Dipole moments of diatomic molecule

As mentioned above and discussed in Chapter 2, atomic charges were often obtained in the past from dipole moments of diatomic molecules, assuming that the measured dipole moment equal to the bond length times the atomic charge. This method assumes that the molecular electron density is composed of spherically symmetric electron density distributions, each centered on its own nucleus. That is, the dipole moment is assumed to be due only to the charge transfer moment Mct. and the atomic dipoles Malom are ignored. 

Fig. 3-8.—Curve relating tbo amount of ionic character of a bond to the electronegativity difference of the two atoms. Experimental points, based upon observed values of the electric dipole moment of diatomic molecules, are shown for 18 bonds.

From what has been said so far, we would expect any diatomic molecule with a polar bond (between atoms with different electronegativities) to exhibit a dipole moment. Although this is generally true, the observed dipole moments of diatomic molecules are sometimes smaller than expected. For example, the carbon monoxide molecule CO has a dipole moment of only 0.11 D, much smaller than expected from the polarity of the CO bond. This discrepancy is most likely caused by the lone pairs of electrons on the atoms, which make large contributions to the dipole moment in opposition to that from the bond polarity. We will not explore the details of this situation here. The dipole moments of some representative diatomic molecules are listed in Table 13.3. 

Dipole moments of diatomic molecules can be calculated directly. In more complex molecules, vector addition of the individual bond dipole moments gives the net molecular dipole moment. However, it is usually not possible to calculate molecular dipoles directly from bond dipoles. Table 3.8 shows experimental and calculated dipole moments of chloro-methanes. The values calculated from vectors use C—H and C—Cl bond dipole moments of 1.3 X 10 ° and 4.9 X 10 C m, respectively, and tetrahedral bond angles. Clearly, calculating dipole moments is more complex than simply adding the vectors for individual bond moments. However, for many purposes, a qualitative approach is sufficient. 

The early approach to the nature of the bonding in solids as outlined by Paulingb34) and Fajans< > derived from the measurement of dipole moments of diatomic molecules, especially the hydrogen halides, the correlation of these with the percent of ionic behavior (/dipole moment fi) and the rationalization of these numbers in terms of the elemental electronegativities. Thus Hannay and Smyth<79) give (empirically)... 

Calculated and Experimental Dipole Moments of Diatomic Molecules... 

Dipole moments of diatomic molecules Preliminary remarks... 

Valence density depends on the periodic position of an atom, shown for representative elements in Table 14. The simplest situation to model is the polarization that occurs in an alkali halide molecule, also responsible for the largest dipole moments of diatomic molecules. In effect, a singly charged valence shell interacts with a single vacancy in the valence shell of the halogen atom. The polarization of the alkali shell should decrease with atomic size, which is measured by the period number of the valence shell. The implied decrease in valence density from Li to Na, of 8.6/6.4 3/2, suggests v = 1/n as approximate scale factor, which could be complicated by the appearance of (3 and / sublevels.lt is a complementary vacancy density that should be taken into account. 

In Section 2.12, we saw that a polar covalent bond in which electrons are not evenly distributed has a nonzero dipole moment. A polar molecule is a molecule with a nonzero dipole moment. All diatomic molecules are polar if their bonds are polar. An HC1 molecule, with its polar covalent bond (8+H—Clfi ), is a polar molecule. Its dipole moment of 1.1 D is typical of polar diatomic molecules (Table 3.1). All diatomic molecules that are composed of atoms of different elements are at least slightly polar. A nonpolar molecule is a molecule that has no electric dipole moment. All homonuclear diatomic molecules, diatomic molecules containing atoms of only one element, such as 02, N2, and Cl2, are nonpolar, because their bonds are nonpolar. 

We saw that homonuclear diatomic molecules exhibit no pure-rotation or vibration-rotation spectra, because they have zero electric dipole moment for all internuclear separations. The Raman effect depends on the polarizability and not the electric dipole moment homonuclear diatomic molecules do have a nonzero polarizability which varies with varying internuclear separation. Hence they exhibit pure-rotation and vibration-rotation Raman spectra. Raman spectroscopy provides information on the vibrational and rotational constants of homonuclear diatomic molecules. 

