Effects of Nanowire Doping on Plasmon-Enhanced N2 Dissociation

Doping a transition metal element into plasmonic systems can tune the optical properties of the system, which will potentially facilitate the plasmon-enhanced catalytic process. In this study, we applied the linear-response time-dependent density functional theory (LR-TDDFT) method with real-time electron dynamics and mean-field Ehrenfest dynamics methods to computationally investigate the effects of doping silver nanowires on plasmon-enhanced N2 dissociation. We calculated the absorption spectra for different doped systems, applied an external electric field to the system, and performed mean-field Ehrenfest dynamics to examine how plasmonic excitation will affect the N2 activation or dissociation. In addition, we also studied how the transition metal dopant affects the system's electronic structure and potential energy surface.

Effects of Static Electric Fields on the Excitations of Silver Nanowire Dimers

We theoretically studied the introduction of static electric fields to Ag10 nanowire dimer systems, including the effects of this field on optical absorption characteristics and the orbitals responsible for these excitations. Linear-response time-dependent density functional theory computations were performed on three distinct dimer systems: end-to-end, parallel, and 90° angle dimer systems separated by a closest interparticle distance of 7.0 Å. The calculations were performed in the presence of a 0.1 V/Å electric field strength applied in the z and y directions. The orientation of the dimer system and the direction of the applied static electric field each play a significant role in the resulting absorption spectra and the electronic structure of the nanowires. As a result, a dimer system can exhibit a blue shift for the longitudinal excitation and a red shift for the transverse excitation in the presence of one direction of the static electric field but not for the other direction. Notably, the electron density shifts from one nanowire to the other in the presence of the static electric field. Changes in optical characteristics and electronic structure suggest that the usage of a static electric field with a particular spatial configuration of nanowires provides a way to tune the optical properties of the system.

Temperature-Controlled Selective Formation of Silver Nanoclusters and Their Transformation to the Same Product

Herein, two atomically precise silver nanoclusters, Ag54 and Ag33, directed by inner anion templates (CrO4 2- and/or Cl-), are initially isolated as a mixed phase from identical reactants across a wide temperature range (20-80 °C). Interestingly, fine-tuning the reaction temperature can realize pure phase synthesis of the two nanoclusters; that is, a metastable Ag54 is kinetically formed at a low temperature (20 °C), whereas such a system is steered towards a thermodynamically stable Ag33 at a relatively high temperature (80 °C). Electrospray ionization mass spectrometry illustrates that the stability of Ag33 is superior to that of Ag54, which is further supported by density functional theory calculations. Importantly, the difference in structural stability can influence the pathway of 1,4-bis(pyrid-4-yl)benzene induced transformation reaction starting from Ag54 and Ag33. The former undergoes a dramatic breakage-reorganization process to form an Ag31 dimer (Ag31), while the same product can be also achieved from the latter following a noninvasive ligand exchange process. Both the Ag54 and Ag33 have the potential for further remote laser ignition applications. This work not only demonstrates how temperature controls the isolation of a specific phase, but also sheds light on the structural transformation pathway of nanoclusters with different stability.

Biomimetic crystallization for long-pursued -COOH-functionalized gold nanocluster with near-infrared phosphorescence

As an interdisciplinary product, water-soluble gold nanoclusters (AuNCs) stabilized by ligands containing carboxyl (-COOH) group have garnered significant attention from synthetic chemists and biologists due to their immense potential for biomedical applications. However, revealing the crystallographic structures of -COOH-functionalized AuNCs remains a bottleneck. Herein, we successfully applied the salting-out method to obtain a series of high-quality single crystals of -COOH-functionalized Au25 nanoclusters and revealed their crystallographic structures. Particularly, K3Au25(2-Hmna)9(mna)6]- (Au25a) protected by 2-mercaptonicotinic acid features an unprecedented tetrameric Au4(SRS)3(SRS,N)2 staple motifs surrounding the icosahedral Au13 kernel, breaking the traditional perception on the structure of Au25(SR)18. Au25a exhibits a distinct near-infrared emission at 970 nm with long lifetime of 8690 ns, which have been studied by transient absorption spectroscopy and time-dependent density functional theory. This work compensates for the research gap in the experimental structure of -COOH-functionalized AuNCs and opens up a new avenue to explore their structure-property correlations.

