The SCF Case

Going one step further, one may analyse the case of an SCF (i.e. singleconfiguration) dimer calculation. The zeroth-order wavefunction equivalent to a single configuration and hence is a valid first step to consider before going on to the converged dimer SCF wavefunction. Substituting it in (7) one now finds (with -I- Eg = °) 

From the previous discussion it follows that at the SCF level AE is a reasonable tool for partitioning SCF interaction energies obtained from Eq. (6) into terms which correspond to those obtained in the perturbation approach. In the usual partitioning schemes , A itself is partitioned according to 

In the form derived here it will be contaminated with the basis-set superposition error (BSSE) (cf. Section V). Moreover, since dispersion energy is a correlation effect, A will not contain 

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We consider here only the SCF case where the off diagonal < i j > factors vanish. In addition, we assume that the orbitals satisfy the usual symmetry constraint i.e. that they are pure s, p, d. .. functions (RHF approach). On the other hand, no spin constraint is assumed. Then the eq.(lO) is most conveniently written as ... 

The maximum of the radial probability distribution occurs for a higher r value in the SCF case, due to the inclusion of the (averaged) electronic repulsion. 

Returning to the SCF case, we note that the A term in b can also be made small (i.e. els )) by using the full dimer basis (Xa Xb) calculating the monomer SCF wavefunctions, i.e. full CP This leads to a different b, and a different AE - ... 

In this chapter the first of these three points is addressed. However, by way of general introduction to the use of molecular symmetry, it is interesting to consider the SCF case in qualitative terms. 

The basic self-consistent field (SCF) procedure, i.e., repeated diagonalization of the Fock matrix [26], can be viewed, if sufficiently converged, as local optimization with a fixed, approximate Hessian, i.e., as simple relaxation. To show this, let us consider the closed-shell case and restrict ourselves to real orbitals. The SCF orbital coefficients are not the... 

All of the CSFs in the SCF (in which case only a single CSF is included) or MCSCF wavefunction that was used to generate the molecular orbitals (jii. This set of CSFs are referred to as spanning the reference space of the subsequent CI calculation, and the particular combination of these CSFs used in this orbital optimization (i.e., the SCF or MCSCF wavefunction) is called the reference function. 

Adsorption and Desorption Adsorbents may be used to recover solutes from supercritical fluid extracts for example, activated carbon and polymeric sorbents may be used to recover caffeine from CO9. This approach may be used to improve the selectivity of a supercritical fluid extraction process. SCF extraction may be used to regenerate adsorbents such as activated carbon and to remove contaminants from soil. In many cases the chemisorption is sufficiently strong that regeneration with CO9 is limited, even if the pure solute is quite soluble in CO9. In some cases a cosolvent can be added to the SCF to displace the sorbate from the sorbent. Another approach is to use water at elevated or even supercritical temperatures to facilitate desorption. Many of the principles for desorption are also relevant to extraction of substances from other substrates such as natural products and polymers. 

As a final note, be aware that Hartree-Fock calculations performed with small basis sets are many times more prone to finding unstable SCF solutions than are larger calculations. Sometimes this is a result of spin contamination in other cases, the neglect of electron correlation is at the root. The same molecular system may or may not lead to an instability when it is modeled with a larger basis set or a more accurate method such as Density Functional Theory. Nevertheless, wavefunctions should still be checked for stability with the SCF=Stable option. ... 

For conjugated radicals, a contribution to AH° coming from a electrons can be treated as constant within the reaction series. Under this approximation, it is sufficient to consider only the n-electron energies. In general, the SCF values should be preferred, but it appears that a reasonable picture can be obtained in many cases even with HMO data. 

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