Dipole moment electric

In addition, there could be a mechanical or electromagnetic interaction of a system with an external entity which may do work on an otherwise isolated system. Such a contact with a work source can be represented by the Hamiltonian U p, q, x) where x is the coordinate (for example, the position of a piston in a box containing a gas, or the magnetic moment if an external magnetic field is present, or the electric dipole moment in the presence of an external electric field) describing the interaction between the system and the external work source. Then the force, canonically conjugate to x, which the system exerts on the outside world is... 

The electric dipole moment operator jx has components along the cartesian axes ... 

The dipole moment (strictly, the electric dipole moment) of a molecule is a measure of the charge asymmetry and is usually denoted by the symbol /r. 

Nelson, R D, Jr, Lide, D R, Jr, Maryott, A A Selected Values of Electric Dipole Moments in the Gas Phase NSRD NBS 10, Govenunent Pnntmg Office Washmgton, DC, 1967... 

A ferroelectric crystal is one that has an electric dipole moment even in the absence of an external electric held. This arises because the centre of positive charge in the crystal does not coincide with the centre of negative charge. The phenomenon was discovered in 1920 by J. Valasek in Rochelle salt, which is the H-bonded hydrated d-tartrate NaKC4H406.4H 0. In such compounds the dielectric constant can rise to enormous values of lO or more due to presence of a stable permanent electric polarization. Before considering the effect further, it will be helpful to recall various dehnitions and SI units ... 

Theoreticians did little to improve their case by proposing yet more complicated and obviously unreUable parameter schemes. For example, it is usual to call the C2 axis of the water molecule the z-axis. The molecule doesn t care, it must have the same energy, electric dipole moment and enthalpy of formation no matter how we label the axes. I have to tell you that some of the more esoteric versions of extended Hiickel theory did not satisfy this simple criterion. It proved possible to calculate different physical properties depending on the arbitrary choice of coordinate system. 

To look ahead a little, there are properties that depend on the choice of coordinate system the electric dipole moment of a charged species is origin-dependent in a well-understood way. But not the charge density or the electronic energy Quantities that have the same value in any coordinate system are sometimes referred to as invariants, a term borrowed from the theory of relativity. 

Ground to excited state Transition electric dipole moments (Au) ... 

A more thorough analysis shows that one should not expect the electric dipole moment to remain constant, because real molecules have polarizability. The polarization of the dielectric in the electric field of the molecule itself gives rise to a reaction field, which tends to enhance the electrical asymmetry. 

This is not a unique way of classifying molecular properties. For example, Dykstra et al. (1990) concentrate on the response of a system to an apphed external field the electric dipole moment can be defined as the first derivative of the energy with respect to the field, and so on. I will stick with the Boys and Cook nomenclature as a broad basis for discussion. 

In Figure 16.1, we see a pair of point charges Qp, at position vector Fa and <2b at position vector fb. <2a is not necessarily equal to <2b> and one is not necessarily the negative of the other. Their electric dipole moment pe is defined as... 

At the molecular level, electric dipole moments are important because they give information about the charge distribution in a molecule. Examination of the experimental data for a few simple compounds reveals that the electric dipole moment is also a property associated with chemical bonds and their polarity. The... 

At the molecular level, electric quadrupoles can lead to useful structural information. Thus, whilst the absence of a permanent electric dipole in CO2 simply means that the molecule is linear, the fact that the electric quadrupole moment is negative shows that our simple chemical intuition of 0 C" 0 is correct. The definition of quadrupole moment is only independent of the coordinate origin when the charges sum to zero and when the electric dipole moment is zero. 

Breakdown of the Bom-Oppenheimer approximation is responsible for the small but non-zero permanent electric dipole moment of HD (2 x 10 Cm, Trefler and Gush, 1968) but otherwise the effect is negligible to chemical accuracy. 

Table 16.1 Modulus of the electric dipole moment vector of pyridine...

Table 16.2 shows typical results. In all cases, the bond length was optimized. It is of interest to consider the variation of electric dipole moment with internu-clear separation, shown in Table 16.3. 

Similar considerations apply to the electric dipole moment the derivatives of the dipole integrals can be easily obtained whilst the derivatives of the density matrix require the use of coupled Hartree-Fock theory (e.g. Gerratt and Mills, 1968). 

Basis-set sensitivity is important, as it was for the calculation of electric dipole moments. Several experimental values in the literamre refer to measurements corrected neither for zero-point vibrations nor for centrifugal effects. 

Molecules do not consist of rigid arrays of point charges, and on application of an external electrostatic field the electrons and protons will rearrange themselves until the interaction energy is a minimum. In classical electrostatics, where we deal with macroscopic samples, the phenomenon is referred to as the induced polarization. I dealt with this in Chapter 15, when we discussed the Onsager model of solvation. The nuclei and the electrons will tend to move in opposite directions when a field is applied, and so the electric dipole moment will change. Again, in classical electrostatics we study the induced dipole moment per unit volume. 

For the special case of an axially symmetric molecule, the electric dipole moment lies along the axis of highest symmetry, which we usually call the z-axis. The induced dipole due to a field along the molecular axis is usually written... 

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