In diatomic molecules, where there is only one bond, one can associate the dipole moment of the molecule with a property of the bond, the bond moment. In polyatomic molecules, however, the molecular dipole moment is the... 

Fig. 5.37 (a) Chemists usually consider the dipole moment of a diatomic molecule, the vector Qr, to be directed from the positive to the negative atom, (b) The dipole moment of a collection of charges, such as a molecule, arises from the magnitudes of the charges, and their locations (i.e. distances and directions from the origin, (c) The dipole moment of a molecule can be thought of as the vector sum of bond moments... 

A molecule can only absorb infrared radiation if the vibration changes the dipole moment. Homonuclear diatomic molecules (such as N2) have no dipole moment no matter how much the atoms are separated, so they have no infrared spectra, just as they had no microwave spectra. They still have rotational and vibrational energy levels it is just that absorption of one infrared or microwave photon will not excite transitions between those levels. Heteronuclear diatomics (such as CO or HC1) absorb infrared radiation. All polyatomic molecules (three or more atoms) also absorb infrared radiation, because there are always some vibrations which create a dipole moment. For example, the bending modes of carbon dioxide make the molecule nonlinear and create a dipole moment, hence CO2 can absorb infrared radiation. 

Spectral studies of rotational energy levels have proved most profitable for linear molecules having dipole moments, particularly diatomic molecules (for example, CO, NO, and the hydrogen halides). The moment of inertia of a linear molecule may be readily obtained from its rotation spectrum and for diatomic molecules, interatomic distances may he calculated directly from moments of inertia (Exercise 14d). For a mole-... 

The electric dipole moment of a molecule is a valuable characteristic of its structure and also the value of the dipole moment is an important factor determining the cohesion energy. The relation between the dipole moment and the constitution, however, is complicated even for a diatomic molecule or one bond446. 

Predicting the IR absorption behavior of molecules with more than two atoms is not as simple as looking at diatomic molecules. It is not the net dipole moment of the molecule that is important, but any change in the dipole moment on vibration. We need to understand how molecules vibrate. This is relatively simple for diatomic and triatomic molecules. Large molecules cannot be evaluated simply, because of their large number of vibrations and interactions between vibrating atoms. It can be said that most molecules do absorb IR radiation, which is the reason this technique is so useful. 

If the mechanical vibration of the simple harmonic oscillator by which we first represented the nuclear motion of the diatomic molecule in the preceding section is accompanied by an oscillation of the dipole moment of the molecule, then, according to classical physics, radiation will be emitted with the frequency of the oscillator. For small amplitudes of vibration we can take the oscillating part of the dipole moment as being proportional to the elongation cc of the molecule introduced in the preceding section, let us say equal to qx. The amount of radiation emitted by the oscillator in unit time is then given by ... 

The constant electron density contour diagrams of one homonuclear and five heteronuclear diatomic molecules presented in Fig. 8.6 have been obtained by reasonably accurate quantum chemical calculations. The electric dipole moment of F2 is zero by symmetry. The electric dipole moments of heteronuclear molecules like LiFl, LiF, HF, CIF or CO may be calculated from their electron densities using equation (5.2). These dipole moments, in turn, allow us to calculate the ionic characters gic(calc) = /Xei(calc)(calc). In Table 8.1 we compare the calculated ionic characters of 21 heteronuclear diatomic molecules with their experimental counterparts. The agreement between experiment and calculations is good the average deviation between experimental and calculated values is less than 0.02 a.u, the maximum deviation (in KLi) is 0.05 a.u. 

For a molecule to show infrared absorptions it must possess a specific feature, i.e. an electric dipole moment of the molecule must change during the vibration. This is the selection rule for infrared spectroscopy. Figure 1.4 illustrates an example of an infrared-active molecule, a heteronuclear diatomic molecule. The dipole moment of such a molecule changes as the bond expands and contracts. By comparison, an example of an infrared-inactive molecule is a homonuclear diatomic molecule because its dipole moment remains zero no matter how long the bond. 

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