Using density functional theory calculations, we have analyzed second-order nonlinear optical (NLO) properties of a series of 1À 6, 9, 12). This type of modification can induce evident electron transfer between the graphyne and conjugated chain and decrease the transition energy, resulting in the system exhibiting a large static first hyperpolarizability (β 0 ). The β 0 values of the GY[n]À (CH=CH) m À NH 2 /NO 2 show a monotonously increasing trend with lengthening the À (CH=CH) m À NH 2 /NO 2 chain from m = 1 to 12. Further, the NO 2 -modified system has a higher β 0 value than the corresponding NH 2 -modified system with the same π-conjugated length. Compared with the singlemodified GY[1], the À (CH=CH) m À NH 2 /NO 2 co-modified GY[1] systems exhibit better NLO responses. For GY-[n]À (CH=CH) m À NO 2 , when m = 1À 4, the β 0 value increases with increasing the size of graphyne, while for m = 5, 6, 9, 12, the varying order is reversed. Solvent and frequency dispersion effects are also analyzed. The polarizable environment has a significant influence on hyper-Rayleigh scattering first hyperpolarizability (β HRS ).