Electrical multipoles dipole moment

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. 

The condition for this quantity to be non-zero is that the chromophore of interest must have a non-zero magnetic and electric transition dipole moment along the same molecular diiectioa In the absence of pertuibing external fields, this is only trae for molecules that are chiral. Expressions that include higher order multipole contributions to eqs. (8), (9), and (11) can be found in previous theoretical descriptions of CPU theory (Riehl and Richardson, 1976a, 1986). 

The long-range interactions between a pair of molecules are detemiined by electric multipole moments and polarizabilities of the individual molecules. MuJtipoJe moments are measures that describe the non-sphericity of the charge distribution of a molecule. The zeroth-order moment is the total charge of the molecule Q = Yfi- where q- is the charge of particle and the sum is over all electrons and nuclei in tlie molecule. The first-order moment is the dipole moment vector with Cartesian components given by... 

Now, the quadrupole moment can next be calculated by differentiating the potential to get the electric field due to the dipole moment. The reader can now see that an infinite series can be thus generated. The total electric field is simply the sum of all the individual multipole contributions, given by... 

Gaussian also predicts dipole moments and higher multipole moments (through hexadecapole). The dipole moment is the first derivative of the energy with respect to an applied electric field. It is a measure of the asymmetry in the molecular charge distribution, and is given as a vector in three dimensions. For Hartree-Fock calculations, this is equivalent to the expectation value of X, Y, and Z, which are the quantities reported in the output. 

Typical properties of the charge distribution are summarized by its various electric multipole moments. The electric dipole moment p. induced in the system by the external field is obviously... 

FIM can also be used to study properties, such as the surface induced dipole moment and the effective polarizability of some surface atoms, kink site atoms and adsorbed atoms etc. The charge distribution of a surface atom is obviously completely different from that of a free atom because of its interaction with the surface and in addition surface atoms are partially shielded by itinerant charges of the surface. The charge distribution of a surface atom can be described by the magnitudes of the electric multipoles of the atom. 

An important induced dipole component of pairs involving molecules is multipolar induction. Specifically, the lowest-order multipole consistent with the symmetry of H2 is the electric quadrupole. Each H2 molecule may be thought of as being surrounded by an electric field of quadrupolar symmetry that rotates with the molecule.-In that field, a collisional partner X is polarized, thus giving rise to an induced dipole moment which in turn is capable of emitting and absorbing light. For like pairs, molecule 1 will induce a dipole in molecule 2 and 2 will induce one in 1. In... 

Both photon-assisted collisions and collision-induced absorption deal with transitions which occur because a dipole moment is induced in a collisional pair. The induction proceeds, for example, via the polarization of B in the electric multipole field of A. A variety of photon-assisted collisions exist for example, the above mentioned LICET or pair absorption process, or the induction of a transition which is forbidden in the isolated atom [427], All of these photon-assisted collision processes are characterized by long-range transition dipoles which vary with separation, R, as R n with n — 3 or 4, depending on the symmetry of the states involved. Collision-induced spectra, on the other hand, frequently arise from quadrupole (n = 4), octopole (n = 5) and hexadecapole (n = 6) induction, as we have seen. At near range, a modification of the inverse power law due to electron exchange is often quite noticeable. The importance of such overlap terms has been demonstrated for the forbidden oxygen —> lD emission induced by collision with rare gases [206] and... 

The Born equation is based on the simple model of a spherical ion with a single charge at its centre. Such an ion has no dipole moment and no higher multipole moments, but real molecular ions are of course much more complex. Since the electrical charge is distributed among all the atoms of the... 

We will return to the quadrupole interaction in following chapters, but we now re-examine the general expansion of the electrostatic interaction and, in particular, the possibility of other nuclear electrostatic multipole moments. Because our multipole expansion is performed in a coordinate system with origin at the centre of charge of the protons p in the nucleus, the nuclear electric dipole moment is zero. However, this result arises only from our choice of origin and we now show that there are much... 

Linear Dipolar Electric Polarization. Even atoms and microsystems with symmetrically distributed charges are known to exhibit polarization under the influence of an external electric field or the internal (molecular) electric field of a neighbour. Such a system is said to become endowed with an induced electric dipole (or higher multipoles). In many a case it sufiSces to assume that the induced dipole moment p E) is proportional to the field strength inducing it ... 

In non-dipolar dielectrics sufiSciently dense for molecular interaction, the temperature-dependent polarization (241) is generally non-zero. Such interaction will lead to an effect consisting in the induction, in any given molecule immersed in the dense medium, of a dipole moment M by the fluctuating electric field of the permanent quadrupoles, > octu-poles, >hexadecapoles, and in general multipoles" of its nei bours. 

Another important class of forces, induction or polarization forces, involves permanent moments that induces multipoles in a polarizable species. Polarizability, a, measures the ability of an atomic or molecular species to develop an induced dipole moment, as a response to an applied electric field E. Within the limits of linear response theory, the induced dipole moment is given by the product of polarizability tensor times the electric field E. 

The dipole polarizability can be used in place of the dipole moment function, and this will lead to Raman intensities. Likewise, one can compute electrical quadrupole and higher multipole transition moments if these are of interest. 

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