Selection rule Raman transition

If the Schrodinger equation (Section 1.3) is solved using this potential, the resulting eigenvalues are expressed as a function of a quantum number, n. Selection rules for transitions are An = 1 for IR and An = 2 for Raman. The values of a and b must be chosen so that calculated IR and Raman fequencies agree with those observed. As an example, consider 1,3-disilacyclobutane ... 

Is the transition between the ground and lowest excited singlet states of cyclobutadiene allowed by electric dipole selection rules, Raman selection rules, both, or neither ... 

Another related issue is the computation of the intensities of the peaks in the spectrum. Peak intensities depend on the probability that a particular wavelength photon will be absorbed or Raman-scattered. These probabilities can be computed from the wave function by computing the transition dipole moments. This gives relative peak intensities since the calculation does not include the density of the substance. Some types of transitions turn out to have a zero probability due to the molecules symmetry or the spin of the electrons. This is where spectroscopic selection rules come from. Ah initio methods are the preferred way of computing intensities. Although intensities can be computed using semiempirical methods, they tend to give rather poor accuracy results for many chemical systems. 

One effect of mechanical anharmonicity is to modify the Au = t infrared and Raman selection rule to Au = 1, 2, 3,. .., but the overtone transitions with Au = 2, 3,... are usually weak compared with those with Au = t. Since electrical anharmonicity also has this effect both types of anharmonicity may contribute to overtone intensities. 

The rotational selection rule for vibration-rotation Raman transitions in diatomic molecules is... 

Because Raman scattering is also a two-photon process the selection rules for two-photon absorption are the same as for vibrational Raman transitions. For example, for a two-photon electronic transition to be allowed between a lower state j/" and an upper state... 

The selection rule for rotational Raman transitions are AJ = 2. This result relates to the involvement of two photons, each with angular momentum h, in the scattering process. Also allowed is A J = 0, but since such a transition implies zero change in energy it represents Raleigh scattering only. 

Information concerning conformation, tacticity and crystallinity may also be obtained (1). Vibrational transitions accesssible to IR spectroscopy are governed by the selection rule that there must be a change in dipole moment during excitation of the polymer vibrations. Thus symmetric vibrations which are detected by Raman spectroscopy are inaccessible to IR absorption measurements. 

A complete study of the electronic states of the / configuration of CeClj using the electronic Raman effect has been performed by Kiel eta/, Two pure antisymmetric transitions were observed which are forbidden by normal symmetric tensor selection rules. In this paper the general features of the electronic Raman effect are... 

Raman spectroscopy Is a form of vibrational spectroscopy which, like Infrared spectroscopy. Is sensitive to transitions between different vibrational energy levels in a molecule (1). It differs from Infrared spectroscopy In that Information Is derived from a light scattering rather than a direct absorption process. Furthermore, different selection rules govern the Intensity of the respective vibrational modes. Infrared absorptions are observed for vibrational modes which change the permanent dipole moment of the... 

Although similar transitional energy ranges occur in IR and Raman spectroscopies, different selection rules govern the intensities in Raman... 

In our experiment, the coherent superposition of u = 0 and v=l state is created by the impulsive Raman transition. Due to the selection rule of a Raman transition. 

The infra-red and Raman spectra of molecules are dominated by transitions between the ground state and the fundamental levels but, in practice, the number of fundamental frequencies observed does not reach 3JV—6 since (a) some of the Xt are identical (leading to degenerate fundamental levels) and (b) selection rules forbid certain transitions. Both (a) and (b) are determined by the symmetry of the molecule. 

A rotation of the H2 molecule through 180° creates an identical electric field. In other words, for every full rotation of a H2 molecule, the dipole induced in the collisional partner X oscillates twice through the full cycle. Quadrupole induced lines occur, therefore, at twice the (classical) rotation frequencies, or with selection rules J — J + 2, like rotational Raman lines of linear molecules. Orientational transitions (J — J AM 0) occur at zero frequency and make up the translational line. Besides multipole induction of the lowest-order multipole moments consistent with... 

Consideration of the matrix elements m a n of the polarizability shows that the selection rule for a pure-rotational Raman transition of a l2 diatomic molecule is (see Wilson, Decius, and Cross)... 

Stoicheff investigated the pure rotational Raman spectrum of CS2. The first few lines could not be observed because of the width of the exciting line. The average values of the Stokes and anti-Stokes shifts for the first few observable lines (accurate to 0.02 cm-1) are Ap = 4.96, 5.87, 6.76, 7.64, and 8.50 cm-1, (a) Calculate the C=S bond length in carbon disulfide. (Assume centrifugal distortion is negligible. The rotational Raman selection rule for linear molecules in 2 electronic states is AJ = 0, 2.) (b) Is this an R0 or Re value (c) Predict the shift for the 7 = 0—>2 transition. 

Recall that homonuclear diatomic molecules have no vibration-rotation or pure-rotation spectra due to the vanishing of the permanent electric dipole moment. For electronic transitions, the transition-moment integral (7.4) does not involve the dipole moment d hence electric-dipole electronic transitions are allowed for homonuclear diatomic molecules, subject to the above selection rules, of course. [The electric dipole moment d is given by (1.289), and should be distinguished from the electric dipole-moment operator d, which is given by (1.286).] Analysis of the vibrational and rotational structure of an electronic transition in a homonuclear diatomic molecule allows the determination of the vibrational and rotational constants of the electronic states involved, which is information that cannot be provided by IR or microwave spectroscopy. (Raman spectroscopy can also furnish information on the constants of the ground electronic state of a homonuclear diatomic molecule.)... 

The selection rules for Raman vibrational transitions are also readily derived from group theory. Here, the transition probability depends on integrals involving the components of the molecular polarizability matrix a. Since a is symmetric, it has only six independent components axx aw axi axr ayi aMf These six quantities can be shown14 to transform the same way the six functions... 

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