## 3 Results and Discussion
For blue colorants used in color filters for image sensors, the molar extinction coefficient is required to be greater than 1.0 \(\times\) 10\({}^{4}\) L/mol\(\cdot\)cm, with transmittance standards of over 85% at 430 nm and below 12.5% at 650 nm. The molar extinction coefficient was calculated using the Beer-Lambert law, and the optical absorbance properties of the blue colorants were evaluated accordingly. \[A=\varepsilon c\]  
\(A\): absorbance, \(\varepsilon\): molar extinction coefficient, \(c\): molar concentration, \(l\): optical path length  
The synthesized pyrrole derivatives and Disperse Blue 359 showed absorption in the ranges of 300-450 nm and 500-700 nm. The maximum absorption wavelengths (UV\({}_{\text{max}}\)) of BAPCP and HAPCP were 615 nm and 616 nm, respectively, while the commercial blue colorant Disperse Blue 359 exhibited UV\({}_{\text{max}}\) at 612 nm and 651 nm. The synthesized compounds, along with Disperse Blue 359, exhibited very high molar extinction coefficient (\(\varepsilon_{\text{max}}\)) values. Unlike Disperse Blue 359, the two synthesized compounds displayed absorbance intensities exceeding 1. The \(\varepsilon_{\text{max}}\) values at the maximum absorption wavelengths for BAPCP and HAPCP were 6.03 \(\times\) 10\({}^{4}\) and 6.91 \(\times\) 10\({}^{4}\) L/mol\(\cdot\)cm, respectively. Compared to Disperse Blue 359, BAPCP and HAPCP exhibited molar extinction coefficients that were more than four times higher. While the molar extinction coefficients of BAPCP and HAPCP were similar, HAPCP showed a slight increase. This increase may be due to the relatively longer alkyl groups in HAPCP, which could lead to greater molecular spacing. A closer molecular distance may result in energy transfer between molecules, potentially reducing absorption efficiency. Therefore, the increased molar extinction coefficient of HAPCP compared to BAPCP can be attributed to this factor. At 615 nm, the molar absorption coefficients of BAPCP and HAPCP were 6.03 \(\times\) 10\({}^{4}\) and 6.91 \(\times\) 10\({}^{4}\) L/mol\(\cdot\)cm, respectively, demonstrating a difference of over 14% (Figure S7). This variation may have a direct impact on optical efficiency and color fidelity. In conclusion, both synthesized compounds demonstrated molar extinction coefficients exceeding 1.0 \(\times\) 10\({}^{4}\) L/mol\(\cdot\)cm in PGMEA solvent, indicating their excellent potential as candidates for blue colorants. The transmittance properties of the synthesized materials in solution were evaluated, with the resulting data exhibited in Figure 2 and Table 2. The transmittance spectra were measured under identical conditions using a 1 \(\times\) 10\({}^{-4}\) M concentration in PGMEA. For commercial blue colorants used in image sensors, the required transmittance values must be above 85% at 430 nm and below 12.5% at 650 nm. HAPCP showed transmittance values of 99.6% at 430 nm and 0.36% at 650 nm, while BAPCP exhibited transmittance values of 88.6% at 430 nm and 0.73% at 650 nm, meeting all commercial standards. In comparing the transmittance values of the synthesized compounds to those of the commercial blue colorant, Disperse Blue 359, the synthesized compounds demonstrated higher transmittance at 650 nm. This suggests that the synthesized materials have optical properties favorable for commercialization and are likely to offer high color purity when used as blue colorants in image sensor applications. The optimized molecular structures and electronic properties of the synthesized blue materials were analyzed using molecular calculations, with the findings summarized in Figures 3 and 4 as well as Table S1. The B3 LYP-D3 method was selected for molecular calculations due to its high accuracy and efficiency in energy and molecular orbital (MO) calculations. For the basis set, the def2-TZVPP was chosen, considering its balance of computational efficiency and accuracy. The inclusion of polarization functions further optimized it for flexible molecular structures [28].