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In this work, we have implemented the time-dependent density functional theory approximate auxiliary s function (TDDFT-aas) method, which is an approximate TDDFT method. Instead of calculating the exact two-center electron integrals in the K coupling matrix when solving the Casida equation, we approximate the integrals, thereby reducing the computational cost. In contrast to the related TDDFT plus tight-binding (TDDFT+TB) method, a new type of gamma function is used in the coupling matrix that does not depend on the tight-binding parameters. The calculated absorption spectra of silver and gold nanoparticles using TDDFT-aas show good agreement with TDDFT and TDDFT+TB results. In addition, we have implemented the analytical excited-state gradients for the TDDFT-aas method, which makes it possible to calculate the emission energy of molecular systems. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Atomically precise metal nanoclusters (NCs) can be compositionally controlled at the single-atom level, but understanding structure-property correlations is required for tailoring specific optical properties. Here, the impact of Ni atom doping on the optical, structural, and electrochemical properties of atomically precise 1,3-benzene dithiol (BDT) protected Ag 29 NCs is studied. The Ni-doped Ag 29 (NiAg 28 (BDT) 12 ) NCs, are synthesized using a co-reduction method and characterized using electrospray ionization mass spectrometry (ESI MS), ion mobility spectrometry (IMS), and X-ray photoelectron spectroscopy (XPS). Only a single Ni atom doping can be achieved despite changing the precursor concentration. Ni doping in Ag 29 NCs exhibits enhanced thermal stability, and electrocatalytic oxygen evolution reaction (OER) compared to the parent NCs. Density functional theory (DFT) calculations predict the geometry and optical properties of the parent and NiAg 28 (BDT) 12 NCs. DFT is also used to study the systematic single-atom doping effect of metals such as Au, Cu, and Pt into Ag 29 NCs and suggests that with Ni and Pt, the d atomic orbitals contribute to creating superatomic orbitals, which is not seen with other dopants or the parent cluster. The emission mechanism is dominated by a charge transfer from the ligands into the Ag core cluster regardless of the dopant., (© 2024 The Author(s). Small published by Wiley‐VCH GmbH.)

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. Au 24 Pt(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 Au 24 Pt(SR) 18 in comparison with those of [Au 25 (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.

We report the first example of a chiral mixed thiolate/stibine-protected gold cluster, formulated as Au 18 (S-Adm) 8 (SbPh 3 ) 4 Br 2 (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 Au 2 (S-Adm) 3 and Au(S-Adm) 2 staple motifs on an achiral Au 13 core and the subsequent capping of the remaining gold atoms by SbPh 3 and Br - ligands. Interestingly, the structure and properties of this new Au 18 cluster are found to be different from other reported achiral Au 18 clusters and the only other stibine-protected [Au 13 (SbPh 3 ) 8 Cl 4 ] + 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.

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 Au 14 Cd(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.

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 Ag 29 (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 Ag 29 (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 Ag 29 (DHLA) 12 NCs consisting of an icosahedral core with an Ag 16 S 24 shell. Combining the experimental observation with DFT structural analysis of a series of atomically precise NCs, Ag 29- y Au 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.