A correlation is shown between the negative differential conductance of single molecules recorded using scanning tunneling microscopes and gas-phase long-lived negative ions formed upon resonant electron capture by the same molecules with a multiplicity of four (4TNI#) and a spin prohibition on the rapid autodetachment of an additional electron. It is assumed that negative differential conductance in the studied compounds is associated with the formation of 4TNI# ions in scanning tunneling microscopes, which suppress the tunneling current due to a similar spin prohibition. Remarks are made about a possible mechanism for the formation of 4TNI# ions in scanning tunneling microscopes.