The use of oriented external electric fields (OEEF) as a tool to accelerate chemical reactions has recently attracted much interest. A new model to calculate the optimal OEEF of the least intensity to induce a barrierless chemical reaction path is presented. A suitable ansatz is provided by defining an effective potential energy surface (PES), which considers the unperturbed or original PES of the molecular reactive system and the action of a constant OEEF on the overall dipole moment of system. Based on a generalization of the Newton Trajectories (NT) method, it is demonstrated that the optimal OEEF can be determined upon locating a special point of the potential energy surface (PES), the so-called "optimal bond-breaking point" (optimal BBP), for which two different algorithms are proposed. At this point, the gradient of the original or unperturbed PES is an eigenvector of zero eigenvalue of the Hessian matrix of the effective PES. A thorough discussion of the geometrical aspects of the optimal BBP and the optimal OEEF is provided using a two-dimensional model, and numerical calculations of the optimal OEEF for a SN2 reaction and the 1,3-dipolar retrocycloaddition of isoxazole to fulminic acid plus acetylene reaction serve as a proof of concept. The knowledge of the orientation of optimal OEEF provides a practical way to reduce the effective barrier of a given chemical process.
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Affiliation(s)
- Josep Maria Bofill
- Departament de Química Inorgànica i Orgànica, Secció de Química Orgànica, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain.,Institut de Química Teòrica i Computacional, (IQTCUB), Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain
| | - Wolfgang Quapp
- Mathematisches Institut, Universität Leipzig, PF 100920, D-04009 Leipzig, Germany
| | - Guillermo Albareda
- Institut de Química Teòrica i Computacional, (IQTCUB), Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain.,Max Planck Institute for the Structure and Dynamics of Matter and Center for Free Electron Laser Science, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Ibério de P R Moreira
- Institut de Química Teòrica i Computacional, (IQTCUB), Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain.,Departament de Ciència de Materials i Química Física, Secció de Química Física, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain
| | - Jordi Ribas-Ariño
- Institut de Química Teòrica i Computacional, (IQTCUB), Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain.,Departament de Ciència de Materials i Química Física, Secció de Química Física, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain
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Quapp W, Bofill JM. Some Mathematical Reasoning on the Artificial Force Induced Reaction Method. J Comput Chem 2020; 41:629-634. [PMID: 31792984 DOI: 10.1002/jcc.26115] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/02/2019] [Revised: 11/01/2019] [Accepted: 11/04/2019] [Indexed: 11/07/2022]
Abstract
There are works of the Maeda-Morokuma group, which propose the artificial force induced reaction (AFIR) method (Maeda et al., J. Comput. Chem. 2014, 35, 166 and 2018, 39, 233). We study this important method from a theoretical point of view. The understanding of the proposers does not use the barrier breakdown point of the AFIR parameter, which usually is half of the reaction path between the minimum and the transition state which is searched for. Based on a comparison with the theory of Newton trajectories, we could better understand the method. It allows us to follow along some reaction pathways from minimum to saddle point, or vice versa. We discuss some well-known two-dimensional test surfaces where we calculate full AFIR pathways. If one has special AFIR curves at hand, one can also study the behavior of the ansatz. © 2019 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc.
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Affiliation(s)
- Wolfgang Quapp
- Leipzig University, Mathematisches Institut, Universität Leipzig, PF 100920, D-04009, Leipzig, Germany
| | - Josep Maria Bofill
- Universitat de Barcelona, Departament de Química Inorgànica i Orgànica, Universitat de Barcelona, and Institut de Química Teòrica i Computacional, Universitat de Barcelona, (IQTCUB), Martí i Franquès, 1, 08028, Barcelona, Spain
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Bofill JM, Ribas-Ariño J, Valero R, Albareda G, Moreira IDPR, Quapp W. Interplay between the Gentlest Ascent Dynamics Method and Conjugate Directions to Locate Transition States. J Chem Theory Comput 2019; 15:5426-5439. [PMID: 31433636 DOI: 10.1021/acs.jctc.8b01061] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
An algorithm to locate transition states on a potential energy surface (PES) is proposed and described. The technique is based on the GAD method where the gradient of the PES is projected into a given direction and also perpendicular to it. In the proposed method, named GAD-CD, the projection is not only applied to the gradient but also to the Hessian matrix. Then, the resulting Hessian matrix is block diagonal. The direction is updated according to the GAD method. Furthermore, to ensure stability and to avoid a high computational cost, a trust region technique is incorporated and the Hessian matrix is updated at each iteration. The performance of the algorithm in comparison with the standard ascent dynamics is discussed for a simple two dimensional model PES. Its efficiency for describing the reaction mechanisms involving small and medium size molecular systems is demonstrated for five molecular systems of interest.
