Infrared-transition dipole

As explained in section 2.6.1, any infrared-absorption peak is associated with a particular vibrational mode of the polymer chain. For each of these modes there is a particular direction within the polymer chain, called the infrared-transition dipole or transition-moment axis, which is the direction of the absorption dipole p. Infrared radiation is absorbed by a particular chain of the polymer only if two conditions are satisfied the frequency of the radiation must correspond to the frequency of the vibration and there must be a component of the electric vector E of the incident radiation parallel to the transition-dipole axis. If the molecules become oriented, so do the dipole axes hence the absorption of the sample will depend on the polarisation of the radiation. 

Rg. 10.10 Orientation of the infrared transition dipole p with respect to the long axis of the polymer molecule and the set of axes OX1X2X3 fixed in the sample. The axes OX1 and 0X3 are assumed to lie in the plane of the sample. 

As mentioned earlier, an infrared absorption band is associated with a particular vibration mode of the polymer bonds. For each one of these modes there is a particular direction within the polymer chain, which is the direction of the absorption dipole /i, also called infrared-transition dipole or transition moment axis (Bower and Maddams, 1989 Bower, 2002). 

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... 

Infrared spectra are straightforward to predict theoretically, demanding development of a force field (FF) to determine frequencies and dipole derivatives for intensities. These parameters were initially obtained using empirically fitted force constants and simple models for transition dipoles (Krimm and Bandekar, 1986 Torii and Tasumi, 1996). 

Focusing on the 0 ) > 1 ) infrared transition of the fast mode, the dipole... 

Two ingredients are needed to compute the intensities of transitions the wave functions of the initial and final states and the form of the transition operator (Ogilvie and Tipping, 1983). For infrared transitions the appropriate operator is the dipole operator, M(r, 0, (j>). This operator is a vector (tensor of rank 1) and thus can be written as... 

In order to find the coefficients a, for infrared transitions (for which the operator is a dipole operator), one returns to the geometric structure of the molecule and introduces a set of Cartesian coordinates (in the plane x, y), shown in Figure 4.4. The operator f has two components, fx and Ty, given by... 

Different types of chemical reactions involve different types of vibrational modes, e.g. dissociation reactions may be controlled by stretching vibrations, isomerizations by skeletal modes, and so on. The argument that infrared quanta are relatively energy-poor and infrared transitions generally have low absorption cross sections, especially if multiphoton excitation is required, limits the choice of suitable molecular transitions. With respect to these constraints the type of reaction chosen and described below was dissociation, involving molecules with maximal transition dipole moments, comparatively weak bonds to be broken, and vibrational excitation in the mid-infrared spectral range. 

The factor in (6.67) that multiplies the integral (6.73) contains the derivatives of the dipole-moment components with respect to the normal coordinate Qk, evaluated at the equilibrium configuration. We conclude that a radiative infrared transition in which the vibrational quantum number of the A th normal mode changes by one is forbidden unless the Acth mode has a change in dipole moment associated with it. The value of the equilibrium dipole moment de is irrelevant for infrared transitions of a polyatomic molecule. 

Ultraviolet, visible, and infrared spectroscopies refer to analysis of the absorption characteristics of a sample that are linked to various electronic and vibrational transitions within a molecule [17]. These involve relative displacements of electrons and nuclei that are able to couple to incident light if they induce a dipole in the material. The strength of this coupling is measured by the transition dipole moment [17],... 

Vibrational spectroscopy has been used in the past as an indicator of protein structural motifs. Most of the work utilized IR spectroscopy (see, for example, Refs. 118-128), but Raman spectroscopy has also been demonstrated to be extremely useful (129,130). Amide modes are vibrational eigenmodes localized on the peptide backbone, whose frequencies and intensities are related to the structure of the protein. The protein secondary structures must be the main factors determining the force fields and hence the spectra of the amide bands. In particular the amide I band (1600-1700 cm-1), which mainly involves the C=0-stretching motion of the peptide backbone, is ideal for infrared spectroscopy since it has an large transition dipole moment and is spectrally isolated... 

In resonant infrared multidimensional spectroscopies the excitation pulses couple directly to the transition dipoles. The lowest order possible technique in noncentrosymmetrical media involves three-pulses, and is, in general, three dimensional (Fig. 1A). Simulating the signal requires calculation of the third-order response function. In a small molecule this can be done by applying the sum-over-states expressions (see Appendix A), taking into account all possible Liouville space pathways described by the Feynman diagrams shown in Fig. IB. The third-order response of coupled anharmonic vibrations depends on the complete set of one- and two-exciton states coupled to thermal bath (18), and the sum-over-states approach rapidly becomes computationally more expensive as the molecule size is increased. 

This technique was employed to monitor the B —> A transition of DNA as a function of the relative humidity (Pilet and Brahms, 1973 Pohle et al., 1984). The investigated bands are those which reflect the vibrations of the phosphate groups. As shown by Fig. 4.7-3, which presents the polarized infrared spectra of a salmon sperm DNA hydrated film with 93% RH (top, B form) and 58% RH (bottom, A form), the dichroism of the two phosphate bands changes. The B form of the antisymmetric PO2 stretching vibration around 1230 cm is non-dichroic, while that of the A form is perpendicular. The B form of the symmetric PO2 stretching vibration around 1090 cm is perpendicular, while that of the A form is parallel. A simple computation, for instance for the latter band, shows that the value of the angle between the transition dipole moment of this vibration and the double helical axis varies between 68 ° (B form) and 49 ° (A form). This parameter is an extremely sensitive indicator of a B A transition and may also be employed to show the inhibition of a B —> A transition by various classes of molecules, such as proteins (Liquier et al., 1977 Taillandier et al., 1979) or drugs (Fritzsche and Rupprecht, 1990). 

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