Homonuclear diatomic, electronic structure

Ishiguro, E., Kayama, K., Kotani, M., and Mizuno, Y., J. Phys. Soc. Japan 12, 1355, Electronic structure of simple homonuclear diatomic molecules. II. Lithium molecule. ... 

To describe the band structure of metals, we use the approach employed above to describe the bonding in molecules. First, we consider a chain of two atoms. The result is the same as that obtained for a homonuclear diatomic molecule we find two energy levels, the lower one bonding and the upper one antibonding. Upon adding additional atoms, we obtain an additional energy level per added electron, until a continuous band arises (Fig. 6.9). To describe the electron band of a metal in a... 

MO wave functions in the above form give equal importance to covalent and ionic structures, which is unrealistic in homonuclear diatomic molecules like H2. This should be contrasted with (/>Vb> which in its simple form neglects the ionic contributions. Both and i//MO are inadequate in their simplest forms while in the VB theory the electron correlation is overemphasized, simple MO theory totally neglects it giving equal importance to covalent and ionic structures. Therefore neither of them is able to predict binding energies closer to experiment. The MO theory could be... 

Usually the electronic structure of diatomic molecules is discussed in terms of the canonical molecular orbitals. In the case of homonuclear diatomics formed from atoms of the second period, these are the symmetry orbitals 1 og, 1 ou, 2ag,... 

Recall that homonuclear diatomic molecules have no vibration-rotation or pure-rotation spectra due to the vanishing of the permanent electric dipole moment. For electronic transitions, the transition-moment integral (7.4) does not involve the dipole moment d hence electric-dipole electronic transitions are allowed for homonuclear diatomic molecules, subject to the above selection rules, of course. [The electric dipole moment d is given by (1.289), and should be distinguished from the electric dipole-moment operator d, which is given by (1.286).] Analysis of the vibrational and rotational structure of an electronic transition in a homonuclear diatomic molecule allows the determination of the vibrational and rotational constants of the electronic states involved, which is information that cannot be provided by IR or microwave spectroscopy. (Raman spectroscopy can also furnish information on the constants of the ground electronic state of a homonuclear diatomic molecule.)... 

Table 3.3.2. Electronic configurations and structural parameters of homonuclear diatomic molecules of the second period...

Fig. 39 a, b. Schematic pictures of one-electron level structures for a homonuclear diatomic molecule (for further explanations see text)... 

Among the homonuclear diatomic molecules, only N2 and the very small H2 have shorter bond lengths than O2, 1.21 A. Recall that VB theory predicts that O2 is diamagnetic. Experiments show, however, that it is paramagnetic, with two unpaired electrons. MO theory predicts a structure consistent with this observation. For O2, the [Pg.360]

For this Is electron angular momentum plays no part in the reconstruction. As a matter of fact, all homonuclear diatomic molecules probably have such spherical structures, assuming angular momentum vectors to cancel. 

There are many other indications that the electrostatic effects of non-spherical features of the charge distribution, such as lone pairs and n electrons, can be important in determining molecular crystal structures. At the extreme of homonuclear diatomics (X2), the electrostatic potential outside the molecule arises from the non-spherical distribution of the valence electrons. Just as there are considerable variations in the bonding orbitals in the diatomics, there are also considerable variations in the lowest temperature ordered crystal structure. 

Let us consider an element in the first short Period having 2s and 2p orbitals in its valence shell. When two such atoms are combined into a homonuclear diatomic molecule, the two sets of atomic orbitals may combine into various MO s. Before we can specify the electronic structures of the diatomic molecules of these elements, we must know the relative energies of these MO s. 

The first application of the MCP in SOC calculations dates back to 1996 [61]. In this study, Krause and Klobukowski found the agreement between the MCP and AE SOC results to be within 1% for diatomic hydrides of P, As, and Sb. Later, a method to compute both one- and two-electron SOC using MCP was proposed [177] and applied to atoms, hydrides and homonuclear diatomic cations of P, As, and Sb. The agreement with results from AE calculations was within 3%. More recently, MCP was applied in SOC calculations of ions of S2 [178] and the hydrides of C, Si, Ge, and Sn [179], and good agreement with experimental values was found for molecules containing light atoms, with the noticeable deviation for SnH. The error for SnH can be attributed to the truncation of the MCP basis set and the consequent distortion of the inner nodal structure of the valence orbitals [97]. AU the... 

The molecular orbital description of period 2 diatomic molecules leads to bond orders in accord with the Lewis structures of these molecules. Further, the model predicts correctly that O2 should exhibit param pietism, which leads to attraction of a molecule into a magnetic field due to the influence of unpaired electrons. Molecules in which all the electrons are paired exhibit diamagnetism, which leads to weak repulsion from a magnetic field. The molecular orbitals of heteronuclear diatomic molecules are often closely rdated to those of homonuclear diatomic molecules. 

Fig. 3.5 displays Mulliken s [2] generalized orbital correlation diagram for homonuclear diatomic molecules, which has been of seminal importance for the elucidation of the electronic structure of molecules. Only the atomic levels n = 1,2 have been included on its right on the left, the orbitals of the united atom have been extended sufRciently that all of the necessary correlation lines can be drawn. The energetic spacing of the AOs is purely schematic, their order on the left being that common to silicon and sulfur, the united atoms corresponding to N2 and O2. The abcissa, is - of course - quite non-linear. 

It would be instructive to illustrate the use of these rules. As a first example let us consider the core-hole excited states of homonuclear diatomic molecules. When one electron is removed from the core orbital, the original Da,h symmetry of the wavefunction is lowered to Coov This situation is depicted in the figure below where only the Is core electrons are represented. According to the rules in table 2, the Dooh group can be decomposed into two C v components related by a Ci or Cs operation. The two C >v structures (a) and (b) below ... 

Franck-Condon factors. The most common angular momentum coupling cases are discussed, and rotational fine structure in electronic transitions (cf. Fig. 4.3) is rationalized for heteronuclear and homonuclear diatomics using Herzberg diagrams. 

Molecular symmetry offered a relevant diversion from our major task at hand, but the task hasn t disappeared. We still need to solve, to within reasonable approximations, the molecular Hamiltonian. Now we return to that challenge, but this chapter gives away much of the philosophy behind our approach. We will simplify the electronic and vibrational and rotational degrees of freedom by first examining in each case the highest symmetry molecules—homonuclear diatomics—and will only then (and rather reluctantly) move on to the more ornery cases of asymmetric systems. Aside from its utilitarian value, group theory should be appreciated for its ability to elicit some of the native beauty of molecular structure, which is reason enough to study chemistry. 

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