Toward quantitative electronic structure in small gold nanoclusters

Ligand-protected gold nanoclusters (AuNCs) feature a dense but finite electronic structure that can be rationalized using qualitative descriptions such as the well-known superatomic model and predicted using quantum chemical calculations. However, the lack of well-resolved experimental probes of a AuNC electronic structure has made the task of evaluating the accuracy of electronic structure descriptions challenging. We compare electronic absorption spectra computed using time-dependent density functional theory to recently collected high resolution experimental spectra of Au₉(PPh₃)₈ ³⁺ and Au₈(PPh₃)₇ ²⁺ AuNCs with strikingly similar features. After applying a simple scaling correction, the computed spectrum of Au₈(PPh₃)₇ ²⁺ yields a suitable match, allowing us to assign low-energy metal-metal transitions in the experimental spectrum. No similar match is obtained after following the same procedure for two previously reported isomers for Au₉(PPh₃)₈ ³⁺, suggesting either a deficiency in the calculations or the presence of an additional isomer. Instead, we propose assignments for Au₉(PPh₃)₈ ³⁺ based off of similarities Au₈(PPh₃)₇ ²⁺. We further model these clusters using a simple particle-in-a-box analysis for an asymmetrical ellipsoidal superatomic core, which allows us to reproduce the same transitions and extract an effective core size and shape that agrees well with that expected from crystal structures. This suggests that the superatomic model, which is typically employed to explain the qualitative features of nanocluster electronic structures, remains valid even for small AuNCs with highly aspherical cores.

Impact of Ligands on Structural and Optical Properties of Ag29 Nanoclusters

A ligand exchange strategy has been employed to understand the role of ligands on the structural and optical properties of atomically precise 29 atom silver nanoclusters (NCs). By ligand optimization, ∼44-fold quantum yield (QY) enhancement of Ag₂₉(BDT)_12-x(DHLA)_x NCs (x = 1-6) was achieved, where BDT and DHLA refer to 1,3-benzene-dithiol and dihydrolipoic acid, respectively. High-resolution mass spectrometry was used to monitor ligand exchange, and structures of the different NCs were obtained through density functional theory (DFT). The DFT results from Ag₂₉(BDT)₁₁(DHLA) NCs were further experimentally verified through collisional cross-section (CCS) analysis using ion mobility mass spectrometry (IM MS). An excellent match in predicted CCS values and optical properties with the respective experimental data led to a likely structure of Ag₂₉(DHLA)₁₂ NCs consisting of an icosahedral core with an Ag₁₆S₂₄ shell. Combining the experimental observation with DFT structural analysis of a series of atomically precise NCs, Ag_29-yAu_y(BDT)_12-x(DHLA)_x (where y, x = 0,0; 0,1; 0,12 and 1,12; respectively), it was found that while the metal core is responsible for the origin of photoluminescence (PL), ligands play vital roles in determining their resultant PLQY.

Real-Time Electron Dynamics Study of Plasmon-Mediated Photocatalysis on an Icosahedral Al13-1 Nanocluster

Nitrogen bond dissociation is one of the important steps in the Haber-Bosch process, where N₂ is catalytically converted to NH₃; however, the dissociation of the nitrogen triple bond is difficult to achieve. In this study, we investigate the possibility of nitrogen activation using plasmonic excitation of an icosahedral aluminum nanocluster. Real-time time-dependent density functional theory is employed to study the electron dynamics of the Al₁₃^-1 and [Al₁₃N₂]^-1 systems. Step and trapezoidal electric fields with field strengths of 0.001 and 0.01 au and different polarization directions are applied to the systems, and the electron dynamics are analyzed. Because the occupation of nitrogen antibonding orbitals could potentially activate the N-N bond, we investigated the single-particle electronic transitions corresponding to an excitation from an occupied (O) to virtual (V) molecular orbitals (P_OV) of [Al₁₃N₂]^-1. We found that N₂ antibonding orbitals are more likely to become populated with stronger fields and also by using off-resonance fields.

