Using the state-of-art computational techniques, we limelight a structure-property relationship for the position and number of methoxy group(s) to tune the optical and nonlinear optical (NLO) properties (first hyperpolarizability) of chalcone derivatives. Based on our previously synthesized chalcones [system 1 ((E)-1-(2,5-dimethylthiophen-3-yl)-3-(2-methoxyphenyl)prop-2-en-1-one and system 4 (E)-1-(2,5-dimethylthiophen-3-yl)-3-(2,4,5-trimethoxyphenyl)prop-2-en-1-one)], we systematically design several novel derivatives with tuned optical and NLO properties. For instance, the rotation of methoxy group substitutions at three different possible ortho, meta, and para positions on phenyl ring show significant changes in NLO properties of these chalcones derivatives. The system 3 has shown β tot amplitude of 1776 a.u. with terminal 4-methoxyphenyl group (para-methoxy substitution), which is ~2.2 and 2.4 times larger than that of ortho- and meta-methoxyphenyl systems 1 and 2, respectively. Additionally, systems 3a and 4a, which are cyano derivatives of the systems 3 and 4 show significantly large β tot amplitudes of 3280 and 4388 a.u., respectively, which are about 3 and 4 times larger than that of para-nitro aniline (PNA) molecule (a typical donor-acceptor molecule) at the same LC-wPBE/6-311G** level of theory. The origin of larger β tot amplitudes has been traced in lower transition energies and higher oscillator strengths for crucial transitions of designed derives. Thus, our investigation reveals that the chalcones derivatives with para-methoxyphenyl groups possess reasonably large amplitudes of their first hyperpolarizability and good optical transparency (3.0-4.7 eV), which can make them attractive candidates for nonlinear optical applications.