Chiral and Achiral Crystal Structures of Au25 (PET)18 0 Reveal Effects of Ligand Rotational Isomerization on Optoelectronic Properties

The crystal structures of 4 ligand-rotational isomers of Au25 (PET)18 are presented. Two new ligand-rotational isomers are revealed, and two higher-quality structures (allowing complete solution of the ligand shell) of previously solved Au25 (PET)18 clusters are also presented. One of the structures lacks an inversion center, making it the first chiral Au25 (SR)18 structure solved. These structures combined with previously published Au25 (SR)18 structures enable an analysis of the empirical ligand conformation landscape for Au25 (SR)18 clusters. This analysis shows that the dihedral angles within the PET ligand are restricted to certain observable values, and also that the dihedral angle values are interdependent, in a manner reminiscent of biomolecule dihedral angles such as those in proteins and DNA. The influence of ligand conformational isomerism on optical and electronic properties was calculated, revealing that the ligand conformations affect the nanocluster absorption spectrum, which potentially provides a way to distinguish between isomers at low temperature.

Understanding the Ligand-Dependent Photoluminescent Mechanism in Small Alkynyl-Protected Gold Nanoclusters

Alkynyl-protected gold clusters have recently gained attention because they are more structurally versatile than their thiolate-protected counterparts. Despite their flexibility, however, a higher photoluminescent quantum yield (PLQY) has been observed experimentally compared to that of organically soluble thiolate-protected clusters. Previous experiments have shown that changing the organic ligand, or R group, in these clusters does not affect the geometric or electronic properties of the core, leading to a similar absorption profile. This article serves as a follow-up to those experiments in which the geometric, optical, and photoluminescent (PL) properties of Au22(ETP)18 are pieced together to find the photoluminescence mechanism. These properties are then compared between Au22(C≡CR)18 clusters where the ligand is changed from R = ETP to PA and ET (ETP = 3-ethynylthiophene, PA = phenylacetylene, and ET = 3-ethynyltoluene). As the theoretical results do not reproduce the same absorption profile among the different ligands as in the experiment, this article also presents a supplementary benchmark of the geometric and optical properties among the three ligands for different levels of theory. The calculations show that the photoluminescence mechanism with the ETP ligand results in ligand-to-metal-to-metal charge transfer (LMMCT), while PA and ET are likely a result of core-dominated fluorescence. The changes are the result of the Au(I) ring atoms as well as how the aromatic groups are connected to the cluster. Additionally, dispersion, solvent, and polarization functions are all important to creating an accurate chemical environment, but the most useful tool in these calculations is the use of a long-range-corrected exchange-correlation functional.

Effects of Field Strength and Silver Nanowire Size on Plasmon-Enhanced N2 Dissociation

Dissociation of the nitrogen molecule via plasmon-enhanced catalysis using noble metal nanoparticles has been investigated both experimentally and computationally in recent years. However, the mechanism of plasmon-enhanced nitrogen dissociation is still not very clear. In this work, we apply theoretical approaches to examine the dissociation of a nitrogen molecule on atomically thin Ag_n nanowires (n = 6, 8, 10, 12) and a Ag₁₉⁺ nanorod. Ehrenfest dynamics provides information about the motion of nuclei during the dynamics process and real-time TDDFT calculations show the electronic transitions and population of electrons over the first 10 s of fs time scale. The activation and dissociation of nitrogen are typically enhanced when the electric field strength increases. However, the enhancement is not always monotonic with field strength. As the length of the Ag wire increases, nitrogen is typically easier to dissociate and thus requires lower field strengths, even though the plasmon frequency is lower. The Ag₁₉⁺ nanorod leads to faster dissociation of N₂ than the atomically thin nanowires. Overall, our detailed study yields insights into the mechanisms involved in plasmon-enhanced N₂ dissociation, as well as provides information about factors that can be used to improve adsorbate activation.

