Global Mapping of Equilibrium and Transition Structures on Potential Energy Surfaces by the Scaled Hypersphere Search Method:  Applications to ab Initio Surfaces of Formaldehyde and Propyne Molecules

Abstract

Technical details of a new global mapping technique for finding equilibrium (EQ) and transition structures (TS) on potential energy surfaces (PES), the scaled hypersphere search (SHS) method (Ohno, K.; Maeda, S. Chem. Phys. Lett. 2004, 384, 277), are presented. On the basis of a simple principle that reaction pathways are found as anharmonic downward distortions of PES around an EQ point, the reaction pathways can be obtained as energy minima on the scaled hypersphere surface, which would have a constant energy when the potentials are harmonic. Connections of SHS paths between each EQ are very similar to corresponding intrinsic reaction coordinate (IRC) connections. The energy maximum along the SHS path reaches a region in close proximity to the TS of the reaction pathway, and the subsequent geometry optimization from the SHS maximum structure easily converges to the TS. The SHS method, using the one-after-another algorithm connecting EQ and TS, considerably reduces the multidimensional space to be searched to certain limited regions around the pathways connecting each EQ with the neighboring TS. Applications of the SHS method have been made to ab initio surfaces of formaldehyde and propyne molecules to obtain systematically five EQ and nine TS for formaldehyde and seven EQ and 32 TS for propyne.

Sampling reactive pathways with random walks in chemical space: Applications to molecular dissociation and catalysis

“…18,19 Over the last few decades, a wide variety of computational strategies have been developed specifically with the purpose of determining reaction pathways and the associated energetic barriers. For example, the Nudged Elastic Band (NEB) method 20,21 and related approaches, [22][23][24] the zero-and finite-temperature string (FTS) methods, 25,26 and the growing string approach 27 all aim to search for a reaction path given an initial guess path connecting specified reactant and product configurations; the constraint of generating a good initial guess is removed in methods such as Gradient Extremal Following (GEF), 28,29 Scaled Hypersphere Searching (SHS [30][31][32], and reduced gradient following (RGF). 33 Rather than focussing on the search for single reaction paths, methods such as transition path sampling [34][35][36][37][38][39][40][41][42][43] and Onsager-Machlup path sampling 44,45 can instead generate ensembles of reaction pathways; subsequent analysis of the path ensemble, for example, by calculation of commitor probabilities, allows further identification of important features associated with transition states (TSs).…”

Analyses of bifurcation of reaction pathways on a global reaction route map: A case study of gold cluster Au5

“…[2][3][4] A concept of global reaction route mapping (GRRM) has been established as the approach to explore chemical reaction pathways automatically through a combination of ADDF and IRC computations. In this paper, the "global map" stands for a map of IRC paths obtained by the ADDF method.…”

The effect of Mg2+ incorporation on the structure of calcium carbonate clusters: investigation by the anharmonic downward distortion following method

“…Thus, the large-ADD (l-ADD) technique is available for fast searches in ADDF, which is expected to explore the low energy structures along low barrier pathways 31 ; it has been successfully applied to various systems 27,28,31 and is applied also in the present study. The methods used to efficiently find maximal ADD directions in multi-dimensional potential-energy surfaces and the methods used to effectively choose l-ADDs from various ADDs have been described in previous papers [21][22][23][24]31 .…”

“…Therefore, in the present study, we use the anharmonic downward distortion following (ADDF) method [21][22][23][24] to make quantum chemical calculations intended to investigate the stable structure of Mg-containing calcium carbonate clusters. The ADDF method was recently developed to make an automated global exploration for reaction pathways on the quantum chemical potential energy surface (PES) of a given chemical formula possible without any assumptions of initial structures and reaction routes.…”