Rovibrational bound states

The initial wavepackets are built combining the rovibrational bound states with these NACMES s and derivative terms, as expressed in Eq.(17). In Eig.4 the contour plots associated to the initial wavepackets for the EP of the ground vibrational levels of A and B electronic states are shown. The most relevant features is the node appearing along r, the HP vibration. This is the reaction coordinate at... 

Kozin, I.N., Law, M.M., Hutson, J.M., Tennyson, J. Calculating energy levels of isomerizing tetra-atomic molecules. 1. The rovibrational bound states of Ar2HF, J. Chem. Phys. 2003,118,4896-904. 

The numbers N, N2 are the vibron numbers of each bond. As discussed in Chapter 2 they are related to the number of bound states for bonds 1 and 2, respectively. For Morse rovibrators they are given by Eq. (2.111) that is, they are related to the depth of the potentials. They are fixed numbers for a given molecule. The numbers (0], co, X], X2 are related to the vibrational quantum numbers, as discussed explicitly in the following sections. We have written the O] (4) representations as (C0i, 0) and not simply as aq, since for coupled systems one can have representations of 0(4) in which the second quantum number is not zero. The values of (iq and (02 are given by the rule (2.102),... 

The electronic predissociation from different rovibrational levels of the A and B electronic states has been evaluated, to study the effect of the initial excitation on the process. The bounds states chosen are 1,2,3 and 6 for A, and fc=l,2,3,6 and 12 for B, which correspond to the bending progression of states appearing in the... 

Bound electronic states exhibit a discrete spectrum of rovibrational eigenstates below the dissociation energy. The interaction between discrete levels of two bound electronic states may lead to perturbations in their rovibrational spectra and to nonradiative transitions between the two potentials. In the case of an intersystem crossing, this process is often followed by a radiative depletion. Above the dissociation energy and for unbound states, the energy is not quantized, that is, the spectrum is continuous. The coupling of a bound state to the vibrational continuum of another electronic state leads to predissociation. 

Recently, it has become possible to perform essentially exact calculations of bound states, for a given potential surface, in systems with up to six active nuclear degrees of freedom. Such calculations have been made feasible by the introduction of the DVR approach, combined with a sequential truncation-diagonalization scheme to produce a more efficient basis. A similar five-dimensional treatment of the rovibrational states of the water dimer was performed by Althorpe and Clary. The DVR approach has also been applied to the torsional dynamics of the water trimer, including one-dimensional, two-dimensional, and three-dimensional treatments. Two torsional potential eneigy surfaces for the trimer have also been developed by fitting to ab initio data. These calculations are di.scussed further in Section 5. 

The NACME s are multiplied by the corresponding derivatives acting on the initial bound rovibrational states. These derivatives are larger as the excitation of the vibration associated to each coordinate increases. In the excited electronic states, the HF frequency is much larger that those associated to the other two... 

The first type, direct photodissociation, corresponds to the absorption of light that results in a direct transition from a bound molecule to photofragments. One deals here with a transition from a bound rovibrational state of the ground potential energy surface (pes) to an excited repulsive pes. 

A particular effort has been addressed to the study of the dynamics within the dimer and to the characterization of fhe low lying rovibrational states in view of pofenfial inferesf for fhe analysis of spectral features in atmospheric research. Calculations of fhe bound rovibrational states of the dimers have been performed for rofafional sfafes having fofal angular momentum / < 6 by solving the secular problem over the exact Hamiltonian. We have calculated the rovibrational levels for the potential energy surfaces described above of the dimers N2-N2, N2-O2 and for all fhree surfaces (singlet, triplet and quintet) [4,5] of O2-O2. A summary of resulfs and fheir discussion follows. Full accounf of all available data has been given in [5,6,8-10]. 

These extra eigenvalues are shown as a function of energy for both Ai and A2 symmetries of the rovibronic wavefunction in Fig. 10. There are two maxima near 4.41 and 4.62 eV for Ai symmetry, 4.49 and 4.70 eV for A2 symmetry. They correspond to resonances with lifetimes close to 15 fs for Ai symmetry and 10 fs for A2 symmetry. Resonances with similar lifetimes have been computed in [60, 61] and detected experimentally in [68]. The energies of the bound rovibrational states... 

Enantiomeric control is more difficult if the excited molecular potential energy surfaces do not possess an appropriate minimum at the o hyperplane configurations (see Figs. 1 and 2). In this case the method introduced in this section is not applicable. One may however be able to apply the laser distillation procedure by adding a molecule B to the initial L, D mixture to form weakly bound L — B and B - D, which are themselves right- and left-handed enantiomeric pairs [83]. The molecule B is chosen so that electronic excitation of B — D and L — B forms an excited species G, which has stationary rovibrational states that are either symmetric or antisymmetric with respect to reflection through t7>,. The species L - B and B - D now serve as the L and D enantiomers in the general scenario above, and the laser distillation procedure described above then applies. Further, the molecule B serves as a catalyst that may be removed from the final product by traditional chemical means. 

B. Lepetit, Z. Peng, and A. Kuppermann, Calculation of bound rovibrational states on the first electronically excited state of the H, system, Chem. Phys. Lett. 166 572 (1990). 

---