Analytical excited state gradients for time-dependent density functional theory plus tight binding (TDDFT + TB)

Understanding photoluminescent mechanisms has become essential for photocatalytic, biological, and electronic applications. Unfortunately, analyzing excited state potential energy surfaces (PESs) in large systems is computationally expensive, and hence limited with electronic structure methods such as time-dependent density functional theory (TDDFT). Inspired by the sTDDFT and sTDA methods, time-dependent density functional theory plus tight binding (TDDFT + TB) has been shown to reproduce linear response TDDFT results much faster than TDDFT, particularly in large nanoparticles. For photochemical processes, however, methods must go beyond the calculation of excitation energies. Herein, this work outlines an analytical approach to obtain the derivative of the vertical excitation energy in TDDFT + TB for more efficient excited state PES exploration. The gradient derivation is based on the Z vector method, which utilizes an auxiliary Lagrangian to characterize the excitation energy. The gradient is obtained when the derivatives of the Fock matrix, the coupling matrix, and the overlap matrix are all plugged into the auxiliary Lagrangian, and the Lagrange multipliers are solved. This article outlines the derivation of the analytical gradient, discusses the implementation in Amsterdam Modeling Suite, and provides proof of concept by analyzing the emission energy and optimized excited state geometry calculated by TDDFT and TDDFT + TB for small organic molecules and noble metal nanoclusters.

A first glance into mixed phosphine-stibine moieties as protecting ligands for gold clusters

Atomically precise gold clusters have attracted considerable research interest as their tunable structure-property relationships have resulted in widespread applications, from sensing and biomedicine to energetic materials and catalysis. In this article, the synthesis and optical properties of a novel [Au₆(SbP₃)₂][PF₆]₂ cluster are reported. Despite the lack of spherical symmetry in the core, the cluster shows exceptional thermal and chemical stability. Detailed structural attributes and optical properties are evaluated experimentally and theoretically. This, to the best of our knowledge, is the first report of a gold cluster protected via synergistic multidentate coordination of stibine (Sb) and phosphine moieties (P). To further show that the latter moieties give a set of unique properties that differs from monodentate phosphine-protected [Au₆(PPh₃)₆]²⁺, geometric structure, electronic structure, and optical properties are analyzed theoretically. In addition, this report also demonstrates the critical role of overall-ligand architecture in stabilizing mixed ligand-protected gold clusters.

Theoretical Investigations on the Plasmon-Mediated Dissociation of Small Molecules in the Presence of Silver Atomic Wires

Plasmonic nanoparticles can promote bond activation in adsorbed molecules under relatively benign conditions via excitation of the nanoparticle's plasmon resonance. As the plasmon resonance often falls within the visible light region, plasmonic nanomaterials are a promising class of catalysts. However, the exact mechanisms through which plasmonic nanoparticles activate the bonds of nearby molecules are still unclear. Herein, we evaluate Ag₈-X₂ (X = N, H) model systems via real-time time-dependent density functional theory (RT-TDDFT), linear response time-dependent density functional theory (LR-TDDFT), and Ehrenfest dynamics in order to better understand the bond activation processes of N₂ and H₂ facilitated by the presence of the atomic silver wire under excitation at the plasmon resonance energies. We find that dissociation is possible for both small molecules at high electric field strength. Activation of each adsorbate is symmetry- and electric field-dependent, and H₂ activates at lower electric field strengths than N₂. This work serves as a step toward understanding the complex time-dependent electron and electron-nuclear dynamics between plasmonic nanowires and adsorbed small molecules.

Characterization of Pt-doping effects on nanoparticle emission: a theoretical look at Au24Pt(SH)18 and Au24Pt(SC3H7)18

Developments in nanotechnology have made the creation of functionalized materials with atomic precision possible. Thiolate-protected gold nanoclusters, in particular, have become the focus of study in literature as they possess high stability and have tunable structure-property relationships. In addition to adjustments in properties due to differences in size and shape, heteroatom doping has become an exciting way to tune the properties of these systems by mixing different atomic d characters from transition metal atoms. Au₂₄Pt(SR)₁₈ clusters, notably, have shown incredible catalytic properties, but fall short in the field of photochemistry. The influence of the Pt dopant on the photoluminescence mechanism and excited state dynamics has been investigated by a few experimental groups, but the origin of the differences that arise due to doping has not been clarified thoroughly. In this paper, density functional theory methods are used to analyze the geometry, optical and photoluminescent properties of Au₂₄Pt(SR)₁₈ in comparison with those of [Au₂₅(SR)₁₈]^1-. Furthermore, as these clusters have shown slightly different geometric and optical properties for different ligands, the analysis is completed with both hydrogen and propyl ligands in order to ascertain the role of the passivating ligands.

