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  • 1
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    The @journal of physical chemistry 〈Washington, DC〉 95 (1991), S. 8585-8597 
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    The @journal of physical chemistry 〈Washington, DC〉 95 (1991), S. 1047-1053 
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 97 (1992), S. 1353-1364 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Recent research has demonstrated that optimal electromagnetic fields capable of producing selective vibrational excitation in molecules can be designed employing linear quadratic control methods using a cost functional that balances the energy distribution in the molecule, the fluence of the optical field, and a final cost to insure the desired excitation. Practical computations of molecular control theory for large molecules especially with anharmonic potentials become difficult to obtain due to the increased dimensionality and the accompanying uncertainty in the Hamiltonian. In this paper we reduce the complexity of the problem by treating a portion of the molecule including the target and optical dipoles in full detail, while the remainder of the molecule is modeled as an external disturbance of bounded energy. The optimal control field now minimizes the cost functional which is simultaneously maximized with respect to the energy constrained external disturbance to assure robustness. This optimal design process is commensurate with taking the most pessimistic view of the disturbance. This conservative view was born out in the numerical calculations such that practical laboratory studies should reach results much improved over the worst case design. As an illustration we investigate disturbances of varying energy content for a truncated 20 atom molecular chain where the uncontrolled remainder of the chain is the source of the system disturbance. The sensitivity of the system with respect to the disturbance was found to be strongly dependent on the distance of the disturbance to the target bond and the dipole arrangement. In addition, in the range of physically reasonable disturbance energy the optimal field could be accurately predicted from an asymptotic expansion involving only the reference undisturbed case. Although the present paper takes advantage of linear system techniques, the same robust optimal control procedure can be generalized to nonlinear systems by a variety of means.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 97 (1992), S. 852-861 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We present a stable and accurate inversion method for extracting potentials from spectroscopic data of diatomic molecules. The method, which was developed previously for inverting scattering data, is based on first-order functional sensitivity analysis in conjunction with the Tikhonov regularization, singular system analysis, and an exact transformation technique. Besides being numerically stable, it requires neither explicit functional forms nor special basis function expansions for the potential corrections when solving the corresponding linearized integral equation. Instead, we solve the linear equation directly in terms of the probability densities of the unperturbed vibrotation eigenstates. For illustration, we consider the ground electronic state of the H2 molecule. Inversions have been carried out for simulated data free of noise and for those with noise of magnitude comparable to realistic experimental errors. It is found that in both cases, a relatively large deviation of the starting reference potential from the truth may be tolerated to still accurately recover the intended one. The propagation of the spectral errors is analyzed in detail based on the linearization assumption. The variance of the recovered potential reveals the reliability of various regions of the recovered potential.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 97 (1992), S. 276-287 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A molecular system is steered on the ground electronic surface from the initial state to a desired target state at time T via an excited electronic state by using optimally designed coherent laser fields. A new algorithm based on the SU(2) algebra is developed to solve the time-dependent Schrödinger equation for the systems involving two electronic states with time-dependent Hamiltonians. For the design of optimal fields with restricted functional forms the rotating wave approximation is introduced for significantly reducing the computational effort. As a model of unimolecular reactions, a double-well switching problem is studied. The objective is to move the system from one well to the other. It is found that the unrestricted optimal fields which successfully move the system from one well to the other at the target time T are complicated. The objective is achieved through the cooperative interaction between the system and the driving field. The optimal fields with restricted functional forms, such as a train of Gaussian pulses with a single carrier frequency, can also lead to the satisfactory achievement of the objective. However, except for some propitious cases a simple two-pulse pump–dump scheme does not achieve the control objective satisfactorily. Possible further potential applications are discussed briefly.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 94 (1991), S. 7114-7124 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: This paper examines the effect of infinitesimal functional variations in a three-dimensional vibration–rotation He–H2 potential surface on several different levels of physical observables: inelastic cross sections, rate constants, and energy level populations. Earlier equations for a rigid-rotor system are extended and a comparison of the current results with earlier rigid-rotor results is made. A significant difference in the sensitivity of observables to the potential components has been observed between those observables which are purely rotationally inelastic and those which are vibrationally inelastic. The region of highest sensitivity is dependent upon the energy or temperature as well as the states related by the individual observable. Significant information loss has been observed in the transition from the microscopic observables to the macroscopic ones for those observables which are vibrationally inelastic.