# rmgpy.kinetics.Wigner¶

class rmgpy.kinetics.Wigner(frequency)

A tunneling model based on the Wigner formula. The attributes are:

Attribute Description
frequency The imaginary frequency of the transition state

An early formulation for incorporating the effect of tunneling is that of Wigner [1932Wigner]:

$\kappa(T) = 1 + \frac{1}{24} \left( \frac{h \left| \nu_\mathrm{TS} \right|}{ k_\mathrm{B} T} \right)^2$

where $$h$$ is the Planck constant, $$\nu_\mathrm{TS}$$ is the negative frequency, $$k_\mathrm{B}$$ is the Boltzmann constant, and $$T$$ is the absolute temperature.

The Wigner formula represents the first correction term in a perturbative expansion for a parabolic barrier [1959Bell], and is therefore only accurate in the limit of a small tunneling correction. There are many cases for which the tunneling correction is very large; for these cases the Wigner model is inappropriate.

calculateTunnelingFactor(self, double T) → double

Calculate and return the value of the Wigner tunneling correction for the reaction at the temperature T in K.

calculateTunnelingFunction(self, ndarray Elist) → ndarray

Raises NotImplementedError, as the Wigner tunneling model does not have a well-defined energy-dependent tunneling function.

frequency

The negative frequency along the reaction coordinate.

 [1932Wigner] E.Wigner. Phys. Rev. 40, p. 749-759 (1932). doi:10.1103/PhysRev.40.749
 [1959Bell] R. P. Bell. Trans. Faraday Soc. 55, p. 1-4 (1959). doi:10.1039/TF9595500001