Diatomic molecular orbitals

FIGURE 5-12 Correlation Diagram for Homonuclear Diatomic Molecular Orbitals. 

Concepts such as a and n bonds, and bonding and antibonding orbitals, are derived from the consideration of diatomic molecular orbitals. The ideas of directional bonds originate in the hybridization of atomic orbitals to form orbitals with the optimal spatial properties for bonding. More generally, the use of symmetry, molecular or local, helps us to classify orbitals into various bonding types. 

Diatomic molecular orbitals which are either symmetric or antisymmetric with respect to rotation around the bond-axis are designated as o and n. Alternatively, these orbitals have, respectively, 0 and 1 nodal planes (i.e. planes on which the orbital wave-function is zero at all points) that pass through the atomic nuclei and include the bond axis. There are two sets of degenerate Jt-type molecular orbitals. With the z-axis as the bond axis, these orbitals are labelled here as either and Tiy or 71 and n, and have, respectively, the jcz and yz planes as nodal planes. 

It seems now that both Samuel and Wheland held the widespread opinion that valence-bond structures for diamagnetic molecules must only have electron-pair bonds. Samuel and Wheland had attempted to transform the molecular orbital configurations for N2 and NO so that they would obtain electron-pair bonds for N2O. But neither worker used the correct procedure to obtain valence-bond stractures from diatomic molecular orbital configurations with one or more singly-occupied anti-bonding molecular orbitals. The technique that should be used was developed by Linnett in 1956 , and then by Green and Liimett in 1960 °, and it has formed the primary Pauling 3-electron bond basis for the increased-valence theory we use in this book. When this theory is applied to the excited Nj and NO... 

Highest occupied molecular orbital Intermediate neglect of differential overlap Linear combination of atomic orbitals Local density approximation Local spin density functional theory Lowest unoccupied molecular orbital Many-body perturbation theory Modified INDO version 3 Modified neglect of diatomic overlap Molecular orbital Moller-Plesset... 

The molecular orbital (MO) approach to the electronic structure of diatomic, and also polyatomic, molecules is not the only one which is used but it lends itself to a fairly qualitative description, which we require here. 

Figure 7.14 Molecular orbital energy level diagram for first-row homonuclear diatomic molecules. The 2p, 2py, 2p atomic orbitals are degenerate in an atom and have been separated for convenience. (In O2 and F2 the order of

To derive the states arising from a molecular orbital configuration in a diatomic molecule see Sections 7.2.2 and 7.2.4. There are two states, and 11 /2, arising from this configuration and is the lower in energy and, therefore, the ground state. 

Unlike the stable molecule N2O, the sulfur analogue N2S decomposes above 160 K. In the vapour phase N2S has been detected by high-resolution mass spectrometry. The IR spectrum is dominated by a very strong band at 2040 cm [v(NN)]. The first ionization potential has been determined by photoelectron spectroscopy to be 10.6 eV. " These data indicate that N2S resembles diazomethane, CH2N2, rather than N2O. It decomposes to give N2 and diatomic sulfur, S2, and, hence, elemental sulfur, rather than monoatomic sulfur. Ab initio molecular orbital calculations of bond lengths and bond energies for linear N2S indicate that the resonance structure N =N -S is dominant. 

Unlike reactive diatomic chalcogen-nitrogen species NE (E = S, Se) (Section 5.2.1), the prototypical chalcogenonitrosyls HNE (E = S, Se) have not been characterized spectroscopically, although HNS has been trapped as a bridging ligand in the complex (HNS)Fc2(CO)6 (Section 7.4). Ab initio molecular orbital calculations at the self-consistent field level, with inclusion of electron correlation, reveal that HNS is ca. 23 kcal mof more stable than the isomer NSH. There is no low-lying barrier that would allow thermal isomerization of HNS to occur in preference to dissociation into H -1- NS. The most common form of HNS is the cyclic tetramer (HNS)4 (Section 6.2.1). 