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 92 (1990), S. 3957-3976 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We introduce a discrete-continuum hybrid treatment of solid vibrations in order to describe the collisional excitation of adsorbate and defect modes by atom impacts. The inhomogeneous surface is represented by: (a) one or more atom clusters corresponding to the defect sites and their immediate neighbors, which are harmonically coupled to (b) an elastic continuous bulk. The model thus aims at reproducing the long-wavelength spectrum of the lattice as well as the high-frequency localized modes contributed by adsorbates and surface defects. The hybrid model is tested against lattice results in one-dimensional simulations that allow for analytic solution of the surface motion (which would be unfeasible for three-dimensional imperfect lattices); hybrid and lattice results are thus compared in detail under identical conditions. The model is also evaluated under the worst possible conditions for the continuum approximation, since collinear collisions correspond to three-dimensional situations in which the transferred momentum and, therefore, short-wavelength excitations are maximal. Comprehensive tests are presented for He atoms scattering from CO chemisorbed on Pt and on Ni substrates, and from N2 adsorbed on W. The scattering dynamics is treated by time-correlation functions of the transition operator previously developed for polyatomic targets [J. Chem. Phys. 84, 3162 (1987); 85, 2300 (1987); 86, 750 (1987)]. All the energetically open states are thus incorporated, as well as the thermal average over initial states, without need of basis-set expansions. Distributions of transferred energy are presented as would be observed in a one-dimensional scattering "experiment'' using impact energies between 0.1 and 1 eV and with the solid at nonzero temperature. The collisional spectra obtained from the hybrid models are found to be in excellent agreement with those of the corresponding inhomogeneous lattices throughout wide ranges of impact velocity, surface initial temperature (including 0 K) and transferred energy. The results indicate that discrete-continuum treatments provide a powerful tool for analyzing the transfer of energy at the gas–adsorbate–solid interface.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 92 (1990), S. 2927-2937 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Analytic solutions of the optimal fields giving selective local excitation in harmonic molecules are presented, and calculated by a numerically stable algorithm. It is shown that the optimal fields can be decomposed into a finite number of monochromatic laser fields, with the following properties: (a) the number of component frequencies is equal to the number of normal modes of the molecule; (b) the component frequencies go to the molecular vibrational normal mode frequencies in the limit of low amplitude; (c) there is an inverse relationship between the amplitude of the fields (as controlled by the weighting factor for the field fluence term) and the time T at which the objective is reached; (d) there exists a limiting form for the optimal fields as the controlling time T→∞ (which had been observed empirically in previous work and now has a regorous mathematical basis). The intensity of the component laser fields, and thus the optimal field can be reduced to any desired level with a corresponding lengthening of the pulses. Thus by varying the design criteria one may determine a corresponding entire family of optimal fields with each member equivalently leading to the desired final local excitations. The optimization procedure clearly illustrates the trade off between optimal pulse length and amplitude. In order to try and achieve the control objectives with consideration of laboratory constraints on the laser fields a formalism is presented for designing the optimal fields with constrained functional forms. An illustration based on linear chain molecules shows that the objectives may be quite well achieved by using realistically constrained optimized fields.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 92 (1990), S. 364-376 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A quantum mechanical formalism for the optimal control of physical observables of microsystems is developed. The computational procedure for numerical implementation is presented. Three illustrative examples with a model Morse oscillator show that optimal pumping fields can be found to reach the physical objectives: selective excitations, steering a system to a specified state, and breaking a bond.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 97 (1992), S. 6226-6239 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A new approach to calculating quantum functional sensitivity maps of transition probabilities is described in this paper. This approach is based on the log-derivative version of the Kohn variational principle and is applied here to the collinear H+H2 hydrogen exchange reaction. The sensitivity maps provide detailed quantitative information about how variations in the potential energy surface affect the state-to-state transition probabilities. The key issues investigated are (i) the evolution of sensitivity structure in the 0.30–1.50 eV range of total energy; (ii) the comparison of sensitivity structure on the Porter–Karplus, the Liu–Siegbahn–Truhlar–Horowitz, and the double-many-body-expansion potential energy surfaces; and (iii) the range of linearity for first order sensitivity predictions.
    Type of Medium: Electronic Resource
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