Field-free vibrational states

Easy availability of ultrafast high intensity lasers has fuelled the dream of their use as molecular scissors to cleave selected bonds (1-3). Theoretical approaches to laser assisted control of chemical reactions have kept pace and demonstrated remarkable success (4,5) with experimental results (6-9) buttressing the theoretical claims. The different tablished theoretical approaches to control have been reviewed recently (10). While the focus of these theoretical approaches has been on field design, the photodissociation yield has also been found to be extremely sensitive to the initial vibrational state from which photolysis is induced and results for (11), HI (12,13), HCl (14) and HOD (2,3,15,16) reveal a crucial role for the initial state of the system in product selectivity and enhancement. This critical dependence on initial vibrational state indicates that a suitably optimized linear superposition of the field free vibrational states may be another route to selective control of photodissociation. 

The sum is taken over all the discrete vibrational levels if of state g>. Vr (f) is the component of the wavepacket on the g channel evolved up to time t from the field-free vibrational state v > prepared at time f = 0. Note that Pbound(y if) actually represents the total bound state population at any time after tj, since no further decay is then possible, the laser being turned off at such a time. It is clear that Eq. (71) gives a useful approximation for the result of a full time-dependent wavepacket evolution, [Eq. (73)], only if the assumption of an adiabatic transport of Floquet states is valid. 

In the FOIST scheme,the product yield is maximized through the preparation of the initial wave function g(0) as a superposition of the field-free vibrational wave function c ) , of the ground electronic state... 

Fig. 1. Schematic of vertical (a) and non-vertical (b) electronic transitions with the electronic energies represented by displaced harmonic potentials. The initial state is the vibrational ground state on Vi. The wave packet on V2 in (a) is the Franck-Condon wave packet and the dashed arrows mark the positions of the turning points for the oscillation this wave packet will undergo under field-free conditions.

For the HF molecule, we have rigorously evaluated the vibrational-electronic state electrical properties. For about a dozen bond length choices, electrical properties for HF were calculated. An ACCD potential energy curve, accurate enough to predict the r = 0 -mj = 1 field-free transition... 

The pump-dump control concept [17,18] has been realized in different experiments in the gas and the condensed phase (see review [71] and references therein, [30]). The concept includes three successive steps. First step excitation of the system from the ground state (reactant) to an excited state with a femtosecond pump pulse short enough to create a wavepacket in the excited state. Second step field free evolution of the system. Third step interaction with a second pulse to dump the vibrational wavepacket to the target state/region on the electronic ground state. 

Born-Oppenheimer expressions for vibration-rotation energies of diatomic molecules have been derived several times (Herman and Asgharian, 1966 Watson, 1973 Bunker and Moss, 1977 Watson, 1980 Herman and Ogilvie, 1998). Here we will follow mainly the derivation by Brniker and Moss (Bunker and Moss, 1977). After separation of the translation of the whole molecule and transformation to nuclear centre of mass coordinates one can write the field-free Hamiltonian for the electronic ground state of symmetry of a diatomic molecule as... 

In this section we present the nuclear relaxation (NR) contributions to the vibrational (hyper)polarizabilities of Li C6o and [Li C6o]. As previously stated our treatment requires a geometry optimization in the presence of a finite field. A problem can arise when there are multiple minima on the PES separated by low energy barriers. The finite field method works satisfactorily in that event as long as the field-dependent optimized structure corresponds to the same minimum as the field-free optimized structure. This was the case in previous work on ammonia [42], which has a double minimum potential. However, it is sometimes not the case for the endohedral fullerenes considered here, especially Li C6o- In fact, we were unable to determine the NR contribution in the x direction, i.e. perpendicular to the symmetry plane, for that molecule. It was possible to obtain based on the alternative analytical formulation [32-34], utilizing field-free dipole (first) derivatives and the Hessian. The analytical polarizability components in the other two directions were, then, used to confirm the values of the corresponding finite field method for those properties. 

So, the calculation of the shape of an IR spectrum in the case of anticorrelated jumps of the orienting field in a complete vibrational-rotational basis reduces to inversion of matrix (7.38). This may be done with routine numerical methods, but it is impossible to carry out this procedure analytically. To elucidate qualitatively the nature of this phenomenon, one should consider a simplified energy scheme, containing only the states with j = 0,1. In [18] this scheme had four levels, because the authors neglected degeneracy of states with j = 1. Solution (7.39) [275] is free of this drawback and allows one to get a complete notion of the spectrum of such a system. 

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