Nonradiative relaxation dynamics in the [Au25-nAgn(SH)18]-1 (n = 1, 12, 25) thiolate-protected nanoclusters

Evaluation of the electron-nuclear dynamics and relaxation mechanisms of gold and silver nanoclusters and their alloys is important for future photocatalytic, light harvesting, and photoluminescence applications of these systems. In this work, the effect of silver doping on the nonradiative excited state relaxation dynamics of the atomically precise thiolate-protected gold nanocluster [Au_25-nAg_n(SH)₁₈]^-1 (n = 1, 12, 25) is studied theoretically. Time-dependent density functional theory is used to study excited states lying in the energy range 0.0-2.5 eV. The fewest switches surface hopping method with decoherence correction was used to investigate the dynamics of these states. The HOMO-LUMO gap increases significantly upon doping of 12 silver atoms but decreases for the pure silver nanocluster. Doped clusters show a different response for ground state population increase lifetimes and excited state population decay times in comparison to the undoped system. The ground state recovery times of the S₁-S₆ states in the first excited peak were found to be longer for [Au₁₃Ag₁₂(SH)₁₈]^-1 than the corresponding recovery times of other studied nanoclusters, suggesting that this partially doped nanocluster is best for preserving electrons in an excited state. The decay time constants were in the range of 2.0-20 ps for the six lowest energy excited states. Among the higher excited states, S₇ has the slowest decay time constant although it occurs more quickly than S₁ decay. Overall, these clusters follow common decay time constant trends and relaxation mechanisms due to the similarities in their electronic structures.

Correction: Analysis and visualization of energy densities. I. Insights from real-time time-dependent density functional theory simulations

Correction for 'Analysis and visualization of energy densities. I. Insights from real-time time-dependent density functional theory simulations' by Junjie Yang et al., Phys. Chem. Chem. Phys., 2020, 22, 26838-26851, DOI: .

Analysis and visualization of energy densities. I. Insights from real-time time-dependent density functional theory simulations

In this article, we report a scheme to analyze and visualize the energy density fluctuations during the real-time time-dependent density functional theory (RT-TDDFT) simulations. Using Ag4-N2 complexes as examples, it is shown that the grid-based Kohn-Sham energy density can be computed at each time step using a procedure from Nakai and coworkers. Then the instantaneous energy of each molecular fragment (such as Ag4 and N2) can be obtained by partitioning the Kohn-Sham energy densities using Becke or fragment-based Hirshfeld (FBH) scheme. A strong orientation-dependence is observed for the energy flow between the Ag4 cluster and a nearby N2 molecule in the RT-TDDFT simulations. Future applications of such an energy density analysis in electron dynamics simulations are discussed.

Analysis and visualization of energy densities. II. Insights from linear-response time-dependent density functional theory calculations

Inspired by the analysis of Kohn-Sham energy densities by Nakai and coworkers, we extended the energy density analysis to linear-response time-dependent density functional theory (LR-TDDFT) calculations. Using ethylene-tetrafluoroethylene and oxyluciferin-water complexes as examples, distinctive distribution patterns were demonstrated for the excitation energy densities of local excitations (within a molecular fragment) and charge-transfer excitations (between molecular fragments). It also provided a simple way to compute the effective energy of both hot carriers (particle and hole) from charge-transfer excitations via an integration of the excitation energy density over the donor and acceptor grid points.

Ultrafast Nonradiative Decay of a Dipolar Plasmon-like State in Naphthalene

Motivated by the uncertainty in our understanding of ultrafast plasmon decay mechanisms, we examine the effect of nuclear vibrations on the dynamical behavior of the strong plasmon-like dipole response of naphthalene, known as the β peak. The real-time time-dependent density functional (RT-TDDFT) method coupled with Ehrenfest molecular dynamics is used to describe the interconnected nuclear and electronic motion. Several vibrational modes promote drastic plasmon decay in naphthalene. The most astonishing finding of this study is that activation of one particular vibrational mode (corresponding to the B_1u representation in D_2h point group symmetry) leads to a continuous drop of the dipole response corresponding to the β peak into a totally symmetric, dark, quadrupolar electronic state. A second B_1u mode provokes the sharp plasmon-like peak to split due to the breaking of structural symmetry. Nonadiabatic coupling between a B_2g vibrational mode and the β peak (a B_1u electronic state) gives rise to a B_3u vibronic state, which can be identified as one of the p-band peaks that reside close in energy to the β peak energy. Overall, strong nonadiabatic coupling initiates plasmon decay into nearby electronic states in acenes, most importantly into dark states. These findings expand our knowledge about possible plasmon decay processes and pave the way for achieving high optical performance in acene-based materials such as graphene.

