Electron dipole moments

The weak interactions that cause atomic PNC violate not only the symmetry of parity, P, but also the symmetry of charge conjugation, C. However, the product of these, CP, is conserved. Because any quantum field theory conserves CPT, where T is time reversal this is equivalent to saying that T is conserved. However, even this symmetry is known to be violated. To date, this incompletely understood phenomenon has been seen in only two systems, the neutral kaon system, and, quite recently, the neutral B meson system. However, as noted already in the 1950 s by Ramsey and Purcell [62], an elementary particle possessing an intrinsic electric dipole moment also violates T invariance, so that detection of such a moment would be a third way of seeing T noninvariance. 

One can assign an electric dipole moment to the electron by introducing the interaction 

The enhancement factor involves an atomic physics calculation along the lines as described above for PNC transitions. Because only a nonvanishing effect is sought, the demands on the accuracy of the calculation axe not as stringent, with really only the correct order of magnitude needed. This would of course change were a nonvanishing result to be found, but at present only bounds have been set. The bound from cesium is [65] 

These experiments complement the search for an edm of the neutron, which has a history of almost 50 years of increasingly precise limits, with the present result [67] 

Several other atoms and molecules have also been used for edm searches, so far without a positive result. There has been particular interest in polar molecules, for example ytterbium flouride [68], because the intense internal electric fields in such molecules lead to greater sensitivity to a possible electron electric dipole moment. 

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Since the vibrational eigenstates of the ground electronic state constitute an orthonomial basis set, tire off-diagonal matrix elements in equation (B 1.3.14) will vanish unless the ground state electronic polarizability depends on nuclear coordinates. (This is the Raman analogue of the requirement in infrared spectroscopy that, to observe a transition, the electronic dipole moment in the ground electronic state must properly vary with nuclear displacements from... 

Because of difficulties in calculating the non-adiabatic conpling terms, this method did not become very popular. Nevertheless, this approach, was employed extensively in particular to simulate spectroscopic measurements, with a modification introduced by Macias and Riera [47,48]. They suggested looking for a symmetric operator that behaves violently at the vicinity of the conical intersection and use it, instead of the non-adiabatic coupling term, as the integrand to calculate the adiabatic-to-diabatic transformation. Consequently, a series of operators such as the electronic dipole moment operator, the transition dipole moment operator, the quadrupole moment operator, and so on, were employed for this purpose [49,52,53,105]. However, it has to be emphasized that immaterial to the success of this approach, it is still an ad hoc procedure. 

In effect, i is replaced by the vibrationally averaged electronic dipole moment iave,iv for each initial vibrational state that can be involved, and the time correlation function thus becomes ... 

Some substituents induce remarkably different electronic behaviors on the same aromatic system (8). Let us consider, for example, the actions of substituents on an aromatic electron system. Some substituents have a tendency to enrich their electronic population (acceptors), while others will give away some of it (donors). Traditionaly, quantum chemists used to distinguish between long range (mesomeric) effects, mainly u in nature, and short range (inductive) effects, mainly a. The nonlinear behavior of a monosubstituted molecule can be accounted for in terms of the x electron dipole moment. Examples of donor and acceptor substituents can be seen on figure 1. 

This integral of the electronic dipole moment operator is a function of a nuclear coordinate Q. The integral may be expanded in a Taylor series with respect to Q (equation 4) and... 

In the case of direct vibrational excitation, the vibrational transition probability is given by p, where are the intermediate and ground vibrational states, respectively, and is the vibrational transition moment. The electronic transition probability out of the intermediate state is < n < e ng e > n>, where are the excited and ground electronic states, respectively, and is the electronic dipole moment operator and vibrational state in the upper electronic state. Applying the Born-Oppenheimer approximation, where the nuclear electronic motion are separated, S can be presented as... 

Molecular electronic dipole moments, pi, and dipole polarizabilities, a, are important in determining the energy, geometry, and intermolecular forces of molecules, and are often related to biological activity. Classically, the pKa electric dipole moment pic can be expressed as a sum of discrete charges multiplied by the position vector r from the origin to the ith charge. Quantum mechanically, the permanent electric dipole moment of a molecule in electronic state Wei is defined simply as an expectation value ... 

The potential curves and the relevant electronic dipole moments are from I. Schmidt, Ph.D. Thesis, Kaiserslautern University, 1987. 

