Nonadiabatic Dynamics of Cycloparaphenylenes with TD-DFTB Surface Hopping

Abstract

We implemented a version of the decoherence-corrected fewest switches surface hopping based on linear-response time-dependent density functional tight binding (TD-DFTB), enhanced by transition density analysis. The method has been tested for the gas-phase relaxation dynamics of two cycloparaphenylene molecules, [8]CPP and [10]CPP, explaining some important features of their nonadiabatic dynamics, such as the origin of their long fluorescence lifetimes (related to the slow radiative emission from the S state) and the trend of increasing the fluorescence rate with the molecular size (related to an increase in the S-S energy gaps and oscillator strengths in the larger molecule). The quality of the TD-DFTB electronic structure information was assessed through four quantities: excitation energies; charge-transfer (CT) numbers, which estimate the charge transfer character of states; participation ratio (PR), which describes delocalization of electronic density; and participation ratio of natural transition orbitals (PRNTO), which describes the multiconfigurational character of states. These quantities were computed during dynamics and recomputed for the same geometries with the higher-level long-range-corrected TD-LC-DFTB and a lower-level single-determinant approximation for the excited states, SD-(LC)-DFTB. Taking TD-LC-DFTB as the standard, TD-DFTB underestimates the excitation energies by ∼0.5 eV and overestimates CT and PR. SD-DFTB underestimates excitation energies and overestimates CT to the same extent that TD-DFTB does, but it predicts reasonable PR distributions. SD-LC-DFTB leads to an extreme overestimation of the excitation energies by ∼3 eV, overestimates the charge transfer character of the state, but predicts the PR values very close to those obtained with TD-LC-DFTB.

Recent Advances and Perspectives on Nonadiabatic Mixed Quantum–Classical Dynamics

“…Fischer et al 350 322 A reasonable agreement between these methods was found too. Nevertheless, it tends to degrade for delocalized densities.…”

Toward an understanding of electronic excitation energies beyond the molecular orbital picture

“…In the following, we will use PR NTO , considering that this has already found various applications in the literature 75,[85][86][87] despite its ad hoc nature.…”

Density-functional tight-binding: basic concepts and applications to molecules and clusters

“…DFTB, as a density functional method, is not initially designed to use wavefunctions to compute properties. Nevertheless, the most common practice is to use the excited state wavefunctions associated with the single excitation configuration interaction (CIS) approximation spanning the TD-DFTB excited states to determine the non-adiabatic couplings presented above [197][198][199][200][201]. This can be achieved through the calculation of the overlap of the CIS electronic wavefunctions between nuclear time steps t and t þ Δt.…”

“…This procedure is described within the framework of TD-DFTB by Humeniuk and Mitrić [200]. Several implementations of FSSH are available within various open-source DFTB codes, such as DFTBaby [200], DFTB+ coupled with the NewtonX or PYXAID packages [201,202] and DeMonNano [203].…”

“…In addition to the simulation of exciton dynamics in molecular clusters [200,[362][363][364] reported in section 4.3, the FSSH scheme for non-adiabatic dynamics has been used to simulate excimer formation in the pyrene dimer [365] or relaxation of excited fluorene oligomers [200]. Relaxation dynamics enhanced by transition density analysis has been investigated by Stojanović et al for two cycloparaphenylene molecules (labelled [8]CPP and [10]CPP) in ref [201]). Other authors have studied the intraband electron and hole relaxation as well as nonradiative electron-hole recombination in a CdSe quantum dot and the (10,5) semiconducting carbon nanotube [202].…”