Adiabatic ground state potential

Fig. 5. The pseudo-Jahn-Teller effect in ammonia (NH3). (a) CCSD(T) ground state potential energy curve breakdown of energy into expectation value of electronic Hamiltonian (He), and nuclear-nuclear repulsion VNN. (b) CASSCF frequency analysis of pseudo-Jahn-Teller effect showing the effect of including CSFs of B2 symmetry is to couple the ground and 1(ncr ) states to give a negative curvature to the adiabatic ground state potential energy surface for the inversion mode.

Fig. 4.2.2 Potential energy diagram for the Landau-Zener model. Adiabatic potentials (solid lines) and diabatic potentials (dashed lines), with /3i < 0 and (32 > 0. The arrow illustrates the dynamics on the lower adiabatic (ground-state) potential.

The integration limits Si and 2 are the reaction coordinate classical turning points /u-eff is the reduced mass, which introduces the reaction path curvature and V (s) is the adiabatic ground-state potential. 

In practice, we approximate the exact transmission coefficient by a mean-field-type of approximation that is we replace the ratio of averages by the ratio for an average or effective potential. For gas-phase reactions with small reaction-path curvature, this effective potential would just be the vibrationally adiabatic ground-state potential. In the liquid phase and enzymes we generalize this with the canonical mean-shape approximation. In any event, though, the transmission coefficient should not be thought of as a perturbation. The method used here may be thought of as an approximate full-dimensional quantum treatment of the reaction rate. 

Two modes of the same symmetry can mix under electronic excitation. This mixing, which can be depicted as a normal coordinate rotation, is known as the Dushinsky effect (Dushinsky, 1937). If the adiabatic ground-state potentials of the two modes, labeled j = and j = 2, are... 

Figure 6 Plot of the MEP (dotted line) and the vibrationally adiabatic ground-state potential curve as calculated in curvilinear (solid line) and rectilinear (dashed line) coordinates for the H + CH4 reaction.

We obtain values for the vibrationally adiabatic ground-state potential-energy curve at the saddle point of 10.1 kcal/mol for the A state and 11.7 kcal/mol for the A state. In equation (3), 03x and 0)2 are the symmetric stretch and (doubly) degenerate bending frequencies of the transition state. For the A" state, AEi. may be compared to experimentally derived activation energies or 8-10 kcal/mol for reaction (Rl). ... 

Notice that is the classical endoergicity 3nd AEq is quantal ground-state endoergicity. It is also convenient to define the conventional-transition-state-theory approximation to the barrier height of the vibrationally adiabatic ground-state potential energy... 

In this chapter we shall not emphasize the results of quantal corrections to the reaction-coordinate motion for three-dimensional collisions. However such corrections may be carried out using essentially the same techniques as discussed above for collinear reactions. In particular, we use adiabatic transmission coefficients obtained by calculating quantal transmission through and across the one-dimensional adiabatic ground-state potential barrier... 

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