We have revisited the problem of anomalously diffusing species, modelled at the mesoscopic level using continuous time random walks, to include linear reaction dynamics.If a constant proportion of walkers are added or removed instantaneously at the start of each step then the long time asymptotic limit yields a fractional reaction-diffusion equation with a fractional order temporal derivative operating on both the standard diffusion term and a linear reaction kinetics term. If the walkers are added or removed at a constant per capita rate during the waiting time between steps then the long time asymptotic limit has a standard linear reaction kinetics term but a fractional order temporal derivative operating on a non-standard diffusion term.Results from the above two models are compared with a phenomenological model with standard linear reaction kinetics and a fractional order temporal derivative operating on a standard diffusion term.We have also developed further extensions of the CTRW model to include more general reaction dynamics.

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The gas phase vibrational overtone spectrum of propane is measured using conventional near infrared (NIR) spectroscopy for the ΔvCH=2–5 regions and intracavity dye laser photoacoustic spectroscopy (IDL-PAS) for the ΔvCH=5 and 6 regions. The peaks are assigned in terms of the local mode model. Experimental oscillator strengths are compared to values calculated for the CH-stretching components of the spectrum. The calculations use a harmonically coupled, anharmonic oscillator local mode model to obtain the vibrational wave functions, and ab initio MO calculations at the SCF level with a 6-31G* basis set to obtain the dipole moment function. The importance of intermanifold coupling is explored. The calculations can account for the fall-off in intensity with increasing v, and can give a reasonably quantitative account of the relative intensities of the individual peaks within a given vibrational manifold. The questions of the relative intensities of primary and secondary CH bonds, and of the relative intensities of different methyl CH bonds are also explored.

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Vapor phase room temperature overtone spectra of cyclohexane are measured with conventional near infrared spectroscopy for the lower overtones, ΔvCH=2–4, and with intracavity dye laser photoacoustic spectroscopy for the higher overtones, ΔvCH=5–7. The relative intensity of the axial to equatorial peak is explained in terms of the local mode model of harmonically coupled anharmonic oscillators, where all modes but the two CH-stretching modes are neglected. The dipole moment function is expanded in the two CH-stretching coordinates, where the expansion coefficients are determined from ab initio molecular orbital calculations. This simple calculation, which contains no adjustable parameters, can account very well for the observed relative intensity of axial and equatorial pure local mode peaks in the overtone spectra from ΔvCH=3–7. We also investigate different ways of obtaining the dipole moment derivatives, and find that a fourth order series expansion around the equilibrium geometry is a good approximation when calculating the relevant matrix elements.

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The existence of normal modes of vibration is elegantly demonstrated in a film by Crawford and Overend.1 A loosely coupled eccentric motor excites a ball and spring model of the carbon dioxide molecule. As the frequency of rotation of the motor increases, the chaotic motions of the excited "atoms" are resolved into a coherent bending motion. A further increase in the frequency of the motor again procedures chaos until, at some higher frequency, the symmetric stretching motion appears and finally, at even higher frequency, the antisymmetric stretch. Thus we see directly that at these "natural" frequencies each "atom" in the "molecule" is moving with the same frequency and phase so that each "atom" reaches its position of maximum displacement at the same time and each "atom" passes through its equilibrium position at the same time.These are the familar characteristics of normal modes

Gas phase vibrational overtone spectra of 1,3-butadiene are recorded in the ΔvCH=2–6 regions by conventional near infrared–visible spectroscopy, and in the ΔvCH=4–7 regions by intracavity dye/titanium:sapphire, laser photoacoustic spectroscopy (ICL-PAS). Gas phase vibrational overtone spectra of 1,3-butadiene-d6 are recorded in the ΔvCD=2–5 regions with conventional spectroscopy and in the ΔvCD=5–8 regions by ICL-PAS. Oscillator strengths are calculated from wave functions that are obtained from a harmonically coupled anharmonic oscillator (HCAO) local mode model and from a dipole moment function that is obtained from ab initio calculations. The experimental oscillator strengths are compared to the values that are calculated for both the CH- and CD-stretching components of the spectrum. Our simple calculations, which contain no adjustable parameters, are in very good agreement with the relative intensities of the peaks corresponding to the three different CH oscillators in 1,3-butadiene. As expected, the local mode description is not as good for the CD oscillators in 1,3-butadiene-d6. Nonetheless, the calculations can provide a reasonable explanation of the CD-stretching intensity distribution in the higher overtone spectra of 1,3-butadiene-d6. Small hydrogen impurities in the fully deuterated sample give rise to isolated CH-stretching overtones. The relative intensities of the CD peaks and the CH impurity peaks in the 1,3-butadiene-d6 sample spectra are predicted by the calculations. A comparison of the 1,3-butadiene-d6 sample spectra in the CH-stretching region with the CH-stretching overtone spectra in 1,3-butadiene dramatically illustrates the effects of vibrational coupling between CH oscillators.