Eigenvector Following optimization method

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. 

The RFO and EF family of optimization methods can proceed toward the transition structure even when started outside the quadratic region. However, the Hessian must have a suitable lowest eigenvector that leads uphill to the appropriate transition structure. It is possible to follow an eigenvector other than the lowest one by rescaling the coordinate system so that the desired eigenvector is the lowest one. Note, however, that not all transition structures can be reached by EF from a minimum. 

Aq becomes asymptotically a g/ g, i.e., the steepest descent fomuila with a step length 1/a. The augmented Hessian method is closely related to eigenvector (mode) following, discussed in section B3.5.5.2. The main difference between rational fiinction and tmst radius optimizations is that, in the latter, the level shift is applied only if the calculated step exceeds a threshold, while in the fonuer it is imposed smoothly and is automatically reduced to zero as convergence is approached. 

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