SCF components

Extrapolation of the SCF component of TAE from the small , medium , and large basis sets (Wl) or medium , large , and extra-large basis sets (W2), by means of either the geometric... 

We should note that inner polarization is strictly an SCF-level effect while, for instance, switching from an A VDZ to an A,VDZ+2d basis set affects the computed atomization energy of SO3 by as much as 40 kcal/mol ( ), almost all of this effect is seen in the SCF component of the TAE [28], In fact, we have recently found [29] that the effect persists if the (1, v, 2s, 2p) orbitals on the second-row atom are all replaced by a pseudopotential. What is really getting polarized here is the inner part of the valence orbitals, which requires polarizations functions that are much tighter (higher-exponent) than those required for the outer part of the valence orbital. The fact that these inner polarization functions are in the same exponent range as the d and / functions required for correlation out of the (2s, 2p) orbitals is merely coincidental the inner polarization effect has nothing to do with correlation, let alone with inner-shell correlation. 

The valence correlation component of TAE is the only one that can rival the SCF component in importance. As is well known by now (and is a logical consequence of the structure of the exact nonrelativistic Bom-Oppenheimer Hamiltonian on one hand, and the use of a Hartree-Fock reference wavefunction on the other hand), molecular correlation energies tend to be dominated by double excitations and disconnected products thereof. Single excitation energies become important only in systems with appreciable nondynamical correlation. Nonetheless, since the number of single-excitation amplitudes is so small compared to the double-excitation amplitudes, there is no point in treating them separately. 

One pragmatic criterion which we have found to be very useful is the percentage of the TAE that gets recovered at the SCF level. For systems that are wholly dominated by dynamical correlation, like CH4 and H2, this proportion exceeds 80 %, while it drops to 50 % for the N2 molecule, 02 is only barely bound at the SCF level, and F2 is even metastable. In the W1 /W2 validation paper [26], we invariably found that large deviations from what appeared to be reliable experimental data tend to be associated with strong nondynamical correlation, and a small SCF component of TAE (e.g. 27 % for NO2, 32 %for F2O, and 15 % for CIO). 

Secondly, let us consider the gaps bridged by the extrapolations. For the SCF component, that gap is a very reasonable 0.3 kcal/mol (0.03 %), but for the CCSD valence correlation component this rises to 5 kcal/mol (1.7 %) while for the connected triple excitations contribution it amounts to 1 kcal/mol (3.7 % - note however that a smaller basis set is being used than for CCSD). It is clear that the extrapolations are indispensable to obtain even a useful result, let alone an accurate one, even with such large basis sets. 

As for the difference of about 0.4 kcal/mol between the old-style and new-style SCF extrapolations in Wlh and W1 theories, comparison with the W2h SCF limits clearly suggests the new-style extrapolation to be the more reliable one. (The two extrapolations yield basically the same result in W2h.) This should not be seen as an indication that the Eoo + A/L5 formula is somehow better founded theoretically, but rather as an example of why reliance on (aug-)cc-pVDZ data should be avoided if at all possible. Users who prefer the geometric extrapolation for the SCF component could consider carrying out a direct SCF calculation in the extra large (i.e. V5Z) basis set and applying the Eoo + A/BL extrapolation to the medium , large , and extra large SCF data. 

For a supercritical fluid (SCF) component, the pure component parameters were obtained by fitting P-v data on isotherms (300-380K). Preliminary data for these substances suggest that although the computed v is a weak function of temperature, exl is a constant within regression error. 

Mixtures containing a cosolvent SCF (component l)-solute (usually solid) (2)-cosolvent (usually a subcritical liquid) (3). 

Type II (Solid-Fluid) System. In type II systems (when the solid and the SCF component are very dissimilar in molecular size, structure, and polarity), the S-L-V line is no longer continuous, and the critical (L = V) mixture curve also is not continuous. The branch of the three-phase S-L-V line starting with the triple point of the solid solute does not bend as much toward lower temperature with increasing pressure as it does in the case of type I system. This is because the SCF component is not very soluble in the heavy molten solute. The S-L-V line rises sharply with pressure and intersects the upper branch of the critical mixture (L = V) curve at the upper critical end point (LfCEP), and the lower temperature branch of the S-L-V line intersects the critical mixture curve at the lower critical end point (LCEP). Between the two branches of the S-L-V line there exists S-V equilibrium only (13). 

Type II Ternary (Liquid-Liquid-Fluid). Type II ternary phase behavior is characterized by the appearance within the P-x prism of the L-L-V region (13), which does not extend to the sides of the prism, each side depicting the P-x behavior of a constituent binary, as schematically shown in Figure 5c. At pressures below the critical pressure of the SCF component, two liquid phases appear along with an L-L-V region and expand considerably with increasing pressure. At pressures above the mixture critical pressure of the SCF component and one liquid component, the L-L-V region disappears and the phase behavior becomes identical with that for a type I ternary system. 

Type I P-T trace. This S-L-V line has a negative slope of P vs T. This type occurs when the SCF component has high solubility in the molten solute. 

Type II P-T trace. The SCF component is slightly soluble in the molten solute. As a result, the melting point is increased owing to an increase in the hydrostatic pressure. 

Type III P-T trace. There is a minimum temperature due to two competing opposite effects of increasing solubility of the SCF component in the molten solute and also increasing melting point with increasing hydrostatic pressure. 

Figure 1 Angular variation of components of the two-body interaction energy in (HF)3 in a planar Cii, configuration. SCF components are labeled as follows ES = electrostatic, EX = exchange, def = deformation energy (AE - - ES - EX). The dispersion energy 6cjisp ° computed by perturbation theory is denoted disp. The curve representing the complete two-body interaction through third-order Mpller-Plesset perturbation theory is labeled as full. All terms have been computed in the dimer-centered basis set. (Data taken from ref. 120.)...

Commercial plants for soKd extraction with SCFs have so far been used mainly in the food and pharmaceutical industry and employ solely carbon dioxide as the SCF component The most important processes among them are described below. SCFs have also been used as solvents to separate liquid mixtures. One example is the Residuum Oil Supercritical Extraction (ROSE) process for extracting residual petroleum reservoirs with sc butane and/or pentane [2, 3]. 

Obtained from W1-F12 theory, unless otherwise indicated Percentages of the valence CCSD(T)/CBS atomization eneigy accounted for by the SCF component... 

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