Classical physics dipole moments

The next section in this chapter provides a brief comparison of the dipole moment (magnitude and direction) for a set of simple alcohols. Experimental gas phase dipole moments45 are compared to ab initio and as molecular mechanics computed values. It is important to note that the direction of the vector dipole used by chemists is defined differently in classical physics. In the former definition, the vector points from the positive to the negative direction, while the latter has the orientation reversed. 

Model correlation functions. Certain model correlation functions have been found that model the intracollisional process fairly closely. These satisfy a number of physical and mathematical requirements and their Fourier transforms provide a simple analytical model of the spectral profile. The model functions depend on the choice of two or three parameters which may be related to the physics (i.e., the spectral moments) of the system. Sears [363, 362] expanded the classical correlation function as a series in powers of time squared, assuming an exponential overlap-induced dipole moment as in Eq. 4.1. The series was truncated at the second term and the parameters of the dipole model were related to the spectral moments [79]. The spectral model profile was obtained by Fourier transform. Levine and Birnbaum [232] developed a classical line shape, assuming straight trajectories and a Gaussian dipole function. The model was successful in reproducing measured He-Ar [232] and other [189, 245] spectra. Moreover, the quantum effect associated with the straight path approximation could also be estimated. We will be interested in such three-parameter model correlation functions below whose Fourier transforms fit measured spectra and the computed quantum profiles closely see Section 5.10. Intracollisional model correlation functions were discussed by Birnbaum et a/., (1982). 

Modem structural chemistry differs from classical structural chemistry with respect to the detailed picture of molecules and crystals that it presents. By various physical methods, including the study of the structure of crystals by the diffraction of x-rays and of gas molecules by the diffraction of electron waves, the measurement of electric and magnetic dipole moments, the interpretation of band spectra, Raman spectra, microwave spectra, and nuclear magnetic resonance spectra, and the determination of entropy values, a great amount of information has been obtained about the atomic configurations of molecules and crystals and even their electronic structures a discussion of valence and the chemical bond now must take into account this information as well as the facts of chemistry. 

The dipole moment operator is qirh just as in classical physics. If the same wavefunctions are introduced in eqn. 2.14, then the permanent dipole... 

Equation (1-239) relates the interaction-induced part of the dipole moment of the complex AB to the distortion of the electron density associated with the electrostatic, exchange, induction, and dispersion interactions between the monomers. The polarization contributions to the dipole moment through the second-order of perturbation theory (A/a, A/a, and A/a ) have an appealing, partly classical, partly quantum, physical interpretation. The first-order multipole-expanded polarization contribution (F) is due to the interactions of permanent multipole moments on A with moments induced on B by the external field F, and vice versa. The terms... 

As one can see from relation (13.112), the wavefield at the point r D may be viewed at the moment of time t as the sum of elementary fields of point and dipole sources distributed over the surface S with densities dP r,t)/dn and P r,t) respectively. The interference of these fields beyond the domain D results in complete suppression of the total wavefield. Thus, the Kirchhoff integral formula can be treated as the mathematical formulation of the classical physical Huygens-Fresnel principle. 

Electric polarization, dipole moments and other related physical quantities, such as multipole moments and polarizabilities, constitute another group of both local and molecular descriptors, which can be defined either in terms of classical physics or quantum mechanics. They encode information about the charge distribution in molecules [Bbttcher et al, 1973]. They are particularly important in modelling solvation properties of compounds which depend on solute/solvent interactions and in fact are frequently used to represent the -> dipolarity/polarizability term in - linear solvation energy relationships. Moreover, they can be used to model the polar interactions which contribute to the determination of the -> lipophilicity of compounds. 

In classical physics, the magnetic dipole can lie in any direction with respect to the magnetic field. In real atoms this is not possible, and the direction of the magnetic moment vector can only take values such that the projection of the vector on the magnetic field direction, z, has values of Mj, where Mj is given by ... 

Raman spectroscopy (RS) is a well known technique to detect the vibrational characteristics of molecules in various media and is therefore extensively used in physics chemistry and biologyGenerally this technique is easily implemented, and does not require sample preparation. In addition RS has the advantage that it can be applied in water solutions, in contrast to IR absorption. In a classical picture RS results from the inelastic interaction between a molecular system and the electromagnetic field of a laser source." The electronic polarizability is modulated by the vibration mode associated with the motion of the molecule, at a frequency (Raman shift) which is the difference (Stokes scattering) or the sum (anti-Stokes scattering) between the laser and the molecular frequencies. The induced dipole moment can be written as ... 

If the mechanical vibration of the simple harmonic oscillator by which we first represented the nuclear motion of the diatomic molecule in the preceding section is accompanied by an oscillation of the dipole moment of the molecule, then, according to classical physics, radiation will be emitted with the frequency of the oscillator. For small amplitudes of vibration we can take the oscillating part of the dipole moment as being proportional to the elongation cc of the molecule introduced in the preceding section, let us say equal to qx. The amount of radiation emitted by the oscillator in unit time is then given by ... 

If a normal mode in a crystal, connected for example with a phonon or the photoionization of an impurity, gives rise to any change in the electric dipole moment p, then the dynamic dipole moment p = 9p/9 i is nonzero. Here qi is the normal coordinate, which characterizes the corresponding normal mode and can be derived from normal coordinate analysis based on classical physics [55], The value of p depends on the relative ionicity of the species and can be obtained only by quantum-chemical calculatious (see Ref. [61] and the literature therein). In general, the more polar the bond, the larger the p term. The matrix element of the dynamic dipole moment, (y p i), is called the transitional dipole moment (TDM) of the corresponding normal mode. 

In Sections 4.1 and 4.2 we discussed the fact that the electric moments of molecules play an important role in the description of the intermolecular forces between two molecules separated by a large distance. Their contribution to the interaction energy is of purely classical, i.e. electrostatic nature. Here, we want to show now that also the contribution from quantum mechanical dispersion or London forces, i.e. the dispersion energy E, can be related to molecular properties of the two interacting molecules. In particular, we will see that it is related to the frequency-dependent polarizabilities, which is in line with the physical interpretation of the dispersion forces as arising from the interaction of induced dipole moments, which implies that both charge distributions are perturbed by their interaction. 

The attraction between two neutral atoms, already introduced in 1873 by Van Der Waals to explain the properties of non-ideal gases and liquids, has been explained by three different effects. Two of them, the interaction of the dipole moments and the polarising action of a dipole in one molecule on the other molecule can be understood on the lines of classical physics. London however showed that also between apolar atoms an attraction exists which is a typical quantum mechanical effect, and which, in ail cases except for extremely polar molecules like H2D or NH3, is stronger than the Debye and the Keesom effect. 

The basis for the decision of this problan is formula (5.1.32) a force working on a magnetic dipole depends on both the nonuniformity of the magnetic field and the orientation of the atomic magnetic momoits relative to the quantization axis z. If the atomic magnetic moments submit to laws of classical physics, there could be any values of angles and the experiment would result in a fuzzy maximum. However, in quantum mechanics this is not a case ... 

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