Some Heteronuclear Diatomic Molecules

To take into account the energy inequalities between the participating atomic orbitals the wave functions have extra c terms, as in the example  

The NO molecule, because of its single unpaired electron, is sometimes written as NO, the dot signifying the odd electron. This has given rise in the biochemical literature to some serious misunderstandings, particularly in the role of NO as a chemical messenger, with the formulae NO and NO being ascribed to species having different chemical properties  

Q Which of the molecules N, or NO would you expect to have the larger first ionization energy State your reasoning. 

would be expected to have a larger first ionization energy than NO since the latter molecule has an anti-bonding electron that is easily removed. 

The normalization factors are included in equations 4.11 and 4.12 and the minus sign in equation 4.12 means combine the 2s orbital with the 2p orbital after it has been reversed so that its positive lobe is directed in the opposite direction from that in equation 4.1 V. 

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Some heteronuclear diatomic molecules, such as nitric oxide (NO), carbon monoxide (CO) and the short-lived CN molecule, contain atoms which are sufficiently similar that the MOs resemble quite closely those of homonuclear diatomics. In nitric oxide the 15 electrons can be fed into MOs, in the order relevant to O2 and F2, to give the ground configuration... 

Some heteronuclear diatomic molecules were described in detail. Differences in electronegativity coefficients between the combining atoms were shown to be important. 

P. Politzer, Theor. Chim. Acta, 23, 203 (1971). Properties of Atoms in Molecules III. Atomic Charges and Centers of Electronic Charge in Some Heteronuclear Diatomic Molecules. 

This presents a problem when we discuss the dipole moment of a polar heteronuclear diatomic molecule, AX, where X will be the more electronegative. In the chemical picmre, it is quite common to say that in the ground state the molecule lies along some axis and that it has a definite dipole moment. In the physical picmre, we say that the molecule has no measurable dipole moment in the ground state. 

Classification of the remaining heteronuclear diatomic molecules is somewhat arbitrary, and we have grouped together those molecules containing some particular electronegative element B, rather than consider isoelectronic species. 

Heteronuclear diatomic molecules are naturally somewhat more complicated than the homonuclear comprehensive comparisons with homonuclear molecules were given by Mulliken [15]. The atomic orbital coefficients in the molecular orbitals ofheteronu-clear diatomic molecules are no longer determined by symmetry alone, and the electrons in the molecular orbitals may be shared equally between atoms, or may be almost localised on one atom. The molecular orbitals can still be classified as a or n, but in the absence of a centre-of-symmetry the g/u classification naturally disappears. Some heteronuclear molecules contain atoms which are sufficiently similar that the molecular orbitals resemble those shown in figure 6.7. In many other cases, however, the atoms are very different. This is particularly the case for hydride systems, like the HC1 molecule,... 

Let us now consider heteronuclear diatomic molecules. Start with the fact that hydrogen fluoride, HF, is a gas at room temperature. This tells us that it is a covalent compound. We also know that the H—F bond has some degree of polarity because H and F are not identical atoms and therefore do not attract the electrons equally. But how polar will this bond be ... 

A considerable contribution to the theoretical study of isoelectronic diatomic molecules was made by Laurenzi (1969, 1972, 1976, 1981), who obtained the equations describing the behavior of Re, De, and k2 as functions of nuclear charges in both cases of homo- and heteronuclear diatomic molecules. In particular, Laurenzi (1976, 1981) solved exactly these equations for one-electron diatomics with some empirical diatomic potential functions (Morse and Varshni III). 

There are only a few heteronuclear diatomic molecules that are formed from elements of the first and second rows of the Periodic Table and are stable as diatomic molecules in the gas phase at normal temperatures and pressures. These are HF, CO and NO. Others have been observed at high temperatures, in discharge lamps, in flames or in space. Examples are LiH, LiF, OH, BeH, BeO, BF, BH, CH, CN and NH. Some of the molecules in this second list will be stable with respect to the two separate atoms but not at normal temperatures and pressures with respect to other forms of the compound. LiH, LiF and BeO are normally found as ionic solids. The other molecules are unstable with respect to covalent compounds in which the atoms have their normal valencies H20, BeH2, BF3, B2H6, CH4, (CN)2 and NH3. 

