No abstract

Systems of interacting harmonic oscillators have recently received considerable attention as models for describing a variety of physical problems. %'e have investigated the validity of the rotating-wave approximation which constitutes the traditional approach to the solution of the dynamical problem by comparing it with the exact solution. A numerical comparison has been made and the limits of validity of the rotating-wave approximation has been established in terms of the strength of oscillator interaction.In particular, the time development of dynamical operators and certain transition probabilities have been compared. In the region where the rotating-wave approximation is valid, the time evolution of the quasiprobability distribution P(e, t) of one oscillator is given for several initial conditions. A counting scheme similar to the argument given by Feynman for the driven harmonic oscillator, is proposed for the interpretation of the time-dependent transition &.mplitudes between number states.

The two-vibrational-mode model proposed by Toyozawa and Mahr to account for the Urbach rule is considered both in the semiclassical approximation and in the full quantum theory. The semiclassical line shape accounts for both the exponential Urbach tail and the central Gaussian region of the absorption band.Quantum modifications make the semiclassical line shape incorrect for an excited state stable to odd-parity lattice distortions. The quantum line shape for an unstable excited state is shown to be qualitatively similar to the semiclassical line shape. In particular the two line shapes agree at high temperatures, but diller quantitatively at low temperatures. It is suggested that the hypothesis of an unstable excited state is consistent with recent experimental results on intrinsic luminescence in alkali halides.

The hydrogen bond stretching vibration, vu, in the far-infrared region is studied for substituted phenols with trimethylamine N-oxide (TMAO) as well as with 1,2-bis((dimethylamino)methyl)benzene Nfl-dioxide (DMAMBO) solutions in a 2:l mixture of chloroform and acetonitrile as a function of the pKa of the phenols. It is found and explained that the position of this vibration is only slightly dependent on the mass of the substituted phenols. In the case of the phenol + TMAO systems, vu first shifts with decreasing pKa of the phenols toward higher wavenumbers showing a maximum with the 3,4-dinitrophenol + TMAO system and shifts then again toward smaller wavenumbers. The position of this band reflects the strength of these hydrogen bonds. Always only a single hydrogen bond stretching vibration is observed. With the systems with more asymmetrical double minimum proton potentials, the ground state of the proton is not split; Le., only one of the two proton limiting structures OH-ON * O---H+ON is realized if the system is in the ground state. In the most symmetrical system, O--H+-.ON bonds are built; hence also only one hydrogen bond stretching vibration is expected. In the cases in which the double minimum proton potentials are almost largely symmetrical, the lowest level is split. Both proton limiting structures are realized in the ground state. Hence the result that only one hydrogen bond stretching vibration is found in these cases demonstrates that the proton fluctuates with a frequency larger than lo'* s-I within these hydrogen bonds. In the case of the phenol + DMAMBO systems, the nature of the hydrogen bonds is equivalent to those in the phenol + TMAO systems. But with decreasing pKa of the phenols beginning with the 4-cyanophenol + DMAMBO system intramolecular homoconjugated NO-H+-ON hydrogen bonds are also formed. If the pK, of the phenols decreases further, with the 3,4-dinitrophenol + DMAMBO systems only such homoconjugated hydrogen bonds are found and the phenolates are present as free ions. This formation of homoconjugated hydrogen bonds can be explained by sterical reasons.

Pyridine-borabenzene (1) and pyridine-2-boranaphthalene (2) can be coordinated to group 6A metals M to form compounds of the type (OC)3M·1 and (OC)3M·2, respectively. X-ray structure determinations prove the ligands to be η6-bonded to the metal via the boron-containing six-membered ring.