Dipolar electron notation

The dipolar contributions and the anisotropy of the orbital parts have been neglected the notation Jforb simply reflects our ignorance of the details of the expression for the orbital relaxation. If the applied field Bo is parallel to the molecular axis, the relaxation is associated with jumps of an electron from a cr or JT orbital just below Ei to a r or a orbital just above F). If the field is perpendicular, w e must consider jumps between a a orbital and one type of n orbital as well as those between the two different types of n orbitals. (AU these jumps change only the orbital symmetry, without electron spin flip.) Currently, no values are known for these a-n and 71-71 transition matrix elements. It is clear, however, that a higher f-LDOS wiU lead to a higher value for 33Xorb -... 

Thus, the electronic mechanism of concerted 1,3-dipolar cycloadditions is now well established. It may be written with the usual notations of organic chemists ... 

Let us start with the field-free SO effects. Perturbation by SO coupling mixes some triplet character into the formally closed-shell ground-state wavefunction. Therefore, electronic spin has to be dealt with as a further degree of freedom. This leads to hyperfine interactions between electronic and nuclear spins, in a BP framework expressed as Fermi-contact (FC) and spin-dipolar (SD) terms (in other quasirelativistic frameworks, the hyperfine terms may be contained in a single operator, see e.g. [34,40,39]). Thus, in addition to the first-order and second-order ct at the nonrelativistic level (eqs. 5-7), third-order contributions to nuclear shielding (8) arise, that couple the one- and two-electron SO operators (9) and (10) to the FC and SD Hamiltonians (11) and (12), respectively. Throughout this article, we will follow the notation introduced in [58,61,62], where these spin-orbit shielding contributions were denoted... 

In addition to these two representative kinds of polarization processes (electronic and dipolar), we may have conduction by means of macroscopic charge transport. Again, because the latter conduction processes are often thermally activated, there will appear a phase lag of the conductive response to the applied field and we may write the conductivity due to charge transport phase conductivity (i.e., the observed conductivity) is... 

The appropriate perturbative terms to add to the Hamiltonian for electric-dipole and magnetic-dipole radiation are proportional to E-D and H (L + 2S), respectively, where D is the sum over all the electrons i of r,. The vectors and H characterize the radiation field, whose direction of propagation, k, makes no appearance in the dipolar perturbations. As for the quadrupolar term, we can take advantage of a very useful notational device introduced by Innes and Ufford (1958) whereby two tensors T and t/ , when coupled to a resultant of rank w, are written as (j " (/( >)< " . We get, for the term in question, an expression proportional to where the quadrupole tensor is given by the sum over i of the... 

Consider a molecular system described by the Hamiltonian operator Ho (r, R) in interaction with a pulsed laser field with slowly varying envelope and frequency. Below, for ease of notation, the dependence of the various operators and wavefunctions on the electronic and nuclear coordinates r and R is dropped. In the semiclassical dipolar approximation, the total Hamiltonian operator of the system reads... 

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