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Affiliation(s)
| | | | | | - Guillermo Albareda
- Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science , Luruper Chaussee 149 , 22761 Hamburg , Germany
| | | | - Wolfgang Quapp
- Mathematisches Institut , Universität Leipzig , PF 100920 , D-04009 Leipzig , Germany
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Bofill JM, Quapp W. Calculus of variations as a basic tool for modelling of reaction paths and localisation of stationary points on potential energy surfaces. Mol Phys 2019. [DOI: 10.1080/00268976.2019.1667035] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- Josep Maria Bofill
- Institut de Química Teòrica i Computacional (IQTCUB), and Departament de Química Inorgànica i Orgànica, Secció de Química Orgànica, Universitat de Barcelona, Martí i Franquès, Barcelona, Spain
| | - Wolfgang Quapp
- Mathematisches Institut, Universität Leipzig, Leipzig, Germany
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9
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Affiliation(s)
- W. Quapp
- Mathematisches Institut, Universität Leipzig, Leipzig, Germany
| | - J. M. Bofill
- Departament de Química Inorgànica i Orgànica, Secció de Química Orgànica, and Institut de Química Teòrica i Computacional, (IQTCUB), Universitat de Barcelona, Barcelona, Spain
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Bofill JM, Ribas-Ariño J, García SP, Quapp W. An algorithm to locate optimal bond breaking points on a potential energy surface for applications in mechanochemistry and catalysis. J Chem Phys 2017; 147:152710. [PMID: 29055306 DOI: 10.1063/1.4994925] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023] Open
Abstract
The reaction path of a mechanically induced chemical transformation changes under stress. It is well established that the force-induced structural changes of minima and saddle points, i.e., the movement of the stationary points on the original or stress-free potential energy surface, can be described by a Newton Trajectory (NT). Given a reactive molecular system, a well-fitted pulling direction, and a sufficiently large value of the force, the minimum configuration of the reactant and the saddle point configuration of a transition state collapse at a point on the corresponding NT trajectory. This point is called barrier breakdown point or bond breaking point (BBP). The Hessian matrix at the BBP has a zero eigenvector which coincides with the gradient. It indicates which force (both in magnitude and direction) should be applied to the system to induce the reaction in a barrierless process. Within the manifold of BBPs, there exist optimal BBPs which indicate what is the optimal pulling direction and what is the minimal magnitude of the force to be applied for a given mechanochemical transformation. Since these special points are very important in the context of mechanochemistry and catalysis, it is crucial to develop efficient algorithms for their location. Here, we propose a Gauss-Newton algorithm that is based on the minimization of a positively defined function (the so-called σ-function). The behavior and efficiency of the new algorithm are shown for 2D test functions and for a real chemical example.
