Linear and Quadratic Synchronous Transit

A related idea is used in the Line Then Plane (LTP) algorithm where the constrained optimization is done in the hyperplane perpencheular to the interpolation line between the two end-points, rather than on a hypersphere. 

Illustration of the saddle method. Energy minima on the hyperspheres are denoted 

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Figure 14.5 Illustration of the linear and quadratic synchronous transit methods. Energy maxima and minima are denoted by and , respectively...

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... 

In HyperChem, two different methods for the iocation of transition structures are available. The eigenvector following method is appropriate for unimolecuiar processes or any molecular system where a natural vibrational mode of the system tends to lead to a transition state. Synchronous transit methods are especially useful when reactant and product systems are very different, or In cases where It Is desirable to specify a sequence of structures intermediate between reactants and products. Both linear and quadratic synchronous transit methods have been implemented in HyperChem. 

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. 

Fig. 10.5. Model potential energy surface illustrating linear synchronous transit (LST) and quadratic synchronous transit (QST) paths (from Ref. [72] with permission).

Fig. 4. The linear synchronous transit (LST) and quadratic synchronous transit (QST) methods for finding transition structures R, reactants P, prc ucts TS, true transition structure 1, maximum on LST path (full curveV, 2, minimum perpendicular to LST path 3, maximum on QST path (broken curve). The model surface is constructed from two...

The linear synchronous transit (LST) and quadratic synchronous transit (QST) approaches may be useful for getting closer to the transition structure. In the LST approach, the reaction path between reactants and products is approximated by a straight line (usually in distance matrix space or in internal coordinates) and a maximum is found along this line. Figure 3 shows some examples of LST and QST paths. The... 

IlyperChem supplies two differeiii types or algorithms for transition state search eigenvector I ollowing and synchronous transit (linear and quadratic search ). 

HyperChein has two synch ron ons transit meth ods im piemen ted. The linear synchronous transit method (LST) searches for a maximum along a linear path between reactants and products. It may happen that this method will end up with a structure having two or more negative eigenvalues. The quadratic synchronous transit method (QSTlisan improvement of LST approach and searches for a maximum along a parabola connecting reactants and products, and for a minimum in all directions perpendicular to the parabola. 

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