Morokuma analysis

Alternatively, the height of the crossing point can be calculated with any MO-based method, by determining the energy of the reactant wave function at zero iteration (see Appendix 23A), by constrained optimization of block-localized wavefunctions [44], or by an energy decomposition scheme of the Morokuma-analysis type [45]. Lastly, the height of the crossing point can be computed by means of molecular mechanical methods [46], or related empirical VB calculations [47,48]. 

Morokuma analysis was widely used in the years after its introduction it is less popular now as some problems have been encountered when trying to interpret the results with the larger basis sets that are feasible with today s faster computers and improved algorithms. In particular, when diffuse basis sets are used then there is a substantial amount of intermolecular overlap even at relatively large distances, which can make it difficult to factor out the different components. Nevertheless, the approach is certainly a useful way to assess the major causes of a particular type of intermolecular interaction, if only to provide a qualitative picture. 

To overcome these drawbacks, the scheme was modified by Morokuma and Kitaura and is the popular EDA tool currently used. Similar to the Morokuma analysis in KM scheme, the energies of isolated monomers are first evaluated and the energy of the unperturbed complex is expressed as the sum of their energies ... 

The natural energy decomposition analysis (the keyword is NEDA) of Glendening and Streitwieser provides a more comprehensive picture of the various energy components contributing to intermolecular interactions. The NEDA decomposition mimics in some ways the older Kitaura-Morokuma analysis, but it avoids the use of non-orthogonal (and exclusion principle-violating) wavefiinctions for the two monomers, with the attendant interpretational ambiguities. 

TABLE 10. Morokuma-Kitaura component analysis of the SCF interaction energy of the water dimer ... 

In order to leam more about the nature of the intermolecular forces we will start with partitioning of the total molecular energy, AE, into individual contri butions, which are as close as possible to those we defined in intermolecular perturbation theory. Attempts to split AE into suitable parts were undertaken independently by several groups 83-85>. The most detailed scheme of energy partitioning within the framework of MO theory was proposed by Morokuma 85> and his definitions are discussed here ). This analysis starts from antisymmetrized wave functions of the isolated molecules, a and 3, as well as from the complete Hamiltonian of the interacting complex AB. Four different approximative wave functions are used to describe the whole system ... 

TABLE 6.8. Energy Contributions to the Total Energy Obtained for Three Complexes Using Morokuma s Analysis... 

Morokuma, K. Kitaura, K. Energy Decomposition Analysis of Molecular Interactions in Chemical Applications of Atomic and Molecular Electrostatic Potentials, Politzer, P Ed. Plenum New York, 1981, pp. 215-242. 

Singh UC, Kollman PA (1985) A water dimer potential based on ab-initio calculations using Morokuma component analysis. J Chem Phys 83 4033-4040... 

Yamabe S, Morokuma K (1975) Molecular orbital studies of hydrogen bonds. IX. Electron distribution analysis. J Am Chem Soc 97 4458 -4465... 

To assess the reliability of the particular ONIOM scheme employed in the analysis of the aldol addition, Ojea and coworkers" considered the difference between the activation energies of the most stable transition structures 136 and 137 in the favored disolvated reaction channel (130 and 131) as a convenient parameter for the -value test proposed by Morokuma" . In this manner the error of the ONIOM(I) and ONIOM(II) extrapolations, with respect to their benchmark calculations at the B3LYP/6-31- -G //HF/6-31G level, were 0.86 and 0.60 kcalmol", respectively. When the geometry optimizations at the ONIOM(II) level were followed by single-point energy evaluations at the B3LYP/6-31-l-G level, the error was reduced to less than 0.10 kcalmoG. ... 

Table 1.6 Comparison between Morokuma-Kitaura and natural energy decomposition analysis (NEDA) " . All values in kcal/mol, calculated with 4-3IG basis set. 

Decomposition of interaction energies is desired for qualitative chemical analyses of complicated multi-valent interactions in supramolecular aggregates but such a decomposition cannot be uniquely defined within fundamental physical theory. A popular semi-quantitative decomposition method with nice formal features to be mentioned in this context is Weinhold s natural bond orbital (NBO) approach to intermolecular interactions [232, 233]. Comparable is the recently proposed energy decomposition analysis by Mo, Gao and Peyerimhoff [234, 235] which is based on a block-localized wave function. Other energy decomposition schemes proposed are the energy decomposition analysis (EDA) by Kitaura and Morokuma [236] and a similar scheme by Ziegler and Rauk [237]. 

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