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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.

 

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. 

The crystal structures of 4 ligand‐rotational isomers of Au₂₅(PET)₁₈are 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)₁₈clusters are also presented. One of the structures lacks an inversion center, making it the first chiral Au₂₅(SR)₁₈structure solved. These structures combined with previously published Au₂₅(SR)₁₈structures enable an analysis of the empirical ligand conformation landscape for Au₂₅(SR)₁₈clusters. 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.

 

The synthesis and characterization of an Au 20 (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 Au 20 (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 Au 20 (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.