Isogyric and Isodesmic reactions

The SEC acronym refers to the case where the reference wave function is of the MCSCF type and the correlation energy is calculated by a MR-CISD procedure. When the reference is a single determinant (HF), the SAC nomenclature is used. In the latter case the correlation energy may be calculated for example by MP2, MP4 or CCSD, producing acronyms such as MP2-SAC, MP4-SAC and CCSD-SAC. In the SEC/SAC procedure, the scale factor E is assumed to be constant over the whole surface. If more than one dissociation channel is important, a suitable average F may be used. 

The Parameterized Configuration Interaction (PCI-X) method simply takes the correlation energy and scales it by a constant factor X (typical value -1.2), i.e. it is assumed that the given combination of method and basis set recovers a constant fraction of the correlation energy. 

The introduction of various empirical corrections, such as scale factors for frequencies and energy corrections based on the number of electrons and degree of spin contamination, blurs the distinction between whether they should be considered ab initio, or as belonging to the semi-empirical class of methods such as AMI and PM3. Nevertheless, the accuracy that these methods are capable of delivering makes it possible to calculate absolute stabilities (heat of formation) for small- and medium-sized systems that rival (or surpass) experimental data, often at a substantially lower cost than that for actually performing the experiments. 

In many cases, however, it is possible to choose less demanding reference systems than the isolated atoms. Consider for example calculating the C—H dissociation energy of CH4. In a direct calculation this is given as the difference in total energy of CFLt and CH3 + H. 

There are a few other correction procedures that may be considered as extrapolation schemes. The Scaled External Correlation (SEC) and Scaled All Correlation (SAC) methods scale the correlation energy by a factor such that calculated dissociation energy 

The Parameterized Confisuration Interaction (PCI-X) method simply takes the 

The introduction of various empirical corrections, such as scale factors for frequencies 

The most Hiffiniilt part in calculating absolute stabilities (heat of formationi is the 

The most difficult part in calculating absolute stabilities (heat of formation) is the correlation energy. For calculating energies relative to isolated atoms, the goal of tire 

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Modified Neglect of Diatomic Overlap Parametric Method Number 3 (MNDO-PM3) 3.10.6 The MNDO/d Method 88 89 5.5 5.6 5.4.5 Correlation Consistent Basis Sets Extrapolation Procedures Isogyric and Isodesmic Reactions 162 164 169... 

JANAF thermochemical tables [160a] estimate the heat of formation of FCO radicals to be —41 15 kcal mol". MacNeil and Thynne [171] determined the F—CO bond energy from electron impact ionization study of CFjO, arriving at a heat of formation of —42 kcal mol . Henrici et al. [172] suggested a value of —34 5 kcal mol from shock tube experiments. Bowers and Chau [173] estimated a value of -42 + 4 kcal mol . Using isogyric and isodesmic reaction schemes and ab initio methods, Francisco and Zhao [174] estimated the heat of formation of FCO as -42.9 0.8 kcal mol", consistent with the measurements of Bower and Chau. 

Reactions in which the numbers of paired electrons are not conserved are classified as nonisogyric reactions. Examples include homolytic bond dissociations and transition state calculations. In contrast, isogyric reactions conserve the number of paired electrons, such as in heterolytic bond dissociations and some isomerizations. Last, isodesmic reactions are bond conserving and not only maintain the division of electrons into shared and unshared pairs, but also maintain the number and type of bonds between heavy atoms (nonhydrogen). 

Several classes of reactions have been defined that display some degree of similarity in reactants and products. These include isogyric, isodesmic, and homodesmotic reactions. In isogyric reactions (Pople et al. 1983), the numbers of pairs of electrons in reactants and products is the same (and hence so is the number of unpaired electrons). For example, the following are isogyric processes ... 

In addition to kinetic parameters, thermodynamic quantities can also be calculated via electronic structure methods. In particular, isodesmic reactions (in which the same numbers and types of bond are conserved) and isogyric reactions (in which the total number of electron pairs is conserved) are often used to determine reliable enthalpies of formation for previously unexplored... 

An indirect means of dealing with the correlation problem when the molecule is too large to be treated by advanced methods such as the G2 is to include it in a reaction (often hypothetical) in which the reactants and products are similar in terms of one or more of several electronic and structural factors, e.g. number of electron pairs, types of bonds, atom environments, etc. [15,20,21], It is hoped that in computing AH(298 K) for such a process, the errors for the reactants and products will largely cancel. The desired AHf can then be obtained if the AHf of all of the other species are known. There are several categories of such reactions isogyric ones conserve the number of electron pairs, isodesmic maintain unchanged... 

Several theoretical studies were performed on the FO2 radical. The best and more recent one is that by Francisco et al (56). References to previous work on the subject are given there. The calculation of AH o for the direct reaction proved to be exceedingly difficult and inaccurate. Therefore, the authors studied also some other isodesmic and/or isogyric reactions, namely FO2 + HO —> HO2 + FO... 

Recent theoretical results by Nicolaides and Radom , who employed isodesmic and isogyric reactions for an accurate determination of the heats of formation of both ions at the G2 level of theory, suggest that the silabenzyl cation 85 is more stable than the silatropylium ion 86 by approximately 40 kcalmol For the corresponding [C7,H7]+ surface, they found a reverse ordering, here the tropylium ion is 29 kcalmol more stable than the benzyl cation. These findings presumably reflect the well-documented inability of silicon to form 7r-bonds with significant strength. 

The main difficulty in representing these reactions is that they are neither isodesmic nor isogyric. Errors do not compensate then, and only an equally accurate description of the radicals and the neutral molecules afford reasonable values for the reactions. As observed in the table, B3LYP is nearly useless for the description, since errors up to 17 kcal/mol occur. The BMK method exhibits both a MAD and RMSE of almost one-fourth those of B3LYP. The results are comparable to G4 and better than MP2, but not as good as CCSD(T) or CBS-APNO. 

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