Moment, electric

Spackman M A 1992 Molecular electric moments from X-ray diffraction data Chem. Rev. 92 1769... 

The quadrupole is the next electric moment. A molecule has a non-zero electric quadrupole moment when there is a non-spherically symmetrical distribution of charge. A quadrupole can be considered to arise from four charges that sum to zero which are arranged so that they do not lead to a net dipole. Three such arrangements are shown in Figure 2.8. Whereas the dipole moment has components in the x, y and z directions, the quadrupole has nine components from all pairwise combinations of x and y and is represented by a 3 x 3 matrix as follows ... 

The three moments higher than the quadrupole are the octopole, hexapole and decapoli. Methane is an example of a molecule whose lowest non-zero multipole moment is the octopole. The entire set of electric moments is required to completely and exactly describe the distribution of charge in a molecule. However, the series expansion is often truncated after the dipole or quadrupole as these are often the most significant. 

The electric moments are examples of tensor properties the charge is a rank 0 tensor (which i the same as a scalar quantity) the dipole is a rank 1 tensor (which is the same as a vectoi with three components along the x, y and z axes) the quadrupole is a rank 2 tensor witl nine components, which can be represented as a 3 x 3 matrix. In general, a tensor of ran] n has 3" components. 

VVe therefore return to the point-charge model for calculating electrostatic interactions. If sufficient point charges are used then all of the electric moments can be reproduced and the multipole interaction energy. Equation (4.30), is exactly equal to that calculated from the Coulomb summation. Equation (4.19). 

Onsager L 1936. Electric Moments of Molecules in Liquids. Journal of the American Chemical Society 58 1486-1493. 

Finally, the package gives us skeletal information about molecular properties in the form of electric moments (Figure 10.15). 

Since we normally deal with electrostatic field perturbations that are small, we can profitably expand the electric moments as a Taylor series in the external field ... 

Under the influence of an electric field a gas whose molecules have a permanent electric moment and in addition can have a further moment induced in them by deformation becomes polarized in the direction of the field, the amount of polarization per unit volume being1... 

Here e is the dielectric constant of the gas, F the strength of the applied field, N the number of molecules in unit volumes, n the permanent electric moment of a molecule, and a the coefficient of induced polarization of a molecule cos 9 is the average value of cos 9 for all molecules in the gas, and cos 9 is the time-average of cos 9 for one molecule in a given state of motion, 6 being the angle between the dipole axis and the lines of force of the applied field. 

The electric moment found for hydrogen chloride is equal to that of a dipole composed of a proton and an electron 0.0694 A apart for hydrogen bromide the equivalent distance is 0.0528 A. 

The existence of this residual entropy of ice at very low temperatures was discovered by Giauque and Ashley (ref. 7), who preliminarily ascribed it to the persistence of rotation of ortho-water molecules (comprising 3/< of the total) about their electric-moment axes, giving an entropy of 3/ R In 2 = 1.03 E. U. 

This oscillating dipole will radiate a secondary wave of the same frequency, which may be observed along the direction OP making an angle 6 with the direction (x-axis) of the incident wave. The scattered wave will be polarized in the plane defined by P and the 2 -axis. The electric intensity Es c of the scattered wave will depend on the acceleration of the induced electric moment, i.e., on d pldC-. Specifically the amplitude o.sec of the wave scattered in the direction OP will depend on the amplitude of (1/c ) d pldt ) calculated from Eq. (14), on the projection of the moment perpendicular to the direction P in the plane, and inversely on the distance r from the scatterer. Thus,... 

In his pioneering work Baetzold used the Hartree-Fock (HF) method for quantum mechanical calculations for the cluster structure (the details are summarized in Reference 33). The value of the HF procedure is that it yields the best possible single-determinant wave function, which in turn should give correct values for expectation values of single-particle operators such as electric moments and... 

Julg, A. On the Description of Molecules Using Point Charges and Electric Moments. 58, 1-37 (1975). 

Examples of p(r) are energy density, charge density, current density (see Section 4.6), difference density (difference between a final density and an initial density), electric moment density, magnetic moment density, local reactivity functions (see Section 4.5.2), force density, etc. Note that, for ensuring the stability of matter, the net force density must vanish everywhere in space. The concept of a PDF has generated many significant developments in interpretative quantum chemistry. 

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