Higher-level correction

The second, third, and fourth corrections to [MPd/b-Jl lG(d,p)] are analogous to A (- -). The zero point energy has been discussed in detail (scale factor 0.8929 see Scott and Radom, 1996), leaving only HLC, called the higher level correction, a purely empirical correction added to make up for the practical necessity of basis set and Cl truncation. In effect, thermodynamic variables are calculated by methods described immediately below and HLC is adjusted to give the best fit to a selected group of experimental results presumed to be reliable. 

Step 9. G2 theory makes a modification to the higher-level correction of G1 theory b dding 0.00114np into the final energy calculation (which we denote... 

The final correction is to add an empirical higher-level correction which is chosen to give agreement between the G1 values for hydrogen atom, hydrogen molecule and experiment. In the original G1 theory, a value of An — Bua was used. Here ria is the number of a-spin electrons, the number of 6-spin electrons, A — 4.81 x 10 h and B = 0.19 x lO"" Eh. 

A new family of methods, referred to as G3S (G3 Scaled), has been developed recently [29], where the additive higher-level correction is replaced by a multiplicative scaling of the correlation and Hartree-Fock components of the G3 energy. The scale factors have been obtained by fitting to the G2/97 test set of energies. This test set is substantially larger than that used in previous fits and can provide a reliable assessment of the use of such a scaling approach to computational thermochemistry. 

The increase in the mean absolute deviation for all three methods is primarily due to large errors in the calculated enthalpies of formation of some of the non-hydrogen species in the expanded G3/99 test set. This is similar to the results for the G3 methods based on the higher-level correction per electron pair. The G3S mean absolute deviation of 3.37 kcal/mol for the 13 non-hydrogen species in the G3-3 subset is more than twice that of 1.60 kcal/mol for the 34 non-hydrogens in the G2/97 set. Similar increases in the mean absolute deviations occur for the G3S(MP3) and G3S(MP2) theories. 

Figure 3.4 Effect of inclusion of higher level corrections on the mean absolute deviations of G3, B3LYP, and BLYP methods for the enthalpies of formation in the G3/99 test set.

Since application of a higher-level correction for electron pairs works well in the G2 and G3 methods to reduce deficiencies per electron pair,... 

G3 theory based on multiplicative scaling of the energy terms (G3S) instead of the additive higher-level correction has a mean absolute deviation of 1.08 for the G3/99 test set, an increase from 0.99 for the G2/97 test set. As in the case of G3 theory, the increase is largely due to the new non-hydrogen species in the test set. However, systems such as the highly strained P4 molecule perform poorly with the scaled methods. 

The density functional methods assessed in this study (B3LYP, BLYP, and LDA) all perform much worse for the enthalpies of formation of the larger molecules in the G3/99 set. This is due to a cumulative effect in the errors for the larger molecules in this test set. The errors are found to be approximately proportional to the number of pairs of electrons in the molecules but the methods are not improved significantly when a higher-level correction such as that used in G2 or G3 theory is added the DFT methods. Further correction schemes may be necessary to improve the performance of density functional methods for large molecules. 

A higher level correction (HLC) is added to give the total electronic... 

Variations of G3 Theory At least two variations of G3 theory have been proposed. The first does the basis set extensions at the second-order Mailer-Plesset level. This method, referred to as G3(MP2) theory,97 has an average absolute deviation from experiment of 1.30 kcal/mol for the G2/97 test set and 1.18 kcal/mol for the subset of 148 neutral enthalpies (see Table 5). This is a significant improvement over the related G2(MP2) theory. The new method provides significant savings in computational time compared to G3 theory (see Figure 2). The modification to step 4 in G3 theory is shown in Table 6, along with the new higher level correction parameters. 

Several empirical corrections are added to the resulting energies in the CBS methods to remove the systematic errors in the calculations (see Table 10). The CBS-Q method contains a two-electron correction term similar in spirit to the higher level correction used in G2 theory, a spin correction term to account for errors resulting from spin contamination in UHF wavefunctions for open-shell systems, and a correction to the sodium atom to account for core-valence correlation effects. The CBS-4 and CBS-q methods also contain a one-electron... 

Atomic spin-orbital corrections, sometimes empirical, and a higher-level correction , HLC, to (hopefully) take any remaining inadequacies into account... 

Gaussian-2 methods that correspond effectively to energy calculations at the QCISD(T)/6-311+G(3df,2p)//MP2(full)/6-31G(d) level with ZPE from HF/6-31G(d) level and higher level corrections Hartree-Fock... 

A higher level correction ( (HLC)) is added to take into account the remaining deficiencies in the energy calculations the HLC is —An — B(n — rip) where rip and are the number of )3 and a valence electrons, respectively, with > rip. The number of valence electron pairs corresponds to rip. Thus, A is the correction for pairs of valence electrons in the system and B is the correction for unpaired electrons in the system. For G2 theory, A = 4.81 mhartrees, B = 0.19 mhartrees. The parameter B was derived to give the exact energy for H atom and the parameter A was derived to give zero mean deviation for the 55 molecules in the G2-1 test set. 

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