Synthesis of two new thioesters bearing ferrocene: Vibrational characterization and ab initio calculations. X-ray crystal structure of S-(2-methoxyphenyl)ferrocenecarbothioate

Structural and conformational properties of S-benzyl ferrocenecarbothioate (I) and S-(2-methoxyphenyl) ferrocenecarbothioate (II) are analyzed using data obtained from X-ray diffraction, vibrational data and theoretical calculations. According to chemical quantum calculations, the synperiplanar and antiperiplanar forms are found as the first and second more stable conformations, respectively, for the title compounds. The geometric parameters and normal modes of vibration were calculated using a density functional theory method (B3LYP) and the 6-31+G∗∗ basis set for all atoms except for iron. For this atom the calculations were carried out with the Lanl2dz basis set. The calculated parameters are in good agreement with the corresponding X-ray diffraction values. The combined experimental and theoretical approach allows a consistent assignment for most of the fundamental modes.     

Preparation, IR spectroscopy, and time-of-flight mass spectrometry of halogenated and methylated Si(111)

The preparation of chlorine-, bromine-, and iodine-terminated silicon surfaces (Si(111):Cl, Br, and I) using atomically flat Si(111)-(1×1):H is described. The halogenated surfaces were obtained by photochemically induced radical substitution reactions with the corresponding dihalogen in a Schlenk tube by conventional inert gas chemistry. The nucleophilic substitution of the Si-Cl functionality with the Grignard reagent (CH₃MgCl) resulted in the unreconstructed methylated Si(111)-(1×1):CH₃ surface. The halogenated and methylated silicon surfaces were characterized by Fourier transform infrared (FTIR) spectroscopy and laser-induced desorption of monolayers (LIDOM). Calibration of the desorption temperature via analysis of time-of-flight (TOF) distributions as a function of laser fluence allowed the determination of the originally emitted neutral fragments by TOF mass spectrometry using electron-impact ionization. The halogens were desorbed atomically and as SiX _n (X = Cl, Br) clusters. The methyl groups mainly desorbed as methyl and ethyl fragments and a small amount of ⁺SiCH₃.     

Strichartz estimates for Schrödinger equations on irrational tori in two and three dimensions

In this paper, we prove new multilinear Strichartz estimates, which are obtained by using techniques of Bourgain. These estimates lead to new critical well-posedness results for the nonlinear Schrödinger equation on irrational tori in two and three dimensions with small initial data. In three dimensions, this includes the energy critical case. This extends recent work of Guo–Oh–Wang.     

Quantum Crystallography and Complementary Bonding Analysis of Agostic Interactions in Titanium Amides

Agostic interactions involving titanium are textbook examples for C−H bond activation. Therefore, it is surprising that there is no study in the literature in which the hydrogen atom in the C−H⋅⋅⋅Ti interaction has been determined reliably, although nearly all the criteria for assessing the strength and character of the agostic interaction depend on the hydrogen atom and its position. Here, we demonstrate with quantum crystallographic techniques how hydrogen atoms in a series of three titanium amides can indeed be localized accurately and precisely based on routine single-crystal X-ray diffraction data. Once the hydrogen positions have been established, theoretical and experimentally fitted bonding analyses reveal that the C−H⋅⋅⋅Ti interaction becomes stronger with increasing inter-ligand London dispersion stabilization of bulky alkyl groups.     

Unconditionally Stable Methods for Hamilton–Jacobi Equations

We present new numerical methods for constructing approximate solutions to the Cauchy problem for Hamilton–Jacobi equations of the form u_t+H(D_xu)=0. The methods are based on dimensional splitting and front tracking for solving the associated (non-strictly hyperbolic) system of conservation laws p_t+D_xH(p)=0, where p=D_xu. In particular, our methods depend heavily on a front tracking method for one-dimensional scalar conservation laws with discontinuous coefficients. The proposed methods are unconditionally stable in the sense that the time step is not limited by the space discretization and they can be viewed as “large-time-step” Godunov-type (or front tracking) methods. We present several numerical examples illustrating the main features of the proposed methods. We also compare our methods with several methods from the literature.     

