Infrared intensities transition moments

If the vibration does not produee a modulation of the dipole moment (e.g., as with the symmetrie streteh vibration of the CO2 moleeule), its infrared intensity vanishes beeause 0 i/3Ra) = 0. One says that sueh transitions are infrared "inaetive". 

A powerful characteristic of RAIR spectroscopy is that the technique can be used to determine the orientation of surface species. The reason for this is as follows. When parallel polarized infrared radiation is specularly reflected off of a substrate at a large angle of incidence, the incident and reflected waves combine to form a standing wave that has its electric field vector (E) perpendicular to the substrate surface. Since the intensity of an infrared absorption band is proportional to / ( M), where M is the transition moment , it can be seen that the intensity of a band is maximum when E and M are parallel (i.e., both perpendicular to the surface). / is a minimum when M is parallel to the surface (as stated above, E is always perpendicular to the surface in RAIR spectroscopy). 

One of the most familiar uses of dipole derivatives is the calculation of infrared intensities. To relate the intensity of a transition between states with vibrational wavefunctions i/r and jfyi it is necessary to evaluate the transition dipole moment... 

In the normal-incident transmission measurements of LB films deposited on transparent substrates, the electric vector of the infrared beam is parallel to the film surface (Figure 5A). Therefore, only absorption bands which have the transition moments parallel to the film surface can be detected by this method. On the other hand, in the above-mentioned RA measurements, in which the p-polarized infrared beam is incident upon the LB film prepared on Ag-evaporated substrates at a large angle of incidence, we have a strong electric field perpendicular to the film surface as shown in Figure 5B. Therefore, in this case, only absorption bands which have the transition moments perpendicular to the film surface can be detected with a large intensity enhancement. Thus, if the molecules are highly oriented in the LB films, the peak intensities of particular bands should be different between the transmission and RA spectra. 

We noted earlier (Section I. 1.) that the intensity of an absorption band is proportional to the square of the changing dipole moment in the molecule (i. e., transition moment) during the corresponding normal vibration. The intensity also depends upon the direction that the electric vector in the incident radiation makes with the transition moment. In particular, the intensity is proportional to the square of the scalar product of the transition moment and electric field vectors. This implies, for example, that if the electric field vector is perpendicular to the transition moment vector no absorption will occur. This fundamental relationship is the basis for the utilization of polarized infrared radiation as a powerful tool in the study of the spectra and structure of oriented polymers. We consider below some aspects of this technique. 

Raman Selection Rules. For polyatomic molecules a number of Stokes Raman bands are observed, each corresponding to an allowed transition between two vibrational energy levels of the molecule. (An allowed transition is one for which the intensity is not uniquely zero owing to symmetry.) As in the case of infrared spectroscopy (see Exp. 38), only the fundamental transitions (corresponding to frequencies v, V2, v, ...) are usually intense enough to be observed, although weak overtone and combination Raman bands are sometimes detected. For molecules with appreciable symmetry, some fundamental transitions may be absent in the Raman and/or infrared spectra. The essential requirement is that the transition moment F (whose square determines the intensity) be nonzero i.e.. 

In analyzing the photodissociation spectra, line frequencies and transition moments based on an assumed molecular structure, as well as decay rates, are convoluted through Eq.(l). The parameters are adjusted to give the best agreement with observations. Band positions and infrared intensities also reflect the van der Waals interactions. Summarized in this section are the important conclusions regarding the structures and interactions in the van der Waals molecules we have studied. 

In addition to the energies and intensities we have also included the transition moment directions in Table IX. These quantities, obtained in UV or infrared (IR) linear dichroism experiments, have been used... 

Here Uab is the Raman transition moment, fic is the infrared transition moment, g and V refer to ground and excited vibrational states, coir is the input infrared frequency, coq is the resonance frequency of the adsorbate, and T is a damping factor [8, 14—17]. Thus, the SFG intensity is related to the product of an (anti Stokes) Raman transition and an infrared transition. The SFG intensity is enhanced when the input infrared wavelength coincides with a vibrational mode of the adsorbate and the result of an SFG spectrum corresponds to the vibrational levels of the molecule. This situation is shown schematically in Fig. 5.1. From (5), non-zero SFG intensity will occur only for transitions that are both Raman and IR allowed. This situation occurs only for molecules lacking inversion symmetry [19]. 

