Dipole polarizability electrical properties

Equations (6.5) and (6.12) contain terms in x to the second and higher powers. If the expressions for the dipole moment /i and the polarizability a were linear in x, then /i and ot would be said to vary harmonically with x. The effect of higher terms is known as anharmonicity and, because this particular kind of anharmonicity is concerned with electrical properties of a molecule, it is referred to as electrical anharmonicity. One effect of it is to cause the vibrational selection mle Au = 1 in infrared and Raman spectroscopy to be modified to Au = 1, 2, 3,. However, since electrical anharmonicity is usually small, the effect is to make only a very small contribution to the intensities of Av = 2, 3,. .. transitions, which are known as vibrational overtones. 

Five large basis sets have been employed in the present study of benzene basis set 1, which has been taken from Sadlej s tables [37], is a ( ()s6pAdl6sAp) contracted to 5s >p2dl >s2p and contains 210 CGTOs. It has been previously adopted by us in a near Hartree-Fock calculation of electric dipole polarizability of benzene molecule [38]. According to our experience, Sadlej s basis sets [37] provide accurate estimates of first-, second-, and third-order electric properties of large molecules [39]. 

Abstract Although the electronic structure and the electrical properties of molecules in first approximation are independent of isotope substitution, small differences do exist. These are usually due to the isotopic differences which occur on vibrational averaging. Vibrational amplitude effects are important when considering isotope effects on dipole moments, polarizability, NMR chemical shifts, molar volumes, and fine structure in electron spin resonance, all properties which must be averaged over vibrational motion. 

Methods for determining permanent dipole moments and polarizabilities can be arbitrarily divided into two groups. The first is based on measuring bulk phase electrical properties of vapors, liquids, or solutions as functions of field strength, temperature, concentration, etc. following methods proposed by Debye and elaborated by Onsager. In the older Debye approach the isotope effects on the dielectric constant and thence the bulk polarization, AP, are plotted vs. reciprocal temperature and the isotope effect on the polarizability and permanent dipole moment recovered from the intercept and slope, respectively, using Equation 12.5. 

The static dipole polarizability is the linear response of an atomic or molecular system to the application of a weak static electric field [1], It relates to a great variety of physical properties and phenomena [2-5]. Because of its importance, there have been numerous ab initio calculations of isolated atomic and molecular polarizabilities [6-14]. Particular theoretical attention has been dedicated to the polarizability of free atomic anions [15-21] because of its fragility and difficulty in obtaining direct experimental results. In recent years theoretical studies have... 

Molecular dynamic studies used in the interpretation of experiments, such as collision processes, require reliable potential energy surfaces (PES) of polyatomic molecules. Ab initio calculations are often not able to provide such PES, at least not for the whole range of nuclear configurations. On the other hand, these surfaces can be constructed to sufficiently good accuracy with semi-empirical models built from carefully chosen diatomic quantities. The electric dipole polarizability tensor is one of the crucial parameters for the construction of such potential energy curves (PEC) or surfaces [23-25]. The dependence of static dipole properties on the internuclear distance in diatomic molecules can be predicted from semi-empirical models [25,26]. However, the results of ab initio calculations for selected values of the internuclear distance are still needed in order to test and justify the reliability of the models. Actually, this work was initiated by F. Pirani, who pointed out the need for ab initio curves of the static dipole polarizability of diatomic molecules for a wide range of internuclear distances. 

A variety of properties can be defined and calculated I will restrict attention to the operators involved in the calculation of dipole polarizabilities and NMR parameters, corresponding to the introduction of a uniform electric field E represented by the scalar potential... 

Another approach developed by McIntosh and his co-workers 112-117) has been to measure the electrical properties of the adsorbates while they are adsorbed it is found that changes in the capacitance curves take place at the monolayer point. However, interpretation of the data to provide, say, the polarizability of the adsorbed species has proved to be difficult. An apparent dipole moment of infinity was obtained for sulfur dioxide adsorbed on rutile. It was concluded 116) that no satisfactory way of obtaining the apparent electrical properties of adsorbed matter has been developed, and until this is achieved, no great clarification of the observations seems likely. 

These effects are related to the electric properties of the reacting molecules, like their dipole moments and polarizability, as well as to solvent properties, like their dielectric constants and viscosity. 

Among the molecular properties introduced above are the permanent electric dipole moment /xa and traceless electric quadrupole moment a(8, the electric dipole polarizability aajg(—w to) [aiso(to) = aaa(—or, o>)], the magnetizability a(8, the dc Kerr first electric dipole hyperpolarizability jBapy(—(o a>, 0) and the dc Kerr second electric-dipole hyperpolarizability yapys(— ( >, 0,0). The more exotic mixed hypersusceptibilities are defined, with the formalism of modern response theory [9]... 

Birefringences are mostly observed in condensed phases, especially pure liquids or solutions, since the strong enhancement of the effects allows for reduced dimensions (much shorter optical paths) of the experimental apparatus. Nowadays measurements of linear birefringences can be carried out on liquid samples with desktop-size instruments. Such measurements may yield information on the molecular properties, molecular multipoles and their polarizabilities. In some instances, for example KE, CME and BE, measurements (in particular of their temperature dependence) have been carried out simultaneously on some systems. From the combination of data, information on electric dipole polarizabilities, dipole and quadrupole moments, magnetizabilities and higher order properties were then obtained. 

Let us now consider the second-order molecular properties. The static electric dipole-polarizability tensor is given by the expression... 

