Bond additivity correction

There are two major sources of uncertainty in the BAG-MP4 heats of formation. First, there are imcertainties resulting from incomplete knowledge of the appropriateness of the chosen theoretical methods for a given molecule. Second, systematic imcertainties exist that result from the lack of good reference compounds needed to estabhsh the bond additivity corrections. The magnitude of the first is estimated using an ad hoc method developed previously that uses the results from lower-level calculations (Table 1). 

A somewhat more chemically based empirical correction scheme is the bond-additivity correction (BAG) methodology. In the BAG-MP4 approach, for instance, the energy of a molecule is computed as... 

Zachariah, M. R. and Melius, C. F. 1998. Bond-additivity Correction of Ab Initio Computations for... 

Zachariah, M. R. and Melius, C. F. Bond-additivity Correction of Ab Initio Computations for Accurate Prediction of Thermochemistry in Computational Thermochemistiy, ACS Symposium Series, Vol. 677, Irikura, K. K., and Frurip, D. J., Eds., American Chemical Society Washington, DC, 162. 

Bond additivity correction, 243, 371 Bond critical point, 316 Bond dipole moment, 33 Bond dissociation energy, 20-21, 148, 156,... 

It is instructive to compare the implications of each value for the other s measurements. If the combustion value is correct, it implies that the AH°( value for the aqueous solution reaction is —245.9 kJ mol-1 instead of —200.1 kJ mol-1 as measured, an error of ca 23%, well outside the quoted 0.7%. If the —245.9 kJmol-1 value is correct, then A//f (combustion) = —5538 kJmol-1 instead of —5583 kJmol-1 as measured, an error of 0.8% compared to the quoted 0.07%. To the impartial assessor, the second scenario seems more likely than the first. A more detailed discussion of potential sources of uncertainty is contained in the paper of van der Vis and Cordfunke83, which also lists earlier measurements. The BAC-MP4 calculation24, while nearer to combustion value, is probably not definitive, since there are too few reliable reference compounds on which to base the Bond Additivity corrections. 

Finally we describe several methods that combine molecule-dependent empirical parameters with a moderate level ab initio molecular orbital method. The BAC-MP4 method of Melius and coworkers115-118 combines a computationally inexpensive molecular orbital method with a bond additivity correction. This procedure uses a set of accurate experimental data to obtain a correction for bonds of different types that is then used to adjust calculated thermochemical data such as enthalpies of formation. Quite accurate results can be obtained if suitable reference molecules are available and if the errors in the calculation are systematic. The computational methodology is based on an MP4/6-31G(d,p)//HF/6-/31G(d) calculation. A pairwise additive empirical bond correction is derived for different bonds from fitting to experimental enthalpies of formation or in some cases to high quality ab initio computations. In addition, for open-shell molecules an additional correction is needed to compensate for spin contamination of the wavefunction from higher spin states in the unrestricted Hartree-Fock (UHF) method. 

Plane et al. made further DPT calculations on the OlO + NO system [54], These included bond-additivity corrections for I2 and 10, absorbed into "spin-orbit" corrections for 1 and 10. The bond strengths shown in Table 9.4 are derived from the differences between the computed reaction enthalpies reported by Plane et al. [54], as noted by Golden [55], and are reasonably close to the present values, both falling about 8 kj mol smaller. 

To aid the modelers in developing improved reaction mechanisms as well as to aid the experimentalists in their interpretation of the data, we have calculated the energetics of molecular intermediates and products arising from these reactions. Our approach was to use the highly accurate fourth order M ller-Plesset perturbation theory (24) with bond-additivity corrections. (2 )... 

These theoretical calculations are subject to systematic errors arising from basis set truncation and neglect of higher perturbation order electron correlation effects. Therefore, we have added a second step to our procedure in which we attempt to account for these deficiencies by adding empirically derived Bond-Additivity-Correction (BAC) factors that are based on the types of bonds present in the given molecule. The correction factors for NH (9.4 kcal-mole" ) and OH (10.7 kcal-mole" ) bonds are obtained as the difference between the theoretical and... 

In a similar fashion, correction factors for the nitrogen-oxygen and oxygen-oxygen bond types are developed from a comparison of the theoretical results with various experimental values of N-O-H containing molecular species. In this case the bond additivity corrections depend both on the bond distance as well as the bond type. An additional correction factor for spin contamination in the spin-unrestricted Hartree-Fock wavefunction is included. 

The calculational approach used here involving fourth-order fipller-Plesset perturbation theory with bond additivity corrections (BAC-MP4), has been shown to be a powerful tool for determining heats of formation of molecular species and for analyzing possible reaction pathways. For NH2 and NH reacting with 0 and O2 we have been able to distinguish between likely and unlikely reaction products based on the stability of various reaction intermediates compared to the reactants and products. 

The enthalpy of formation of methylformate, CH30CH=0, is calculated at -82.2 kcal moT by the G3MP2B3 method and at -83.4 kcal moT with the B3LYP/6-311G(d,p) method. There are previous calculations on methylformate by Sumathi and Green [146] using CBS-Q with spin-orbit and bond additivity corrections they reported a value at -85.87 kcal mol. ... 

The BAC-MP4 method allows the enthalpy of formation of a chemical species to be estimated. The calculation of electronic structures (geometry and vibration frequencies) can be carried out using the GAUSSIAN 94 computer program. The corrections are carried out using the Mdller-Plasset (MP) theory of perturbations and the Bond Additivity Corrections are also carried out using the same theory. 

Bond additivity corrections for quantum chemistry methods ... 

The bond additivity correction is typically computed only for atom pairs with interatomic distances within a preset cutoff. For studying chemical reactions in which bonds are made and broken it is necessary to force the BAG to be computed for some pairs of atoms at all distances to insure continuity of potential energy curves. In the present study the BAG is applied to all the hydrogen-bonded interactions, although in the standard application it is not. This introduces approximately an additional 0.8 kcal/mol of binding for each hydrogen-bonded interaction at the equilibrium hydrogen-bonded intemuclear distance. 

Figure 1. Hierarchial diagram of the BAC-MP4 method for determining thermochemical properties of molecules. First, a Hartree-Fock calculation provides the molecular geometries and frequencies. Fourth-order M0ller-Plesset perturbation theory (MP4) provides the ab initio electronic energy to which bond-additivity corrections (BAC) are then added to obtain chemical bond energies. Finally, statistical mechanics calculations are used to determine the enthalpy, entropy, and free energy of the molecule.

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