The dipole strength

The dipole strength is defined as the absolute square of the matrix element for the transition  

Indeed, only the difference is significant. This difference is drastically increased by applying a magnetic field this is the basis of magnetic optical rotation and MCD. 

Circularly polarized light can only propagate along an optical axis, where a m+ j) = a m j)f, so that 

In Einstein s theory, the dipole strength is defined for an isotropic radiation bath  

This has implications for the formulation of the oscillator strength, introducing a factor 1/3 that was very misleading in MCD theory. In our pedestrian development we have tried to unravel these difficulties step by step and will always use the dipole strengths D andD as defined by Eqs. (113), (116), (117), (119), (120), (122), (123), (125) and, when necessary, use Disotropic (see Eq. (126)). 

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The intermolecular interaction described above provides information about the magnitude of spectral shifts, but it does not explain why the absorption spectra of molecular aggregates usually have either an H- or J-band. The square of transition dipole moment (in Debye2 units) is usually termed the dipole strength and is related to the intensity of the absorption band as (van Amerongen et al. 2000)... 

The intensity of a vibrational transition 1 - 0 for the fundamental of normal mode Qa is proportional to the dipole strength, D,o, defined as... 

Once the normal modes are computed, the nature or properties of the excited vibrational states can also be of use for structural studies. The most obvious of these is the dipole strength, directly proportional to the IR absorption intensity, which will depend on the environment and stereochemistry of the amide group. A key element in utilizing these calculational results is the use of intensities, through spectral simulation, to compare pre-... 

A parameter that has proven useful in the interpretation of experimental MCD spectra is the dipole strength. The dipole strength of a transition to state J, Dj, can be derived from an absorption spectrum. Dj is defined as... 

The dipole strength is a measure of the intensity of the transition to state J in the absorption spectrum and is closely related to the oscillator strength. The MCD intensity and thus MCD parameters produced by a particular transition are proportional to the absorption intensity of that transition. 

The dipole strength parameter is straightforward to obtain in a TDDFT calculation. 

The strength or intensity of absorption is related to the dipole strength of transition D or square of the transition moment integral M m , and is pressed in terms of oscillator strength / or integrated molar extinction jfe Jv. A transition with /= 1, is known as totally allowed transition. But the transitions between all the electronic, vibrational or rotational states are not equally permitted. Some are forbidden which can become allowed under certain conditions and then appear as weak absorption bands. The rules which govern such transitions are known as selection rules. For atomic energy levels, these selection rules have been empirically obtained from a comparison between the number of lines theoretically... 

For a few systems, two empirical models are entered in the table. While the parameters may differ widely, at the spectroscopically significant separations the dipole strengths are consistent. For the isotropic overlap components, significant separations R range from a few percent below a to roughly 1.2 a. Outside of the range of validity, the empirical dipole models may be seriously in error and must not be used. 

This expression may be viewed as a sum of two terms. The first one, the integral over the squared derivative of the dipole function, p R), models those contributions which arise from the variation of the dipole strength with the separation R. The second models the contributions due to the variation of direction, p, as the rather natural separation of the kinetic energy operator into a radial and angular part suggests [314]. 

An explanation was offered by van Kranendonk many years after the experimental discovery. Van Kranendonk argued that anticorrelations exist between the dipoles induced in subsequent collisions [404], Fig. 3.4. If one assumed that the induced dipole function is proportional to the intermolecular force - an assumption that is certainly correct for the directions of the isotropic dipole component and the force, and it was then thought, perhaps even for the dipole strength - an interference is to be expected. The force pulses on individual molecules are correlated in... 

The dipole strength of the fundamental excitation of mode i is then... 

Within the HA, the prediction of a vibrational absorption spectrum amounts to the calculation of the harmonic normal mode frequencies, vi7 and dipole strengths, Dt. The frequencies are obtained from the harmonic force field (HFF). With respect to Cartesian displacement coordinates, this is the Hessian (d2WG/dXXadXx,a,)0. Diagonalization (after mass-weighting) yields the force constants ky the frequencies, vy and the normal coordinates, <2 , i.e. the transformation matrices, SXa4. The dipole strengths depend in addition on the APTs these require calculation of (dtpG/dXXa)0. 

The quantity Rqj is called the Rotatory Strength, in analogy to the dipole strength of a... 

Here, T.. is the distance vector between dipoles ft. and fi., v is the center frequency (in wavenumbers) of the unperturbed transition, and the Subscript k refers to the k th exciton component (1 < k < n ). The infrared absorption intensities can be obtained from the dipole strengths D, defined by... 

Unfortunately the calculation of transition probabilities has not been attempted in many instances and the results are not encouraging. Apart from a valiant early attempt by Davies173 for Na2 in a calculation where not all electrons were specifically considered, the first serious attempt to compute transition probabilities from ab initio wavefunctions was due to La Paglia.174 In this important paper La Paglia considered the dipole strengths of various 1 -iE transitions for some first-row diatomic molecules. 

Further, the dipole strength (D) is related to the molar extinction coefficient c by ... 

VA intensity is proportional to the electric dipole strength. In the harmonic approximation, Dlm, the dipole strength for the th normal mode of a fundamental vibrational transition (0 —> 1) can be expressed as... 

In the complexes [Ln(H20)y]3+, [Ln(oda)3]3, the dynamic polarization first-order electric dipole transition moment is minimized by negative interference due to the out-of-phase relation between the contributions of the [ML3] and [ML6] ligand sets [109,110]. For [Ln(oda)3]3 and other D3 complexes, only the anisotropic polarizability contributions are non-zero for AMj = 1 transitions in the [Eu(H20) ]3+ and [Eu(oda)3]3 complexes the contribution of the cross-term to the dipole strength of the 7Fo —> 5D2 and5 Do — 7F2 transitions has a magnitude comparable with that of the dominant crystal field or dynamic polarization contribution [111]. 

Quantitative analysis provides values for the ground and excited state magnetic dipole moments and the -factors based on determination of the Faraday terms and the dipole strength of the corresponding electronic absorption band. 

The dipole strength of the absorption intensity in the absence of an applied field is... 

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