Figure 17.2 Schematic molecular orbital energy diagram for diatomic halogen molecules. (For F2 the order of the upper and 7T bonding MOs is inverted.).

To illustrate molecular orbital theory, we apply it to the diatomic molecules of the elements in the first two periods of the periodic table. 

Among the diatomic molecules of the second period elements are three familiar ones, N2,02, and F2. The molecules Li2, B2, and C2 are less common but have been observed and studied in the gas phase. In contrast, the molecules Be2 and Ne2 are either highly unstable or nonexistent. Let us see what molecular orbital theory predicts about the structure and stability of these molecules. We start by considering how the atomic orbitals containing the valence electrons (2s and 2p) are used to form molecular orbitals. 

Hurley, A. C., Proc. Roy. Soc. [London) A216, 424, The molecular orbital theory of chemical valency. XIII. Orbital wave functions for excited states of a homonuclear diatomic molecule."... 

Wallis, R. F., and Hulburt, H. M., J. Chem. Phys. 22, 1774, "Approximation of molecular orbitals in diatomic molecules by diatomic orbitals."... 

The se the orie s are inevitablj based upem analyse s of the interactions and transformations of molecular orbitals, and consequently the accurate construction and re presentation of molecular orbitals has become essential, furthermore, although the forms of molecular orbitals in diatomics and of delocalized tt orbitals in conjugated systems are familiar, a general, non-computational method for determining the qualitative nature of or and t orbitals in arbitrary molecules has been lacking. 

In the molecular orbital description of homonuclear diatomic molecules, we first build all possible molecular orbitals from the available valence-shell atomic orbitals. Then we accommodate the valence electrons in molecular orbitals by using the same procedure we used in the building-up principle for atoms (Section 1.13). That is,... 

We shall illustrate these rules first with H2 and then with other diatomic molecules. The same principles apply to polyatomic molecules, but their molecular orbitals are more complicated and their energies are harder to predict. Mathematical software for calculating the molecular orbitals and their energies is now widely available, and we shall show some of the results that it provides. 

FIGURE 3.31 Atypical molecular orbital energy-level diagram for the homonuclear diatomic molecules Li2 through N2. Each box represents one molecular orbital and can accommodate up to two electrons. 

The ground-state electron configurations of diatomic molecules are deduced by forming molecular orbitals from all the valence-sbell atomic orbitals of the two atoms and adding the valence electrons to the molecular orbitals in order of increasing energy, in accord ivith the building-up principle. 

FIGURE 3.33 A typical d molecular orbital energy-level diagram for a heteronuclear diatomic molecule AB the relative contributions of the atomic orbitals to the molecular orbitals are represented by the relative sizes of the spheres and the horizontal position of the boxes. In this case, A is the more electronegative of the two elements. 

The molecular orbital energy-level diagrams of heteronuclear diatomic molecules are much harder to predict qualitatitvely and we have to calculate each one explicitly because the atomic orbitals contribute differently to each one. Figure 3.35 shows the calculated scheme typically found for CO and NO. We can use this diagram to state the electron configuration by using the same procedure as for homonuclear diatomic molecules. 

FIGURE 3.35 The molecular orbital schemes typical of those calculated for a diatomic oxide molecule, EO (where E = C for CO and E = N for NO). Note that the D-orbitals are formed from mixtures of s- and p/-orbitals on both atoms accordingly, we label them simply Id,... 

The molecular orbital theory of polyatomic molecules follows the same principles as those outlined for diatomic molecules, but the molecular orbitals spread over all the atoms in the molecule. An electron pair in a bonding orbital helps to bind together the whole molecule, not just an individual pair of atoms. The energies of molecular orbitals in polyatomic molecules can be studied experimentally by using ultraviolet and visible spectroscopy (see Major Technique 2, following this chapter). 

Construct and interpret a molecular orbital energy-level diagram for a homonuclear diatomic species (Sections 3.9 and 3.10). 

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