Theory electric dipole transition moment

Coupled oscillator models are extensions to the simple models developed for electronic circular dichroism. They are well known under the name exciton theory (see e.g. Harada and Nakanishi, 1972). These models, extended to vibrational transitions, describe the coupling of pairs of electric dipole transition moments. They predict equal amounts of positive and negative VCD intensity ... 

Since the crystal structures of Rps. viridis [1] and of Rb. sphaeroides [2] have become available, attempts have been made to explain the spectroscopic properties of the reaction centres of photosynthetic bacteria, using exciton theory to describe the coupling between the electric dipole transition moments of the various pigments and comparing calculated spectra with the observed reaction centre (RC) spectra. 

The most intuitively acceptable explanation for the breakdown of the theory relating IR dichroism and the uniaxial molecular orientation is that some of the molecular structural parameters, such as i and Aq, are indeed affected by dynamic orientation processes. In other words, molecules undergoing dynamic reorientation processes do not always rotate as rigid and independent entities. Changes in local molecular environments and molecular conformations induced by the macroscopic perturbations imposed on the system significantly affect the submolecular spatial relationship between the individual electric dipole transition moments arising from the vibrations of the molecular constituents and the principal orientation axis of the molecule. 

In practice values of B are also often quoted in cm-1. For the simple rigid rotor the rotational quantum number J takes integral values, J = 0, 1, 2, etc. The rotational energy levels therefore have energies 0, 2B, 6B, 12B, etc. Elsewhere in this book we will describe the theory of electric dipole transition probabilities and will show that for a diatomic molecule possessing a permanent electric dipole moment, transitions between the rotational levels obey the simple selection rule A J = 1. The rotational spectrum of the simple rigid rotor therefore consists of a series of equidistant absorption lines with frequencies 2B, 4B, 6B, etc. 

There is only one other ab initio implementation of the theory of optical activity to calculate optical rotatory strengths, that due to Hansen and Bouman, based on the random-phase approximation (RPA) and implemented in the program package, RPAC. The RPA method is intended to include those first-order correlation effects that are important both for electronic transition intensities and for excitation energies. The electric and magnetic dipole transition moments in RPA are given by equations (14), (15), and (16) (analogous to equations 7, 8, and 9, above). 

Analogously to UV/ECD, IR and VCD intensities are proportional to the quantities dipole (D) and rotational (R) strengths, respectively, which are calculated using equations (16) and (17), at the same level of theory employed in the optimization step. However, in the case of VCD, the electric (jx) and magnetic (m) dipole transition moment vectors include the wavefunctions of the ground (0) and the first excited vibrational state (1), within the ground electronic state of the molecule. Furthermore, in the harmonic approximation, the dipole strength in the normal mode Qa is proportional to ... 

Unlike the near-field dyadic of Forster, which has no frequency dependence, the dyadics appearing in the above expression are explicitly frequency-dependent due to the range of the interaction. In particular, T p is the appropriate dyadic with the sphere in place, and fdip is the dyadic in the absence of the sphere. Although Td,p is easily obtained from dipole radiation theory, f,p must be obtained bv solvine the appropriate boundary value problem. When one considers that T( d, ra, co) - id is the electric field at the acceptor [see Eq. (8.14)], it becomes apparent that A(co) 2 is simply a ratio of intensities. For the case of transition moments which are normal to the surface as depicted in Figure 8.19, the numerator of Eq. (8.21) reduces to... 

The quantity that connects theory with experiment in CD spectroscopy is the rotational strength R. On an experimental level, R is determined by the area under a resolved CD transition (Figure 1.6b), while from theory the rotational strength is proportional to the projection of the electric dipole moment of a T g —> vPe transition... 

In group theory, the electric dipole operator transforms according to the operations of translation, and the magnetic dipole operator transforms as a rotation. It is not difficult to show that the individual transition moments are invariably orthogonal as long as the molecular point group contains improper axes of rotation. This rule is often trivialized to... 

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