represents the group velocity of i th band for α component. From the figure , it is apparent that C 58 B 1 N 1 shows conductivity (σ /τ) behaviour at lower temperature as compared to C 60 and C 54 B 3 N 3 . The computed values of conductivity of qHP's of C 60 , C 58 B 1 N 1 and C 54 B 3 N 3 at 300 K are 2.59 × 10 10 , 9.80 × 10 12 , and 5.09 × 10 10 , in units of Ω -1 cm -1 s -1 , respectively. Here It was found that qHP C 58 B 1 N 1 shows a thousand times (× 1,000) higher conductivity compared to the other two systems. Interestingly the qHP C 54 B 3 N 3 also shows higher conductivity compared to qHP C 60 . In previous work on qTP C 60 and its similar doped systems, the conductivity at 300 K for C 54 B 3 N 3 is found to be zero and only shows conductivity at higher temperature . It can be concluded that replacing a CC pair with a BN pair in the C 60 fullerene sheet significantly affects the system's conductivity due to the generation of polarity into the bond. The work function (Φ) of all the compounds is calculated using the equation Φ = E vaccum -E f ermi , which represents the energy needed to remove an electron from the Fermi level to a point far away in the vacuum. The work function is a crucial parameter in surface science, catalysis, and related fields, as it characterizes a given surface. The computed work function of the pristine qHP C 60 is 4.91 eV, demonstrating good congruence with the experimental value of 4.56 eV for graphene and 4.85 qTP C 60 . The work function for qHP of C 58 B 1 N 1 and C 54 B 3 N 3 is found to be 4.82 eV and 4.78 eV, respectively and is shown in Figure . The work function of impurity-doped graphene varies depending on the concentration of the impurity defects. . The frequency-dependent complex dielectric constant was calculated using Density Functional Theory (DFT) within the random phase approximation (RPA) . This calculation assesses and characterizes the optical properties of materials. The real (ε 1 ) and imaginary (ε 2 ) parts of the dielectric function (ε) were com- puted using relevant equations (Equation No. 5) . This complex dielectric constant is crucial for understanding optical characteristics such as optical absorption, electron energy loss spectra, refractivity, extinction coefficient, reflectivity, and transmittance .