Electronic dipole

In these expressions, e and N refer to electron and nucleus, respectively, Lg is the orbital angular moment operator, rg is the distance between the electron and nnclens. In and Sg are the corresponding spins, and reN) is the Dirac delta fnnction (eqnal to 1 at rgN = 0 and 0 otherwise). The other constants are well known in NMR. It is worth mentioning that eqs. 3.8 and 3.9 show the interaction of nnclear spins with orbital and dipole electron moments. It is important that they not reqnire the presence of electron density directly on the nuclei, in contrast to Fermi contact interaction, where it is necessary. 

The other model is also principally possible. Europium initially enters the barite lattice as Eu" ", which oxidizes to Eu + at 700 °C. The relatively small difference between the Ba " and the Eu" ionic radii (1.5 and 1.7 A) makes this substitution possible. The luminescence of Eu was still not observed in minerals, but is known in luminofors (Gorobets et al. 1968). Eu has 6s electron configuration and the mostly probable are electric-dipole electron transitions 6s -6p, taking place between uneven and even 2,3,4 Ps,4,5 terms. 

Even if the liquid molecules have no net dipole, electrons in the molecule will be affected by an electric field. The ability of electrons to move in the presence of an electric field is called their polarizability. The movement of electrons results in an induced dipole, and the alignment of the induced dipoles with the electric field gives induced polarization. 

Recall that homonuclear diatomic molecules have no vibration-rotation or pure-rotation spectra due to the vanishing of the permanent electric dipole moment. For electronic transitions, the transition-moment integral (7.4) does not involve the dipole moment d hence electric-dipole electronic transitions are allowed for homonuclear diatomic molecules, subject to the above selection rules, of course. [The electric dipole moment d is given by (1.289), and should be distinguished from the electric dipole-moment operator d, which is given by (1.286).] Analysis of the vibrational and rotational structure of an electronic transition in a homonuclear diatomic molecule allows the determination of the vibrational and rotational constants of the electronic states involved, which is information that cannot be provided by IR or microwave spectroscopy. (Raman spectroscopy can also furnish information on the constants of the ground electronic state of a homonuclear diatomic molecule.)... 

A condition for such a reaction to take place is a certain similarity of the interacting HOMO and LUMO orbitals, depending on the relative orbital energies of both the dipolarophile and the dipole. Electron-withdrawing groups on the dipolarophile normally favour an interaction of the LUMO of the dipolarophile with the HOMO of the dipole that leads to the formation of the new bonds, whereas electron donating groups on the dipolarophile normally... 

The manifestation of the dipole-dipole approximation can be seen explicitly in Equation (3.134) as the R 6 dependence of the energy transfer rate. In Equation (3.134) the electronic and nuclear factors are entangled because the dipole-dipole electronic coupling is partitioned between k24>d/(td R6) and the Forster spectral overlap integral, which contains the acceptor dipole strength. Therefore, for the purposes of examining the theory it is useful to write the Fermi Golden Rule expression explicitly,... 

Figure 9.25. Zeeman splitting of the N = 1 and 2 rotational levels in the CN radical. In region 1 the rotational transition is electric dipole allowed and magnetically tunable. In region 3 the magnetically-tunable transitions are magnetic dipole electron spin transitions the electric dipole transitions are not magnetically tunable. Region 2 is intermediate between these limiting cases.

Cells Heat of AH Dipole Electron Ioni- log P Ehomo -Elumo V X to M.W. Length... 

Compd. HL-60 HSC-2 HSC-3 HSC-4 T98G Heat of AH Dipole Electron Ionization Ehomo Elumo V X o) M.W. Length log ... 

Compd.HSG HL-60 HSC-3HSC-2 MT-4 Heat of AH Dipole Electron Ionization logP-Ehomo E lumo >1 X r > M.W. Length Surface Volume... 

In a static linear dichroism experiment, one measures the sample absorbance using light propagating along the laboratory z axis and polarized along either the x or y axis. For a single electric-dipole electronic transition from state 0 to state n, the parallel and perpendicular absorbance components are then proportional to... 

One view of the interaction of matter with magnetic fields stems from the electrons acting as revolving charges, setting up a magnetic dipole. Electrons paired in orbitals cancel one another (the small residual effects are lumped... 

Farinha JPS, Spiro JG, Winnik MA (2004) Dipole-dipole electronic energy transfer fluorescence decay functions for arbitrary distributions of donors and acceptors in systems with cylindrical symmetry. J Phys Chem B 108(42) 16392-16400. doi 10.1021/jp048807... 

There are many approaches to compute the polarizabilities and hyperpolarizabilities and also different ways to classify them. One convenient division is between perturbation theory approaches, which express the (hyperjpolarizability using Summation-Over-States (SOS) expressions and those techniques, which are based on the evaluation of derivatives of the energy (or another property). SOS approaches consist in evaluating energies and transition dipoles that appear in the (hyper)polarizability expressions. For instance, in the case of the frequency-dependent electric-dipole electronic first hyperpolarizability, the SOS expression reads ... 

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