The set or toolkit of potential surfaces corresponding to a discrete set of electric-field values between and . The surfaces were calculated using 2-RDM techniques.
Three dipole moment surfaces corresponding to electric-field values of , 0, and are shown. Potential energy surfaces were generated with the 2-RDM method with the electric field included, and then the dipole surfaces were calculated by centered finite differences. In the dipole approximation the set of potential energy surfaces, generated from a single dipole surface in the absence of the electric field, does not include field-induced polarization effects. The figure shows that the dipole surfaces at the minimum and maximum electric-field values are qualitatively different. These qualitative differences cannot be corrected simply with the addition of a polarization term.
Population dynamics of the HF molecule under the influence of an optimized electric field where the field is optimized (a) with potential surfaces from the dipole approximation and (b) with a set of precalculated Born-Oppenheimer potential energy curves corresponding to a set of electric-field amplitudes. The initial state of the system is the ground state, and the target state is the fifth vibrational level.
The magnitude of the optimized control field that drives the population of HF from its ground vibrational state to its fifth state is shown. Only the last 10% of the time interval is shown, but the remainder of the electric field exhibits similar behavior. The field was optimized with the toolkit of precalculated Born-Oppenheimer potential energy curves corresponding to a set of electric-field amplitudes.
The power spectrum of the optimized control field that drives the population of HF from its ground vibrational state to its fifth state is shown. The frequencies of the control field are an order of magnitude smaller than those corresponding to the lowest electronic transition. The field was optimized with a toolkit of precalculated Born-Oppenheimer potential energy curves corresponding to a set of electric-field amplitudes.
Population dynamics of the HF molecule modeled by a set of potential surfaces beyond the dipole approximation but subjected to an optimal field computed by surfaces within the dipole approximation. The field from the dipole approximation is unable to drive an appreciable amount of the population from the ground state into the target fifth-excited state and scarcely fills the third excited state.
Population dynamics from a control calculation using a toolkit of Born-Oppenheimer potential energy surfaces precalculated by full configuration interaction. The basis set and parameters are the same as those in Fig. 3(b) where the toolkit of Born-Oppenheimer surfaces is computed with the variational 2-RDM method. The exhibited mechanism is similar to that of the 2-RDM calculation, but the populations have different timings and peak heights.
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