Classical barrier height

One of the simplest chemical reactions involving a barrier, H2 + H —> [H—H—H] —> II + H2, has been investigated in some detail in a number of publications. The theoretical description of this hydrogen abstraction sequence turns out to be quite involved for post-Hartree-Fock methods and is anything but a trivial task for density functional theory approaches. Table 13-7 shows results reported by Johnson et al., 1994, and Csonka and Johnson, 1998, for computed classical barrier heights (without consideration of zero-point vibrational corrections or tunneling effects) obtained with various methods. The CCSD(T) result of 9.9 kcal/mol is probably very accurate and serves as a reference (the experimental barrier, which of course includes zero-point energy contributions, amounts to 9.7 kcal/mol). 

Table 13-7. Computed classical barrier heights AE [kcal/mol] for the reaction H2 + H — [ II II 111 —> H2 + H (6-311++G(,3pd) basis set) data compiled from Johnson et al., 1994, and Csonka and Johnson, 1998.

The energy threshold of a reaction corresponds to the minimum relative translational energy that must be supplied to the reactants in order to produce products. This energy threshold will differ from the classical barrier height, even when the reac-... 

For the F+H2 reaction high levels of theory are required. The Hartree-Fock limit for the classical barrier height is about 67 kJ/mol [J. Phys. Chem. 89, 5336 (1985)], that is, almost ten times larger than the exact value ... 

Fig. 6.1.1 An illustration of the barrier height Eo- The zero-point energy levels of the activated complex and the reactants are indicated by solid lines. Note that the zero-point energy in the activated complex comes from vibrational degrees of freedom orthogonal to the reaction coordinate. In the classical barrier height Ec 1, vibrational zero-point energies are not included.

The classical threshold energy Ec, which we also refer to as the classical barrier height, is the energy that can be inferred directly from the potential energy surface. 

The reaction rate depends critically on the barrier height and the shape of the potential energy surface in the vicinity of the saddle point. As an illustration of this, we consider again the F + H2 —> HF + H reaction, where a second saddle point has been identified (Section 3.1) which corresponds to a linear activated complex with a classical barrier height that is slightly higher than for the bent complex. An evaluation of the rate constant based on the linear activated complex would have resulted in a rate constant that is about ten times smaller than the experimental result. 

The potential energy surface for the reaction has been calculated and the classical barrier height associated with the activated complex is Ec = 90.8 kJ/mol. The relevant vibrational frequencies are given in the table below. (Note that the imaginary frequency of the activated complex is not included in the table.)... 

The unimolecular rate constant k(E) is described within the framework of RRKM theory. In the following, we neglect the rotational energy in HCN as well as in the activated complex. The classical barrier height is Ec = 1.51 eV. 

K.A. Peterson, D.E. Woon, T.H. Duiming, Benchmark calculations with correlated molecular wave-functions. 4. The classical barrier height of the H -F H2 H2 -F H reaction, /. Chem. Phys. 100 (10) (1994) 7410-7415. 

Table 19.3. Classical barrier heights and energies of reaction (in kcal mol ) for modelsl l of the hydrogen abstraction for methylmalonyl-CoA mutase.

Figure 6.27 ID Tunnelling barrier Schematic illustration of a tunnelling barrier of length Sz. Incident current density, /i, is transformed into transmitted current density, jt, by tunnelling through the barrier which takes place even though electron energy does not exceed Ej, a value less than the classical barrier height l o-...

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