Quadratic Synchronous Transit optimization

It uses a linear or quadratic synchronous transit approach to get closer to the quadratic region of the transition state and then uses a quasi-Newton or eigenvalue-following algorithm to complete the optimization. 

Illustrating the Concepts 264 11.1 Geometry Convergence 264 11.1.1 Ah Initio Methods 264 11.1.2 DFT Methods 267 14.4 Choice of Coordinates 322 14.5 Transition Structure Optimization 327 14.5.1 Methods Based on Interpolation Between Reactant and Product 327 14.5.2 Linear and Quadratic Synchronous Transit 328... 

One-structure interpolation methods coordinate driving, linear and quadratic synchronous transit, and sphere optimization... 

Gradient methods are very efficient for minimizations however, to locate transition structures they must be modified or constrained to overcome the problems caused by the Hessian not being positive-definite. One approach is to partition the AT-dimensional optimization into a one-dimensional space for maximization, and an (N — l)-dimensional space for minimization. This partitioning in effect chooses a transition vector. The transition vector may be fixed, or may be allowed to vary in a restricted manner (e.g. according to a quadratic synchronous transit path). The search for a maximum in the... 

For D3, the manually-optimized transition state structure was refined using gradient optimization procedures and Quadratic Synchronous Transit (QST) techniques force constant matrix calculations were also performed to classify various points along the reaction path. For D3, all positive force constants, and thus, proper local minima, were found for the reactants, addition complex, and insertion product a single negative force constant was found for the 3-21G TS structures, thus verifying a proper transition state. The manually-optimized transition state has not been refined nor has force constant matrix analyses been performed for the KOH-D4 reaction path. 

BFGS = Broyden - Fletcher - Goldfarb - Shanno DFP = Davidson-Fletcher-Powell EF = eigenvector following GDIIS = geometry optimization by direct inversion of the iterative subspace LST = linear synchronous transit QST = quadratic synchronous transit RFO = rational function optimization. 

CPR = conjugate peak refinement GDIIS = geometry direct inversion in the iterative subspace GE = gradient extremal LST = linear synchronous transit LTP = line then plane LUP = locally updated planes NR = Newton-Raph-son P-RFO = partitioned rational function optimization QA = quadratic approximation QST = quadratic synchronous transit SPW = self-penalty walk STQN = synchronous transit-guided quasi-Newton TRIM = trust radius image minimization TS = transition structure. 

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