Unraveling substituent effects on frontier orbitals of conjugated molecules using an absolutely localized molecular orbital based analysis

It is common to introduce electron-donating or electron-withdrawing substituent groups into functional conjugated molecules (such as dyes) to tune their electronic structure properties (such as frontier orbital energy levels) and photophysical properties (such as absorption and emission wavelengths). However, there lacks a generally applicable tool that can unravel the underlying interactions between orbitals from a substrate molecule and those from its substituents in modern electronic structure calculations, despite the long history of qualitative molecular orbital theory. In this work, the absolutely localized molecular orbitals (ALMO) based analysis is extended to analyze the effects of substituent groups on the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) of a given system. This provides a bottom-up avenue towards quantification of effects from distinct physical origins (e.g. permanent electrostatics/Pauli repulsion, mutual polarization, inter-fragment orbital mixing). For the example case of prodan (a typical dye molecule), it is found that inter-fragment orbital mixing plays a key role in narrowing the HOMO-LUMO gap of the naphthalene core. Specifically, an out-of-phase mixing of high-lying occupied orbitals on the naphthalene core and the dimethylamino group leads to an elevated HOMO, whereas an in-phase combination of LUMOs on the naphthalene core and the propionyl group lowers the LUMO energy of the entire molecule. We expect this ALMO-based analysis to bridge the gap between concepts from qualitative orbital interaction analysis and quantitative electronic structure calculations.