The complex Kohn method

2 Kohn variational theory 8.2.3 The complex Kohn method 

The derivation given above of the stationary Kohn functional [ K] depends on logic that is not changed if the functions Fo and l of Eq. (8.5) are replaced in each channel by any functions for which the Wronskian condition mm — m 0 = l is satisfied [245, 191]. The complex Kohn method [244, 237, 440] exploits this fact by defining continuum basis functions consistent with the canonical form cv() = I.a = T, where T is the complex-symmetric multichannel transition matrix. These continuum basis functions have the asymptotic forms 

This transformed representation of the asymptotic wave functions can easily be verified for potential scattering. The asymptotic radial wave function in a given i-channel satisfies the identity 

Using these asymptotic continuum functions, the derivation given above implies that for Tt = —such that mio + mnTt = 0, then 

Introduced in the context of heavy-particle reactive collisions [440], the complex Kohn method has been successfully applied to electron-molecule scattering [341], It is accurate but computationally intensive, since continuum basis orbitals do not have the Gaussian form that is exploited in most ah initio molecular bound-state studies. The method has been implemented using special numerical methods [341] developed for these integrals. These numerical methods mitigate another practical 

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