MO Treatment of Heteronuclear Diatomic Molecules

The treatment of heteronuclear diatomic molecules is similar to that for homonuclear diatomic molecules. We first consider the MO description. 

As in homonuclear diatomics, the heteronuclear diatomic MOs are approximated as linear combinations of atomic orbitals. The coefficients are found by solving the Roothaan equations (13.157). For example, a minimal-basis-set SCF calculation using Slater AOs (with nonoptimized exponents given by Slater s rules) gives for the CO 5 r, lir, and 2ir MOs at R = [B. J. Ransil, Rev. Mod. Phys., 32,245 (I960)]  

We see from Fig. 11.2 that the 2pf AO lies well below the 2sb AO. This causes the 2pap AO to contribute substantially to lower-lying MOs and the 2sb AO to contribute substantially to higher-lying MOs, as compared with what happens in N2. (This effect occurs in CO, although to a lesser extent. Note the very substantial contribution of 2sc to the 5a MO also, the 4a MO in CO has a very substantial contribution from 2paQ.) 

For a diatomic molecule AB where each atom has s and p valence-shell AOs (this excludes H and transition elements) and where the A and B valence AOs differ widely in energy, we may expect the pattern of valence MOs to be a a TT a TT tr, but it is not so easy to guess which AOs contribute to the various MOs or the bonding or antibonding character of the MOs. By feeding the valence electrons into these MOs, we can make a plausible guess as to the number of unpaired electrons and the ground term of the AB molecule (Problem 13.34). 

Diatomic hydrides are a special case, since H has only a Is valence AO. Consider HF as an example. The ground-state configurations of the atoms are Is for H and ls 2s 2p for F. We expect the filled Is and 2s F subshells to take little part in the bond- 

In general, for a heteronuclear diatomic molecule AB where the valence AOs of each atom are of s and p type and where the valence AOs of A do not differ greatly in energy from the valence AOs of B, we can expect the Fig. 13.17 pattern of 

For a diatomic molecule AB where each atom has 5 and p valence-shell AOs (this excludes H and transition elements) and where the A and B valence AOs differ widely in 

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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. 

We now use the U2 MOs developed in the last section to discuss many-electron homonuclear diatomic molecules. (Homonuclear means the two nuclei are the same heteronuclear means they are different.) If we ignore the interelectronic repulsions, the zeroth-order wave function is a Slater determinant of H -like one-electron spin-orbitals. We approximate the spatial part of the spin-orbitals by the LCAO-MOs of the last section. Treatments that go beyond this crude first approximation will be discussed later. 

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