Field optimized initial state method

We study optimal control problems of quantum chaos systems. Our goal of control is to obtain an optimal field s(t) that guides a quantum chaos system from an initial state target state (pj) at some specific time t = T. One such method is optimal control theory (OCT), which has been successfully applied to atomic and molecular systems [4]. 

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. 

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