An experimental examination of the spin forbidden transitions of molecular oxygen dissolved in various solvents and in the gas phase reveals the following selection rules governing the intermolecular enhancement of these transitions: (i) Nonheavy atom solvents selectively enhance the 1Δg← 3Σg− transition (factor of 1000) but not the 1Σg+← 3Σg− transition; (ii) the bimolecular oxygen enhancement of the 1Δg← 3Σg−(0,0) transition is selectively suppressed in solution by a factor of ∼ 3; (iii) heavy atom solvents enhance the 1Σg+← 3Σg− transition (factor of 10 in iodine containing solvents) but not the 1Δg← 3Σg− transition. The possible origins of these different selection rules are discussed in terms of previous theoretical treatments of the interaction of oxygen with electronically excited molecules.

The infrared and visible spectra of gaseous oxygen have been examined at temperatures around 90°K using a long path absorption cell. At all temperatures the infrared and visible spectra show a broad band which can be assigned as collision-induced absorption. However, at low temperatures small but discrete features appear with integrated intensities dependent on the square of the gas density. These features are assigned to bound state van der Waals molecules of the type (O2)2. The visible absorption of (O2)2 studied corresponds to the Δg1 (ν=0)+1 Δg(ν=1) ←3Σg−(ν=0) simultaneous transition. The part of the spectrum attributed to bound dimers shows a progression of eight fine structure bands superimposed on the broad simultaneous transition absorption. The fine structure has been assigned to combinations of electronic and vibrational transitions involving the stretching mode of the van der Waals bond of (O2)2. In the ground state each oxygen molecule is in the Σg-3(ν=0) state, while in the excited state one oxygen molecule is in the Δg1(ν=0) state and the other is in the Δg1(ν=1) state. The spacings and convergence of the dimer vibrational levels provide a determination of the dissociation energy of the ground and excited dimer states, giving De″=87 and De′=50 cm−1. The infrared spectrum of (O2)2 occurs near the infrared inactive fundamental vibration of O2 and shows three regions of discrete absorption superimposed on the broad collision-induced band. The discrete absorption bands have been assigned to fundamental and combination bands of (O2)2. The combination band features involve hindered rotor transitions associated with the internal rotations of the O2 molecules within the dimer. From an analysis of the infrared vibration-rotation band contour of one of the dimer fundamentals, an average distance of 4.8 Å between the centers of mass of the two O2 molecules was determined for the (O2)2 van der Waals molecule. Applying the usual band analysis formulas to determine the geometry is an uncertain procedure since the data indicate that (O2)2 is weakly bonded and has a floppy structure. It was subsequently not possible to choose among possible linear or nonlinear dimer equilibrium configurations with the present experimental or theoretical information. All the spectroscopic evidence obtained here is consistent with the description of the weak bonding in (O2)2 as due to van der Waals-type interactions. There is no need to suggest a pairing of the electrons in oxygen into some sort of weak chemical bond that might stabilize (O2)2.

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L O " ( b) Flgure 7. Possible approaches of DDQ toward the crown ether in the complex formation (see text).

The study of fractal dimensionality for complex sutures in deer skulls and ammonites reveals their extremely long and elaborate lengths in relation to the defined areas they bound. These sutures often show various scales of self-similarity (where the parent pattern is elaborated in miniature, again and again), and empirical fractal dimensions calculated lie between one and two. In the scaling elaborations of Cervid sutures, some elaborations seem isolated from the continuous suture. Small "islands" are seen in similar theoretical fractal curves as well. The evolutionary and developmental specialization of intricate sutures improves the bonds; such fitness is essential owing to extraordinary stresses. Autocorrelation (where nearby sides or elaborations tend to resemble a basic pattern and, therefore, resemble one another) of the elaborations of the sutures serves to lengthen the boundaries and theoretically enhances the development of self-similar patterns. When autocorrelation and self-similarity in the sutures are favored by an evolutionary process plastic enough to elaborate intricate form, ensuring fitness, and natural selection does not directly limit the lengths while concomitantly defining the bounded areas, then the intricacy is manifest as fractal phenomena, and practically described as such.

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