It is interesting to note that a similar radiative association process is not possible for the two hydrogen atoms. On the symmetry grounds the dipole moment of the H — H system (which is inversion symmetric) vanishes. In that case the nuclear dipole moment is identically 0 and the electronic dipole moments induced in the two approaching atoms have opposite orientations and cancel each other. For the H — H system (which lacks the inversion symmetry) the dipole moment (in the adiabatic and non-relativistic approximation) is finite. In that case the hadronic moment is e R and the induced leptonic moments of H and H have the same orientations and add together to a non vanishing dipole moment (which tends to 0 in the limit of infinite separation R between the atoms). 

The general features of the nonadiabatic coupling and its relation to molecular properties are surveyed. Some consequences of the equation of motion , formally expressing a smoothness of a given molecular property within the diabatic basis, are demonstrated. A particular emphasis is made on the relation between a smoothness of the electronic dipole moment and the generalized Mulliken-Hush formula for the diabatic electronic coupling. 

The other techniques can be divided into a few categories (see also Ref. [14c]). One of them goes back to the idea first coined by Mulliken [41], Hush [42] and Lichten [8] of using molecular properties to determine the diabatic basis and is actually based on the Werner-Meyer-Macfas-Riera formula [32,33] for the adiabatic-to-diabatic mixing angle in terms of electronic dipole moments. This... 

SMOOTHNESS OF THE ELECTRONIC DIPOLE MOMENT AND THE GENERALIZED MULLIKEN-HUSH APPROACH... 

Consider the electronic dipole moment matrix M = (mH = ((1P"ilrl1fr/)))H. and project it on a given direction in 1R3. This gives the matrix m = (mkl)kl. Imposing a smoothness condition of this matrix within the two-state diabatic basis, one readily obtains the ADT mixing angle in terms of the electronic dipole moment [32, 33,37,68]... 

Fig. 4. (A) The general case of a dipole-dipole interaction. The angles 0, and 02 define the orientation of the two electronic dipole moments and with respect to the vector r, which passes from the center of one dipole to the next. The magnitude of the vector is the separation of the two dipoles. (B) The colinear dipole-dipole interaction, the enthalpically optimal case. (C) The antiparallel dipole-dipole interaction, which is often seen between macroscopic helix dipoles in proteins. (D) The parallel dipole-dipole interaction, which is enthalpically unfavorable. (E) The behavior of dipole-dipole interaction enthalpy as a function of the parameter 02 with 0, = 0°.

Dipole-dipole interactions are still weaker and of shorter range than the charge-dipole interaction. The strength of the interaction depends on the distance (r) between the centers of the two dipoles, their dipole moments Hi and h2. and the angles i and 2 between each electronic dipole moment and the vector r, and is given by... 

We note that the coexistence of symmetric and antisymmetric componenti e dipole moment is with respect to plane rotates with the molee ah operation is said to be body-fixed (or molecule-fixed ). Both the body-1 symmetric ds and the body-fixed antisymmetric dfl dipole-moment components occur in A —> A electronic transitions whenever the geometry of a bent B molecule deviates considerably from the points on the a hyperplane, characte by the points of equidistance (C2 ) geometries (where du = 0) (see Fig. 8 1S deviation of da from zero on the a plane necessitates going beyond the 1L Condon approximation, which assumes that the electronic dipole moment, dofni change as the molecule vibrates. (In the terminology of the theory df... 

The excitation of a chromophore group is accompanied by a change in the electron dipole moment of the molecule. This involves a change in the interaction energy with the surrounding molecules, which manifests itself by a shift of the time-dependent frequency maximum of the fluorescence spectra, (relaxation shift) (Bakhshiev, 1972) ... 

Dipole moments have been measured in the piperazine series in an attempt to correlate those of noncyclic nitramines and nitrosamines with the moments of some homologous dinitroso- and dinitropiperazines (1674), to examine the conformation of certain 1,4-disubstituted piperazines (1675), and to examine the effective size of the lone pair on nitrogen (1676). Infrared spectral measurements of the first overtone and electronic dipole moment measurements indicate that the N-H in a... 

Fluorescence is defined simply as the electric dipole tranation from an excited electronic state to a lower state, usually the ground state, of the same multiplicity. Mathematically, the probability of an electric-dipole induced electronic transition between specific vibronic levels is proportional to R f where Rjf, the transition moment integral between initial state i and final state f is given by Eq. (1), where represents the electronic wavefunction, the vibrational wavefunctions, M is the electronic dipole moment operator, and where the Born-Oppenheimer principle of parability of electronic and vibrational wavefunctions has been invoked. The first integral involves only the electronic wavefunctions of the stem, and the second term, when squared, is the familiar Franck-Condon factor. 

In the presence of an external field, additional terms contribute to ft, the electronic dipole moment of a molecule. These contributions may be expanded in powers of the applied field... 

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