Fast vs Accurate: Evaluating TD-DFTB for Large-Scale Screening of Organic Dyes

Abstract

The effectiveness of the semi-empirical TD-DFTB (Time-Dependent Density Functional Tight Binding) method in reproducing the spectral properties of organic dyes was investigated using the example of a library of isomers of the thiophene-containing donor-acceptor Effenberger dye, known for its pronounced solvatochromism. The aim of the work was to find out how suitable the accelerated TD-DFTB approach is for modern molecular design tasks, with a necessity to quickly and reliably identify compounds with intense electronic transitions in the long-wavelength region of the UV-Vis spectrum. The library contained 60 structures in which the positions of the donor (N,N-dimethylamine) and acceptor (NO₂) substituents, as well as the degree of planarity of the π-framework, were systematically varied. For each isomer, the geometry was first optimized at the DFTB level, after which the excitation energies were calculated using the TD-DFTB method. The obtained values were compared with TD-DFT calculations (B3LYP and CAM-B3LYP functionals) performed with geometries, obtained both at DFT and DFTB methods. Such a hybrid scheme significantly reduces the computational costs, allowing screening of large libraries without losing the accuracy. The correlation between excitation energies calculated by TD-DFTB and TD-DFT is given. As obtained, TD-DFTB tends to systematically underestimate the excitation energies, but largely reflects compounds with minimal excitation energies and large oscillator strengths, which makes it a reliable tool for initial screening. Several isomers with long-wavelength absorption and sufficient transition intensity were identified, which are promising for further modification. Thus, TD-DFTB in combination with TD-DFT on optimized DFTB geometries demonstrates an optimal balance between accuracy and speed for prescreening donor-acceptor dyes with given spectral parameters, which significantly enhances the capabilities of rational design of functional organic materials.