According to the vibronic theory of infrared intensities, the vibronic contribution to the transition dipole moment of the vibrational mode Q is related to... 

Finally, let us consider the relationship between the vibrational motions and the infrared (IR) absorption spectra. The IR spectra show the frequencies corresponding to the energy gaps in the transitions between vibrational eigenstates, with the peak intensities proportional to the transition moments. The transitions between vibrational states have rules called selection principles for the harmonic oscillator, transitions take place for the eigenstate pairs with A = 1. This selection principle comes from the fact that the transition moment, which is proportional to the transition dipole moment. 

Infrared dichroism is based on the interaction between linearly polarized infrared radiation and the oriented material. The atoms of a polymer molecule vibrate in characteristic normal modes, each of which produces a change in dipole moment (the transition moment) that has a specific direction. Each mode absorbs infrared energy at a characteristic frequency, giving rise to peaks in the infrared spectrum. The peak intensity (i.e. the absorbance) depends on the angle between the transition moment and the electric field vector of the radiation, and it is this that provides information on the molecular orientation. The orientation is defined in terms of the second moment of the orientation function Pjlcos 0), where ... 

The intensity of an infrared absorption band is proportional to the square of the transition moment (or infrared active dipole moment). The absolute intensity of an infi ared band also depends upon the direction of the transition moment (dipole electric field vector) and the field direction vector (electric field vector) of the incident infrared radiation. The proportion of the transition moment (TMp) in the direction of the infrared electric field direction vector (E) is given as... 

The contributions of the various intermolecular interactions to the vibrational coupling in Van der Waals complexes have been calculated explicitly for (SFe)25 (SiF4)2 and (81114)2. To try and simulate the dimer vibrational spectra (see Section 4) in the frequency range from 880 to 1100 cm , we have also calculated the infrared intensities of the dipole allowed transitions. We concentrate, in particular, on the dependence of the calculated spectra on the monomer orientations. In line with the atom-atom model used for the intermolecular potential, we write the following expression for the vibrational dipole moment operator of a dimer... 

These spectra serve to illustrate the sensitivity of rotational fine structure to the transition moment orientations and rotational constants. In practice, individual rotational lines cannot be resolved in most infrared vibration-rotation spectra, because the rotational constants are too small. In spectra such as that in Fig. 6.14, the bunched groups of Q-branch lines frequently materialize as single intense bands, while the more sparse P and R branches form weak continua. Rotational structures are frequently analyzed by comparing them with computer-generated spectra derived from assumed rotational constants and selection rules. By weighting the rotational line intensities with appropriate Boltzmann factors (cf. Eq. 3.28) and assigning each rotational line a frequency width commensurate with the known instrument resolution, realistic simulations of experimental spectra are possible if the rotational constants and selection rules are properly adjusted. 

P. Lazzeretti and R. Zanasi, Chem. Phys. Lett., 112, 103 (1984). Connection between the Nuclear Electric Shielding Tensor and the Infrared Intensities. P. Lazzeretti, R. Zanasi, and P. J. Stephens, J. Phys. Chem., 90, 6761 (1986). Magnetic Dipole Transition Moments and Rotational Strengths of Vibrational Transitions An Alternative Formalism. 

The intensity of an infrared absorption band is proportional to the square of the transition moment (or changing dipole moment) of the molecular vibration causing the band. The band intensity also depends on the relative... 

Acrylamide has four molecules per unit cell so that for every normal mode of vibration of the acrylamide molecule there were four modes for the unit cell (see Fig. 2.9). Two modes are infrared inactive because acrylamide crystallizes into two pairs of dimers, each with a center of symmetry. The two infrared active modes will have transition moments parallel and perpendicular to the direction of crystal growth as seen from a direction normal to the BC plane. The parallel and perpendicularly polarized spectra thus isolate the two active modes which have nearly the same but not identical frequencies. The relative band intensities of the two modes yield information about the direction of the vibrational transition moment of the molecule. 

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