  We calculate characteristic correlation functions for the Anderson model with
additional phonon-assisted coupling to the odd conduction channel. This model
describes, for example, the behavior of a molecule embedded between two
electrodes in linear transport experiments where the position of the molecule
with respect to the leads affects the tunneling amplitudes. We use variational
projection-operator method and numerical renormalization group (NRG) method.
The spin is Kondo screened either by even or odd conduction channel depending
on the gate voltage and electron-phonon coupling. However, in all regimes the
gate-voltage dependence of the zero temperature conductance is found to be
qualitatively the same as in the model with no coupling to the vibrational
mode.
