High accuracy methods

The atomic systems in the previous examples have s, p, and/or d valence electrons. Here we discuss the energy levels of the Pr ion, which has an P configuration. The spectrum is well charax terized experimentally [60] and provides a good test for high-accuracy methods incorporating relativity and correlation. 

The emitted beam has both a specific intensity distribution profile and specific polarization properties. High-accuracy methods of computation of SR allow the calculation of the spectral flux and intensity distributions of emitted radiation in the near- and in the far-field regions.24 In Fig. 3.3(a) three distribution profiles... 

Note that these calculations of the heat of formation of methanol are not purely ab initio (quite apart from the empirical correction terms in the multistep high-accuracy methods), since they required experimental values of either the heat of atomization of graphite (atomization and formation methods) or the heat of formation of methane (formation method). The inclusion of experimental values makes the calculation of heat of formation with the aid of ab initio methods a semiempiri-cal procedure (do not confuse the term as used here with semiempirical programs... 

Both G3(MP2) and CBS-4M give reasonably satisfactory heats of formation for these quinones by the atomization method, but it must be conceded that, in general, an isodesmic approach with currently practical high-accuracy methods at least, gives more accurate heats, and especially free energies, of formation CBS-QB3 was somewhat limited in the size of molecule it could handle [191] ... 

Table 7.4 Reaction enthalpies (kJ mol-1), calculated with three functionals and two basis sets, 6-31G and 6-311++G(2df, 2p), and with three high-accuracy methods (but CBS-APNO is unable to handle Cl species). The calculated reaction enthalpies follow from the calculated 298 K product enthalpies minus the reactant enthalpies...

Useful source of information on the calculation of energy quantities heats of formation, reaction energies, bond energies, activation energies, high-accuracy methods (G2, CBS, etc.), energies of solvation. 

For the purpose of this guide high accuracy methods arc considered to be those that provide measurements closest to the true value. 

The efficient computation of molecular response properties such as optical rotation is of paramount importance, and schemes for reducing the computational effort required for high-accuracy methods such as coupled cluster theory become even more crucial for larger, chemically relevant molecules. However, algorithmic improvements must not come at the expense of the overall accuracy of the theory, and the EOM-CCl approach of Sekino and Bartlett provides a reasonable com-... 

Ideally, one would apply these high-accuracy methods as a routine for thermochemistry and kinetics studies. However, these methods can be very expensive for even a moderate system. For example, a G2(MP2) calculation on a octane molecule exceeds 100 cpu hours on a CRAY-YMP supercomputer. Petersson (1998) did extensive benchmark study and his conclusion is that most of the CBS and G2 methods are not practical for systems that have more than a half dozen non-hydrogen atoms. Table 2 shows the summary of error measurements for the G2 test set of 125 reactions. Most of these reactions involve very small gas molecules. 

Calorimetry is generally a high-accuracy method for determination of thermodynamic properties. A particular variant is the high-temperature drop calorimetry where the oxide phase is dissolved in a suitable melt and enthalpies of formation from oxides are evaluated from the thermal effect. Drop-calorimetry data (Rian 1992, Zhou and Navrotsky 1992, Lamberti et al. 1997) obtained for phases fiom the R(0)-Ba(0)-Cu(0) phase diagram are summarized in table 26. Similar, but much more scattered data were obtained in numerous early studies by various aqueous-solution calorimetry techniques for recent more precise data by the latter technique on RBa2Cu306.9 (R = Gd, Ho, Y), see Matskevich and McCallum (1999). Only a few adiabatic calorimetry studies have focused on determination of thermodynamic properties of the superconducting phases. 

---