Dipole moment of transition

For forbidden transitions in atoms and molecules this phenomenon may be experimentally observed in spectra induced by collisions. As is known, the selection rules on some transitions may be cancelled during collision. The perturbers are able to induce a dipole moment of transition having the opposite direction in successive collisions due to intercollisional correlation. Owing to this, the induced spectra do involve the gap (Fig. 1.7), the width of the latter being proportional to the gas density [46, 47], Theorists consider intercollisional correlation to be responsible for the above phenomenon [48, 49, 50]. 

The calculation of accurate dipole moments of transition metal oxides is very difficult (see, e.g., ref [17]). Our calculated dipole moments axe given in Table... 

This is a consequence of the crudeness of the models and the lack of independent methods for the evaluation of the dipole moments of transition states. These quantities are obtained from the slopes of the approximately linear plots of AC vs. (es) or

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SYMMETRY ANALYSIS OF NORMAL VIBRATIONS AND DIPOLE MOMENTS OF TRANSITION GENERATED THEREFROM... 

This analysis illustrates a particular case of one fundamental IR spectroscopy rule The dipole moment of transition is characterized by the same symmetry mode as the normal vibration, which generates it [57]. This means that colinear moments of transition and bands of equal dichroic ratio correspond to vibrations belonging to the same symmetry class. This conclusion is of principal importance for the application of IR-LD spectroscopy for the identification of the IR bands. The statement is supported by the example given in Figure 1.8. 

FIGURE 1.7 Direction of the dipole moment of transition for v -stretching, v -stretching, and 5-bending vibrations. 

The theoretical model of the IR linear dichroism suggests a single-axis orientation of a molecular assembly with axial (cylindrical) synunetry. This means that the molecules are located with their longest axis in the direction, which induces the anisotropy, determined by the director n, and the side groups are randomly fixed or rotate along the length of this axis. Under these conditions, the dipole moments of transition caused by the normal vibrations form conical surfaces with director n (Figure 1.2) [2,3,6-8]. 

It turns out that there is another branch of mathematics, closely related to tire calculus of variations, although historically the two fields grew up somewhat separately, known as optimal control theory (OCT). Although the boundary between these two fields is somewhat blurred, in practice one may view optimal control theory as the application of the calculus of variations to problems with differential equation constraints. OCT is used in chemical, electrical, and aeronautical engineering where the differential equation constraints may be chemical kinetic equations, electrical circuit equations, the Navier-Stokes equations for air flow, or Newton s equations. In our case, the differential equation constraint is the TDSE in the presence of the control, which is the electric field interacting with the dipole (pemianent or transition dipole moment) of the molecule [53, 54, 55 and 56]. From the point of view of control theory, this application presents many new features relative to conventional applications perhaps most interesting mathematically is the admission of a complex state variable and a complex control conceptually, the application of control teclmiques to steer the microscopic equations of motion is both a novel and potentially very important new direction. 

The interaction of the electron spin s magnetic dipole moment with the magnetic dipole moments of nearby nuclear spins provides another contribution to the state energies and the number of energy levels, between which transitions may occur. This gives rise to the hyperfme structure in the EPR spectrum. The so-called hyperfme interaction (HFI) is described by the Hamiltonian... 

C3.4.13)). The dimer has a common ground state and excitation may temrinate in eitlier tire or excited state (see tire solid arrows in figure C3.4.3). The transition dipole moments of tliese transitions are defined as ... 

In a combined experimental/computational study, the vibrational spectra of the N9H and N7H tautomers of the parent purine have been investigated [99SA(A) 2329]. Solvent effects were estimated by SCRF calculations. Vertical transitions, transition dipole moments, and permanent dipole moments of several low-lying valence states of 2-aminopurine 146 were computed using the CIS and CASSCF methods [98JPC(A)526, 00JPC(A)1930]. While the first excited state of adenine is characterized by an n n transition, it is the transition for 146. The... 

The form of the Plmn will be discussed later, because it is instructive to develop the argument by considering next the information which is obtained from any spectroscopic technique. Figure 2a shows a direction within a unit of structure which is defined by the polar and azimuthal angles (, r ). For example, this could be the direction defining the change in dipole moment (the transition moment vector) in an infra-red spectroscopic measurement. The spectroscopic measurements provide... 

The intercept, 1/Po, is called the anisotropy of the molecule and is an indication of the nonrotational depolarization of the molecule. This intrinsic depolarization is due to the segmental motion of the fluorophores within the molecule the depolarization due to energy transfer and the angular difference in transition dipole moments of the absorbing and emitting states. 

Fig. 7.3 Effect of magnetic dipole interaction (7/m), electric quadmpole interaction (Hq), and combined interaction// = Hu + //q, Em> q on the Mossbauernuclear levels of Ni. The larger spacings between the sublevels of the ground state are due to the somewhat larger magnetic dipole moment of the nuclear ground state as compared to the excited state. The relative transition probabilities for a powder sample as well as the relative positions of the transition lines are indicated by the stick spectra below...

The PPP-MO method is capable of calculating not only the magnitude of the dipole moment change on excitation, but it can also predict the direction of the electron transfer. The vector quantity that expresses the magnitude and direction of the electronic transition is referred to as the transition dipole moment. For example, the direction of the transition dipole moment of azo dye 15f as calculated by the PPP-MO method is illustrated in Figure 2.15. 

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