Electric moment second order

There are several different definitions for the second order electric moments. In order to be consistent with the above, the quadrupole moment is defined in a similar way ... 

The poles con espond to excitation energies, and the residues (numerator at the poles) to transition moments between the reference and excited states. In the limit where cj —> 0 (i.e. where the perturbation is time independent), the propagator is identical to the second-order perturbation formula for a constant electric field (eq. (10.57)), i.e. the ((r r))Q propagator determines the static polarizability. 

G2, to G3, and to G4, the effective enhancement was 10%, 36%, and 35% larger than the value estimated by the simple addition of monomeric values. The enhancement included the local field effect due to the screening electric field generated by neighboring molecules. Assuming the chromophore-solvent effect on the second-order susceptibility is independent of the number of chro-mophore units in the dendrimers, p enhancement can be attributed to the inter-molecular dipole-dipole interaction of the chromophore units. Hence, such an intermolecular coupling for the p enhancement should be more effective with the dendrimers composed of the NLO chromophore, whose dipole moment and the charge transfer are unidirectional parallel to the molecular axis. 

For weak electric fields the magnitude of the induced polarization is linearly proportional with the amplitude of the electric field. Yet, when the field strength increases, the linear relationship no longer holds, and nonlinear terms have to be taken into account. In this case, the induced dipole moment and polarization can be expressed up to second order in the electric field as11... 

In order to describe second-order nonlinear optical effects, it is not sufficient to treat (> and x<2) as a scalar quantity. Instead the second-order polarizability and susceptibility must be treated as a third-rank tensors 3p and Xp with 27 components and the dipole moment, polarization, and electric field as vectors. As such, the relations between the dipole moment (polarization) vector and the electric field vector can be defined as ... 

If the hfs of the nucleus under consideration is not resolved in the EPR spectrum, all nuclear spin states are simultaneously saturated and a sign determination using ENDOR line intensities is not possible. In this case the relative signs may sometimes be determined from second order hf contributions. This method has been applied by DuVarney and Spaeth74) to determine the sign of the 41K electric quadrupole moment using F centres in KC1. 

Second-order perturbation sums are a second example in which one is interested in an average or integral over a spectral density. For example, the dynamic polarizability a of a system at a frequency co0 is related to the spectral density /(co) of the electric dipole moment of the system by... 

In the limit of the oriented gas model with a one-dimensional dipolar molecule and a two state model for the polarizability (30). the second order susceptibility X33(2) of a polymer film poled with field E is given by Equation 4 where N/V is the number density of dye molecules, the fs are the appropriate local field factors, i is the dipole moment, p is the molecular second order hyperpolarizability, and L3 is the third-order Langevin function describing the electric field induced polar order at poling temperature Tp - Tg. 

However, non-centrosymmetry does not automatically imply a dipolar molecule, or, more generally, vectorial properties. Also molecules without a dipole moment can exhibit second-order nonlinear optical properties. Tetrahedral molecules, such as CC14, and trigonal molecules, such as BC13, also lack centrosymmetry. However, they cannot be oriented in an electric field, due to the absence of a dipole moment. Therefore, they can simply not be measured by EFISHG. Also ionic species cannot be measured, since these migrate, rather than rotate, under the influence of an applied field. 

Electrostatic potentials and fields of classical molecules are generated by a collection of point charges—generally on atoms—obtained from QM calculations and defined such that they at least reproduce the vacuum dipole moment [103], or also the quadrupole moment [69], i.e., the first- and second-order sources of the electric field... 

The spacing of the different energy levels studied by NQR is due to the interaction of the nuclear quadrupole moment and the electric field gradient at the site of the nucleus considered. Usually the electric quadrupole moment of the nucleus is written eQ, where e is the elementary charge Q has the dimension of an area and is of the order of 10 24 cm2. More exactly, the electric quadrupole moment of the nucleus is described by a second order tensor. However, because of its symmetry and the validity of the Laplace equation, the scalar quantity eQ is sufficient to describe this tensor. 

The dipole polarizability also expresses the second-order effect of an electric field on the energy levels of an atom or molecule. We can write, for an atom (which has no dipole moment and therefore, in general, no first-order effect) ... 

Having set up the Hamiltonian, we may calculate the first- and second-order properties in the eigenvector representation. For the permanent electric and magnetic dipole moments, we obtain... 

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