Now we study in detail how the macroscopic susceptibilities are related to the molecular properties. A thorough understanding of these relations is essential for both the rational design of molecular NLO materials as well as the experimental determination of the molecular electric properties. Models for the interpretation of macroscopic susceptibilities in terms of molecular dipole moments and polarizabilities usually assume additive molecular contributions (Liptay et al., 1982a,c). Thus, an nth-order susceptibility can be represented by (99) as a sum of terms that are proportional to concentrations Cj (moles per cubic metre, mol m ) of the different constituents J of the medium. 

Nuclear magnetic resonance (NMR) has been used to determine electrical properties in a conventional setup [23], but recently, applied electric fields have been incorporated for the determination of properties [24, 25]. Polar liquids and solutions of polar molecules align when a strong electric field (about 300 kV/cm) is applied. The anisotropic spin interactions essentially modify the NMR spectrum, and determinations of the lowest order dipole polarizability can be made. To low order, the interaction energy may be taken to be... 

The vibrational excursions of a molecule may cause it to have sharply changing electrical properties from state to state. This, of course, is essential for mechanisms of absorption and emission of radiation. How sharp these changes may be is illustrated for HF in Figure 3. The curves show the axial elements of a. A, and P in the vicinity of the equilibrium bond length as a function of the H-F distance. The types of changes that may be found in a polyatomic molecule are illustrated by Figures 4 and 5. They show contours of the dipole polarizability and hyperpolarizability elements over the two stretching coordinates of HCN. Both and P yy have zero contours... 

To understand the complete role of vibration in determining electrical properties, it is useful to consider a diatomic molecule in the harmonic oscillator approximation, where the stretching potential is taken to be quadratic in the displacement coordinate. The doubly harmonic model takes the various electrical properties to be linear functions of the coordinate. This turns out to be most reasonable in the vicinity of an equilibrium structure, but it breaks down at long separations. Letting x be a coordinate giving the displacement from equilibrium of a one-dimensional harmonic oscillator, the dipole moment, dipole polarizability, and dipole hyperpolarizability, within the doubly harmonic (dh) model, may be written in the following way ... 

The dipole moments just discussed are permanent dipole moments, intrinsic properties of a molecule. A net separation of charge may also be induced in any molecule by application of an external electric field. The induced dipole moment /x(ind) so created is approximately proportional to the strength of the applied field. Thus, for molecule, /x,4(ind) = where E is the applied field strength and a a is the polarizability of A. If the source of the electric field is a pemiaiient dipole in a neighboring molecule B, then the contribution to U from the permanent dipole/induced dipole interaction is ... 

Molecular electric properties give the response of a molecule to the presence of an applied field E. Dynamic properties are defined for time-oscillating fields, whereas static properties are obtained if the electric field is time-independent. The electronic contribution to the response properties can be calculated using finite field calculations , which are based upon the expansion of the energy in a Taylor series in powers of the field strength. If the molecular properties are defined from Taylor series of the dipole moment /x, the linear response is given by the polarizability a, and the nonlinear terms of the series are given by the nth-order hyperpolarizabilities ()6 and y). 

As an example, explicit expressions of /3 can be given in the case of the dipole polarizability of the H atom and for a few simple VdW interactions which depend on the electrical properties of the molecules such as electric dipole moments and polarizabilities (Stone, 1996). As we have already said, these dipole moments, and the higher ones known generally as multipole moments, can be permanent (when they persist in absence of any external field) or induced (when due, temporarily, to the action of an external field and disappear when the field is removed). 

Equilibrium bond distances and electric properties (permanent moments4 up to / = 3 and isotropic dipole polarizabilities) of a few polar molecules are collected in Table 5.2 (Magnasco et al., 2006). Data for H2O are taken from recent accurate work by Torheyden and Jansen (2006). 

In the present review article 1985 s results obtained in applications of the concept of vibronic interactions to the investigation of electric properties of molecules (dipole and multipole moments and polarizabilities) are presented. Molecular aspects of these topics are almost untouched in the publications listed in the preceding paragraph. The idea of dipole instability was used first as a basis of the so-called vibronic theory of ferroelectricity (Bersuker, 1966 Bersuker and Vekhter, 1978). Meanwhile, the manifestation of the electronic or vibronic degeneracy in the electric responses of molecules, being no less essential than other vibronic effects, has some special features. 

The analysis of the preceding results leads to several important conclusions about the electric properties of vibronic systems. First, in accordance with the results obtained in the preceding, nonpolar molecules may have both types of behavior of the mean dipole moment—that for rigid dipole molecules and that for nondipolar ones. Only in the cases of limit values of temperatures or vibronic coupling constants can they be related to either the former or the latter. This statement can be illustrated by the case of a molecule with two dipolar-type minima [Eq. (19)]. Consider the two limit cases A kT. In the former case the function a(T) transforms into the classical linear dependence on 11 kT inherent to rigid dipole molecules. In the limit case of low temperatures, a(T) is reduced to a constant value equal to the static polarizability of molecules that have no proper dipole moment. 

Second, the development of methods and concrete numerical calculations of the constants (reduced matrix elements of the dipole and quadru-pole moments, polarizability, and hyperpolarizabilities, vibronic constant, etc.) determining the effects of electronic degeneracy on electric properties of molecules predicted in this paper seems to be one of the most up-to-date problem in the topics under consideration. Such calculations are quite possible, in principle, provided that the wave functions of the degenerate electronic term (for the calculation of the dipole moment), as well as the excited ones (for the calculation of the polarizabilities), are known. Considering the advances in quantum chemistry, the solution of the problem is quite possible from the practical point of view, especially if one takes into account that in the cases under consideration one can determine numerically the wave function of the system in the presence of an electric field instead of a calculation of excited states. 

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