We investigated spin states of stable neutral pure-organic radical molecules of 1,3,5-triphenyl-6-oxoverdazyl (TOV) and 1,3,5-triphenyl-6- thioxoverdazly (TTV) adsorbed on an Au(111) surface, which appears as a Kondo resonance because of spin-electron interaction. By using scanning tunneling spectroscopy (STS), a clear Kondo resonance was detected for the TOV molecule. However, no Kondo resonance was detected for TOV molecules with protrusions in the occupied state image and for TTV molecules. Spin-resolved DFT calculations showed that an unpaired π electron was delocalized over the adsorbed TOV molecule, which was the origin of the Kondo resonance. For the TOV molecules with protrusions, we proposed a model in which an additional H atom was attached to the TOV molecule. Calculations showed that, upon transfer of an electron to the verdazyl ring, the unpaired π electron disappeared, accounting for the absence of a Kondo resonance in the STS spectra. The absence of a Kondo resonance for the TTV molecule can be explained in a similar manner. In other words, electron transfer to the verdazyl ring occurs because of Au-S bond formation.