Search for stationary points on multidimensional surfaces

Khait, Yu. G.; Puzanov, Yu. V.

doi:10.1016/s0166-1280(97)00036-5

Cited by 10 publications

(10 citation statements)

References 33 publications

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“…The algorithms for locating TSs can be generally divided into two classes, namely, (i) the chain-of-states methods and (ii) the surface-walking methods. The former class locates the TS by simultaneously optimizing a few connected structure images on the potential energy surface (PES) to identify the reaction path. − The latter class requires only one image on the PES, and local information such as the gradient (force) or the second derivative (Hessian) of the PES is utilized to manipulate the image toward the TS. − Despite the huge progress made in the field, the current theoretical methods for simulating reaction pathways are still not sufficiently efficient, and both computational power and human experiences are highly demanding. Specifically, the chain-of-states methods require a knowledge of the exact final state, and the success of the surface-walking method relies heavily on the input (TS-like) structures.…”

Section: Introductionmentioning

confidence: 99%

“…Among all of the methods for TS searching, the Hessian-involved methods such as the P-RFO approach are perhaps the most efficient when the (analytic) Hessian is cheaply available. − By modifying and following the eigenvalue of the Hessian (eigenvector following), these methods can maximize energy in one degree of freedom while minimize energy in all the others. To reduce the computational cost in calculating the Hessian, the Quasi-Newton-based methods have been utilized to update the Hessian, such as Powell-symmetric-Broyden (PSB) and Symmetric rank 1 (Murtagh–Sargent), − and the hybrid approach developed by Bofill. − In practice, a constraint on the step length is often implemented to deal with the overstepping problem .…”

Section: Introductionmentioning

confidence: 99%

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Constrained Broyden Dimer Method with Bias Potential for Exploring Potential Energy Surface of Multistep Reaction Process

Shang

Liu

2012

J. Chem. Theory Comput.

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To predict the chemical activity of new matter is an ultimate goal in chemistry. The identification of reaction pathways using modern quantum mechanics calculations, however, often requires a high demand in computational power and good chemical intuition on the reaction. Here, a new reaction path searching method is developed by combining our recently developed transition state (TS) location method, namely, the constrained Broyden dimer method, with a basin-filling method via bias potentials, which allows the system to walk out from the energy traps at a given reaction direction. In the new method, the reaction path searching starts from an initial state without the need for preguessing the TS-like or final state structure and can proceed iteratively to the final state by locating all related TSs and intermediates. In each elementary reaction step, a reaction direction, such as a bond breaking, needs to be specified, the information of which is refined and preserved as a normal mode through biased dimer rotation. The method is tested successfully on the Baker reaction system (50 elementary reactions) with good efficiency and stability and is also applied to the potential energy surface exploration of multistep reaction processes in the gas phase and on the surface. The new method can be applied for the computational screening of new catalytic materials with a minimum requirement of chemical intuition.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Constrained Broyden Dimer Method with Bias Potential for Exploring Potential Energy Surface of Multistep Reaction Process

Shang

Liu

2012

J. Chem. Theory Comput.

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“…Here, there are two commonly used possibilities to select the diagonal matrix elements: an uniform shift or individual shifts for each degree of freedom. The Restricted Step Rational Function Optimization (RS‐RFO), Augmented Hessian, stabilized Newton‐Raphson, and Trust Radius Newton methods are used the uniform shift computed in a way that the final step lies inside the “trust‐region,” that is,:

| | Δ {boldq}^{λ} | | \leq R .

…”

Section: Methodsmentioning

confidence: 99%

A new module for constrained multi‐fragment geometry optimization in internal coordinates implemented in the MOLCAS package

2013

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A parallel procedure for an effective optimization of relative position and orientation between two or more fragments has been implemented in the MOLCAS program package. By design, the procedure does not perturb the electronic structure of a system under the study. The original composite system is divided into frozen fragments and internal coordinates linking those fragments are the only optimized parameters. The procedure is capable to handle fully independent (no border atoms) fragments as well as fragments connected by covalent bonds. In the framework of the procedure, the optimization of relative position and orientation of the fragments are carried out in the internal "Z-matrix" coordinates using numerical derivatives. The total number of required single points energy evaluations scales with the number of fragments rather than with the total number of atoms in the system. The accuracy and the performance of the procedure have been studied by test calculations for a representative set of two- and three-fragment molecules with artificially distorted structures. The developed approach exhibits robust and smooth convergence to the reference optimal structures. As only a few internal coordinates are varied during the procedure, the proposed constrained fragment geometry optimization can be afforded even for high level ab initio methods like CCSD(T) and CASPT2. This capability has been demonstrated by applying the method to two larger cases, CCSD(T) and CASPT2 calculations on a positively charged benzene lithium complex and on the oxygen molecule interacting to iron porphyrin molecule, respectively.

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Section: Introductionmentioning

confidence: 99%

“…As a result, these methods are much less demanding in computational power. Belonging to this category are the methods, such as the partitioned rational function optimizer (P-RFO), [12][13][14][15] the hybrid eigenvector following, 16,17 the dimer, [18][19][20][21] and the bond-length constrained minimization methods. 22,23 Among all the methods in searching for TS, the Hessian involved methods, such as the P-RFO approach, are perhaps the most efficient when the (analytic) Hessian is cheaply available.…”

Section: Introductionmentioning

confidence: 99%

Constrained Broyden Minimization Combined with the Dimer Method for Locating Transition State of Complex Reactions

Shang

Liu

2010

J. Chem. Theory Comput.

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To determine transition state (TS) and, thus, to predict chemical activity has been a challenging topic in theoretical simulations of chemical reactions. In particular, with the difficulty to compute the second derivative of energy (Hessian) in modern quantum mechanics packages with a non-Gaussian basis set, the location usually involves a high demand in computational power and lacks stability in the algorithm, especially for complex reaction systems with many degrees of freedom. Here, an efficient TS searching method is developed by combining the constrained Broyden minimization algorithm with the dimer method that was first proposed by Henkelman and Jo ´nsson. In the new method, the rotation of the dimer needs only one energy and gradient calculation for determining a rotation angle; the translation of the dimer is continually carried out until a termination criterion is met, and the translational force parallel to the dimer direction is damped to optimize the searching trajectory. Based on our results of the Baker reaction system and of a heterogeneous catalytic reaction, our method is shown to increase the efficiency significantly and is also more stable in finding TSs.

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Search for stationary points on multidimensional surfaces

Cited by 10 publications

References 33 publications

Constrained Broyden Dimer Method with Bias Potential for Exploring Potential Energy Surface of Multistep Reaction Process

Constrained Broyden Dimer Method with Bias Potential for Exploring Potential Energy Surface of Multistep Reaction Process

A new module for constrained multi‐fragment geometry optimization in internal coordinates implemented in the MOLCAS package

Constrained Broyden Minimization Combined with the Dimer Method for Locating Transition State of Complex Reactions

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