Locating saddle points of any index on potential energy surfaces by the generalized gentlest ascent dynamics

Quapp, Wolfgang; Bofill, Josep María

doi:10.1007/s00214-014-1510-9

Cited by 15 publications

(20 citation statements)

References 34 publications

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“…[22,31,32] We use the coordinate systems of internal coordinates where the curvilinear metric has to be included in the GAD formulas. The GAD method is a "growing string" method for the exploration of a PES like following an NT.…”

Section: Discussionmentioning

confidence: 99%

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Embedding of the saddle point of index two on the PES of the ring opening of cyclobutene

Quapp

Bofill

2015

Int. J. Quantum Chem.

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The ring opening of cyclobutene is characterized by a competition of the two different pathways: a usual pathway over a saddle of index one (SP 1 ) along the conrotatory behavior of the end groups, as well as a "forbidden" pathway over a saddle point of index two (SP 2 ) along the disrotatory behavior of the end CH 2 groups. We use the system of ordinary differential equations for the method of the gentlest ascent dynamics (GAD) to determine saddle points of the potential energy surface (PES) of the ring opening of cyclobutene to cis-butadiene. We apply generalized GAD formulas for the search of a saddle point of index two. To understand the relation of the different regions of the PES (around minimums, around SPs of index one or two) we also calculate valley-ridge inflection (VRI) points on the PES using Newton trajectories (NT). VRIs and the corresponding singular NTs subdivide the regions of "attraction" of the different SPs. We calculate the connections of the SP 2 (in its different symmetry versions) with different SPs of index one of the PES by different "reaction pathways." We compare the possibilities of the tool of the GAD curves for the exploration of PESs with these of NT. The barrier of the disrotatory SP 2 is somewhat higher than the barrier of the conrotatory SP 1 , however, pathways across the slope to the SP 2 open additional reaction valleys. IntroductionMathematics has had a profound impact on science, providing a means to understand the world around us in unprecedented ways.[1] With the advantage of the computer age, the subject of modelization has hugely grown in importance. In particular, over the last decades significant advances in our understanding of the world of chemistry have culminated in the development of a very large set of concepts. Some of these concepts are the potential energy surface (PES) [2][3][4] and the chemical reaction path (RP) [5] being the basic concepts for the theories of chemical dynamics and chemical transformations. The PES is a continuous function of the coordinates of the nuclei over an IR N , thus it is an N-dimensional hypersurface. It should have continuous derivatives of at least second order for our treatments. If Cartesian coordinates are used, then N53 n, however, we may also use N53 n26 nonredundant, internal coordinates for an n-atomic molecule. The PES can be seen as formally divided in catchments associated with local minima.[2] For such a picture, one has in mind steepest descent (SD) curves. The first order saddle points or transition states (TSs) are located at the deepest points of the boundary of the basins. TSs and minima correspond to stationary points of the PES. Two adjacent minima of the PES can be connected through a TS via a continuous curve in the N-dimensional coordinate space, describing the coordinates of the nuclei. The curve characterizes a RP. The concept of the RP has found a widespread use in descriptions of reaction mechanisms, which are based on geometrical rearrangements of the atoms comprising a given chemical system. [6] Mor...

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Section: Discussionmentioning

confidence: 99%

“…[31] The behavior of the GAD concept was studied for the isomerization of the radical, CH 3 concerted, see also elsewhere. [32] Recently, an application of the GAD to Physical Chemistry is demonstrated for point defect activity on a surface. [24,33] We will apply GAD to a single molecule in the empty space.…”

Section: Full Paper Wwwq-chemorgmentioning

confidence: 99%

Embedding of the saddle point of index two on the PES of the ring opening of cyclobutene

Quapp

Bofill

2015

Int. J. Quantum Chem.

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“…In 2011, E and Zhou [58] proposed the so-called Gentlest Ascent Dynamics (GAD) method that reformulates the procedure of uphill walking from a minimum basin through a set of ordinary differential equations whose solutions converge to first index saddle points [14,[59][60][61][62][63]65]. The set of equations that governs the GAD is…”

Section: Gentlest Ascent Dynamicsmentioning

confidence: 99%

Calculus of variations as a basic tool for modelling of reaction paths and localisation of stationary points on potential energy surfaces

Bofill

Quapp

2019

Molecular Physics

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The theory of calculus of variations is a mathematical tool which is widely used in different scientific areas in particular in physics and chemistry. This theory is strongly related with optimization. In fact the former seeks to optimize an integral related with some physical magnitude over some space to an extremum by varying a function of the coordinates. On the other hand reaction paths and potential energy surfaces, in particular their stationary points, are the basis of many chemical theories, in particular reactions rate theories. We present a review where it is gathered together the variational nature of many types of reaction paths: steepest descent, Newton trajectories, artificial force induced reaction (AFIR) paths, gradient extremals, and gentlest ascent dynamics (GAD) curves. The variational basis permits to select the best optimization technique in order to locate important theoretical objects on a potential energy surface.

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“…, where the superscript T means transposition. The equations that describe the GAD method are [9][10][11][12][13][14]:…”

Section: The Variational Nature Of the Gentlest Ascent Dynamics Rmentioning

confidence: 99%

“…It has been shown that the improved ART converges quadratically to the saddle point along the eigenmode of negative curvature while it converges linearly in perpendicular directions. More recently it has been proposed the gentlest ascent dynamics (GAD) [9][10][11][12][13][14]. Also based on the eigenmode philosophy, it consists of a set of dynamic equations whose solutions converge to saddle points.…”

Section: Introductionmentioning

confidence: 99%

Exploring potential energy surfaces with gentlest ascent dynamics in combination with the shrinking dimer method and Newtonian dynamics

et al. 2018

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We revisit the so-called Gentlest Ascent Dynamics reaction path model for finding saddle points of any index in multidimensional potential-energy surfaces. The variational nature of the method is analyzed in detail and an algorithm for the integration of its equations of motion is proposed based on the optimization-based shrinking dimer method. By means of three different two-dimensional model potentialenergy surfaces, we argue that the combination of the proposed method with Newtonian (dissipative) dynamics could lead to a practical scheme for the exhaustive exploration of potential-energy landscapes. ± Dedicated to the memory of Professor Claudio María Zicovich-Wilson.

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Locating saddle points of any index on potential energy surfaces by the generalized gentlest ascent dynamics

Cited by 15 publications

References 34 publications

Embedding of the saddle point of index two on the PES of the ring opening of cyclobutene

Embedding of the saddle point of index two on the PES of the ring opening of cyclobutene

Calculus of variations as a basic tool for modelling of reaction paths and localisation of stationary points on potential energy surfaces

Exploring potential energy surfaces with gentlest ascent dynamics in combination with the shrinking dimer method and Newtonian dynamics

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