TD-DFTB study of optical properties of silver nanoparticle homodimers and heterodimers

The absorption spectra for face-centered cubic nanoparticle dimers at various interparticle distances are investigated using time-dependent density functional tight binding. Both homodimers and heterodimers are investigated in this work. By studying nanoparticles at various interparticle distances and analyzing their vertical excitations, we found that as the interparticle distance decreases, a red shift arises from contributions of the transition dipole moment that are aligned along the z-axis with nondegenerate features; blue shifts occur for peaks that originate from transition dipole moment components in the x and y directions with double degeneracy. When the nanoparticles are similar in size, the features in the absorption spectra become more sensitive to the interparticle distances. The best-fit curves from vertical excitation energy in the form of AR^-b for ΔE_redshift/ΔE_blueshift vs R are determined. In this way, we determined trends for absorption peak shifts and how these depend on the interparticle distance.

A topological isomer of the Au25(SR)18- nanocluster

Energetically low-lying structural isomers of the much-studied thiolate-protected gold cluster Au25(SR)18- are discovered from extensive (80 ns) molecular dynamics (MD) simulations using the reactive molecular force field ReaxFF and confirmed by density functional theory (DFT). A particularly interesting isomer is found, which is topologically connected to the known crystal structure by a low-barrier collective rotation of the icosahedral Au13 core. The isomerization takes place without breaking of any Au-S bonds. The predicted isomer is essentially iso-energetic with the known Au25(SR)18- structure, but has a distinctly different optical spectrum. It has a significantly larger collision cross-section as compared to that of the known structure, which suggests it could be detectable in gas phase ion-mobility mass spectrometry.

Electronic relaxation dynamics in [Au25(SR)18]−1 (R = CH3, C2H5, C3H7, MPA, PET) thiolate-protected nanoclusters

Excited state decay times in thiolate-stabilized gold nanoclusters exhibit a degree of dependence on the passivating ligand.

Understanding plasmon coupling in nanoparticle dimers using molecular orbitals and configuration interaction

We perform a theoretical investigation of the electronic structure and optical properties of atomic nanowire and nanorod dimers using DFT and TDDFT. In both systems at separation distances larger than 0.75 nm, optical spectra show a single feature that resembles the bonding dipole plasmon (BDP) mode. A configuration interaction (CI) analysis shows that the BDP mode arises from constructive coupling of transitions, whereas the destructive coupling does not produce significant oscillator strength for such separation distances. At shorter separation distances, both constructive and destructive coupling produce oscillator strength due to wave-function overlap, which results in multiple features in the calculated spectra. Our analysis shows that a charge-transfer plasmon (CTP) mode arises from destructive coupling of transitions, whereas the BDP results from constructive coupling of the same transitions at shorter separation distances. Furthermore, the coupling elements between these transitions are shown to depend heavily on the amount of exact Hartree-Fock exchange (HFX) in the functional, which affects the splitting of CTP and BDP modes. With 50% HFX or more, the CTP and BDP modes mainly merge into a single feature in the spectra. These findings suggest that the effects of exact exchange must be assessed during the prediction of CTP modes in plasmonic systems.

[Au18(dppm)6Cl4]4+: a phosphine-protected gold nanocluster with rich charge states

A diphosphine-protected 18-gold-atom nanocluster was isolated via a facile reduction of an Au^I precursor by NaBH₄.

