Eigenvector following

HyperChem supplies two different types or algorithms for transition state search eigenvector following and synchronous transit (linear and quadratic search). 

HyperChem uses the eigenvector following method described in Baker, J, An Algorithm for the Location of Transition States,  

---

I he eigenvector-following (or Hessian mode) method implemented in HyperChem is based on an effieien t quasi-Newton like algorithm for loca tin g tran sitiori states, wh ieh can locate tran si-tion states for alternative rearran gern eri t/dissoeiation reactions, even when startin g from th e wron g regio n on th e poten tial en ergy surface. 

The Eigenvector Following method is in some ways similar to the Newton-Raph son method. Instead of explicitly calculating the second derivatives, it uses a diagonalized Hessian matrix to implicitly give the second derivatives of energy with respect to atomic displacements. The initial guess is computed empirically. 

HyperChem offers a Reaction Map facility under the Setup menu. This is needed for the synchronous transit method to match reactants and products, and depending on X (a parameter having values between 0 and 1, determining how far away from reactants structures a transition structure can be expected) will connect atoms in reactants and products and give an estimated or expected transition structure. This procedure can also be used if the eigenvector following method is later chosen for a transition state search method, i.e., if you just want to get an estimate of the transition state geometry. 

In HyperChem, two different methods for the location of transition structures are available. Both arethecombinationsofseparate algorithms for the maximum energy search and quasi-Newton methods. The first method is the eigenvector-following method, and the second is the synchronous transit method. 

A recent development uses the quadratic synchronous transit approach to get close to a transition state, and then a Newton or eigenvector-following algorithm to complete the optimization. It performs optimizations in redundant internal coordinates. The key reference is due to Peng, Ayala and Schlegel. 

Topological analysis of X-ray protein relative density maps utilizing the eigenvector following method... 

---