Erik Pedersen

Synthesis and magnetic and structural characterization of the binuclear complex di-μ-hydroxobis{[tris(2-pyridylmethyl)amine]chromium(III)} perchlorate tetrahydrate, [(tpa)CrOH]2(ClO4)4·4H2O

Abstract The binuclear complex di-μ-hydroxobis{[tris(2-pyridylmethyl)amine]chromium(III)} perchlorate tetrahydrate, [Cr(C18H18N4)OH]2(ClO4)4·4H2O or [Cr(tpa)OH]2(ClO4)4·4H2O, has been synthesized and characterized. The complex crystallizes in space group P21/n of the monoclinic system with two binuclear units in a cell of dimensions a = 11.381(5), b = 17.856(4), c = 13.050(7) A, β = 111.83(4)°. The structure has been refined to a final value of the conventional R factor of 0.056 on the basis of 3546 independent intensities. The geometry at the chromium is roughly octahedral, and the bridging unit has a Crue5f8Oue5f8Cr angle (φ) of 100.53(8)°. The Crue5f8Cr separation is 3.003(1) A, and the hydrogen atom on the bridging OH group sits 0.30 A from the Cr2O2 plane, leading to a dihedral angle θ of 26.6°. The magnetic susceptibility of the complex indicates antiferromagnetic coupling, with the ground state singlet lying 30.58(6) cm−1 below the lowest lying triplet state.

Synthesis and characterization of the dimeric chromium(III) complex di-μ- hydroxobis[{N,N′-bis(2-pyridylmethyl)-1,3-propanediamine}-chromium(III)] perchlorate, [(bispictn)Cr(OH)]2(ClO4)4·3H2O

Abstract The synthesis and spetroscopic properties of two isomers of the complex [(bispictn)Cr(OH)] 2 4+ where bispictn = N,N′-bis(2-pyridylmethyl)-1,3-propanediamine, C 15 H 20 N 4 , are described. The crystal structure of the perchlorate salt trihydrate of the violet isomer has been determined from 3-dimensional counter X-ray data. The complex crystallizes in the monoclinic space group C2/c with eight dinuclear formula units in a cell of dimensions α = 38.323(11), b = 14.458(7), c = 17.027(7) A, β = 106.24(3)°. The structure has been refined to a final R-factor of 0.065 based on 3710 independent intensities. The crystals contain a racemic mixture, but in any given molecule the configurations at both chromium centers are the same (ΔΔ or ΛΛ). Both ligands bind in the cis -β form, the configurations at all four secondary nitrogen atoms being the same, so the complex is best described as a racemic mixture of the {Λ(β)(RR′)Λ(β)(RR′)} and {Δ(β)(SS′)} isomers. The six-membered chelate rings from a chair conformation at one metal and a skew-boat at the other. The magnetic susceptibility of the complex indicates antiferromagnetic coupling between the chromium centers, the triplet state lying approximately 32.5 cm −1 higher in energy than the ground state singlet.

Mean curvature flow

Mean curvature flow is the negative gradient flow of volume, so any hypersurface flows through hypersurfaces in the direction of steepest descent for volume and eventually becomes extinct in finite time. Before it becomes extinct, topological changes can occur as it goes through singularities. If the hypersurface is in general or generic position, then we explain what singularities can occur under the flow, what the flow looks like near these singularities, and what this implies for the structure of the singular set. At the end, we will briefly discuss how one may be able to use the flow in low-dimensional topology.

Synthesis and magnetic characterization of the dioxo- and oxohydroxo-bridged dimeric chromium(III) cations di-μ-oxobis[bis{1-(2-pyridyl)ethylamine}-chromium(III)] and μ-oxo-μ-hydroxobis[bis{1-(2-pyridyl)ethylamine}-chromium(III)], and structure of the bromide salt of the oxohydroxo complex

