# Assessment of simple and intuitive semiempirical approximations for non-adiabatic coupling vectors in the frame of (LC)-TDDFTB

## TL;DR

This paper introduces two semiempirical methods for approximating non-adiabatic coupling vectors in quantum chemistry, benchmarking their qualitative performance and exploring their implications for electronic coupling and fluorescence in extended molecular systems.

## Contribution

It presents two simple semiempirical schemes for calculating non-adiabatic coupling vectors and evaluates their qualitative effectiveness within the (LC)-TDDFTB framework.

## Key findings

- Atomic NAC vectors are often qualitatively reproduced.
- Quantitative accuracy of NAC magnitudes is limited.
- Size-dependent trends in fluorescence yields are qualitatively predicted.

## Abstract

In this study, two different simple and intuitive semiempirical schemes for computing approximate non-adiabatic coupling vectors (NACVs) between the ground and excited electronic states are presented. The first approximation makes use of Mulliken transition charges, while the second is based on derivative coupling vectors between localized molecular orbitals. Both approximations lend themselves easily to implementation within a whole spectrum of semiempirical quantum-chemical semiempirical methods. Here we present the implementation within the tight-binding DFT and benchmark its performance against analytical TD-DFT NAC vectors for a range of planar fluorescent chromophores at the Franck-Condon point. The pattern of the atomic NAC vectors is often reproduced, but the relative magnitude and total length of the NAC vector are often in serious error. Although quantitative predictions are not possible, these simple and intuitive approximations allow to explain, in a qualitative way, trends in the electronic coupling in extended molecular systems and complex materials. In this context, we investigate how the non-adiabatic coupling depends on the delocalization length of an excitation in chromophoric oligomers based on a simple model. Finally, we make general qualitative predictions on the size dependence of the fluorescence quantum yields in extended molecular systems, and illustrate those on the example of triply fused porphyrin tapes with increasing length.