Molecular properties external electric fields

Polyelectrolytes such as the ion exchange plastics form an interesting group of materials because of their ability to interact with water solutions. They have been used in medical applications involving the removal of heavy metal ions from the human body. They can be used to interact with external electric fields and change their physical properties drastically as is illustrated by the fact that some electrically active liquid crystals are polyelectrolytes of low molecular weight. 

An important aspect of the study of water under electrochemical conditions is that one is able to continuously modify the charge on the metal surface and thus apply a well-defined external electric field, which can have a dramatic effect on adsorption and on chemical reactions. Here we briefly discuss the effect of the external electric field on the properties of water at the solution/metal interface obtained from molecular dynamics computer simulations. A general discussion of the theoretical and experi-... 

Lee, Rasaiah, and Hubbard presented one of the first molecular dynamic studies of the effect of an external field on the properties of a dipolar fluid between charged walls. They simulated a film of 206 Stock-mayer fluid molecules (a Lennard-Jones core in which a point dipole is imbedded) between two flat walls under the influence of external electric fields of intensities ranging from 0 to 4 V/nm. We summarize their results here because they can be used as a reference point for the more complicated case of water. 

The average polarizability a, defined by equation 9, is a global property, which pertains to a molecule as a whole. It is a measure, to the first order, of the overall effect of an external electric field upon the charge distribution of the molecule. We are unaware of any experimentally determined a for the molecules that are included in this chapter. However, they can be estimated using equation 12 and the atomic hybrid polarizabilities, and corresponding group values, that were derived empirically by Miller. These were found to reproduce experimental molecular a with an average error of 2.8%. The relevant data, taken from his work, are in Table 7. 

A more comprehensive discussion of the theoretical background can be found in the first part of this review.1 This necessarily more abbreviated account focuses on those aspects relevant to third-order properties. As discussed in the first part,1 a convenient way to describe the nonlinear optical properties of organic molecules is to consider the effect on the molecular dipole moment p of an external electric field ... 

In the relations between the macroscopic susceptibilities y , y and the microscopic or molecular properties a, ft, y, local field corrections have to be considered as explained above. The molecule experiences the external electric field E altered by the polarization of the surrounding material leading to a local electric field E[oc. In the most widely used approach to approximate the local electric field the molecule sits in a spherical cavity of a homogenous media. According to Lorentz the local electric field [9] is... 

To end this section and the review, we mention briefly the first results from the simulation on laboratory-frame cross-correlation of the type (v(f)J (0)). Here v is the molecular center-of-mass linear velocity and J is the molecular angular momentum in the usual laboratory frame of reference. For chiral molecules the center-of-mass linear velocity v seems to be correlated directly in the laboratory frame with the molecule s own angular momentum J at different points r in the time evolution of the molectilar ensemble. This is true in both the presence and absence of an external electric field. These results illustrate the first direct observation of elements of (v(r)J (0)) in the laboratory frame of reference. The racemic modification of physical and molecular dynamical properties depends, therefore, on the theorem (v(r)J (0)) 0 in both static and moving frames of reference. An external electric field enhances considerably the magnitude of the cross-correlations. 

We have seen how the molecular properties in nonlinear optics are defined by the expansion of the molecular polarization in orders of the external electric field, see Eq. (5) beyond the linear polarization this definition introduces the so-called nonlinear hyperpolarizabilities as coupling coefficients between the two quantities. The same equation also expresses an expansion in terms of the number of photons involved in simultaneous quantum-mechanical processes a, j3, y, and so on involve emission or absorption of two, three, four, etc. photons. The cross section for multiphoton absorption or emission, which takes place in nonlinear optical processes, is in typical cases relatively small and a high density of photons is required for these to occur. 

Let us return to the problem of solving the response of the quantum mechanical system to an external electric field. The zeroth-order wave function of the quantum mechanical system is obtained by use of any of the standard approximate methods in quantum chemistry and the coupling to the field is described by the electtic dipole operator. There exist a number of ways to determine the response functions, some of which differ in formulation only, whereas others will be inherently different. We will give a short review of the characteristics of tire most common formulations used for the calculation of molecular polarizabilities and hyperpolarizabilities. The survey begins with the assumption that the external perturbing fields arc non-oscillatory, in which case we may determine molecular properties at zero frequencies, and then continues with the general situation of time-dependent fields and dynamic properties. 

When the external electric field is time-dependent, there is no well-defined energy of the molecular system in accordance with Eq. (100), and the wave function response can thus not be retrieved from a variational condition on the energy as in the analytic derivative approach described above. Instead the response parameters have to be determined from the time-dependent Schrodinger equation, a procedure which was illustrated in Section 3 for the exact state case. In approximate state theories, however, our wave function space only partially spans the 7V-electron Hilbert space, and the response functions that correspond to an approximate state wave function will clearly be separate from those of the exact state wave function. This fact is disregarded in the sum-over-states approach, and, apart from the computational aspect of slowly converging SOS expressions, it is of little concern when highly accurate wave function models are used. But for less flexible wave function models, the correct response functions should be used in the calculation of nonlinear optical properties. 

Our discussion has so far been concerned with the microscopic response of a molecule to an external electric field, and thus with an expansion of the molecular energy in orders of the response with respect to the external field, giving rise to the molecular (hyper)polarizabilities. Although experimental data for nonlinear optical properties of molecules in the gas phase do exist [55], the majority of experimental measurements are done in the liquid or solid states, as these states also are the ones that are of greatest interest with respect to developing materials with specifically tailored (non)linear optical properties. 

It is possible to define the nonlinear optical properties of a molecule in terms of the response of molecular properties other than the dipole, such as the energy or polarizabilities, to an external electric field. The appropriate expressions within the convention used in this chapter are given by Eqs. [6] and 7]. 

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