Initial state selection

Figure B3.4.6. Reaction probabilities for the initial-state-selected process H2(v = 0,J = 0)+OH(v,y = 0) — H2O+H, for zero total angular momentum. Taken from [75] with pennission.

The methodology presented so far allows the calculations of state-to-state. S -matrix elements. However, often one is not interested in this high-level of detail but prefers instead to find more average infomiation, such as the initial-state selected reaction probability, i.e. the probability of rearrangement given an initial state Uq. In general, this probability is... 

At times, however, even the infomiation presented by "nis too detailed. If one wants to rigorously calculate the themial rate of rearrangement reactions, the initial vibrational state is not important. The relevant quantity is the sum of tire initial-state-selected probabilities... 

Fig. 15. Comparison of the theoretical thermal rate, fc(T), with experimental results.74 Also shown are the initial state selected rate coefficient for the (0,0) state, and an approximate theoretical thermal rate coefficient, fcest(T).

Sometimes the atoms (or molecules) in molecular beams are put into selected electronic, vibrational and rotational states. The initial state selection can be made with lasers. A laser beam of appropriate frequency is shined onto a molecular beam and the molecule goes onto an appropriate excited state. The efficiency of selection depends upon the absorption coefficient. We can attain sufficient absorption to get highly vibrationally excited molecule with the laser. A spin forbidden transition can also be achieved by using a laser. 

Abstract. Over the last deeade, advances in quantum dynamics, notably the development of the initial state selected time-dependent wave packet method, coupled with advances in constructing ab initio potential energy surfaces, have made it possible for some four-atom reactions to be addressed from first principles, in their full six internal degrees of freedom. Attempts have been made to extend the time-dependent wave packet method to reactions with more internal degrees of freedom. Here, we review the full-dimensional theory for the A + BCD four-atom reaction and use it to guide the reduced-dimensionality treatment of the X + YCZ3 reaction. Comparison of rigorous calculations with recent experiments are presented for (a) the benchmark H + H2O abstraction reaction, and (b) the H + CH4 H2 + CH3 reaction. 

These strong non-adiabatic effects observed in the cone-states of the upper sheet contrast with the absence of any significant effect in the H-I-H2 reactive collision. Eor instance, Mahapatra et al. [69] examined the role of these effects in the H -f H2 (v = 0, = 0) reaction probability for / = 0 and found negligible nonadiabatic coupling effects in the initial state selected probability. Subsequently, Mahapatra and co-workers [70] reported initial state-selected ICS and thermal rate constants of H -I- H2(HD) for total energies up to the three body dissociation. Again, they... 

Once the initial state-selected total reaction probability is obtained from Eq. (95), one can calculate the integral cross section and thermal rate constant using standard... 

The initial state-selected total dissociation probability of the diatom is obtained by projecting out the energy-dependent reactive flux. If i /,) denotes the time-independent (TI) full scattering wavefunction, where the labels i and E denote the initial state and energy, the total dissociation probability from an initial state i can be obtained by the flux formula (95). We choose the diatomic distance r to be the 5 coordinate in Eq. (96). The full TI scattering wave function is normalized as (if/,) NV/. ) = 2/nhh(E - E ). The total dissociation probability, according to Eq. (98), is given by... 

In gas-phase dynamics, the discussion is focused on the TD quantum wave packet treatment for tetraatomic systems. This is further divided into two different but closed related areas molecular photofragmentation or half-collision dynamics and bimolecular reactive collision dynamics. Specific methods and examples for treating the dynamics of direct photodissociation of tetraatomic molecules and of vibrational predissociation of weakly bound dimers are given based on different dynamical characters of these two processes. TD methods such as the direct projection method for direct photodissociation, TD golden rule method and the flux method for predissociation are presented. For bimolecular reactive scattering, the use of nondirect product basis and the computation of the initial state-selected total reaction probabilities by flux calculation are discussed. The descriptions of these methods are supported by concrete numerical examples and results of their applications. 

In this review seven chemical reactive systems are discussed for which quantum mechanical energy-dependent initial state-selected (total) cross sections and temperature-dependent rate constants were calculated. In all cases PESs based on ab m/r/ovalues were used. The calculations are characterized by two features namely (a) in each case they were done in the reagents AC only, applying reagents Jacobi coordinates and (b) the reactive ACs were eliminated using the appropriate NIPs. Two triatom systems, namely F + H2 and F +... 

Using DMBE IV potential, Meijer and coworkers carried out wavepacket calculations of the initial state selected total cross sections for the H + O2, including partial waves up to / = 35. All of the projections of J onto the intermolecular axis have been incorporated in the calculations. They found that the calculated cross sections are lower than the experiment, which indicated the deficiencies in the DMBE IV potentials. In 2005, Xu et al. constructed a new potential (XXZLG PES) for this reaction at the internally contracted multireference configuration interaction plus the Davidson correction level with the augmented correlation consistent polarized valence quadruple zeta (aug-cc-pVQZ) basis set. It has been shown that there is remarkable improvement over the previous DMBE IV potential. Based upon this new potential and using the recent developed RGB quantum wave packet method. Sun et al. calculated state-to-state DCS and ICS of the H + O2 reaction up to 1.5 eV. 

However, being interested in less detailed information, one might ask for the probability of reaction if the reactants are prepared in a given initial state Up. These initial state-selected reaction probabilities are obtained by summing all state-to-state transition probabilities corresponding to the initial state... 

In contrast to S-matrix elements, these observables do not depend on the entire potential energy surface. Pn is infiuenced only by the potential energy surface on the reactant side of the reaction barrier and the region in the vicinity of the barrier. The potential energy surface further on the product side has no impact on pn It only decides upon the specific quantum states in which the products are formed. Thus, the calculation of initial state-selected reaction probabilities only requires the treatment of a reduced portion of the potential energy surface. It causes less numerical effort than a full S-matrix calculation. 

Molecular beam and bulb experiments have two goals. First, reaction cross sections can be transformed into reaction rate constants, which provide important kinetic information regarding chemical reaction rates. The rate constant with reactant state selection may be particularly important for technological applications. Indeed, a chemical mixture which reacts exothermically from one reactant state, and is inert from all other reactant states might provide a useful energy source to complement fossil fuels. For more fundamental reasons, we focus on the initial state selected rate constant for the D+H2 —> DH+H reaction in Chapter 5. 

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