Rotation-vibration eigenstate

A rotation-vibration eigenstate is typically sensitive to the global potential-energy surface. In time-dependent language, in order to resolve individual... 

It is possible to encode an enormous amount of amplitude and phase information into a short pulse of electromagnetic radiation. The pulse can be designed to direct the intra-molecular dynamics toward an a priori specified target state, the pulse can be modified empirically based on some sort of learning algorithm to maximize a desired dynamical outcome (e.g., a specified photofragment) (Judson and Rabitz, 1992 Bardeen, et al., 1997 Feurer, et al., 2001 Rice and Zhao, 2000 Levis, et al., 2001 Weinacht, et al., 2001 Levis and Rabitz, 2002), or the pulse can be tailored to create a F(t) in which the amplitudes and phases of individual electronic or rotation-vibration eigenstates could be used as a multibit memory element in a quantum computer (Ahn, et al., 2000 Ballard, et al., 2002). 

Using the same formulation of the Hamiltonian as in Sec. VII [specifically Eqs. (67)—(70)], the two-step process makes use of five pairs of rovibrational states (specified explicitly below). The vibrational eigenstates correspond to the combined torsional and S-D asymmetric stretching modes. The rotational eigenfunctions are the parity-adapted symmetric top wave functions. Each eigenstate has additionally an Si A label denoting its symmetry with respect to inversion. Within the pairs used, the observable chiral states are composed as... 

The autocorrelation function picture of a frequency domain spectrum (Heller, 1981) is derived as follows. Consider the e,v e <— g, t>" electronic absorption spectrum. In the Franck-Condon limit (constant transition moment) and neglecting rotation, the eigenstate spectrum observed from the v" vibrational level... 

The information contained in a diatomic molecule rotation-vibration-electronic wavefunction is enormous. But this is dwarfed by the information content of a time-evolving wavefunction that originates from a non-eigenstate pluck. A simplified, reduced-dimension representation, rather than an exact numerical description, is prerequisite to visualization and understanding. The concepts and techniques presented in this book, developed explicitly for diatomic molecule spectra and dynamics, are applicable to larger molecules. Indeed, any attempt... 

As we demonstrated above, CVPT can be used to compute properties of rotation-vibration states of H2CO. To calculate the rotation-vibration spectrum, we must also be able to calculate the intensity of the transition between the energy eigenstate vT M J ) and vfM7). Here the eigenstates are defined in terms of their total angular momentum... 

The results presented in this chapter show that the use of proper effective models, in combination with calculations based on the exact vibrational Hamiltonian, constitutes a promising approach to study the laser driven vibrational dynamics of polyatomic molecules. In this context, the MCTDH method is an invaluable tool as it allows to compute the laser driven dynamics of polyatomic molecules with a high accuracy. However, our models still contain simplifications that prevent a direct comparison of our results with potential experiments. First, the rotational motion of the molecule was not explicitly described in the present work. The inclusion of the rotation in the description of the dynamics of the molecule is expected to be important in several ways. First, even at low energies, the inclusion of the rotational structure would result in a more complicated system with different selection rules. In addition, the orientation of the molecule with respect to the laser field polarization would make the control less efficient because of the rotational averaging of the laser-molecule interaction and the possible existence of competing processes. On the other hand, the combination of the laser control of the molecular alignment/orientation with the vibrational control proposed in this work could allow for a more complete control of the dynamics of the molecule. A second simplification of our models concerns the initial state chosen for the simulations. We have considered a molecule in a localized coherent superposition of vibrational eigenstates but we have not studied the preparation of this state. We note here that a control scheme for the localiza-... 

Figure 6-4. The vibrational-rotational energy eigenstates for a diatomic molecule arc shown. The ground-state corresponds to v = 0, J = 0.

This completes our introduction to the subject of rotational and vibrational motions of molecules (which applies equally well to ions and radicals). The information contained in this Section is used again in Section 5 where photon-induced transitions between pairs of molecular electronic, vibrational, and rotational eigenstates are examined. More advanced treatments of the subject matter of this Section can be found in the text by Wilson, Decius, and Cross, as well as in Zare s text on angular momentum. 

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