Efficient Calculation of Electronic Absorption Spectra by Means of Intensity-Selected Time-Dependent Density Functional Tight Binding

Abstract

During the last two decades density functional based linear response approaches have become the de facto standard for the calculation of optical properties of small and medium-sized molecules. At the heart of these methods is the solution of an eigenvalue equation in the space of single-orbital transitions, whose quickly increasing number makes such calculations costly if not infeasible for larger molecules. This is especially true for time-dependent density functional tight binding (TD-DFTB), where the evaluation of the matrix elements is inexpensive. For the relatively large systems that can be studied the solution of the eigenvalue equation therefore determines the cost of the calculation. We propose to do an oscillator strength based truncation of the single-orbital transition space to reduce the computational effort of TD-DFTB based absorption spectra calculations. We show that even a * To whom correspondence should be addressed sizeable truncation does not destroy the principal features of the absorption spectrum, while naturally avoiding the unnecessary calculation of excitations with small oscillator strengths. We argue that the reduced computational cost of intensity-selected TD-DFTB together with its ease of use compared to other methods lowers the barrier of performing optical properties calculations of large molecules, and can serve to make such calculations possible in a wider array of applications.

Chemical Control and Spectral Fingerprints of Electronic Coupling in Carbon Nanostructures

“…However, previous studies have shown that the TD-DFTB method on conjugated systems such as C 60 produces reasonably good agreement with the experimental values. 22,23 …”

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

“…Calculation of spin-orbit coupling was interfaced by Gao et al [144] for TD-DFT approaches, including TD-DFTB. From a computational efficiency point of view, intensity-selected TD-DFTB has been introduced by Rüger et al [145], delivering similar accuracy as the linear response TD-DFTB, but at a lower computational cost. More details about the TD-DFTB method as well as some other examples of applications can be found in the review paper of T. A. Niehaus [146].…”

DFTBaby: A software package for non-adiabatic molecular dynamics simulations based on long-range corrected tight-binding TD-DFT(B)

“…Alternatively the excitation space could be truncated by selecting the single-orbital transitions with the highest oscillator strengths down to a certain threshold as proposed in Ref. 42 . If the active space is chosen reasonably, the only side-effect is a small systematic increase in the excitation energies as shown in the appendix A.…”