0000000000398784
AUTHOR
Stefan Adams
Large systems of path-repellent Brownian motions in a trap at positive temperature
We study a model of $ N $ mutually repellent Brownian motions under confinement to stay in some bounded region of space. Our model is defined in terms of a transformed path measure under a trap Hamiltonian, which prevents the motions from escaping to infinity, and a pair-interaction Hamiltonian, which imposes a repellency of the $N$ paths. In fact, this interaction is an $N$-dependent regularisation of the Brownian intersection local times, an object which is of independent interest in the theory of stochastic processes. The time horizon (interpreted as the inverse temperature) is kept fixed. We analyse the model for diverging number of Brownian motions in terms of a large deviation princip…
Über gemischte bindungen in der IV. hauptgruppe
Abstract Reaction of Ph3SnLi with Ph2SiCl2 or Ph2GeCl2 at −78°C in THF yields (Ph3Sn)2SiPh2 (1) and (Ph3Sn)2GePh2 (2). The crystal structure of 1 (R = 0.075) exhibits SnSi distances of 257.2(4) and 257.9(5) pm, an SnSiSn angle of 118.5(2)°, and a central C3SnSiC2SnC3 molecular skeleton with symmetry close to C2. The geminal NMR coupling 2J(119Sn ⋯ 119Sn) in 1, and in a tri-, tetra- and pentastannane series shows a linear correlation to their respective non-bonded d(Sn ⋯ Sn) distances (I(t-Bu2Sn)4I: 20 Hz/496 pm; 1: 724 Hz/443 pm).
Über polystannane
Abstract The compound I(t-Bu2Sn)4I has been synthesized by controlled cleavage of the related cyclotetrastannane (t-Bu2Sn)4 with iodine in toluene. Both compounds have been investigated by mass, NMR and vibrational spectra. I(t-Bu2Sn)4I: δ(119Snterminal) 67.7, δ(Sncentral) 17.4 ppm; 1J(SnSn) 2199 (terminal-central) and 1575 (central-central), 2J(SnSn) 20 (terminal-central), 3J (SnSn) 307 Hz (terminal-terminal); ν(SnSn) 119, ν(SnI) 167 cm−1. (t-Bu2Sn)4: δ(Sn) 87.4 ppm; ν(SnSn) 125 cm−1. The crystal structure of I(t-Bu2Sn)4I has been determined (R = 0.071): bond lengths SnSn 289.5(1) (terminal-central) and 292.4(1) (central-central), SnI 275.3(1) pm. The conformation of the chain ISn…
Über polystannane
Abstract The three compounds Ph4Sn2(X3CCO2)2 were synthesized from Ph2SnH2 and X3CCOOH (X = H, Cl) or by cleavage of two phenyl groups in Ph6Sn2 with Stoichiometric amounts of X3CCOOH (X = Cl, F). The crystal structures (R = 0.041, 0.030, 0.058) show that the Ph4Sn2 units are bridged by two isobidentate acetates resulting in five-coordinated tin atoms. Five crystallographically independent centrosymmetric molecules form three distinct conformers. Bonding parameters (compared with Ph6Sn2): distances d(SnSn) 269, 271, 272, 277 pm; NMR couplings (CDCl3 solution) 1J(SnSn) 16870, 9443, 12915, 4480 Hz; stretching vibrations ν(SnSn) 152, 155, 157, 159 cm−. The ion pairs [Ph4Sn2]2+ [(X3CCO2)2]2−…