Black and white local invariants of mappings from surfaces into three-space

Goryunov proved that the space of local invariants of Vassiliev type for generic maps from surfaces to three-space is three-dimensional. The basic invariants were the number of pinch points, the number of triple points and one linked to a Rokhlin type invariant. In this paper we show that, by colouring the complement of the image of the map with a chess board pattern, we can produce a six-dimensional space of local invariants. These are essentially black and white versions of the above. Simple examples show how these are more effective. This revised version was published online in August 2006 with corrections to the Cover Date.     

Bouquet and join theorems for disentanglements

The disentanglement of certain augmentations is shown to be the topological join of a disentanglement and a Milnor fibre. The kth disentanglement of a finite map is defined and for corank 1 maps from ℂ ⁿ to ℂ ^{n +1} it is shown that they are homotopically equivalent to a wedge of spheres. Applications to the Mond conjecture are given. Oblatum 24-VII-2000 & 5-VII-2001?Published online: 12 October 2001     

Quantum yields for product formation in the 120-133 nm photodissociation of O2

The photodissociation of O(2) in the region from 120-133 nm has been investigated using product imaging. The spectrum in this region is dominated by transitions from the ground state to the first three vibrational levels of the E (3)Sigma(u) (-) state. The O((1)D)+O((3)P) channel is the only product channel observed by product imaging for dissociation at either 124.4 nm or 120.4 nm. The O((1)D(2)) product is aligned in the molecular frame in such a way that its J vector is perpendicular to the relative velocity vector between the O((1)D) and the O((3)P). The variation in the anisotropy of dissociation is approximately predicted by considering transitions on individual lines and then taking into account the coherent excitation of overlapping resonances. At 132.7 nm, both the O((1)D)+O((3)P) and the O((3)P)+O((3)P) channels are observed with branching ratios of 0.40+/-0.08 and 0.60+/-0.09, respectively. At 130.2 nm, the quantum yield for production of O((1)D) is 0.76+/-0.28.     

Improved isotope separation in laser dissociation of trifluoromethyl halides: Scavenging of CF3 with HI

The efficiency of¹³C isotope separation by multiphoton dissociation using a CO₂ laser has been shown to increase by ∼33% upon addition of small amounts of HI to the starting mixture. The reason for this increase is that the CF₃ radicals are scavenged by HI more rapidly than they recombine with free iodine atoms to reform the starting material. For Torr and for 0.5J/cm² roughly 65% of the CF₃ and I radicals reform the starting material in the absence of HI. The results of this study indicate that at −80°C the rate constants for CF₃+CF₃→C₂F₆ and CF₃+I→CF₃I are about equal and are roughly 8 times higher than that for CF₃+HI→CF₃H+I.     

Absorption spectra and photochemistry of the toluene cation and benzyl radical in solid argon

Toluene diluted in argon subjected to continuous argon discharge radiation during condensation at 21 K revealed absorptions at 310.5 and 449.6 nm due to benzyl radical, and 317 nm due to a C₇7H₉ radical. A photosensitive 430 nm band, in agreement with photodissociation spectra of the toluene parent cation, is assigned to this species.     

Photophysics and redox behavior of chiral transition metal polymers

The absorption and emission spectra, excited-state lifetimes, quantum yields, and electrochemical measurements have been obtained for a new series of chiral complexes based on three different chiral 2,2':6',2' '-terpyridine ligands, (-)-ctpy, (-)-[ctpy-x-ctpy], and (-)-[ctpy-b-ctpy], with one, two, or multiple Ru metal centers. The room-temperature absorption and emission maxima of [[((-)-ctpy)Ru]-(-)-[ctpy-b-ctpy]-[Ru((-)-ctpy)]](PF(6))(4) and ((-)-[ctpy-b-ctpy])-[[Ru((-)-[ctpy-b-ctpy])](PF(6))(2)](n) were shifted to lower energies and also exhibited significantly longer luminescence lifetimes when compared to [Ru((-)-ctpy)(2)](PF(6))(2), [[((-)-ctpy)Ru]-(-)-[ctpy-x-ctpy]-[Ru((-)-ctpy)]](PF(6))(4), and ((-)-[ctpy-x-ctpy])-[[Ru((-)-[ctpy-x-ctpy])](PF(6))(2)](n). In terms of their electrochemical behavior, all of the complexes studied exhibited one Ru-centered and two ligand-centered redox waves and the [[((-)-ctpy)Ru]-(-)-[ctpy-x-ctpy]-[Ru((-)-ctpy)]](PF(6))(4), ((-)-[ctpy-x-ctpy])-[[Ru((-)-[ctpy-x-ctpy])](PF(6))(2)](n), and ((-)-[ctpy-b-ctpy])-[[Ru((-)-[ctpy-b-ctpy])](PF(6))(2)](n)() complexes were found to electrodeposit upon ligand-based reduction. The difference between the formal potentials of the Ru-centered and the first ligand-centered (least negative) waves corresponded linearly with the changes in the observed emission energies. The shifts in energy are discussed using a particle-in-a-box model, and the luminescence lifetimes are discussed in terms of the structure of the excited-state manifold.     

