# Design and Color Prediction of Anthracene-Based Dyes Based on Quantum Chemical Calculations

## TL;DR

This paper uses quantum calculations to predict the colors of anthracene-based dyes and provides a model for designing new pigments with high efficiency.

## Contribution

The study introduces a computational model linking quantum calculations to color prediction for anthracene derivatives.

## Key findings

- Frontier molecular orbital analysis showed an inverse correlation between conjugation extent and HOMO-LUMO energy gap.
- TD-DFT calculations predicted excitation wavelengths of 438 nm, 441 nm, 464 nm, and 496 nm for four anthracene derivatives.
- Complementary color theory predicted visual colors of yellow, yellow, red, and orange based on absorption characteristics.

## Abstract

We systematically investigated the parent anthracene (abbreviated as en-1, C14H10) and three N,N′-disubstituted derivatives: the 1,5-diethylanthracene (en-2, C18H18), the 1,5-divinylanthracene (en-3, C18H14), and the 1,5-diphenylanthracene (en-4, C26H18), using a rigorous density functional theory (DFT)/time-dependent density functional theory (TD-DFT) approach. Following full geometric optimization and frequency validation (no imaginary frequencies), frontier molecular orbital analysis revealed an inverse correlation between conjugation extent and the HOMO-LUMO energy gap. Electrostatic potential (ESP) analysis further indicated a progressive increase in surface potential variance upon substitution, reflecting charge redistribution. TD-DFT calculations yielded vertical excitation wavelengths of 438 nm, 441 nm, 464 nm, and 496 nm for en-1, en-2, en-3, and en-4, respectively. Complementary color theory predicts visual colors of yellow, yellow, red, and orange for these compounds based on their absorption characteristics. This work establishes a closed-loop “computation-spectra-color” model for anthracene-based dyes, providing a transferable design paradigm for novel functional pigments with high molar extinction coefficients.