Field-dependent dipole moment definition

An important consequence of the presence of the metal surface is the so-called infrared selection rule. If the metal is a good conductor the electric field parallel to the surface is screened out and hence it is only the p-component (normal to the surface) of the external field that is able to excite vibrational modes. In other words, it is only possible to excite a vibrational mode that has a nonvanishing component of its dynamical dipole moment normal to the surface. This has the important implication that one can obtain information by infrared spectroscopy about the orientation of a molecule and definitely decide if a mode has its dynamical dipole moment parallel with the surface (and hence is undetectable in the infrared spectra) or not. This strong polarization dependence must also be considered if one wishes to use Eq. (1) as an independent way of determining ft. It is necessary to put a polarizer in the incident beam and use optically passive components (which means polycrystalline windows and mirror optics) to avoid serious errors. With these precautions we have obtained pretty good agreement for the value of n determined from Eq. (1) and by independent means as will be discussed in section 3.2. 

Over the last years, the basic concepts embedded within the SCRF formalism have undergone some significant improvements, and there are several commonly used variants on this idea. To exemplify the different methods and how their results differ, one recent work from this group [52] considered the sensitivity of results to the particular variant chosen. Due to its dependence upon only the dipole moment of the solute, the older approach is referred to herein as the dipole variant. The dipole method is also crude in the sense that the solute is placed in a spherical cavity within the solute medium, not a very realistic shape in most cases. The polarizable continuum method (PCM) [53,54,55] embeds the solute in a cavity that more accurately mimics the shape of the molecule, created by a series of overlapping spheres. The reaction field is represented by an apparent surface charge approach. The standard PCM approach utilizes an integral equation formulation (IEF) [56,57], A variant of this method is the conductor-polarized continuum model (CPCM) [58] wherein the apparent charges distributed on the cavity surface are such that the total electrostatic potential cancels on the surface. The self-consistent isodensity PCM procedure [59] determines the cavity self-consistently from an isodensity surface. The UAHF (United Atom model for Hartree-Fock/6-31 G ) definition [60] was used for the construction of the solute cavity. 

The conventional description of molecules, which is obviously much more intuitive and straightforward than its quantum-mechanical counterpart, is often adequate. Nevertheless, the manifestations of quantum effects are easily detectable experimentally. For example, species such as HfeCD, HD, or CH D, which are clearly nonpolar by the conventional definition, do possess temperature-dependent % and observable microwave spectra, and do deflect in inhomogeneous electric fields [11,16]. In fact, if one insists upon the conventional approach, these observations can be consistently accounted for by assuming the presence of small (of the order of 0.01 [D]) permanent dipole moments in these molecules. However, a rigorous quantum-mechanical treatment of such cases is clearly preferable. 

In the previous section we have defined the cartesian components of the magnetizability tensor as second derivatives of the energy E B) in the presence of a magnetic induction B, Eq. (5.39), or alternatively as first derivatives of the magnetic-field-dependent electronic magnetic dipole moment ma B), Eq. (5.32). Both definitions can be used to derive quantum mechanical expressions for the magnetizability. 

Table B.l Definitions of tensor components of the electric polarizabilities and hyperpolarizabilities as derivatives of components of the field-dependent electric dipole Ha S,S) and quadrupole Qji(S, ) moments or of the field-dependent energy E , ). All derivatives have to be evaluated at zero field and field gradient.

In the previous section we have defined the tensor components aap, - a,p-y and Cap -ys of the electric dipole, dipole uadrupole and quadrupole-quadrupole polarizability tensors as derivatives of the energy E , ) in the presence of a field and field gradient, Eqs. (4.65) to (4.67), or alternatively as derivatives of the perturbation dependent electric dipole p , ) and quadrupole moment 0(5,f), Eqs. (4.46) to (4.48), see also Table B.l. Furthermore, we have seen in Sections 3.3 and 4.3 that the electronic contributions to the electric dipole and quadrupole moments can be expressed as expectation values of the electric dipole and quadrupole moment operators, j2 Ro) and Ro) for the electrons, respectively. Both definitions can be used to derive quantum mechanical expressions for the polarizabilities. 

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