Transition dipole moment, rotational spectra

SAC-CI method was applied to calculate the electronic CD spectrum of uridine [43], Based on theoretical CD and absorption spectra, observed peaks in the experimental spectra were assigned. The rotational strength (R) in the length form [44] was calculated as imaginary part of the inner product of the electric transition dipole moment (ETDM) and magnetic transition dipole moment (MTDM). 

Figures 7.5 and 7.6 show the experimental absorption spectra of HCl and DCl, respectively, together with the spectra calculated using wavepacket propagation and the reflection principle. It can be seen that the wavepacket method is in good agreement with the experimental results. For both HCl and DCl the wavepacket propagation method yields the correct frequency for the absorption peak. The wavepacket propagation method is exact and the deviation from the experimental spectrum must be attributed to the use of only two electronic states and/or inaccurate transition dipole moments and/or potential energy curves and/or not treating the rotations of the molecule. The experimental results are quite accurate.

Write a computer program to calculate the relative intensities of the spectral fines in the fundamental band of the vibration-rotation spectrum of a diatomic molecule, assuming that the absorbance is displayed in the spectrum. Set the maximum absorbance of the first line of the P branch equal to 1. Assume the Boltzmann probability distribution and assume that the transition dipole moments for all transitions are equal. Use your program to calculate the relative intensities for the first 15 lines in each branch of the HCl spectrum... 

For molecules in which at least one internal rotating part has a dipole moment component perpendicular to the axis of rotation, there should appear directly in the infrared spectrum transitions between the torsional states. For most cases these would be quite far in the infrared region and therefore more difficult to observe. Nevertheless a few molecules of this type have been studied in this region, and such transitions have been reported.6... 

Detection of hydrogen is a particularly important problem for astrochemists because to a first approximation all visible matter is hydrogen. The hydrogen molecule is the most abundant molecule in the Universe but it presents considerable detection problems due to its structure and hence spectroscopy. Hydrogen does not possess a permanent dipole moment and so there is no allowed rotation or vibration spectrum and all electronic spectrum transitions are in the UV and blocked by the atmosphere. The launch of the far-UV telescope will allow the detection of H2 directly but up to now its concentration has been inferred from other measurements. The problem of detecting the H atom, however, has been solved using a transition buried deep in the hyperflne structure of the atom. 

In the ideal case of free Eu + ions, we first must observe that the components of the electric dipole moment, e x, y, z), belong to the irreducible representation in the full rotation group. This can be seen, for instance, from the character table of group 0 (Table 7.4), where the dipole moment operator transforms as the T representation, which corresponds to in the full rotation group (Table 7.5). Since Z)° x Z) = Z) only the Dq -> Fi transition would be allowed at electric dipole order. This is, of course, the well known selection rule A.I = 0, 1 (except for / = 0 / = 0) from quantum mechanics. Thus, the emission spectrum of free Eu + ions would consist of a single Dq Ei transition, as indicated by an arrow in Figure 7.7 and sketched in Figure 7.8. 

Rotational Raman spectroscopy is a powerful tool to determine the structures of molecules. In particular, besides electron diffraction, it is the only method that can probe molecules that exhibit no electric dipole moment for which microwave or infrared data do not exist. Although rotational constants can be extracted from vibrational spectra via combination differences or by known correction factors of deuterated species the method is the only one that yields directly the rotational constant B0. However for cyclopropane, the rotational microwave spectrum, recording the weak AK=3 transitions could be measured by Brupacher [20],... 

We previously found the selection rule A7 = 1 for a 2 diatomic-molecule vibration-rotation or pure-rotation transition. The rule (4.138) forbids A/ = 1 for homonuclear diatomics this gives us no new information as far as vibration-rotation spectra are concerned, since the absence of a dipole moment insures the absence of a vibration-rotation or pure-rotation spectrum, anyway. 

Symmetric tops with no dipole moment have no microwave spectrum. For example, planar symmetric-top molecules have a C axis and a ak symmetry plane such molecules cannot have a dipole moment. Thus benzene has no microwave spectrum. For a symmetric top with a permanent electric dipole moment, the selection rules for pure-rotation transitions are... 

Aside from the possession of a permanent dipole moment and sufficient volatility, a molecule must be reasonably small for its microwave spectrum to be profitably studied. Large molecules have many low-frequency vibrational modes these modes will be appreciably populated at room temperature, giving many strong pure-rotation transitions between levels with nonzero vibrational quantum numbers. The microwave spectrum of a large molecule will thus have so many lines that assignment of the lines will be virtually impossible. 

In spite of the prohibition on the A2<—>A1 combination as an electric dipole transition the electronic origin appears very weakly in the spectrum as a type A band (Brand, 1956). This was first attributed to a mixing of the A2 state with the higher Al states by rotation (species a2) about the twofold symmetry axis (Pople and Sidman, 1957) but this explanation is now known to be incorrect and the electronic origin is explained as a transition allowed by virtue of the change in magnetic dipole moment (Callomon and Innes, 1962). 

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