The syntheses of the title complex cations, di-μ-oxobis[bis{1-(2-pyridyl)ethylamine}chromium(III)], [(2-picetam) 2 Cr(O)] 2+ 2 or [(C 7 H 10 N 2 ) 2 Cr(O)] 2+ 2 , and μ-oxo-μ-hydroxobis[bis{1-(2-pyridyl)ethylamine}chromium(III)], [Cr 2 (2-picetam) 4 (OH)(O)] 3+ or [(C 7 H 10 N 2 ) 4 Cr 2 (O)(OH)] 3+ , are reported, and their electronic and circular dichroism spectra in a variety of media are compared. The crystal and molecular structure of the μ-oxo-μ-hydroxo complex as the bromide salt, [(2-picetam) 4 Cr 2 (O)(OH)]Br 3 ·5H 2 O, has been determined from three-dimensional X-ray counter data. The complex crystallizes in the tri-clinic space group P with two binuclear complexes in a cell of dimensions a = 13.491(5), b = 13.762(3), c = 11.389(4) A, α = 104.41(2), β = 106.39(3), and γ = 84.44(2)°. Least-squares refinement of the structure using 2969 independent intensities has yielded a weighted R-factor (on F) of 0.052. The cation consists of two roughly octahedral chromium(III) centers, with terminal Crue5f8N distances in the range 2.057(5)–2.130(6) A. The Crue5f8Cr separation is 2.883(2) A. and the bridging Crue5f8Oue5f8Cr angles at the oxo and hydroxo oxygen atoms are 100.6(2)° and 95.0(2)°, respectively. The Crue5f8O distances to the oxo oxygen atom are 1.869(4) and 1.878(4) A, while those to the hydroxo bridge are 1.960(4) and 1.950(4) A. The magnetic susceptibility of this μ-oxo-hydroxo complex shows a maximum near 100 K. A Fit of the data to a model assuming independent triplet, quintet, and septet energies is almost consistent with the Heisenberg model corrected for biquadratic exchange, and leads to a triplet energy of 46.45(2) cm −1 . In the di-μ-oxo complex, examined as the chloride salt, the triplet energy is approximately 83 cm −1 .

Synthesis, structure and magnetic properties of the binuclear chromium(III) complex di-μ-hydroxobis [(1,4,7,10-tetraazacyclododecane)chromium(III)] dithionate tetrahydrate, [(cyclen)CrOH]2(S206)2·4H2O

Abstract The dark blue dimeric complex di-μ-hydroxo- bis [(1,4,7,10-tetraazacyclododecane)chromium(III)] dithionate tetrahydrate, [Cr(C8H20N4)OH]2(S2O6)2· 4H2O or [Cr(cyclen)OH]2(S2O6)2·4H2O, has been synthesized. The crystal structure of the complex has been determined from threeodimensional counter X-ray data. The complex crystallizes in space group P21/n of the monoclinic system with two dimeric formula units in a cell of dimensions a = 8.837(5), b = 14.472(8), c= 13.943(6) A andβ=95.83(4)o. The structure has been refined by full-matrix least- squares methods to a final value of the weighted R-factor of 0.059 on the basis of 1774 independent intensities. The geometry of the cyclen macrocycle is unsymmetrical, the observed conformations being λδδλ and its enantiomer. The strained ligand conformation leads to significant deviations from octahedral geometry at the chromium centers, and to a bridged geometry in which the Crue5f8Oue5f8Cr angle o and the Cr···Cr separation of 104.1(1)o and 3.086(2) A are the largest observed in dimers of this kind. The magnetic susceptibility of the complex indicates antiferromagnetic coupling, with the ground state singlet lying 21.56(6) cm−1 below the lowest lying triplet state. The structural parameters have been used to calculate the triplet energy by means of the Glerup- Hodgson- Pedersen (GHP) model, and the calculated value of 22.3 cme−1 is very similar to the observed value.

Carbonyl sulfides as possible intermediates in the photolysis of oxathiiranes

Abstract Diphenyl oxathiirane, formed by irradiation of thiobenzophenone S-oxide at 77 K, is photochemically converted into a blue, thermally unstable compound which decomposes at ca 100–110 K (λ max 550 nm, (ϵ ca 11,000). Lack of change in magnetic susceptibility during the light induced conversion of sulfine to ketone via the oxathiirane and the subsequent blue intermediate implies the absence of triplet and biradical singlet transients. The unknown carbonyl sulfide functionality, R 2 Cue5fbOue5fbS, thereby emerges as a strong candidate for producing the visible absorption. Comparison of the wave functions for CH 2 ue5fbSue5fbO and CH 2 ue5fbOue5fbS arising from MNDO limited CI geometry optimizations leads to the conclusion that the carbonyl sulfide structure is best described as a zwitterion rather than as a singlet biradical. The failure to observe cycloaddition products between the blue species and several dipolarophiles is rationlized in terms of a labile carbonyl suffide intermediate capable of facile sulfur extrusion from a long, weak O-S bond. Finally, the electronic absorption spectra of a series of para -substituted benzaldehyde O-sulfide model system have been calculated with CNDO/S-CI and correlated with the λ max s of the corresponding series of diaryl blue substrates. The sum of the available experimental and theoretical data is consistent with the existence of closed shell carbonyl sulfides as observable, though labile, intermediates from the photolysis of oxathinanes.