Is (benzene)Cr(CO)3 really more aromatic than benzene?

(benzene)Cr(CO)3 was claimed to be more aromatic than benzene, based on the central 1H Me chemical shifts in dimethyldihydropyrene annulated to it. In this paper, several dihydropyrenes are computationally investigated. NICS-scan methods are used to assess the ring current properties, and NMR calculations are used for obtaining NMR chemical shifts. The parent and four benz-annulated dihydropyrenes show excellent agreement with the experimental results, reported by R. Mitchell in several papers. The effect of annulating the antiaromatic cyclobutadiene was shown to be larger than that of benzene and to change the type of ring currents; while benz-annulated dihydropyrenes maintain local 14-annulene and local benzenic ring currents, the cyclobutadiene-annulated dihydropyrenes show global (and local) ring currents. A NICS-scan study of (benzene)Cr(CO)3 and a NICS-XY-scan study of the (CO)3Cr(C6H4)-annulated to dihydropyrene show that the benzene in the Cr complex is at most aromatic as benzene, probably somewhat less. A detailed study of the 1H chemical shifts suggests that the experimental results were somewhat misinterpreted, and that (benzene)Cr(CO)3 is at most as aromatic as benzene.