Configuration spaces, reducing size

One approach to a complete solution of the Pauling-Wheland resonance-theoretic model is to treat it as a quantum-chemical configuration-interaction problem, now defined on a space of reduced size (corresponding only to those VB structures which are Kekule structures). However this space still has a size that often increases exponentially with the size of G. Thence one (ultimately) wishes further simplifications in dealing with the Hamiltonian and overlap matrixes H and S. 

Another means to reduce the scale of the problem is to shrink the size of the CAS calculation, but to allow a limited number of excitations from/to orbitals outside of the CAS space. This secondary space is called a restricted active space (RAS), and usually the excitation level is limited to one or two electrons. Thus, while all possible configurations of electrons in the CAS space are permitted, only a limited number of RAS configurations is possible. Remaining occupied and virtual orbitals, if any, are restricted to occupation numbers of exactly two and zero, respectively. 

Van Zele and Diener 1990 To investigate the effectiveness of water sprays in reducing hazards from HF releases. Many key variables were studied to enhance HF removal efficiency. Water-to-HF ratio is key. Upflow water sprays are more efficient than downflow sprays. Removal efficiency depends on spray nozzle configuration, nozzle size, spray pattern, spacing, etc. 

In compounds containing heavy main group elements, electron correlation depends on the particular spin-orbit component. The jj coupled 6p j2 and 6/73/2 orbitals of thallium, for example, exhibit very different radial amplitudes (Figure 13). As a consequence, electron correlation in the p shell, which has been computed at the spin-free level, is not transferable to the spin-orbit coupled case. This feature is named spin-polarization. It is best recovered in spin-orbit Cl procedures where electron correlation and spin-orbit interaction can be treated on the same footing—in principle at least. As illustrated below, complications arise when configuration selection is necessary to reduce the size of the Cl space. The relativistic contraction of the thallium 6s orbital, on the other hand, is mainly covered by scalar relativistic effects. 

Unfortunately, even with an incomplete one-electron basis, a full Cl is computationally intractable for any but the smallest systems, due to the vast number of. V-electron basis functions required (the size of the Cl space is discussed in section 2.4.1). The Cl space must be reduced, hopefully in such a way that the approximate Cl wavefunction and energy are as close as possible to the exact values. By far the most common approximation is to begin with the Hartree-Fock procedure, which determines the best single-configuration approximation to the wavefunction that can be formed from a given basis set of one-electron orbitals (usually atom centered and hence called atomic orbitals, or AOs). This yields a set of molecular orbitals (MOs) which are linear combinations of the AOs ... 

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