TD-DFT+TB: An Efficient and Fast Approach for Quantum Plasmonic Excitations

Abstract

We study the quantum plasmonic features of gold and silver nanoparticles using TD-DFT+TB, a new density functional theory approach to the calculation of excited states, which combines a full DFT ground state with tight-binding approximations in the linear response calculation. In this framework, the optical properties of closed-shell Ag, Au and bimetallic Ag–Au nanoparticles with tetrahedral symmetry (with 20, 56, 120, and 165 atoms) and icosahedral structure (with 13, 55, and 147 atoms) were obtained and compared to full linear response time-dependent density functional theory (TD-DFT) as a reference and also to time-dependent density functional based tight binding (TD-DFTB) as a low-cost alternative approach. We find an excellent agreement of TD-DFT+TB calculated absorption spectra with the TD-DFT reference with errors less than 0.15 eV in peak positions, while TD-DFTB shows larger errors of about 1 eV. The computational cost for the ground state calculation is identical for TD-DFT and TD-DFT+TB, but the excited state calculation becomes about a hundred times faster when applying the TB approximation and is then almost negligible for the overall timing of the calculation. In contrast to TD-DFTB, which can only be applied to element combinations for which a suitable DFTB parametrization is available, TD-DFT+TB can be applied to any combination of elements. To assess the accuracy of TD-DFT+TB for different combinations of atoms, the plasmonic properties of bimetallic clusters with different ratios of Ag and Au atoms were obtained and the trend of energy and intensity reproduced in good agreement with TD-DFT, which is not possible using TD-DFTB with standard parameter sets.

Effect of the Metal–Ligand Interface on the Chiroptical Activity of Cysteine‐Protected Nanoparticles

“…This behavior is consistent with the current knowledge that, at this size range there would be a coexistence of shapes and morphologies, [ 46 ] displaying high intensity absorption peaks between 300 and 400 nm, as has been shown in several TD‐DFT calculations. [ 47–51 ] In the case of Au NPs, the observed band (Figure S4a, Supporting Information), indicates a molecular‐like absorption that may be attributed to the discrete electronic sp <‐ d interband transitions arising from the presence of small (with diameters in the size range of 1.5–3.5 nm) NPs in the sample solution. [ 49,51,52 ] This turn to “molecule‐like behavior” from a “metallic behavior” has been suggested to happen in a crossover region (≈2 nm) from 150 to 250 gold atoms, where the optical response of gold NPs changes considerably.…”

“…[ 47–51 ] In the case of Au NPs, the observed band (Figure S4a, Supporting Information), indicates a molecular‐like absorption that may be attributed to the discrete electronic sp <‐ d interband transitions arising from the presence of small (with diameters in the size range of 1.5–3.5 nm) NPs in the sample solution. [ 49,51,52 ] This turn to “molecule‐like behavior” from a “metallic behavior” has been suggested to happen in a crossover region (≈2 nm) from 150 to 250 gold atoms, where the optical response of gold NPs changes considerably. [ 53,54 ] The absorption spectra of l ‐ and d ‐cysteine showed the same signal for both enantiomers centered around 200 nm as expected for this amino acid (Figure S5a, Supporting Information).…”

First principle simulation of coated hydroxychloroquine on Ag, Au and Pt nanoparticles

“…The interactions of HCQ with icosahedral silver and gold clusters with 147 atoms were investigated at the PBE-D3/TZP level of the theory under the influence of the relativistic effect (ZORA). To determine the effect of HCQ drug on the electronic structures and the plasmonic absorption spectra of noble metal particles, the recently developed time-dependent density functional approach, TD-DFT + TB method 48 , 49 which combines a full DFT ground state with tight-binding approximations, was applied. The excited states calculations were performed at optimized geometries using the asymptotically corrected LB94 xc-functional 50 , and the absorption spectra were obtained in the range of 0.0–6.0 eV.…”

Modeling of plasmonic properties of nanostructures for next generation solar cells and beyond

“…In Ref. [145] LR TD-DFT was used to compute spectra including plasmonic peaks of small (up to 165 atoms) silver, gold, and bimetallic Au-Ag particles of different shapes and sizes. The accuracy can be judged from the comparison with the experimental spectrum for Ag 55 shown in Figure 6 and is more qualitative than quantitative.…”

“…The method needs to be parameterized with the so-called Slater-Koster (SK) parameters and allows for the formulation of TD-DFTB based on the Casida formalism [89,90]. Asadi-Aghbolaghi et al [145] compared (LR) TD-DFTB with (LR) TD-DFT calculations with their proposed method which combines a full DFT ground state calculation with tight-binding approximations in the linear response calculation (called TD-DFT+TB), when computing optical properties of Ag, Au and bimetallic Ag−Au nanoparticles with tetrahedral icosahedral structures with up to 165 atoms. The number of included excited states ranged 3,000 − 30,000 depending on the cluster.…”