Electronic and Geometric Structure, Optical Properties, and Excited State Behavior in Atomically Precise Thiolate-Stabilized Noble Metal Nanoclusters

Ligand-protected noble metal nanoclusters are of interest for their potential applications in areas such as bioimaging, catalysis, photocatalysis, and solar energy harvesting. These nanoclusters can be prepared with atomic precision, which means that their stoichiometries can be ascertained; the properties of these nanoclusters can vary significantly depending on the exact stoichiometry and geometric structure of the system. This leads to important questions such as: What are the general principles that underlie the physical properties of these nanoclusters? Do these principles hold for all systems? What properties can be "tuned" by varying the size and composition of the system? In this Account, we describe research that has been performed to analyze the electronic structure, linear optical absorption, and excited state dynamics of thiolate-stabilized noble metal nanoclusters. We focus primarily on two systems, Au₂₅(SR)₁₈^- and Au₃₈(SR)₂₄, as models for understanding the principles underlying the electronic structure, optical properties, luminescence, and transient absorption in these systems. In these nanoclusters, the orbitals near the HOMO-LUMO gap primarily arise from atomic 6sp orbitals located on Au atoms in the gold core. The resulting nanocluster orbitals are delocalized throughout the core of these systems. Below the core-based orbitals lies a set of orbitals that are primarily composed of Au 5d and S 3p atomic orbitals from atoms located around the exterior gold-thiolate oligomer motifs. This set of orbitals has a higher density of states than the set arising from the core 6sp orbitals. Optical absorption peaks in the near-infrared and visible regions of the absorption spectrum arise from excitations between core orbitals (lowest energy peaks) and excitations from oligomer-based orbitals to core-based orbitals (higher energy peaks). Nanoclusters with different stoichiometries have varying gaps between the core orbitals themselves as well as between the band of oligomer-based orbitals and the band of core orbitals. These gaps can slow down nonradiative electron transfer between excited states that have different character; the excited state electron and hole dynamics depend on these gaps. Nanoclusters with different stoichiometries also exhibit different luminescence properties. Depending on factors that may include the symmetry of the system and the rigidity of the core, the nanocluster can undergo large or small nuclear changes upon photoexcitation, which affects the observed Stokes shift in these systems. This dependence on stoichiometry and composition suggests that the size and the corresponding geometry of the nanocluster is an important variable that can be used to tune the properties of interest. How does doping affect these principles? Replacement of gold atoms with silver atoms changes the energetics of the sp and d atomic orbitals that make up the nanocluster orbitals. Silver atoms have higher energy sp orbitals, and the resulting nanocluster orbitals are shifted in energy as well. This affects the HOMO-LUMO gap, the oscillator strength for transitions, the spacings between the different bands of orbitals, and, as a consequence, the Stokes shift and excited state dynamics of these systems. This suggests that nanocluster doping is one way to control and tune properties for use in potential applications.

TD-DFT and TD-DFTB Investigation of the Optical Properties and Electronic Structure of Silver Nanorods and Nanorod Dimers

Here, we perform theoretical investigation using time-dependent density functional theory (TD-DFT) and time-dependent density functional tight binding (TD-DFTB) for the electronic structure and optical properties of silver nanorods. TD-DFTB generally performs well for the accurate description of optical properties with respect to the size and type of dimer assembly of silver nanorods compared to TD-DFT. However, the energies and intensities of the longitudinal and transverse peaks of the nanorods are somewhat underestimated with TD-DFTB compared to the values calculated at the TD-DFT level. By exploiting the computational efficiency of TD-DFTB, we also extend our investigation to longer nanorods and their dimers containing up to ∼2000 atoms. Our results show that the coupling between nanorods and the resulting optical properties of the dimer assemblies are quite dependent on the length of the monomers. In all cases, the energy shifts in dimers as a function of the gap distance deviate significantly from the dipole-dipole interaction model. Moreover, a comparison of the best-fit curves for the dependence of the fractional shifts (Δλ/λ₀) on nanorod length indicates that the parameters of the plasmon ruler equation depend on the length of the nanorods and the type of the assembly rather than approaching a universal value. These insights are enabled by the computational efficiency of TD-DFTB and its ability to treat quantum mechanical effects in large nanorod dimer systems.