Dipole of molecule

The competition between the polar and steric dipoles of molecules may also lead to internal frustration. In this case, the local energetically ideal configuration cannot be extended to the whole space, but tends to be accomodated by the appearance of a periodic array of defects. For example, the presence of the strong steric dipole at the head of a molecule forming bilayers will induce local curvature. As the size of the curved areas increases, an increase in the corresponding elastic energy makes energetically preferable the... 

Here, the pt are the permanent dipoles of molecules i = 1 and 2, and the ptj( r, i 2, Rij) are the dipoles induced by molecule i in molecule j the are the vectors pointing from the center of molecule i to the center of molecule j and the r, are the (intramolecular) vibrational coordinates. In general, these dipoles are given in the adiabatic approximation where electronic and nuclear wavefunctions appear as factors of the total wavefunction, 0(rf r) ( ). Dipole operators pop are defined as usual so that their expectation values shown above can be computed from the wavefunctions. For the induced dipole component, the dipole operator is defined with respect to the center of mass of the pair so that the induced dipole moments py do not depend on the center of mass coordinates. For bigger systems the total dipole moment may be expressed in the form of a simple generalization of Eq. 4.4. In general, the molecules will be assumed to be in a electronic ground state which is chemically inert. 

Van der Waals never speculated about the nature of the intermolecular forces that hold substances together. He was working in a time when many scientists did not believe in atoms or molecules, and those that did had no knowledge of their internal structure. But, by 1921, scientists had figured out the source of van der Waals forces. It was the attraction between the electric dipoles of molecules. 

The van der Waals forces are the interactive forces between dipoles of molecules. The dispersion force, a type of van der Waals force between dipoles that arises from thermal fluctuation or electric field induction, is always present between molecules. The van der Waals forces (FV(jw) between tip and sample can be estimated by the following equation, if we assume the tip is a sphere with radius, R. 

The van der Waals forces act between dipoles of molecules. These forces are referred to as dipole-dipole, dipole-induced and dispersion forces. 

In the previous relations, p is the number density of molecules, P=l/kT, and nie is the effective dipole of molecules along their symmetry axes. 

Molecular models for chloromethane, dichloromethane, and trichloromethane are given to show the direction of the dipole of molecule more clearly. Calculated dipoles for these three molecules are 2.87, 2.50, and 1.72 Debye, respectively, and it is clear that the directional nature of the individual bond dipoles plays a role in the overall magnitude of the dipole moment for the molecrde. With three chlorine atoms directed to different regions of space, chloroform is the least polar of the three molecules, despite the presence of three polarized bonds. 

In order to calculate P it is desirable to introduce the field Eij, which accounts for the electric field at the position n generated by the dipole of molecule j. 

The true origin of van der Waals attraction is based on quantum mechanics. Quantum theory in its simplest form tells us that everywhere in space there is Planck s quantized radiation field. Everywhere in space photons are moving randomly. These photons are constantly scattered by any particles which are present, so that instantaneous induced dipoles are formed. Each instantaneous dipole p " of molecule i induces a dipole of molecule j, which in turn lowers the energy of the instantaneous dipole i, see Fig. Ic. The interaction potential of both molecules is obtained by substituting the instantaneous polarization p-" for pi into Eq. (1.5) and averaging over the time,... 

Van der Waals forces result from attractions between the electric dipoles of molecules, as described in Section 1.2. Attractive van der Waals forces between colloidal particles can be considered to result from dispersion interactions between the molecules on each particle. To calculate the effective interaction, it is assumed that the total potential is given by the sum of potentials between pairs of molecules, i.e. the potential is said to be pairwise additive. In this approximation, interactions between pairs of molecules are assumed to be unaffected by the presence of other molecules i.e. many-body interactions are neglected. The resulting pairwise summation can be performed analytically by integrating the pair potential for molecules in a microscopic volume dVi on particle 1 and in volume dVi on particle 2, over the volumes of the particles (Fig. 3.1). The resulting potential depends on the shapes of the colloidal particles and on their separation. In the case of two flat infinite surfaces separated in vacuo by a distance h the potential per unit area is... 

Long-range coupling through space can occur by the direct interaction of nuclear magnetic dipoles of molecules with one another. In liquids this is averaged to zero because of the rapid molecular motions. In solids, however, molecules have a fixed orientation with respect to one another and one can therefore observe dipolar coupling. 

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... 

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... 

Both infrared and Raman spectroscopy provide infonnation on the vibrational motion of molecules. The teclmiques employed differ, but the underlying molecular motion is the same. A qualitative description of IR and Raman spectroscopies is first presented. Then a slightly more rigorous development will be described. For both IR and Raman spectroscopy, the fiindamental interaction is between a dipole moment and an electromagnetic field. Ultimately, the two... 

It will be noted that hydration enthalpy decreases with increasing ionic radius and increases very sharply with increase in ionic charge, these results being what we should expect for an electrostate interaction between a charged ion and the dipole of a water molecule (p, 44). 

The dipole moments of the hydrogen halides decrease with increasing atomic number of the hydrogen, the largest difference occurring between HF and HCl, and association of molecules is not an important factor in the properties of FICl, HBr and HI. This change in dipole moment is reflected in the diminishing permittivity (dielectric constant) values from HF to HI. 

The reaction field method. The shaded arrow represents the mm of the dipoles of the other molecules within sphere. 

Many molecules, such as carbon monoxide, have unique dipole moments. Molecules with a center of inversion, such as carbon dioxide, will have a dipole moment that is zero by symmetry and a unique quadrupole moment. Molecules of Td symmetry, such as methane, have a zero dipole and quadrupole moment and a unique octupole moment. Likewise, molecules of octahedral symmetry will have a unique hexadecapole moment. 

The dielectric constant is a property of a bulk material, not an individual molecule. It arises from the polarity of molecules (static dipole moment), and the polarizability and orientation of molecules in the bulk medium. Often, it is the relative permitivity 8, that is computed rather than the dielectric constant k, which is the constant of proportionality between the vacuum permitivity so and the relative permitivity. 

Table 1 3 lists the dipole moments of various bond types For H—F H—Cl H—Br and H—I these bond dipoles are really molecular dipole moments A polar molecule has a dipole moment a nonpolar one does not Thus all of the hydrogen halides are polar molecules To be polar a molecule must have polar bonds but can t have a shape that causes all the individual bond dipoles to cancel We will have more to say about this m Section 1 11 after we have developed a feeling for the three dimensional shapes of molecules... 

---