Conjugate Peak Refinement

Figure 5,30 reprinted from Chemical Physical Letters, 194, Fischer S and M Karplus. Conjugate Peak Refinement An Algorithm for Finding Reaction Paths and Accurate Transition States in Systems with Many Degrees of Freedom. 252-261, 1992, with permission from Elsevier Science. 

Figure 9 The refinement of an initial straight line path to a smooth transition pathway using the conjugate peak refinement algorithm. The initial guess is a straight line path. That path is refined by the addition of an intermediate point (the long-stemmed arrow). Two additional intermediates are added to create a path of three intermediates before four more intermediates are inserted. The process can be continued until the desired level of smoothness m the transition pathway is obtained.

The Conjugate Peak Refinement (CPR) method may be eonsidered as a dynamical version of the chain method, where points are added or removed based on a sequenee of maximizations along line segments and minimizations along the conjugate directions. 

An alternative means of calculating reaction pathways is employed in so-called global methods. These methods treat the entire path as a succession of points [71] which are found simultaneously. Methods of this type (for example the conjugate peak refinement algorithm [72], available in the TRAVEL module of CHARMM, which has the advantage of requiring only first derivatives of the energy) have been used to determine reaction paths in a number of proteins [4, 73]. 

Using the conjugate peak refinement method, Fischer et al. [20a] calculated the reaction path of the motion of the biological water molecules. They also compared the computed transition state and activation energy to those in ice. Their calculation shows that the motion of the water molecules, buried in the proteins, involves exchange of two water hydrogen atoms and involves two successive rotations around orthogonal axes. 

Multi-structure interpolation methods chain, locally updated planes, self-penalty walk, conjugate peak refinement and nudged elastic band... 

Minimum energy paths and their TSs were calculated using the conjugate peak refinement (CPR) method [61] as implemented in the TREK module of CHARMM. 

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. 

S. Fischer and M. Karpins. Conjugate peak refinement An algorithm for finding reaction paths and accurate transition states in systems with many degrees of freedom. Chem. Phys. Lett. 194,1992, 252-261. 

---