  We give a simple toy model to study a famous Jahn-Teller type molecule.
Finite lifetime due to non-adiabatic coupling and finite temperature effect
results in the effective Hamiltonian to be non-Hermitian. This effect pulls a
conical intersection into a pair of connected Weyl points, bridged by a Fermi
arc. The length of the Fermi arc depends on the strength of non-hermicity. This
is a unique feature of non-Hermitian topology with no Hermitian analogue. We
predict the existence of Weyl points in molecules which cause anomalous
Jahn-Teller effects and fractional quantum number.