Ruthenium Complexes Containing "Noninnocent" o-Benzoquinone Diimine/o-Phenylenediamide(2-) Ligands. Synthesis and Crystal Structure of the Nitrido-Bridged Complex [{LRu(o-C(6)H(4)(NH)(2))}(2)(&mgr;-N)](PF(6))(2).3CH(3)CN.C(6)H(5)CH(3)

Reaction of LRu(III)Cl(3) (L = 1,4,7-trimethyl-1,4,7-triazacyclononane) with 1,2-phenylenediamine (opdaH(2)) in H(2)O in the presence of air affords [LRu(II)(bqdi)(OH(2))](PF(6)) (1), where (bqdi) represents the neutral ligand o-benzoquinone diimine. From an alkaline methanol/water mixture of 1 was obtained the dinuclear species [{LRu(II)(bqdi)}(2)(&mgr;-H(3)O(2))](PF(6))(3) (1a). The coordinated water molecule in 1 is labile and can be readily substituted under appropriate reaction conditions by acetonitrile, yielding [LRu(II)(bqdi)(CH(3)CN)](PF(6))(2) (2), and by iodide and azide anions, affording [LRu(II)(bqdi)I](PF(6)).0.5H(2)O (3) and [LRu(bqdi)(N(3))](PF(6)).H(2)O (4), respectively. Heating of solid 4 in vacuum at 160 degrees C generates N(2) and the dinuclear, nitrido-bridged complex [{LRu(o-C(6)H(4)(NH)(2))}(2)(&mgr;-N)](PF(6))(2) (5). Complex 5 is a mixed-valent, paramagnetic species containing one unpaired electron per dinuclear unit whereas complexes 1-4 are diamagnetic. The crystal structures of 1, 1a.3CH(3)CN, 3, 4.H(2)O, and 5.3CH(3)CN.0.5(toluene) have been determined by X-ray crystallography: 1 crystallizes in the monoclinic space group P2(1)/m, Z = 2, with a = 8.412(2) ?, b = 15.562(3) ?, c = 10.025 ?, and beta = 109.89(2) degrees; 1a.3CH(3)CN, in the monoclinic space group C2/c, Z = 4, with a = 19.858(3) ?, b = 15.483(2) ?, c = 18.192(3) ?, and beta = 95.95(2) degrees; 3, in the orthorhombic space group Pnma, Z = 4, with a = 18.399(4) ?, b = 9.287(2) ?, and c = 12.052(2) ?, 4.H(2)O, in the monoclinic space group P2(1)/c, Z = 4, with a = 8.586(1) ?, b = 15.617(3) ?, c = 16.388(5) ?, and beta = 90.84(2) degrees; and 5.3CH(3)CN.0.5(toluene), in the monoclinic space group P2(1)/c, Z = 4, with a = 15.003(3) ?, b = 16.253(3) ?, c = 21.196(4) ?, and beta = 96.78(3) degrees. The structural data indicate that in complexes 1-4 the neutral o-benzoquinone diimine ligand prevails. In contrast, in 5 this ligand has predominantly o-phenylenediamide character, which would render 5 formally a mixed-valent Ru(IV)Ru(V) species. On the other hand, the Ru-N bond lengths of the Ru-N-Ru moiety at 1.805(5) and 1.767(5) ? are significantly longer than those in other crystallographically characterized Ru(IV)=N=Ru(IV) units (1.72-1.74 ?). It appears that the C(6)H(4)(NH)(2) ligand in 5 is noninnocent and that formal oxidation state assignments to the ligands or metal centers are not possible.     

Electronic coupling through intramolecular π-π interactions in biscobaltocenes: a structural, spectroscopic, and magnetic study

The paramagnetic dinuclear complexes 1,8-bis(cobaltocenyl)naphthalene (2) and 1,8-bis[(pentamethyl-η(5)-cyclopentadienyl)(η(5)-cyclopentadiendiyl)cobalt(II)]naphthalene (4) were synthesized. The molecular structures were characterized by X-ray structure analysis and consisted of two cobaltocenes linked through a distorted naphthalene clamp. Electronic interactions between the two cobalt atoms were observed by cyclic voltammetric studies. Superconducting quantum interference device (SQUID) measurements of the pure compounds and diluted in their diamagnetic iron derivatives, as well as variable-temperature NMR spectroscopy experiments in solution are presented. Magnetic measurements revealed an antiferromagnetic coupling of the electrons in complexes 2 and 4. From NMR spectroscopy experiments, Curie behavior in the temperature range from -60 to +60 °C can be deduced. The electronic structure and magnetic behavior is supported by results of broken-symmetry DFT and multireference calculations along with UV/Vis spectroscopic data, which revealed an intramolecular through space π-π interaction between the cobaltocene units.