Dipole moment, electric atomic unit

For relatively small electric fields in isotropic substances P = ) E, where is the electric susceptibility. If the medium is made up of N atoms (or ions) per unit volume, the polarization is P = N wherep is the average dipole moment per atom. The polarizability a can be defined as p = ctE , where is the local field at the position of the atom. Using the Lorentz method to calculate the local field one finds ... 

The dielectric polarization, or simply polarization, within dielectric materials is a vector physical quantity, denoted by P, and its module is expressed in C.m Electric polarization arises due to the existence of atomic and molecular forces and appears whenever electric charges in a material are displaced with respect to one another under the influence of an apphed external electric field strength, E. On the other hand, the electric polarization represents the total electric dipole moment contained per unit volume of the material averaged over the volume of a crystal cell lattice, V, expressed in cubic meters (m ) ... 

The table lists the element and atomic mass in the first two columns. The nuclear spin (I) is in column 3. The magnetic dipole moment /i) in units of nuclear magnetons is in column 4. The spectroscopic electric quadrupole moment (Q) in units of barns is in column 5. 

We consider first the polarizability of a molecule consisting of two or more polarizable parts which may be atoms, bonds, or other units. When the molecule is placed in an electric field the effective field which induces dipole moments in various parts is not just the external field but rather the local field which is influenced by the induced dipoles of the other parts. The classical theory of this interaction of polarizable units was presented by Silberstein36 and others and is summarized by Stuart in his monograph.40 The writer has examined the problem in quantum theory and finds that the same results are obtained to the order of approximation being considered. 

When the net charge on a species is zero but its electric dipole moment p is nonzero, classical electrostatics predicts that the interaction with an ion is described by an ion dipole interaction of the form (in atomic units)... 

A piezoelectric crystal is one that develops an electrical voltage when subject to mechanical stress for example if pressure is applied to it, and conversely develops strain when an electric field is applied across it. Application of an electric field causes a slight movement of atoms in the crystal so that a dipole moment develops in the crystal. For it to be piezoelectric, a crystal must be made up from units that are non-centrosymmetric (i.e., they do not possess a centre of symmetry). Of the 32 crystal classes (see Chapter 1), 11 possess a centre of symmetry and one other cannot be piezoelectric because of other symmetry elements it possesses. 

However, it would be a serious error to confuse electronegativity or ionization energy with hardness . The clearest counter-example is Tl(III) which is a rather soft central atom but which must have a rather high ionization energy. There are other physical properties which accentuate the opposite inequality signs of (1) even more, for instance the electric polarizability. Table 1 contains many values for this quantity a in the unit 10-24 cm3. Gaseous atoms and positive ions have polarizabilities which can be calculated from wavefunctions (9) by evaluating the sum of matrix elements of induced dipole moment ... 

Molecular dipole moments are often expressed in the non-SI unit debye, where D 3.335 64 x 10"30 C m. The SI unit C m is inconvenient for expressing molecular dipole moments, which results in the continued use of the deprecated debye (D). A convenient alternative is to use the atomic unit, ea0. Another way of expressing dipole moments is to quote the electric dipole lengths, lp = p/e, analogous to the way the nuclear quadrupole areas are quoted (see pp.21 and 98). This gives the distance between two elementary charges of the equivalent dipole and conveys a clear picture in relation to molecular dimensions. 

Table 3.20 Changes of electric field gradient and dipole moment caused by H-bonding (atomic units) and rms HCl Ubrational angle (degs) calculated with [642/531/31] basis set for [C1,P/N/H]. ...

---