In this paper, a joint strategy was proposed to investigate the microscopic origin of the second-harmonic-generation (SHG) response in nonpolar ABCO(3)F compounds. The SHG coefficients of ABCO(3)F were, evaluated using finite-field and sum-over-states methods. The tendency of the obtained SHG tensors is in-good agreement with the powder SHG response. The atomic contribution was investigated using variation of the atomic charges and bandwidth of occupied atomic states. The results show that oxygen states play a key role in determining the SHG response, and the neighboring divalent cations exert a indirect influence via covalent interaction. The bidentate bonding pattern is beneficial to obtaining a largely enhanced SHG response.