Moments of molecules

The leading tenn in the electrostatic interaction between the dipole moment of molecule A and the axial quadnipole moment of a linear, spherical or synunetric top B is... 

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

The HyperChem log file includes calculated dipole moments of molecules. To set the amount of information collected in the log file, change the value of the QuantumPrintLevel setting in the chem.ini file. Note that the sign convention used in the quantum mechanical calculation of dipoles is opposite to that used in molecular mechanics dipole calculations this reflects the differing sign conventions of physics and chemistry. 

This greatly simplifies the theory of the magnetic moments of molecules and complex ions. The magnetic moment of a molecule or complex ion is determined entirely by the number of unpaired electrons, being equal to... 

Table 6-3. Comparison of the dipoles of the isolated individual monomers (dipole M) compare to the dipole moments of molecules within the dimer (dipole D) via the interaction, calculated with different functionals. Units are atomic units, and we give as well the difference in length and orientation ...

Quantities that have both magnitude and direction are called vectors. Examples of vectors in chemistry include things like the dipole moments of molecules, magnetic and electric fields, velocities and angular momenta. It is convenient to represent vectors geometrically and the simplest example is... 

W.Liptay, Dipole Moments of Molecules in Excited States and the Eifect of External Electric Fields on the Optical Absorption of Molecules in Solution, in Modem Quantum Chemistiy, ed by O.Subabiglu, Academic Press, New York, 1965. 

When a constant electric field is suddenly applied to an ensemble of polar molecules, the orientation polarization increases exponentially with a time constant td called the dielectric relaxation time or Debye relaxation time. The reciprocal of td characterizes the rate at which the dipole moments of molecules orient themselves with respect to the electric field. 

Geometry of molecules and ions, structural isomerism of simple organic molecules and coordination complexes, dipole moments of molecules, relation of properties to structure... 

In this chapter we will also focus on the dipole moment of molecules. With these, some of the most interesting phenomena are the molecules for which the electric moment is in the wrong direction insofar as the atomic electronegativities are concerned. CO is probably the most famous of these cases, but other molecules have even more striking disagreements. One of the larger is the simple diatomic BF. We will take up the question of the dipole moments of molecules like BF in Chapter 12. In this chapter we will examine in a more general way how various sorts of structures influence electric moments for two simple cases. For some of the discussion in this chapter we restrict ourselves to descriptions of minimal basis set results, since these satisfactorily describe the physics of the effects. In other cases a more extensive treatment is necessary. 

Contribution of Unshared Electron Pairs to the Electric Dipole Moments of Molecules.—In the preceding chapter we discussed the dipole moments of molecules, in relation to the partial ionic character of bonds, without considering the possible contribution of unshared electron pairs. A simple treatment based on hybrid orbitals provides some justification of this procedure. 

The Effect of Resonance on the Electric Dipole Moments of Molecules.—It was pointed out by Sutton27 in 1931 that resonance of the... 

Fig. 12.5 Illustration of the orientation angles used in the Stockmayer intermolecular potential. Molecule j consists of atoms A and B, and molecule i consists of atoms C and D. The vector ry runs from the center of mass of molecule i to the center of mass of molecule j. The vector JTJ gives the orientation and magnitude of the dipole moment of molecule i, with a similar definition for JTj. A ghost copy of molecule j is shifted to left to more easily visualize the orientation angle ifr. See Eqs. 12.11 to 12.13 and accompanying text for definition and description of these angles.

In a ferroelectric material, the dipole moments of molecules remain aligned in the absence of an external field. This alignment gives the material a permanent electric polarization. 

So far we have discussed 2D density modulated phases that are formed by deformation or breaking of the layers. However, there are also 2D phases with more subtle electron density modulations. In some cases additional peaks observed in the XRD pattern (Fig. 10) are related to a double layer periodicity in the structure. As double layer periodicity was observed in the bent-core liquid crystals formed by the asymmetric as well as symmetric molecules [22-25] it should be assumed that the mechanism leading to bilayers must be different from that of the pairing of longitudinal dipole moments of molecules from the neighboring layers, which is valid for smectic antiphases made by asymmetric rod-like molecules. 

The dipole moments of molecules are often treated as being equal to the vector sum of the bond dipoles of the various bonds in the molecules. It is almost impossible to measure the dipole moment of an individual bond within a molecule. For example, molecules such as methane, carbon tetrachloride, and p-dichlorobenzene have no dipole moments, whereas molecules such as methylene chloride and m-dichlorobenzene do. The vector sum treatment could be made to agree quantitatively with all known dipole moments if the bond moments were treated as variables that depend on the nature of the particular molecule in which the bonds were located. 

Again uq(R) is the hard sphere potential. This is necessary to keep the molecules from overlapping. The parameter is the dipole moment of molecule i. The factor D(i, j) is a term that depends on the orientation of the dipoles i and j and need not concern us here. We can call this potential the dipolar hard sphere potential. 

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