Compiling data from literature and the Atacama Large Millimeter/submillimeter Array archive, we show enhanced HCN(4-3)/HCO + (4-3) and/or HCN(4-3)/CS(7-6) integrated intensity ratios in circumnuclear molecular gas around active galactic nuclei (AGNs) compared to those in starburst (SB) galaxies (submillimeter HCNenhancement). The number of sample galaxies is significantly increased from our previous work. We expect that this feature could potentially be an extinction-free energy diagnostic tool of nuclear regions of galaxies. Non-LTE radiative transfer modelings of the above molecular emission lines involving both collisional and radiative excitation, as well as a photon trapping effect, were conducted to investigate the cause of the high line ratios in AGNs. As a result, we found that enhanced abundance ratios of HCNtoHCO + and HCNtoCS in AGNs as compared to SB galaxies by a factor of a few to even 10 are a plausible explanation for the submillimeter HCNenhancement. However, a counterargument of a systematically higher gas density in AGNs than in SB galaxies can also be a plausible scenario. Although we cannot fully distinguishthese two scenarios at this moment owing to an insufficient amount of multi-transition, multi-species data, the former scenario is indicative of abnormal chemical composition in AGNs. Regarding the actual mechanism to realize the composition, we suggest that it is difficult with conventional gas-phase X-ray-dominated region ionization models to reproduce the observed high line ratios. We might have to take into account other mechanisms such as neutral-neutral reactions that are efficiently activated in high-temperature environments and/or mechanically heated regions to further understand the high line ratios in AGNs.