A Quadratically-Converging Nudged Elastic Band Optimizer

Bohner, Matthias U.; Meisner, Jan; Kästner, Johannes

doi:10.1021/ct400323z

Cited by 19 publications

(26 citation statements)

References 28 publications

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“…The images along the NEB path were optimized to the minimum energy path (MEP) through a force projection procedure, in which the potential forces act perpendicular to the path whereas the spring forces act along the path. [31][32][33][34] Free Energy Calculations along the NEB Reaction Path. The potential of mean 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 7 force (PMF) along the above NEB optimized path, min r v , was obtained by computing the free energy difference,…”

Section: Qm/mmmentioning

confidence: 99%

QM/MM Investigation of ATP Hydrolysis in Aqueous Solution

2015

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Adenosine-5'-triphosphate (ATP) hydrolysis represents a most important reaction in biology. Despite extensive research efforts, the mechanism for ATP hydrolysis in aqueous solution still remains under debate. Previous theoretical studies often predefined reaction coordinates to characterize the mechanism for ATP hydrolysis in water with Mg(2+) by evaluating free energy profiles through these preassumed reaction paths. In the present work, a nudged elastic band method is applied to identify the minimum energy path calculated with a hybrid quantum mechanics and molecular mechanics approach. Along the reaction path, the free energy profile was obtained to have a single transition state and the activation energy of 32.5 kcal/mol. This transition state bears a four-centered structure that describes a concerted nature of the reaction. In the More-O'Ferrall-Jencks diagram, the results show that the reaction proceeds through a concerted path before the system reaches the transition state and along an associative path after the transition state. In addition, the calculated reaction free energy is -7.0 kcal/mol, in good agreement with experiment, capturing the exothermic feature of MgATP(2-) hydrolysis in aqueous solution, whereas the reaction was often shown to be endothermic in the previous theoretical studies. As Mg(2+) is required for ATP hydrolysis in cells, its role in the reaction is also elucidated.

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Section: Qm/mmmentioning

confidence: 99%

QM/MM Investigation of ATP Hydrolysis in Aqueous Solution

2015

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“…Previously, 43 we have shown that the analytic Jacobian of the NEB force, the matrix of derivatives of the NEB force with respect to the coordinates, can be used to significantly improve the convergence of a NEB minimization in a Newton-Raphson-like manner.…”

Section: Nudged Elastic Band In the Free Energy Surfacementioning

confidence: 99%

“…It contains 6 components corresponding to translation and rotation. 43 Thus, it is singular and cannot directly be inverted to form a Newton-Raphson step of the form…”

Section: Nudged Elastic Band In the Free Energy Surfacementioning

confidence: 99%

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Nudged-elastic band used to find reaction coordinates based on the free energy

Bohner

Zeman

Smiatek

et al. 2014

The Journal of Chemical Physics

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Transition paths characterize chemical reaction mechanisms. In this paper, we present a new method to find mean reaction paths based on the free energy. A nudged elastic band (NEB) is optimized using gradients and Hessians of the free energy, which are obtained from umbrella integration. The transition state can be refined by a Newton-Raphson search starting from the highest point of the NEB path. All optimizations are done using Cartesian coordinates. Independent molecular dynamics (MD) runs are performed at each image used to discretize the path. This makes the method intrinsically parallel. In contrast to other free energy methods, the algorithm does not become more expensive when including more degrees of freedom in the active space. The method is applied to the alanine-dipeptide as a test case and compared to pathways that have been derived from metadynamics and forward flux sampling.

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“…An approach by Bohner et.al. 8 for removing rotation and translation from an NEB calculation relies on modifying the energy minimization algorithm by eliminating the six 5 smallest eigenvalues of the Jacobian matrix of NEB forces. This approach has good convergence properties but is computationally quite demanding since it requires finding the eigenvalues at each iteration.…”

Section: Introductionmentioning

confidence: 99%

Removing External Degrees of Freedom from Transition-State Search Methods using Quaternions

Melander¹,

Laasonen²,

Jónsson

2015

J. Chem. Theory Comput.

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In finite systems, such as nanoparticles and gas-phase molecules, calculations of minimum energy paths (MEPs) connecting initial and final states of transitions as well as searches for saddle points are complicated by the presence of external degrees of freedom, such as overall translation and rotation. A method based on quaternion algebra for removing the external degrees of freedom is described here and applied in calculations using two commonly used methods: the nudged elastic band (NEB) method for MEPs and the DIMER method for finding the minimum mode in minimum mode following searches of first-order saddle points. With the quaternion approach, fewer images in the NEB are needed to represent MEPs accurately. In both NEB and DIMER calculations of finite systems, the number of iterations required to reach convergence is significantly reduced. The algorithms have been implemented in the Atomic Simulation Environment (ASE) open source software.

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A Quadratically-Converging Nudged Elastic Band Optimizer

Cited by 19 publications

References 28 publications

QM/MM Investigation of ATP Hydrolysis in Aqueous Solution

QM/MM Investigation of ATP Hydrolysis in Aqueous Solution

Nudged-elastic band used to find reaction coordinates based on the free energy

Removing External Degrees of Freedom from Transition-State Search Methods using Quaternions

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