Singlet instabilities

A second type of instability is known as a singlet instability, which... 

In OCC and BCC theories, the wave function has the form of a standard coupled-cluster wave function with vanishing singles amplitudes. However, unlike standard coupled-cluster theory, where the orbitals are determined in a separate optimization of the reference state HF), the OCC and BCC orbitals are determined simultaneously with the optimization of the cluster amplitudes, making them more suitable for the description of correlation, in a manner reminiscent of MCSCF theory. In practice, the differences between the standard coupled-cluster wave functions and the BCC and OCC wave functions are small, except in systems characterized by Hartree-Fock singlet instabilities such as the allyl radical in Section 10.10.6. In such cases, the Harlree—Fock instability makes the standard approach unsuitable - the BCC and OCC models, by contrast, suffer from no such instabilities. 

SINDO model, 84 Singles, singly excited states, 100 Singlet instability, 76 Size consistency, 117 Size extensivity, 117 Slater Determinant (SD), 58, 59, 100 Slater Type Orbitals (STO), 150 Slater-Condon rules, 104 Slow growth method, 381 Small component, in relativistic wave functions, 207... 

To illustrate the problems that may arise in connection with singlet instabilities, we consider the allyl radical C3H5, a planar molecular species of C2v symmetry. When the geometry of this system is optimized at the Hartree-Fock level with no spatial symmetry restrictions applied, a minimum of Cs symmetry is obtained - in disagreement with experiment and also with more elaborate calculations. In the following, we shall study the allyl radical at the RHF and UHF levels of theory in order to understand this behaviour [26]. The allyl radical is shown in Figure 10.4, which also illustrates the coordinates used in this study. 

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