Molecular Dipole Moment and Polarizability

Molecular electronic dipole moments, pi, and dipole polarizabilities, a, are important in determining the energy, geometry, and intermolecular forces of molecules, and are often related to biological activity. Classically, the pKa electric dipole moment pic can be expressed as a sum of discrete charges multiplied by the position vector r from the origin to the ith charge. Quantum mechanically, the permanent electric dipole moment of a molecule in electronic state Wei is defined simply as an expectation value  

The electric dipole moment operator for a molecule includes summation over both the electronic and nuclear charges  

Polarizability is the relative tendency of a charge distribution o(r), that is, the electron cloud of an atom or molecule, to be distorted from its normal shape by an external electric field, F, which may be caused by the presence of a nearby ion or dipole. The interaction of an electronic charge distribution with a uniform electric field gives an energy contribution, 

Accordingly, dipole moment and polarizability calculations are sensitive to both the quantum chemistry method and the basis set used. Accurate calculations typically require the use of D FTor Hartree-Fock methods with the inclusion of M P2 treatment of electron correlation [53, 54]. Furthermore, Gaussian basis sets should be augmented with diffuse polarization functions to provide an adequate description of the tail regions of density (the most easily polarized regions of the molecule). 

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Jasien, P. G., and G. Fitzgerald. 1990. Molecular dipole moments and polarizabilities from local density functional calculations Applications to DNA base pairs. J. Chem. Phys. 93, 2554. 

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. 

For a molecule that has little or no symmetry, it is usually correct to assume that all its vibrational modes are both IR and Raman active. However, when the molecule has considerable symmetry, it is not always easy to picture whether the molecular dipole moment and polarizability will change during the vibration, especially for large and complex molecules. Fortunately, we can easily solve this problem by resorting to simple symmetry selection mles. The molecular vibration is active in IR absorption if it belongs to the same representation as at least one of the dipole moment components fjix, iiy, jj z) or, since the dipole moment is a vector, as one of the Cartesian coordinates (x, y, z). In contrast, the molecular vibration is active in Raman scattering if it belongs to the same representation as at least one of the polarizability components, etc.) or, since the polarizability is a tensor, as... 

These interactions (dd, di, ii) are a function of dipole moment and polarizability. It has been shown that the dipole moment cannot be replaced entirely by the use of electrical effect substituent constants as parameters52. This is because the dipole moment has no sign. Either an overall electron donor group or an overall electron acceptor group may have the same value of /x. It has also been shown that the bond moment rather than the molecular dipole moment is the parameter of choice. The dipole moments of MeX and PhX were taken as measures of the bond moments of substituents bonded to sp3- and sp2-hybridized carbon atoms, respectively, of a skeletal group. Application to substituents bonded to sp-hybridized carbon atoms should require a set of dipole moments for substituted ethynes. 

Molecular properties such as dipole moment and polarizability, although in certain fully empirical models, bond dipoles and lone-pair contributions have been incorporated (although again only for conventional chemical bonding situations). 

In this section we have examined the three major contributions to what is generally called the van der Waals attraction between molecules. All three originate in dipole-dipole interactions of one sort or another. There are two consequences of this (a) all show the same functional dependence on the intermolecular separation, and (b) all depend on the same family of molecular parameters, especially dipole moment and polarizability, which are fairly readily available for many simple substances. Many of the materials we encounter in colloid science are not simple, however. Hence we must be on the lookout for other measurable quantities that depend on van der Waals interactions. Example 10.2 introduces one such possibility. We see in Section 10.7 that some other difficulties arise with condensed systems that do not apply to gases. 

The intensities of the infrared absorptions and of the inelastic scattered light (Raman) are determined by such electrical factors as dipole moments and polarizabilities. At the time of the pioneering studies on the infrared spectra of carbohydrates by the Birmingham school,7"11 calculations of the vibrational frequencies had been performed only for simple molecules of fewer than ten atoms.27,34,35 However, many tables of group frequencies, based on empirical or semi-empirical correlations between spectra and molecular structure, are available.32,34"37... 

Molecular Polarizability, Molecular Dipole Moment and Atomic Electronegativities in AB and AB Molecules. 

These equations show that the spectra contain information concerning microscopic molecular quantities, such as dipole moment and polarizability. It is therefore very useful to consider using the second dimension of the spectra and to develop calculation methods for the intensities. Thus, knowing the normal coordinate g, we have to calculate the variation of the dipole moment and of the polarizability with g, i.e., determine both quantities for geometries of the deformed molecule according to the normal mode. Both quantities, fj, and a, can be obtained by classical and quantum chemical methods. 

This method is based on a proposition by Wolkenstein (1941) and has been developed further and used extensively in the last few years (Gussoni, 1979). This approach involves writing the molecular dipole moment and the polarizability as sums over all bonds of the molecule ... 

Augmented Gaussian basis sets of triple and quadruple zeta valence quality for the atoms H and from Li to Ar applications, in HF, MP2, and DFT calculations-of molecular dipole moment and dipole (h5q)er)polarizability ... 

As far as possible only SI units have been used in writing equations and presenting experimental data. Angstroms and calories, which still appear in the scientific literature, are avoided. Instead, nanometers and picometers are used for atomic and molecular dimensions, and joules for units of energy. Pressure is discussed in terms of pascals and bars rather than torrs and atmospheres. Equations involving the molecular dipolar properties, namely the dipole moment and polarizability, assume units of coulomb meters and farad square meters, respectively, for these quantities. However, tabulated data are given in the more familiar cgs system with debyes for the dipole moment and cubic nanometers for the polarizability. This follows the usage in most data tabulations at the present time. The connection between the SI and cgs units is explained in chapter 2. The symbols recommended by the International Union of Pure and Applied Chemistry [1] are used as much as possible. 

Over the last decades, there has been an increasing interest in theoretical (1,2) and experimental (3) studies of weakly interacting complexes, the so-called van der Waals molecules. One of the reasons for this interest is that the spectra of these complexes depend very sensitively on the intermolecular potentials and other properties, such as interaction-induced dipole moments and polarizabilities, the knowledge of which is crucial for understanding the behavior of molecular bulk species. 

When very accurate dipole moments are deduced, it is proper to query the significance of a breakdown of the Bom-Oppenheimer approximation. This approximation justifies the assignment of molecular property tensors, such as dipole moments and polarizabilities, to specific directions in a molecule-fixed frame and supports the use of a property function or surface representing the variation of the property with nuclear position. The dipole moment of HD (5.85 X 1(T4 D)26 arises solely from the breakdown of the approximation and may have the sense H D-.27-29 In HC1 and DC1, there is an isotope effect on the dipole moment that has been attributed to a violation of the Born-Oppen-heimer approximation30 there is an apparent difference of 0.0010 0.0002 D between the dipole functions of HC1 and DC1, with HC1 having the bigger moment. This result is in accord with a recent theoretical analysis by Bunker.31... 

On the Efifects of Spin-Orbit Coupling on Molecular Properties Dipole Moment and Polarizability of PbO and Spectroscopic Constants for the Ground and Excited States... 

In the present chapter the method is tested for the PbO molecule. This molecule was chosen because a number of properties are known experimentally and because it has recently been studied with other high level quantum chemical methods, which allow a comparison of them with the present approach [13-18]. The molecule has a large dipole moment and polarizability, which can be used to test the importance of SOC on molecular... 

Electric properties were obtained for the ground state using finite perturbation theory. An electric field, E, along the molecular axis was varied in steps of 0.005 a.u. and the resulting energies were fitted to a fourth-order polynomial in E. The first and second derivative then gave the dipole moment and polarizability along file molecular axis. 

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