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.     

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.     

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.     

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.     

Spectral and scattering theory for a Schrödinger operator with a class of momentum-dependent long-range potentials

Let be the selfadjoint operator for the static electromagnetic field where W _j for 0, 1, 2, ..., n is a sum of (i) a short-range potential and (ii) a smooth long-range potential decreasing at as |x|^- with in (0, 1]. Then for >1/2, asymptotic completeness holds for the scattering system (H, H ₀).     

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.     

Reactions of Neomycin B under Mitsunobu Conditions: A Correction of the Literature

Reaction of N‐Boc neomycin with triphenylphosphine and diissopropyl azodicarboxylate in either toluene or THF results in an epoxide in ring IV, not an aziridine or azetidine as previously reported.