We compare optical and hard X-ray identifications of active galactic nuclei (AGNs) using a uniformly selected (above a flux limit of f 2-8 keV = 3.5 × 10–15?erg?cm–2?s–1) and highly optically spectroscopically complete (80% for f 2-8 keV 10–14?erg?cm–2?s–1 and 60% below) 2-8?keV sample observed in three Chandra fields (CLANS, CLASXS, and the CDF-N). We find that empirical emission-line ratio diagnostic diagrams misidentify 50% of the X-ray-selected AGNs that can be put on these diagrams as star formers. We confirm that there is a large (two orders of magnitude) dispersion in the ratio of the [O III]λ5007 (hereafter [O III]) to hard X-ray luminosities for the non-broad-line AGNs, even after applying reddening corrections to the [O III] luminosities. We find that the dispersion is similar for the broad-line AGNs, where there is not expected to be much X-ray absorption from an obscuring torus around the AGN nor much obscuration from the galaxy along the line of sight if the AGN is aligned with the galaxy. We postulate that the X-ray-selected AGNs that are misidentified by the diagnostic diagrams have low [O III] luminosities due to the complexity of the structure of the narrow-line region, which causes many ionizing photons from the AGN not to be absorbed. This would mean that the [O III] luminosity can only be used to predict the X-ray luminosity to within a factor of ~3 (1σ). Despite selection effects, we show that the shapes and normalizations of the [O III] and transformed hard X-ray luminosity functions show reasonable agreement, suggesting that the [O III] samples are not finding substantially more AGNs at low redshifts than hard X-ray samples.
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