Water exchange from the oxo-centered rhodium(III) trimer [Rh3(mu3-O)(mu-O2CCH3)6(OH2)3]+: a high-pressure 17O NMR study

Water exchange from the oxo-centered rhodium(III) trimer, [Rh3(mu3-O)(mu-O2CCH3)6(OH2)3]+, was investigated using variable-temperature (272.8-281.6 K) and variable-pressure (0.1-200 MPa) 17O NMR spectroscopy. The exchange reaction was also monitored at three different acidities (pH = 1.8, 2.9, and 5.7) in which the molecule is in the fully protonated form (pKa = 8.3 (+/-0.2), I = 0.1 M, T = 298 K). The temperature dependence of the pseudo-first-order rate coefficient for water exchange yields the following kinetic parameters: k(ex)298 = 5 x 10(-3) s(-1), deltaH(double dagger) = 99 (+/-3) kJ mol(-1), and deltaS(double dagger) = 43 (+/-10) J K(-1) mol(-1). The enhanced reactivity of the terminal waters, some 6 orders of magnitude faster than water exchange from Rh(H2O)6(3+), is likely due to trans-labilization from the central oxide ion. Also, another contributing factor is the low average charge on the metal ions (+0.33/Rh). Variation of reaction rate with pressure results in a deltaV(double dagger) = +5.3 (+/-0.4) cm3 mol(-1), indicative of an interchange-dissociative (I(d)) pathway. These results are consistent with those published by Sasaki et al. who proposed that water substitution from rhodium(III) and ruthenium(III) oxo-centered trimers follows a dissociative mechanism based on highly positive activation parameters (Sasaki, Y.; Nagasawa, A.; Tokiwa-Yamanoto, A.; Ito, T. Inorg. Chim. Acta 1993, 212, 175-182).     

Dissociation of sulfur dioxide by ultraviolet multiphoton absorption between 224 and 232 nm

Multiphoton excitation and dissociation of SO(2) have been investigated in the wavelength range from 224 to 232 nm. Strong evidence is found for two-photon excitation to the H Rydberg state, followed by dissociation to SO + O and ionization of the SO product by absorption of a third photon. The two-photon excitation is resonantly enhanced via the C (1)B(2) intermediate state, and the two-photon yield spectrum thus bears a strong resemblance to the spectrum of this intermediate. Imaging of the O((3)P(2)), S((1)D(2)), and SO products suggests that, following dissociation of SO(2) from the H state, SO is produced in the A and B electronic states. S((1)D(2)) is produced both from two-photon dissociation of SO(2) to give S((1)D(2)) + O(2) and by single-photon dissociation of SO(+). In the former process, the O(2) is likely formed in all of its lowest three electronic states.     

Infrared multiphoton dissociation of CF3Br

The CF₂, Br, and F products of 9.2 μ multiphoton dissociation of CF₃Br have been spectroscopically monitored. Primary dissociation leads to CF₃ + Br, while secondary dissociation of CF₃ leads to CF₂ + F. Both the Br and F atoms are found to have average recoil energies close to those of thermal (300 K) atoms. Comparison of these results to calculations based on RRKM theory indicates that CF₃Br dissociates from levels 2–5 photons above the CF₃ + Br threshold.