Diatomic molecules molecular orbital models

The molecular orbital model as a linear combination of atomic orbitals introduced in Chapter 4 was extended in Chapter 6 to diatomic molecules and in Chapter 7 to small polyatomic molecules where advantage was taken of symmetry considerations. At the end of Chapter 7, a brief outline was presented of how to proceed quantitatively to apply the theory to any molecule, based on the variational principle and the solution of a secular determinant. In Chapter 9, this basic procedure was applied to molecules whose geometries allow their classification as conjugated tt systems. We now proceed to three additional types of systems, briefly developing firm qualitative or semiquantitative conclusions, once more strongly related to geometric considerations. They are the recently discovered spheroidal carbon cluster molecule, Cgo (ref. 137), the octahedral complexes of transition metals, and the broad class of metals and semi-metals. 

In this chapter we shall use lithium hydride, LiH, to discuss the application of the molecular orbital model to a heteronuclear diatomic molecule, and begin by outlining a very simple computational procedure that yields an approximate description of the molecular orbital containing the two valence electrons. We then go on to outline the application of Hartree-Fock (HF) calculations based on a wavefuntion for both the two valence and the two inner-shell electrons. The wavefunction obtained by such calculations indicate that the bonding molecular orbital must be written as a linear combination of the H I5 with both 2s and 2pa atomic orbitals on the Li atom. 

Figure 3.6 shows the LCAO method for generating molecular orbitals of diatomic molecules such as H2. In real molecules, the atomic orbitals of elemental carbon are not really transformed into the molecular orbitals found in methane (CH4). Figure 3.6 represents a mathematical model that mixes atomic orbitals to predict molecular orbitals. Molecular orbitals exist in real molecules and the LCAO model attempts to use known atomic orbitals for atoms to predict the orbitals in the molecule. Molecular orbitals and atomic orbitals are very different in shape and energy, so it is not surprising that the model used for diatomic hydrogen fails for molecules containing other than s-orbitals. 

Using the molecular orbital model for a diatomic molecule, explain the different bond lengths for the ions of oxygen. Also state which ion is diamagnetic. 

Molecular orbital theory is more complex than the hybrid orbital approach, but the foundations of the model are readily accessible. Though complex, molecular orbital theory opens the door to many fascinating aspects of modem chemistry. In this section, we introduce the molecular orbital approach through diatomic molecules. 

Diatomic Molecules.—We shall begin by discussing diatomic molecules, which bear some relation to the models discussed in the previous section. To begin With, the hydrogen molecule has two electrons which both occupy the lowest molecular orbital whose LCAO form is... 

V.B). Experimental distributions obtained for the Ne+-N2 system (Fig. 54) were shown to be intermediate between those predicted by application of the Franck-Condon principle and those predicted by such a statistical model. Finally, it has been suggested by Tomcho and Haugh411 that the molecular orbitals of the transient triatomic system should be considered in predicting vibrational distributions of products from atomic-ion-diatomic-molecule reactions. Calculations based on this approach are in progress for the (Ar-N2)+ system.417... 

The dimer species, M2, was described by Huster (21) as a simple dissolved diatomic molecule. Such a species would be very unstable with respect to the ammoniated species, M + and e and may be ruled out by thermochemical data. The expanded metal dimer model of Becker, Lindquist, and Alder, in which two ammoniated metal ions are held together by a pair of electrons in a molecular orbital located principally between the two ions, is just as difficult to reconcile with optical, volumetric, and NMR data as the expanded metal monomer. In order to account for the similar absorption spectra of e, M, M2 (and any other species such as M or M4 that might exist at moderate concentrations of metal), Gold, Jolly, and Pitzer (16) assumed that species such as M and M2 consist of ionic aggregates in which the ammoniated electrons remain essentially unchanged from their state at infinite dilution. 

If we wish to understand the conditions under which a diatomic molecule such as H2, N2, or CO dissociates on a surface, we need to take two orbitals of the molecule into account - the highest occupied and the lowest unoccupied molecular orbital (the HOMO and LUMO of the so-called frontier orbital concept). Let us take a simple case to start with the molecule A2 with occupied bonding level a and unoccupied antibonding level a. We use jellium as the substrate metal and discuss the chemisorption of A2 in the resonant level model. What happens is that the two levels broaden due to the rather weak interaction with the free electron cloud of the metal. 

We have described the orbital approaches to the electron configurations of diatomic molecules, both the molecular orbital and the united atom models. We now turn to the question of what types of molecular states result from given states of the separate atoms. If Russell Saunders coupling is valid for the separate atoms, the correlation rules, due to Wigner and Witmer [16] provide a valid and complete summary of the molecular states. This information is extremely important for an understanding of both the formation and dissociation of diatomic molecules. 

As an alternative to ab initio methods, the semi-empirical quantum-chemical methods are fast and applicable for the calculation of molecular descriptors of long series of structurally complex and large molecules. Most of these methods have been developed within the mathematical framework of the molecular orbital theory (SCF MO), but use a number of simplifications and approximations in the computational procedure that reduce dramatically the computer time [6]. The most popular semi-empirical methods are Austin Model 1 (AMI) [7] and Parametric Model 3 (PM3) [8]. The results produced by different semi-empirical methods are generally not comparable, but they often do reproduce similar trends. For example, the electronic net charges calculated by the AMI, MNDO (modified neglect of diatomic overlap), and INDO (intermediate neglect of diatomic overlap) methods were found to be quite different in their absolute values, but were consistent in their trends. Intermediate between the ab initio and semi-empirical methods in terms of the demand in computational resources are algorithms based on density functional theory (DFT) [9]. 

Homonuclear diatomic moiecuies are those composed of two identical atoms. In addition to H2 from Period 1, you re also familiar with several from Period 2—N2, O2, and F2—as the elemental forms under standard conditions. Others in Period 2—L12, Be2, B2, C2, and Ne2—are observed, if at all, only in high-temperature gas-phase experiments. Molecular orbital descriptions of these species provide some interesting tests of the model. Let s look first at the molecules from the block. Groups 1 A(l) and 2A(2), and then at those from the p block. Groups 3A(13) through 8A(18). 

The molecular orbital energy-level diagram represented in Fig. 9.35 predicts that the B2 molecule will be diamagnetic, since the MOs contain only paired electrons. Flowever, experiments show that B2 is actually paramagnetic with two unpaired electrons. Why does the model yield the wrong prediction This is yet another illustration of how models are developed and used. In general, we try to use the simplest possible model that accounts for all the important observations. In this case, although the simplest model successfully describes the diatomic molecules up to B2, it certainly is suspect if it cannot describe the B2 molecule correctly. This means we must either discard the model or find a way to modify it. 

The P2 molecule contains phosphorus atoms from the third row of the periodic table. We will assume that the diatomic molecules of the Period 3 elements can be treated In a way very similar to that which we have used so far. Thus we will draw the MO diagram for P2 analogous to that for N2. The only change will be that the molecular orbitals will be formed from 35 and 2p atomic orbitals. The P2 model has 10 valence electrons (5 from each phosphorus atom). The resulting molecular orbital diagram is... 

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 paramagnetism, 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. 

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