Adiabatic correlation

Valuable insight, particularly with regard to the effects of electronic excitation on reaction cross sections and reaction dynamics, has also been achieved without accurate knowledge of the actual potential surfaces, through the use of molecular-orbital correlation diagrams. Adiabatic correlation rules for neutral reactions involving polyatomic intermediates were developed by Shuler 478 These were adapted and extended for ion-neutral interactions by Mahan and co-workers.192,45 479,480 Electronic-state correlation diagrams have been used to deduce the qualitative nature of the potential surfaces that control ion-neutral reaction dynamics. The dynamics of the reaction N+(H2,H)NH+ and in particular the different behavior of the N + (3P) and N + ( Z)) states,123 for example, have been rationalized from such considerations (see Fig. 62). In this case the... 

Fig. 7.10 Adiabatic correlation diagram for the Na nd states obtained from the known d state fine structure splitting, the intermediate field energy ordering, and applying the nocrossing rule for states of the same m (from ref. 3).

It is suggested that the two electronic states fa and l °f noninteracting partners provide a good basis set to be used for constructing orthonormal adiabatic electronic functions fa and fa. At R — oo the functions fa and fa adiabatically correlate with fa and fa, so that the nonadiabatic transition probability calculated for a particular trajectory R(f) refers to the collision-induced transition between the two states of the partners. 

The first excited state, A A , correlates with the ground state products OH (X /7) -I- H and must also be considered for energies higher than 8.4 kJ mol [22], or temperatures above 500 K. The second excited state, B A, adiabatically correlates with excited state products, OH (A X+) - - H. At collinear geometries these two surfaces correspond to a double degenerate 77 state. 

As it can be seen in Figure 3.2, at collinear geometries the ground X A state has X symmetry and adiabatically correlates with an excited A state of the hydroxyl radical. As a result there is a crossing between the X and 77 states. Schatz and co-workers [12,22,23,52] estimated a constant contribution at collinear geometries from the 77 state of approximately 10%, due to the non adiabatic electrostatic coupling between the (X A ) and 77 (B A and A A") states. 

Figure. 15. Contour plots of the two lowest doublet PES, Vi 2 calculated with the contribution of S-O interaction energies are given in kcaPmol solid and dashed contours are for PES indicating the adiabatic correlation between the 1st and 2nd from bottom components of the lowest multiplet 0( P2)+0H( ri3/2) at long distances R and the lowest A" and A states at short distances, respectively.

Shuler, K. E. (1953) Adiabatic Correlation Rules for Reactions Involviag Polyatomic Intermediate Complexes and their Apphcation to the Formation of OH( Z in the H2-O2 Flame, J. Chem. Phys. 21. 624-32. 

Because of the off-diagonal nature of the electronic Hamiltonian in the di-abatic basis, transitions among different electronic states can, and in general will, occur during the forward and backward time evolutions. As a first step towards a computationally convenient expression for the non-adiabatic correlation function, we shall make use of the mapping Hamiltonian formalism to account for these transitions [28-31]. 

Beam studies have until recently been largely confined to systems in which the dynamics are governed by a single potential surface. The use of classical trajectory studies and adiabatic correlation diagrams in predicting the reaction path are both implicitly founded on the Born-Oppenheimer approximation which allows us to deal with only one electronic state during... 

An example of this weak spin-orbit limit nonrelativistic adiabatic correlation is given by the HBr+ system. The lowest energy dissociation asymptote is Br+(3P) +H(2S), thus Si = 1, S2 = 1/2 and S can be 3/2 (quartet state) or 1/2... 

A good way to check that the adiabatic correlation has been done correctly is to check whether the total degeneracy of the molecular states is equal to that of the atomic states. In the case of HBr+ —> H(2S) + Br+(3P), the molecular degeneracy is4 + 8 + 4 + 2 = 18 and the atomic degeneracy is2x3x3 = 18. 

Because of the strength of the spin-orbit coupling in Br+, it is more appropriate to consider the relativistic adiabatic correlations in the intermediate spin-orbit limit. When the spin-orbit splitting(s) of the separated atom states is... 

Figure 7.1 Transition from (A, S) to (Ji,J2) coupling for the 2P + 2S separated atom states which correlate adiabatically with the molecular states of HCI. The specific adiabatic correlations shown are determined by the energy order of the molecular states and the noncrossing rule (from Matsumi, et al., 1990).

These adiabatic correlations imply that the HCI X1E+ ground state belongs to the ct27t4 configuration at Re but at R = oo belongs to the configu-... 

If the electronic states of the primary reaction products from a recoiling atom and a diatomic molecule can be determined, then adiabatic correlation diagrams could be used to deduce the electronic state of the reacting recoil atom, or the symmetry of attack, or both. 

According to the spin conservation along the potential energy surface, the two electrons can couple either as a singlet state, or as a triplet state. The previous configuration thus adiabatically correlates to ... 

Configuration 19 adiabatically correlates to the lowest singlet or to the lowest triplet state of SiNHj having an Aa space-symmetry. The 1 A2 state lies 4.71 eV (108 kcal/mol) above the ground state [62] the reaction is thus strongly endothermic and therefore not possible in the interstellar medium, as is the reaction leading to the l Aa state of SiNHj (in this case, the endothermicity is 89 kcal/mol [117]). 

A completely adiabatic correlation between nQ> and ljQ> states would assume that n equals j a result which unlike the partial 0-correlation is not borne out by coupled channel calculations. Physically this adiabatic correlation is untenable because the spatial character of free-rotor and bending wave-functions is quite different and so non-adiabatic coupling is certain to be large. Thus the change between the free-rotor and bending wavefunctions is better described by a sudden correlation. 

If a strict adiabatic correlation between the n and j-spaces is made then C. = 6 4 in which case... 

The energies Ek(p/) obtained from this diagonalisation give the so-called hyperspherical adiabats when plotted versus p. These hyperspherical adiabats correlate with different quantum states of reactants or products for large p and avoided crossing between them can indicate large reaction probabilities. 

For example, for a system M + Ng ( CO, Clg), the terms U and U adiabatically correlating with the initial (M + Ng) and final (M - - N ) states are crossed by a third term corresponding to the ionic state of the pair (M+ + N ). Near the crossing point, the Massey parameter appears to be low, this providing a high effectivity of non-adiabatic transitions. Thus, for the case considered, the ionic term represents the link between the initial and final electron states so that the process... 

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