  The dominant mechanism of low-energy positron annihilation in polyatomic
molecules is through positron capture in vibrational Feshbach resonances (VFR).
In this paper we investigate theoretically the effect of anharmonic terms in
the vibrational Hamiltonian on the positron annihilation rates. Such
interactions enable positron capture in VFRs associated with multiquantum
vibrational excitations, leading to enhanced annihilation. Mode coupling can
also lead to faster depopulation of VFRs, thereby reducing their contribution
to the annihlation rates. To analyze this complex picture, we use
coupled-cluster methods to calculate the anharmonic vibrational spectra and
dipole transition amplitudes for chloroform, chloroform-$d_1$,
1,1-dichloroethylene, and methanol, and use these data to compute positron
resonant annihilation rates for these molecules. Theoretical predictions are
compared with the annihilation rates measured as a function of incident
positron energy. The results demonstrate the importance of mode coupling in
both enhancement and suppression of the VFR. There is also experimental
evidence for the direct excitation of multimode VFR. Their contribution is
analyzed using a statistical approach, with an outlook towards more accurate
treatment of this phenomenon.
