Accuracy proton affinities

Data on proton affinities (gasphase) ofmany different compounds (see Table 2) demonstrate the high level of accuracy possible in determining energies of related species. In this report by Dewar and Dieter, the enthalpy of formation of is the experimental value (367.2 kcal/mol). The calculated value for is unreliable. 

The original paper defining the Gaussian-2 method by Curtiss, Raghavachari, Trucks and Pople tested the method s effectiveness by comparing its results to experimental thermochemical data for a set of 125 calculations 55 atomization energies, 38 ionization potentials, 25 electron affinities and 7 proton affinities. All compounds included only first and second-row heavy atoms. The specific calculations chosen were selected because of the availability of high accuracy experimental values for these thermochemical quantities. 

This approach may be possible for small molecules because the gas-phase proton affinity can be obtained quantum mechanically with an accuracy of 1-2 kcal/mol [19]. However, the solvation free energy of H+ cannot be calculated and the experimental value is only known approximately, from 259.5 to 262.5 kcal/mol [60]. Also, because the proton affinity and solvation free energies in Eq. (10-7) are on the order of hundreds of kcal/mol, small percentage errors in the calculation can give rise to large error in AGaqP and pKa. Thus, this method for calculation of absolute pifa s remains impractical at the present time [6],... 

To verify the mechanism presented, the quantum-chemical calculations of proton affinity, Aa, were carried out for modifiers, since the corresponding experimental data are quite rare. The calculations were performed for isolated molecules, since the properties of species in the interlayer space are probably closer to the gas phase rather than the liquid. The values of Ah were calculated as a difference in the total energy between the initial and protonated forms of the modifier. Energies were calculated using the TZV(2df, 2p) basis and MP2 electron correlation correction. Preliminarily, geometries were fully optimized in the framework of the MP2/6-31G(d, p) calculation. The GAMESS suite of ah initio programs was employed [10]. Comparison between the calculated at 0 K proton affinities for water (7.46 eV) and dioxane (8.50 eV) and the experimental data 7.50 eV and 8.42 eV at 298 K, respectively (see [11]), demonstrates a sufficient accuracy of the calculation. 

If we use B3LYP/VTZ+1 harmonics scaled by 0.985 for the Ezpv rather than the actual anharmonic values, mean absolute error at the W1 level deteriorates from 0.37 to 0.40 kcal/mol, which most users would regard as insignificant. At the W2 level, however, we see a somewhat more noticeable degradation from 0.23 to 0.30 kcal/mol - if kJ/mol accuracy is required, literally every little bit counts . If one is primarily concerned with keeping the maximum absolute error down, rather than getting sub-kJ/mol accuracy for individual molecules, the use of B3LYP/VTZ+1 harmonic values of Ezpv scaled by 0.985 is an acceptable fallback solution . The same would appear to be true for thermochemical properties to which the Ezpv contribution is smaller than for the TAE (e.g. ionization potentials, electron affinities, proton affinities, and the like). 

W1/W2 theory and their variants would appear to represent a valuable addition to the computational chemist s toolbox, both for applications that require high-accuracy energetics for small molecules and as a potential source of parameterization data for more approximate methods. The extra cost of W2 theory (compared to W1 theory) does appear to translate into better results for heats of formation and electron affinities, but does not appear to be justified for ionization potentials and proton affinities, for which the W1 approach yields basically converged results. Explicit calculation of anharmonic zero-point energies (as opposed to scaling of harmonic ones) does lead to a further improvement in the quality of W2 heats of formation at the W1 level, the improvement is not sufficiently noticeable to justify the extra expense and difficulty. 

Ab initio molecular orbital calculations at the G2 level of theory is found31 consistently to reproduce experimental proton affinities to an accuracy of 10 kJmol-1 for a range of bases with PA spanning ca 500 kJmol-1. 

Measuring physical-chemical properties of the clusters, such as ionization potential (IP), binding energy (BE), electron (EA) and proton affinity (PA), fragmentation channels, electronic structure and so on, provides a basis for the comprehension of the intrinsic forces acting in the clusters and governing their dynamics. Theoretical computation of these quantities may provide a feedback to evaluate the quality of the calculations and the accuracy of the experimental determinations. 

To test the accuracy of the G2 method, Pople and co-workers used a set of very accurate experimental data consisting of 55 atomization energies, 38 ionization energies, 25 electron affinities, and 7 proton affinities of small molecules. Later, these workers also proposed an extended G2 test set of 148 gas-phase heats of formation. For this extended set of data, the average absolute errors for G2 and G3 are 6.7 and 3.8 kJ mol-1, respectively. Furthermore, it is noted that G3 is actually less expensive than G2, which shows the importance of designing a basis set judiciously. Experience indicates that, for systems of up to 10 nonhydrogen atoms, the expected absolute uncertainty for G2/G3 is about 10 to 15 kJ mol-1. 

Similarly revealing is the solution of a long-standing problem offered by Kohler and Lischka for the protonation of C3H4 species. Whereas experimentally determined and theoretically evaluated proton affinities of allene (171) and propyne (172) could be reproduced within experimental accuracy, the calculated proton affinity of cyclopropene... 

A number of proton-transfer equilibrium constants for reactions similar to those shown in Eq. (3) have been measured by ion cyclotron resonance, high-pressure mass spectroscopy, flowing afterglow, MIKES, and MIKES/CID techniques. These studies allowed the relative proton affinities of a variety of bases to be determined with an accuracy of better than +0.2 kcal mol" and compared with related thermodynamic data measured in solution. 

G(d) zero-point energies. Table 1 shows that B3LYP achieves high accuracy for certain energies in the G3/05 set such as proton affinities, while it performs less well for enthalpies of formation. 

Smith and Radom [92-94] showed that the G2(MP2) theoretical procedure is able to estimate proton affinity within a target accuracy of about 2 kcal/mol. The compounds studied by these authors are of small size (containing from 1 to 4 first row atoms) because of the relatively great computational efforts required by the method. Recently, the possibility to use the DF methods in the PA evaluation has been tested by different authors [12,14,17,19] with encouraging results. From these studies it emerges that DF prediction of PA has almost the same accuracy of G2(MP2) one, but in a fraction of computer time. 

While direct measurement of PA and GB via the reactions shown above is practically impossible, these values have been estimated, with the accuracy improving with advances in chemical instrumentation. In the early twentieth century, Bom-Haber thermodynamic cycles were employed to estimate proton affinities. As with all approaches based on thermodynamic cycles (Section 5.3.2), uncertainties in the data used to construct a cycle propagate to the calculated values (in this case the proton affinity). 

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