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Affiliation(s)
- Josep Maria Bofill
- Departament de Química Inorgànica i Orgànica, Secció de Química Orgànica, Universitat de Barcelona, and Institut de Química Teòrica i Computacional, Universitat de Barcelona (IQTCUB), Barcelona, Spain
| | - Jordi Ribas-Ariño
- Departament de Ciència de Materials i Química Física, Secció de Química Física, Universitat de Barcelona and Institut de Química Teòrica i Computacional, Universitat de Barcelona (IQTCUB), Barcelona, Spain
| | - Sergio Pablo García
- Departament de Ciència de Materials i Química Física, Secció de Química Física, Universitat de Barcelona and Institut de Química Teòrica i Computacional, Universitat de Barcelona (IQTCUB), Barcelona, Spain
| | - Wolfgang Quapp
- Mathematisches Institut, Universität Leipzig, PF 100920, D-04009 Leipzig, Germany
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Quapp W, Bofill JM, Ribas-Ariño J. Analysis of the Acting Forces in a Theory of Catalysis and Mechanochemistry. J Phys Chem A 2017; 121:2820-2838. [PMID: 28338327 DOI: 10.1021/acs.jpca.7b00022] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The theoretical description of a chemical process resulting from the application of mechanical or catalytical stress to a molecule is performed by the generation of an effective potential energy surface (PES). Changes for minima and saddle points by the stress are described by Newton trajectories (NTs) on the original PES. From the analysis of the acting forces we postulate the existence of pulling corridors built by families of NTs that connect the same stationary points. For different exit saddles of different height we discuss the corresponding pulling corridors; mainly by simple two-dimensional surface models. If there are different exit saddles then there can exist saddles of index two, at least, between. Then the case that a full pulling corridor crosses a saddle of index two is the normal case. It leads to an intrinsic hysteresis of such pullings for the forward or the backward reaction. Assuming such relations we can explain some results in the literature. A new finding is the existence of roundabout corridors that can switch between different saddle points by a reversion of the direction. The findings concern the mechanochemistry of molecular systems under a mechanical load as well as the electrostatic force and can be extended to catalytic and enzymatic accelerated reactions. The basic and ground ansatz includes both kinds of forces in a natural way without an extra modification.
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Affiliation(s)
- Wolfgang Quapp
- Mathematisches Institut, Universität Leipzig , PF 100920, D-04009 Leipzig, Germany
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The variational nature of the gentlest ascent dynamics and the relation of a variational minimum of a curve and the minimum energy path. Theor Chem Acc 2015. [DOI: 10.1007/s00214-015-1767-7] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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Pulkkinen S. Ridge-based method for finding curvilinear structures from noisy data. Comput Stat Data Anal 2015. [DOI: 10.1016/j.csda.2014.08.007] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Gadzhiev OB, Sennikov PG, Petrov AI, Kachel K, Golka S, Gogova D, Siche D. The role of NH3 and hydrocarbon mixtures in GaN pseudo-halide CVD: a quantum chemical study. J Mol Model 2014; 20:2473. [PMID: 25316343 DOI: 10.1007/s00894-014-2473-4] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2014] [Accepted: 09/21/2014] [Indexed: 12/01/2022]
Abstract
The prospects of a control for a novel gallium nitride pseudo-halide vapor phase epitaxy (PHVPE) with HCN were thoroughly analyzed for hydrocarbons-NH3-Ga gas phase on the basis of quantum chemical investigation with DFT (B3LYP, B3LYP with D3 empirical correction on dispersion interaction) and ab-initio (CASSCF, coupled clusters, and multireference configuration interaction including MRCI+Q) methods. The computational screening of reactions for different hydrocarbons (CH4, C2H6, C3H8, C2H4, and C2H2) as readily available carbon precursors for HCN formation, potential chemical transport agents, and for controlled carbon doping of deposited GaN was carried out with the B3LYP method in conjunction with basis sets up to aug-cc-pVTZ. The gas phase intermediates for the reactions in the Ga-hydrocarbon systems were predicted at different theory levels. The located π-complexes Ga…C2H2 and Ga…C2H4 were studied to determine a probable catalytic activity in reactions with NH3. A limited influence of the carbon-containing atmosphere was exhibited for the carbon doping of GaN crystal in the conventional GaN chemical vapor deposition (CVD) process with hydrocarbons injected in the gas phase. Our results provide a basis for experimental studies of GaN crystal growth with C2H4 and C2H2 as auxiliary carbon reagents for the Ga-NH3 and Ga-C-NH3 CVD systems and prerequisites for reactor design to enhance and control the PHVPE process through the HCN synthesis.
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Affiliation(s)
- Oleg B Gadzhiev
- G.G. Devyatykh Institute of Chemistry of High-Purity Substances, Russian Academy of Sciences, 49 Troponina St., Nizhny Novgorod, 603950, Russia,
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Locating saddle points of any index on potential energy surfaces by the generalized gentlest ascent dynamics. Theor Chem Acc 2014. [DOI: 10.1007/s00214-014-1510-9] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Bofill JM, Quapp W, Caballero M. Locating transition states on potential energy surfaces by the gentlest ascent dynamics. Chem Phys Lett 2013. [DOI: 10.1016/j.cplett.2013.07.074] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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