RHF/UHF instabilities

Ozone is a singlet, but it has an unusual electronic structure and is thus often difficult to model. An RHF Sfable=Opt calculation finds an RHF— UHF instability, and the... 

The optimum value of c is determined by the variational principle. If c = 1, the UHF wave function is identical to RHF. This will normally be the case near the equilibrium distance. As the bond is stretched, the UHF wave function allows each of the electrons to localize on a nucleus c goes towards 0. The point where the RHF and UHF descriptions start to differ is often referred to as the RHF/UHF instability point. This is an example of symmetry breaking, as discussed in Section 3.8.3. The UHF wave function correctly dissociates into two hydrogen atoms, however, the symmetry breaking of the MOs has two other, closely connected, consequences introduction of electron correlation and spin contamination. To illustrate these concepts, we need to look at the 4 o UHF determinant, and the six RHF determinants in eqs. (4.15) and (4.16) in more detail. We will again ignore all normalization constants. 

The optimum value ot c is deiermined by the variational principle. If c — 1, the UHE— wave function is identical to RHF. This will normally be the case near the equUibrium distance. As the bond is stretched, the UHF wave function allows each of the electrons to localize on a nucleus c goes towards 0. The point where the RHF and UHF descriptions start to differ is often referred to as the RHF/UHF instability point. This is... 

The RHF/UHF instability point with this basis occurs when the bond is stretched by 0.46 A. Figure 11.4 shows the behaviour of the energy curves in more detail in tfais ... 

Figure 2 shows the behavior of for various levels of theory as a function of the bond length in hydrogen fluoride. For SCF, MPn, Cl, and CCD methods, S rises rapidly as the bond is stretched beyond the RHF -+ UHF instability (near 1.3 A). For QCISD and CCSD, 5 increases more slowly, indicating they are better able to handle modest levels of... 

Note that multiconfigurational coordination bonding raises a number of difficult technical and computational issues, as discussed in Sidebar 8.2. In this section, we seek to bypass technical issues as far as possible, focusing instead on qualitative aspects of coordination bonding that seem to be adequately described by the DFT-based methods employed throughout this book. However, the student is forewarned that explorations beyond the relatively simple examples described below will typically require dealing with RHF/UHF instability, spin contamination, and other issues alluded to in Sidebar 8.2.]... 

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