Effects of Diglyme on Au Nanocluster Formation: Mechanism, 1H NMR, and Bonding

Recently, diglyme was applied as a solvent in the synthesis of a luminescent gold-thiolate nanocluster. However, the interactions between the diglyme and the gold nanocluster and the intrinsic mechanism of the diglyme-assisted nanocluster growth have not been examined. In this work, we use density functional theory (DFT) to propose a plausible pathway for diglyme-assisted Au(I)-thiolate synthesis; the reaction energies are found to be negative in every step. ¹H NMR calculations are applied to characterize how the environment arising from different gold motifs affects the chemical shifts of the protons on diglyme, which experience strong downfield shifts. Extended transition state-natural orbitals for chemical valence (ETS-NOCV) theory is also utilized to examine the interactions between diglyme and gold clusters as well as a Au₂₀(SR)₁₅ nanocluster. Our work demonstrates that diglyme can play an important role in the synthetic mechanism yielding gold nanoclusters and provides insights into the diglyme-nanocluster binding motifs and resulting NMR chemical shifts.

Sulfide Boosting Near-Unity Photoluminescence Quantum Yield of Silver Nanocluster

Silver nanoclusters have emerged as promising candidates for optoelectronic applications, but their room-temperature photoluminescence quantum yield (PLQY) is far from ideal to access cutting-edge device performance. Herein, two supertetrahedral silver nanoclusters with high PLQY in non-degassed solution at room temperature were constructed by interiorly supporting the core with multiple VO₄^3- and E^2- anions as structure-directing agents and exteriorly protecting the core with a rigid ligand shell of PhC≡C^- and Ph₂PE₂^- (E = S, Ag64-S; E = Se, Ag64-Se). Both clusters have similar outer Ag₅₈ tetrahedral cages and [Ag₆E₄@(VO₄)₄] cores, forming a pair of comparable clusters to decrypt the origin of such a high PLQY, particularly in Ag64-S, where the PLQY reached up to 97%. The stronger suppression effect of inner sulfides for nonradiative decay is critical to boost the PLQY to near unity. Transient absorption spectroscopy is employed to confirm the phosphorescence nature. The quadruple-capping assembly mechanism involving Ag₇ secondary building units on a Ag₃₆ truncated tetrahedron was also established by collision-induced dissociation studies. This work not only provides a strategy of core engineering for the controlled syntheses of silver nanoclusters with high PLQY but also deciphers the origin of a near-unity PLQY, which lays a foundation for fabricating highly phosphorescent silver nanoclusters in the future.

An ultrastable thiolate/diglyme ligated cluster: Au20(PET)15(DG)2

The synthesis and characterization of an Au₂₀(PET)₁₅(DG)₂ (PET = phenylethane thiol; DG = diglyme) cluster is reported. Mass spectrometry reveals this as the first diglyme ligated cluster where diglyme ligands survive ionization into the gas phase. Thermal analysis shows the cluster degrades at 156 °C, whereas the similar Au₂₀(PET)₁₆ cluster degrades at 125 °C, representing markedly increased thermal stability. A combination of NMR spectroscopy and computational modeling suggests that the diglyme molecules bind in a tridentate manner for this cluster, resulting in a binding energy of 35.2 kcal mol^-1 for diglyme, which is comparable to the value of ∼40 kcal mol^-1 for thiolates. IR and optical spectroscopies show no evidence of assembly of this cluster, in contrast to Au₂₀(PET)₁₅(DG), which readily assembles into dimeric species, which is consistent with a tridentate binding motif. Evidence for stacking among Au-bound and non-bound diglyme molecules is inferred from thermal and mass analysis.

