Eigenvector Following optimization

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. 

The semi-empirical molecular orbital calculation software MOPAC in the CAChe Work System for Windows ver. 6.01 (Fujitsu, Inc.) was used in all of calculations for optimization of geometry by the Eigenvector Following method, for search of potential energies of various geometries of intermediates by use of the program with Optimized map, for search of the reaction path from the reactants to the products via the transition state by calculation of the intrinsic reaction coordinate (IRC) [10]. 

Appropriate geometries of both HCl and HF molecules were fixed by calculation with the Eigenvector Following method in MOPAC with various Hamiltonians of AMI [11], PM3 [12], and PMS. The optimization of the state of each molecule was started at the point of initially defaulted value of inter-atomic distance. The calculation was carried out until the cutoff value of less than 1.000 in gradient by root-mean-square (RMS) where the value less than 1.000 means to achieve the self-consistent field (SCF). Tentative heat of formation, AH was obtained by MOPAC calculation. Results are listed in Table 1. In the case of HCl, the cutoff value by AMI reached to the value of less than 1.000 in gradient only in 3 cycles of optimization, and the value of AH was -24.61233 kcal moF with the value of 1.2842 A of inter-atomic distance. Values of AH were obtained as -20.46808 and -30.41903 kcal moF by PM3 and PMS, respectively. In the case of HF, the value by AMI reached to -74.28070 kcal moF in 6 cycles of optimization with the value of 0.8265 A of inter-atomic distance. AH values were obtained as -62.75007 and -67.15007 kcal moF by PM3 and PMS, respectively. Geometries of both HCl and HF by three Hamiltonians were detennined by these optimizations. 

Conjugate-gradient minimization was used to calculate the pathways following small displacements from each transition state. Every CG optimization was followed by eigenvector-following minimization to ensure... 

The principal optimization algorithm in PQS, both for minima and transition states, is the eigenvector following (EF) algorithm developed in 1986 (Baker 1986). It is based on the Rational Functional Optimization (RFO) approach of Simons and coworkers (Banerjee et al. 1985) which was found at the time to provide the best recipe for determining the shift parameter, A. In this approach, the energy on the PES following a step h is written as (see O Eq. 10.1) ... 

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. 

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