The synthesis, spectroscopic, and crystal structures of three heteroleptic thioether/halide platinum(II) (Pt(II)) complexes of the general formula [Pt(9S3)X2] (9S3=1,4,7-trithiacyclononane, X=Cl−, Br−, I−) are presented. All three 9S3/dihalo complexes form very similar structures in which the Pt(II) center is surrounded by a cis arrangement of two halides and two sulfur atoms from the 9S3 ligand. The third sulfur from the 9S3 forms a long distance interaction with the Pt center resulting in an elongated square pyramidal structure with a S2X2+S1 coordination geometry. The distances between the Pt(II) center and axial sulfur shorten with larger halide ions (Cl−=3.260(3) Å>Br−=3.243(2) Å>I−=3.207(2) Å). These distances are consistent with the halides functioning as π donor ligands, and their Pt---S axial distances fall intermediate between Pt(II) thioether complexes involving π acceptor and σ donor ligands. The 195Pt NMR chemical shift values follow a similar trend with an increased shielding of the platinum ion with larger halide ions. The 9S3 ligand is fluxional in all of these complexes, producing a single carbon resonance. Additionally, a related series of homoleptic crown thioether complexes have been studied using 195Pt NMR, and there is a strong correlation between the chemical shift and complex structure. Homoleptic crown thioethers show the anticipated upfield chemical shifts with increasing number of coordinated sulfurs. Complexes containing four coordinated sulfur donors have chemical shifts that fall in the range of −4000 to −4800 ppm while a value near −5900 ppm is indicative of five coordinated sulfurs. However, for S4 crown thioether complexes, differences in the stereochemical orientation of lone pair electrons on the sulfur donors can greatly influence the observed 195Pt NMR chemical shifts, often by several hundred ppm. 相似文献
The emergence of big data has led to so-called convergence complexity analysis, which is the study of how Markov chain Monte Carlo (MCMC) algorithms behave as the sample size, n, and/or the number of parameters, p, in the underlying data set increase. This type of analysis is often quite challenging, in part because existing results for fixed n and p are simply not sharp enough to yield good asymptotic results. One of the first convergence complexity results for an MCMC algorithm on a continuous state space is due to Yang and Rosenthal (2019), who established a mixing time result for a Gibbs sampler (for a simple Bayesian random effects model) that was introduced and studied by Rosenthal (Stat Comput 6:269–275, 1996). The asymptotic behavior of the spectral gap of this Gibbs sampler is, however, still unknown. We use a recently developed simulation technique (Qin et al. Electron J Stat 13:1790–1812, 2019) to provide substantial numerical evidence that the gap is bounded away from 0 as n → ∞. We also establish a pair of rigorous convergence complexity results for two different Gibbs samplers associated with a generalization of the random effects model considered by Rosenthal (Stat Comput 6:269–275, 1996). Our results show that, under a strong growth condition, the spectral gaps of these Gibbs samplers converge to 1 as the sample size increases.