The hydrogen molecule has provided an example of covalent-ionic resonance in a particular bond. Because structures (3-IVb) and (3-IVc) are of importance in an accurate description of the bond from the VB point of view, we say that the bond has some ionic character. However, the polarity that (3-Vb) introduces is exactly balanced by the polarity that (3-Vc) introduces, so that the bond has no net polarity. It is therefore called a nonpolar covalent bond. It is important not to confuse polarity and ionic character, although, unfortunately, the literature contains many instances of such confusion. When we turn to a heteronuclear diatomic molecule, we necessarily have bonds that have both ionic and polar character. Even for the pure covalent canonical structure of HC1 (3-Ia) there is bond polarity... 

In the heteronuclear diatomic molecules, the MOs resemble those of Figure 3.1, but the distribution on the two atoms is different because the energy and size of the AOs are different. Indices g and u are excluded since the inversion center is missing. The final charge distribution is polar to some extent. In LiF, it is reasonable to describe the bond as an ionic bond of the type Li+F, formed by first transferring the Li 2s electron to the F 2p subshell, followed by strong interaction between the ions. The measured dipole moment agrees with this picture. In molecules with nearly the same... 

Now we turn to vibrational Raman spectroscopy, in which the incident photon leaves some of its energy in the vibrational modes of the molecule it strikes or collects additional energy from a vibration that has already been excited. The gross selection rule for vibrational Raman transitions is that the molecular polarizability must change as the molecule vibrates. The polarizability plays a role in vibrational Raman spectroscopy because the molecule must be squeezed and stretched by the incident radiation in order that a vibrational excitation may occur during the photon-molecule collision. Both homonuclear and heteronuclear diatomic molecules swell and contract during a vibration, and the control of the nuclei over the electrons, and hence the molecular polarizability, changes too. Both types of diatomic molecule are therefore vibrationally Raman active. It follows that the information available from vibrational Raman spectra adds to that from infrared spectroscopy. 

The formulae work surprisingly well when tested against a myriad of examples. A self-consistent set of effective exponents n and bond orders for the / -block is shown in Table 9. Readers are urged to verify the numbers against the large volume of data on heteronuclear diatomic molecules [7], some of which are collated in Table 10. The reported = 96kJmol for AsSe appears suspect and has been ignored. 

The symmetry number of any homonuclear diatomic molecule equals 2, corresponding to the result that only half of the conceivable values of J can occur. The symmetry number of a heteronuclear diatomic molecule equals unity, as does that of some polyatomic molecules, so that all values of the rotational quantum numbers can occur. The... 

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. 

The contents of Part 1 is based on such premises. Using mostly 2x2 Hiickel secular equations, Chapter 2 introduces a model of bonding in homonuclear and heteronuclear diatomics, multiple and delocalized bonds in hydrocarbons, and the stereochemistry of chemical bonds in polyatomic molecules in a word, a model of the strong first-order interactions originating in the chemical bond. Hybridization effects and their importance in determining shape and charge distribution in first-row hydrides (CH4, HF, H20 and NH3) are examined in some detail in Section 2.7. 

We have restricted all of this to homonuclear diatomic molecules. These are obviously a very small subset of the possible diatomic molecules. It is time to move on to heteronuclear molecules. We already know what needs to be considered. Let s write some configurations first, then look at the MOs in detail. 

While molecules may be monoatomic (such as the inert gases helium, neon, or krypton), most molecules are diatomic, triatomic, or polyatomic, consisting of two or more atoms (some molecules may be a collection of thousands of atoms). A diatomic molecule may be homonuclear (e.g., O2 or N2) or heteronuclear (e.g., CO or NO). Similarly, a triatomic molecule may be homonuclear (e.g., O3) or heteronuclear (e.g., HCN). 

In this section we consider applications of relativistic quantum methods to calculations of properties of molecules containing heavy atoms. In recent years a number of authors have made relativistic calculations of the electronic and spectroscopic properties of a number of molecules using the methods outlined in the earlier section. There are excellent reviews on applications of relativistic calculations to a number of molecules "While we review some of these calculations for completeness, additional details on these calculations can be found in these reviews. In the present chapter we review more recent developments in this area. We will divide molecules into several categories and discuss the calculations in each category. Sections III.A and III.B consider homonuclear and heteronuclear diatomics, respectively, while Section III.C... 

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