Atomic orbitals heteronuclear diatomic molecules

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. 

Up to now we have been discussing the local properties of the exchange-correlation potential as a function of the spatial coordinate r. However there are also important proi rtira of the exchange-correlation potential as a function of the particle number. In fact there are close connections between the properties as a function of the particle number and the local properties of the exchange-correlation potential. For instance the bumps in the exchange-correlation potential are closely related to the discontinuity properties of the potential as a function of the orbital occupation number [38]. For heteronuclear diatomic molecules for example there are also similar connections between the bond midpoint shape of the potential and the behavior of the potential as a function of the number of electrons transferred from one atomic fragment to another when... 

This is a simple example of a heteronuclear diatomic molecule which is found in a stable molecular substance. We must first choose the basis set. The only AOs that need to be seriously considered are the hydrogen Is, fluorine 2s and fluorine 2p, written for brevity as ls(H), 2s(F) and 2p(F). The fluorine Is orbital lies very low in energy (700 eV lower than 2p) and is so compact that its overlap with orbitals on other atoms is quite negligible. The fluorine 2p level lies somewhat lower than ls(H), as indicated by the higher ionisation potential and electronegativity of F. Interaction between 2p(F) and 2s(H) is very small and can be neglected for all practical purposes. One is tempted to discard 2s(F), which lies more than 20 eV below 2p(F) the 2s-2p separation increases... 

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,... 

FIGURE 6.19 Correlation diagram for heteronuclear diatomic molecules, AB. The atomic orbitals for the more electronegative atom (B) are displaced downward because they have lower energies than those for A. The orbital filling shown is that for (boron monoxide) BO. 

The three 2p orbitals from each atom can be combined to give o bonding and antibonding orbitals and n bonding and antibonding orbitals. In heteronuclear diatomic molecules, these orbitals are simply labelled c or n and do not have subscripts. The subscripts g and u refer to behaviour under inversion through the... 

Molecular orbitals for heteronuclear diatomic molecules can be made by combining atomic orbitals of the same symmetry and of similar energy from the two atoms. 

Because the atomic orbitals combined in heteronuclear diatomic molecules are not of the same energy, the electron in the molecular orbital is not equally shared between the two atoms. 

In this section, we return to MO theory and apply it to heteronuclear diatomic molecules. In each of the orbital interaction diagrams constructed in Section 1.13 for homonuclear diatomics, the resultant MOs contained equal contributions from each atomic orbital involved. This is represented in equation 1.27 for the bonding MO in H2 by the fact that each of the wavefunctions -tpi and contributes equally to ipuOi the representations of the MOs in H2 (Figure... 

The treatment of heteronuclear diatomic molecules by LCAO-MO theory is not fundamentally different from the treatment of homonuclear diatomics, except that the MO s are not symmetric with respect to a plane perpendicular to and bisecting the intemuclear axis. The MO s are still constructed by forming linear combinations of atomic orbitals on the two atoms, but since the atoms are now different we must write them < a+ 0b> where A is not in general equal to 1. Thus these MO s will not in general represent non-polar bonding. As examples let us consider HC1, CO, and NO. 

The homonuclear diatomic molecules discussed Section 5.2 are nonpolar molecules. The electron density within the occupied molecular orbitals is evenly distributed over each atom. A discussion of heteronuclear diatomic molecules provides an introduction into how molecular orbital theory treats molecules that are polar, with an unequal distribution of the electron density in the occupied orbitals. 

Molecular orbital calculations on heteronuclear diatomic molecules, hybridization, and estimation of net atomic charges from calculated electron densities... 

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