Eigenvector following method

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. 

HyperChem uses the eigenvector following method described in Baker, J., J. Comput. Chem., 7, 385-395 (1986), where the details of the procedures can be found. 

The next step will determine optimization convergence. If the criteria are satisfied, HyperChem will stop at this point, having found the position of the transition state. If convergence criteria are not 

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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. 

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

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. 

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