Transition state structures and reaction profiles from constrained optimization procedure. Implementation in the framework of density functional theory

Abstract

A method for finding the transition structures (TS) based on constrained optimization techniques is proposed. The algorithm can be considered as a step-by-step walking uphill process along the minimum energy path, followed by a refining procedure of TS parameters in the saddle point vicinity. By accounting for the constraint conditions in a straightforward manner, it is possible to use efficient quasi-Newton algorithms at every geometry reoptimization step and to manage the moving direction in a reaction valley. This approach may be suitable in the framework of density functional theory. Tests including a potential energy surface model, HNC→HCN and N2H2 trans–cis isomerizations and LiBH4 rearrangements are given. The possible future development of the approach is discussed.

Building Roadmaps of Minima and Transitions in Visual Models

“…owing to looping. Space sweeping methods [10,1,2,4,30,19,28,17] guarantee more systematic progress by using a moving potential or hypersurface to sweep candidate points though the space in such a way that they often pass through transition states. Crippen & Sheraga's early method [10] builds an uphill path by stepping along a prespecified direction and minimizing in the hyperplane orthogonal to the direction at each step.…”

“…However such methods do exist in the computational chemistry / solid state physics community, where transition states are central to the theory of chemical reactions 1 . Both of our classes of transition-state-locating algorithms have roots in chemistry, and both are based on modified forms of local Newton minimization.…”

“…§7 illustrates the methods on a 2D toy problem. §8 presents our main experiments on locating minima during monocular 1 Atomic assemblies can be modeled in terms of the potential energy induced by interactions among their atoms, i.e. by an energy function defined over the high-dimensional configuration space of the atoms' relative positions.…”

Anharmonic Downward Distortion Following for Automated Exploration of Quantum Chemical Potential Energy Surfaces

“…This technique for searching ADDs on the scaled hypersphere is called scaled hypersphere search (SHS) method. Although some methods also use hyperspheres, 28,68,126 the purpose of the use of hypersphere in the SHS method is unique, that is, finding ADDs.…”

“…The artificial force induced reaction (AFIR) method has been developed for finding TSs for associative pathways among two or more components efficiently. 6567 Some approaches, such as the sphere optimization technique, 68 the iso-potential contour following method, 69 and the chemical flooding method, 70 find only a single path starting from a local minimum, where this single path often corresponds to the lowest barrier path. Moreover, there is a rigorous, deterministic approach called ¡BB global optimization method which has been applied to triatomic molecules and the conformational search in simple peptides.…”