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Bond Moments
The dipole moment of a molecule can be interpreted in terms of bond dipole moments, and these, in turn, can be interpreted in terms of percentage of ionic character.
The principle characteristic fo the charge distribution in a molecule that comes from dielectric constant measurements is the extent to which the center of the electron distribution of a molecule fails to coincide with the center of the positive nuclear charge distribution. The charge asymmetry is obtained as the dipole moment of the molecule. This charge asymmetry, as we shall see, may result from an unequal sharing of the bonding electrons, the extreme case of which leads to a molecule with positively and negatively charged ions such as a molecule of NaCl vapor. More subtle electron distribution like the apparent slight asymmetry of the bonding electrons, as in a C – h bond, or the postions of the nonbonding electrons, as the nitrogen atom in ammonia, also lead to molecular dipoles. Dipole moment results allow such aspects of the electronic configuration of molecules to be discussed.
Dipole moment and polarizability of some simple molecules:

The dipole moment of a system of two equal and opposite charges is defined as the product of the charges and the distance separating them. Thus the dipole moment is given by μ = qr. The dipole moment has a direction as well as a magnitude; i.e. it is a vector quantity. It is frequently convenient to represent a dipole moment by an arrow showing the direction from the positive to the negative charge and the magnitude by the length of the arrow.
The concept of a dipole arises when the effect of an assembly of charges at some distant point is investigated. With this approach the dipole moment due to a collection of charges is defined as:
µ = - Σi qiri
Where qi and ri are the charges and vector lengths of the ith charges of the assembly, for a molecule the distribution of the electrons requires an integral form;
µ = - ∫ p (r) r d τ
Where p (r) is the charge density at a position defined by the vector r and d τ is a volume element. The integration over all the electrons and nuclei required can be carried out only for relatively simple molecules, where the electron distribution can be determined by theoretical methods. In general, the detailed electronic distribution is not known, and the molecular dipole moment is obtained by methods. The determinant of this one quantity does not, of course, allow the charge distribution p (r) to be deduced. Usually, one interprets the measured value of the dipole moment of a molecule by depicting the charge asymmetry which it measures in terms of a model, of separated, opposite charges that have the dipole moment of that measured for the molecule.
Dipole moments and ionic character: for diatomic molecules, the measured dipole moment of a molecule gives information about the displacement of the center of negative charge from that of the positive charge along the internuclear unequal sharing of the bonding electrons. The theoretical treatments of heterogeneous percentage, ionic character are the measure of such bonding. For polyatomic molecules it is necessary to try to understand the molecular dipole moment in terms of the contributions of the individual bonds of the molecule in a manner similar to that in which one tried to understand the energy of a molecule in terms of bond energies.
Magnetic measurements are a tool for molecular studies that have not been of such general applicability as electrical measurements. For certain types of compounds, however, magnetic measurements constitute one of the most powerful approaches to the elucidation of the arrangement of the electrons in the compound. The theory of magnetic studies parallels that of electrical studies so closely that detailed treatments need not to be given. Following some mention of the parallels between electrical and magnetic phenomena, the applications of magnetic studies are dealt with.
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The principle characteristic fo the charge distribution in a molecule that comes from dielectric constant measurements is the extent to which the center of the electron distribution of a molecule fails to coincide with the center of the positive nuclear charge distribution. The charge asymmetry is obtained as the dipole moment of the molecule. This charge asymmetry, as we shall see, may result from an unequal sharing of the bonding electrons, the extreme case of which leads to a molecule with positively and negatively charged ions such as a molecule of NaCl vapor. More subtle electron distribution like the apparent slight asymmetry of the bonding electrons, as in a C – h bond, or the postions of the nonbonding electrons, as the nitrogen atom in ammonia, also lead to molecular dipoles. Dipole moment results allow such aspects of the electronic configuration of molecules to be discussed.
Dipole moment and polarizability of some simple molecules:
The dipole moment of a system of two equal and opposite charges is defined as the product of the charges and the distance separating them. Thus the dipole moment is given by μ = qr. The dipole moment has a direction as well as a magnitude; i.e. it is a vector quantity. It is frequently convenient to represent a dipole moment by an arrow showing the direction from the positive to the negative charge and the magnitude by the length of the arrow.
The concept of a dipole arises when the effect of an assembly of charges at some distant point is investigated. With this approach the dipole moment due to a collection of charges is defined as:
µ = - Σi qiri
Where qi and ri are the charges and vector lengths of the ith charges of the assembly, for a molecule the distribution of the electrons requires an integral form;
µ = - ∫ p (r) r d τ
Where p (r) is the charge density at a position defined by the vector r and d τ is a volume element. The integration over all the electrons and nuclei required can be carried out only for relatively simple molecules, where the electron distribution can be determined by theoretical methods. In general, the detailed electronic distribution is not known, and the molecular dipole moment is obtained by methods. The determinant of this one quantity does not, of course, allow the charge distribution p (r) to be deduced. Usually, one interprets the measured value of the dipole moment of a molecule by depicting the charge asymmetry which it measures in terms of a model, of separated, opposite charges that have the dipole moment of that measured for the molecule.
Dipole moments and ionic character: for diatomic molecules, the measured dipole moment of a molecule gives information about the displacement of the center of negative charge from that of the positive charge along the internuclear unequal sharing of the bonding electrons. The theoretical treatments of heterogeneous percentage, ionic character are the measure of such bonding. For polyatomic molecules it is necessary to try to understand the molecular dipole moment in terms of the contributions of the individual bonds of the molecule in a manner similar to that in which one tried to understand the energy of a molecule in terms of bond energies.
Magnetic measurements are a tool for molecular studies that have not been of such general applicability as electrical measurements. For certain types of compounds, however, magnetic measurements constitute one of the most powerful approaches to the elucidation of the arrangement of the electrons in the compound. The theory of magnetic studies parallels that of electrical studies so closely that detailed treatments need not to be given. Following some mention of the parallels between electrical and magnetic phenomena, the applications of magnetic studies are dealt with.
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