Christiansen frequency

At wavenvunbers where the refractive index of the material equals that of the substance it is imbedded in (CO2 gas in the Martian case), the suspended atmospheric dust is least scattering, but still absorbing. The frequency where the index of the particles equals that of the environment is called the Christiansen frequency. If atmospheric gas and dust absorption are not excessive, the spectral region sim-rounding this frequency may provide a suitable window for a measurement of the surface temperature. 

Following the approach of Christiansen-Dalsgaard,24 we can calculate the n —> n + 1 Rabi frequency. We write the Hamiltonian as... 

An upper limit to the required Rabi frequency is found by requiring that it be equal to the detuning. Using this requirement with Eq. (10.31) Christiansen-... 

The calculations give the electronic part of the polarizability. It is thought that the ZPYA correction is the major part of the vibrational contribution and has a value of about 0.29 au at zero frequency. In Table 6 this correction has been added to the electronic part to give the values in the final column, which can be compared with the two possible experimental values in the first two rows. The most accurate of the CCSD type work should be that of Christiansen... 

Figure 1 Dynamic Polarizability, a(w) for H20 in the gas phase. Curves A and B are alternative interpretations of the experimental data (see text) C and D computed curves from Christiansen et al. and Kongsted et al45 filled points are from Poulsen et al46 open points from Jensen et al. All the theoretical values have been increased at all frequencies by 0.29 au, the estimated ZPVA correction...

Curves A and B are alternative interpretations of the experimental situation. Curve B is a plot of the 6 term Cauchy dispersion formula derived by Zeiss and Meath, while curve A is a simple quadratic interpolation (2-term Cauchy formula) between the static value of Cuthbertson40 and the Zeiss-Meath39 value at 514.5 nm (the only point where the polarizability anisotropy has been measured). Theoreticians appear to have taken these two values to heart. Curves C and D are plots of similar formulae [a(co) = 4(1 + Bofi) derived theoretically by Christiansen et al.44 and Kongsted et al.45 respectively, using the methods shown in Table 6 with suitable time-dependent procedures. The points obtained from the MCSCF46 work and the DFT/SAOP method48 are also plotted. The ZPVA correction of 0.29 au has been added at all theoretical points at all frequencies. 

In this complex state of affairs it seemed of interest to examine some reactions at pressures so low that some differentiation between the proposed mechanisms would be possible, or at least some experimental data in a simplified form would be available. It is evident that, at sufficiently low pressures, a profound modification of the velocity constant should take place whether the mechanism be that of Christiansen and Kramers, Lindemann, Perrin or Rodebush. The relation between collision frequency and observed reaction rate at this point would also be of considerable significance.11... 

Polarizabilities and Hyperpolarizabilities of Larger Molecules. - Ab Initio Calculations. At the most highly correlated level Christiansen et al.157 have used the CCS, CC2 and CCSD models to calculate the static polarizability of furan. Dispersion effects are included to make an estimate of the frequency-dependent polarizability. 

A few versions of CC theory have been developed for treating excited states. One such version, the equation-of-motion (EOM) CCSD, has given very good results for vertical excitation energies. Analytic gradients for the EOM-CCSD method are available, allowing calculation of geometries and vibrational frequencies of excited states. For details see R. J. Bartlett in Yarkony, Part II, Chapter 16, Section 9 A. I. Krylov, Amu. Rev. Phys. Chem., 59, 433 (2008). CC excited-state methods are reviewed in K. Sneskov and O. Christiansen, WIRES Comput. Mol. ScL, 2, 566 (2012). 

There is also a possibility that a characteristic frequency for the skeleton -C-N=N-C may exist, as Tetlow [23] has shown that both cis- and trans-azobenzenes show absorption at 927 cm which is absent from hydrazobenzene, and that this band shows a Christiansen filter effect only in the trans-form, which may indicate its association with a skeletal group along the direction of maximum polarisability. 

Bands whose shapes are not Gaussian often appear in the infrared spectrum of a material in a solid matrix. This effect is known as the Christiansen effect and is due to the particle size and refractive index differences between the material and matrix. The radiation loss by scattering is a function of this refractive index difference. At frequencies slightly higher than the absorption maximum of a band, the refractive index of the sample decreases rapidly and approaches the refractive index of the matrix. This results in less scattering and a rapid increase in transmission. At frequencies slightly lower than the absorption maximum, the refractive index of the sample is markedly different than that of the matrix... 

Different approaches to the calculation of vibrational corrections to response properties can be found in the work of Sauer and Pack (2000), Ruud et al. (2000), and Kongsted and Christiansen (2006). The Boltzmann averaging procedure for conformationally flexible molecule has been critically reviewed by Crawford and Allen (2009). Mort and Autschbach (2008) have proposed an approach based on a decoupling of hindered rotations from the remaining (high-frequency) vibrational modes, which allows for a separate calculation of the hindered rotations without invoking the harmonic approximation. 

MP2, the M0ller-Plesset second-order perturbation theory, which in the case of frequency-dependent perturbations has to be replaced by an iterative optimization of the perturbation amplitudes, as described by the CC2 model (Christiansen et al. 1995)... 

Christiansen S, Scholze M, Axelstad M et al (2008) Combined exposure to anti-androgens causes markedly increased frequencies of hypospadias in the rat. Int J Androl 31(2) 241-248. doiilO. 1111/j. 1365-2605.2008.00866.X... 

Christiansen effect A spurious band on the high frequency side of a true absorption band may sometimes be observed when examining the mulls of crystalline materials if the particle size is of the same order of magnitude as the infrared wavelength being used. 

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