Plasmon-induced excitation energy transfer in silver nanoparticle dimers: A real-time TDDFTB investigation

Using real-time quantum dynamics calculations, we perform theoretical investigations of light-induced interactions and electronic excitation transfer in a silver nanoparticle dimer. Real-time time-dependent density functional tight-binding (RT-TDDFTB) calculations provide details of the quantum dynamical processes at an electronic/atomistic level with attosecond resolution. The computational efficiency of RT-TDDFTB allows us to examine electronic dynamics up to picosecond time scales. With time scales varying over six orders of magnitude, we provide insight into interactions between the nanoparticle and laser and between nanoparticles. Our results show that the coupling between nanoparticle monomers is dependent on the separation distance between the nanoparticles in the dimer. As the interparticle distance is varied, the dipole-dipole interactions and electronic excitation transfer mechanisms are markedly different. At large distances (from 50 to 20 Å), the energy transfer from NP1 to NP2 becomes more efficient as the interparticle distance decreases. The total dipole moment of the Ag₁₄ nanoparticle dimer increases linearly at an interparticle distance of 20 Å and reaches its maximum after 1.2 ps. The electronic excitation transfer is also the most efficient at 20 Å. At short distances, back-transfer effects reduce the ability of the dimer and NP1 to accept energy from the incident electric field. We attribute the distance-dependent features of the nanoparticle dimer to the beating between the laser acting on NP1 and the back transfer from NP2 to NP1.

Crystal Structure and Optical Properties of a Chiral Mixed Thiolate/Stibine-Protected Au18 Cluster

We report the first example of a chiral mixed thiolate/stibine-protected gold cluster, formulated as Au₁₈(S-Adm)₈(SbPh₃)₄Br₂ (where S-Adm = 1-adamantanethiolate). Single crystal X-ray crystallography reveals the origin of chirality in the cluster to be the introduction of the rotating arrangement of Au₂(S-Adm)₃ and Au(S-Adm)₂ staple motifs on an achiral Au₁₃ core and the subsequent capping of the remaining gold atoms by SbPh₃ and Br^- ligands. Interestingly, the structure and properties of this new Au₁₈ cluster are found to be different from other reported achiral Au₁₈ clusters and the only other stibine-protected [Au₁₃(SbPh₃)₈Cl₄]⁺ cluster. Detailed analyses on the geometric and electronic structures of the new cluster are carried out to gain insights into its optical properties as well as reactivity and stability of such mixed monolayer-protected clusters.

Theoretical Insights into Excitation-Induced Oxygen Activation on a Tetrahedral Ag8 Cluster

Research on small-molecule dissociation on plasmonic silver nanoparticles is on the rise. Herein, we investigate the effect of various parameters of light, i.e., field strength, polarization direction, and energy of oscillation, on the dynamics of oxygen upon photoexcitation of the O₂@Ag₈ composite using real-time time-dependent density functional theory calculations with Ehrenfest dynamics. From our excited-state dynamics calculations, we found that increasing the strength of the external electric field brings a significant contribution to the O-O dissociation. In addition, the polarization direction of the incident light becomes important, especially at weaker field strengths. The light that is polarized along the direction of charge transfer from the metal to adsorbate and the light that is polarized along the long axis of molecular oxygen were found to enhance the bond breaking of O₂ significantly. We also found that at the weakest electric field strength, the oxygen molecule stays adsorbed to the silver cluster when the incident light resonates with low-energy excited states and desorbs away from the metal cluster with high-energy excitations. With strong electric fields, oxygen either desorbs or dissociates.

Deciphering the dual emission in the photoluminescence of Au14Cd(SR)12: A theoretical study using TDDFT and TDDFT + TB

Determining excited state processes for small nanoclusters, specifically gold, aids in our ability to fine-tune luminescent materials and optical devices. Using TDDFT and TDDFT + TB, we present a detailed theoretical explanation for the dual emission peaks displayed in Au₁₄Cd(S-Adm)₁₂ (Adm = adamantane). As dual emission is relatively rare, we decipher whether the mechanism originates from two different excited states or from two different minima on the same excited state surface. This unique mechanism, which proposes that the dual emission results from two minima on the first excited state, stems from geometrical changes in the bi-tetrahedron core during the emission process.

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.