Experimental reference data

Unfortunately, in the molecular systems the theoretical predictions for the already formidable electronic problem carmot be checked fairly against the experimental data, since the nuclear motions may play major effects. From here the need to check these methods in calculations on atomic systems, where accurate theoretical and comparable experimental reference data are already available. 

Even though the G2 neutral test set is very valuable, it is biased towards small molecules and does not cover all bonding situations that may arise for a given element. The validation of semiempirical methods has traditionally been done using larger test sets which, however, have the drawback that the experimental reference data are often less accurate than those in the G2 set. 

A variance of G3 is the G3S method [149], which replaces the additive HLC of G3 theory by a multiplicative scaling of the correlation and Hartree-Fock parts of the G3 energy. The best results of these methods give errors within 1 kcal/mol with respect to the experimental reference data. A comparison of their performances is given in Refs. 150, 151. 

The parametrization of a given implementation serves to determine optimum parameter values by calibrating against suitable reference data. The most widely used methods (see Section 21.2) adhere to the semiempirical philosophy and attempt to reproduce experiment. However, if reliable experimental reference data are not available, accurate theoretical data (e.g. from high-level ab initio calculations) are now generally considered acceptable as substitutes for experimental data. The quality of semiempirical results is strongly influenced by the effort put into the parametrization. 

What remedies do we have The brute-force device tried in pioneer days, of incorporating core- and core-valence correlation effects into pseudopotentials just by fitting to experimental reference data containing these effects, does not work since the one-electron/one-center PP ansatz is insufficient for this purpose, cf. below. Certainly more reliable is a DFT description of core contributions to correlation effects which is possible with (and actually implied in) the non-linear core corrections discussed in Section 1.4. Another device, which has shown excellent performance in the context of quantum-chemical ab initio calculations180 and has later been adapted to PP work cf. e.g. refs. 139, 181-184), is that of core-polarization potentials (CPP)... 

Originally, there have been two basic strategies for parametrization. Approximate MO methods aim at reproducing ab initio MO calculations with the same minimal basis set (MBS), whereas semiempirical MO methods attempt to reproduce experimental data. Nowadays the limitations of MBS ab initio calculations are well known and the predominant feeling is that approximate MO methods would not be useful enough in practice even if they would exactly mimic MBS ab initio calculations. Hence with the exception of PRDDO [18], current parametrizations usually adhere to the semiempirical philosophy and employ experimental reference data (or possibly, accurate high-level theoretical predictions as substitutes for experimental data see Section III.E). 

The final output file contains an evaluation in tabular form of all simulation and optimized force-field parameters, the simulated properties along with their acmal deviations from the experimental reference data at each temperature, the loss function values, and algorithm-specific information. 

The prediction quality of COSMO-RS was evaluated by experimental reference data taken from the hterature. Further, the influence of the solute solubihty on the reaction rate in a SILP catalyst system was examined for the hydrogenation of propene. 

At the times when DLVO theory was developed, the direct measurement of forces between colloidal particles and surfaces in solution was not possible, and the macroscopic observation of colloidal stability was the only experimental reference data. With increasing technological advancement, setups have been developed for the direct observation of such forces The surface force apparatus (SFA) allows for the measurements of forces between surfaces in solution [6], and with an atomic force microscope (AFM), forces on a colloidal particle can be detected [7]. It is a major success that DLVO theory predicts forces that agree nicely with the measured forces for large particle separations (more than 3-10 nm), but at the same time, it is obvious that in the regime of short particle separations, not aU effects are captured by DLVO. When the barrier for coagulation occurs at such low separations, the DLVO prediction for colloidal stability is not accurate (Fig. 2). 

Table 7.3 Averaged MUEs, MIN MAX Deviations of Anharmonic Vibrational Frequencies (cm ) Computed by Several DFT Models for Pyridine, Furan, Pyrrole, and Thiophene, and Compared to Experimental Reference Data"...

In Figure 15.7, we have plotted the normal distributions of the errors in the calculated bond angles. The main difference from the plots for bond distances in Figure 15.4 is that, for bond angles, the CCSD(T) distributions are less sharply peaked and similar to those of the MP2 model, reflecting the poorer quality of the experimental reference data for bond angles than for bond distances. 

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