Morokuma- Kitaura schemes

Let us take as an example what is probably the most frequently used means of decomposing the interaction energy of various complexes, including H-bonds. In the KM scheme, Ki-taura and Morokuma first compute the wave functions of the two isolated subunits of the complex, / ° and Yb°- They take this pair of wave functions as the starting point for a Hartree-Fock calculation of the complex. 

Note that the electrons of A are anti symmetrized within / °, and similarly for B electrons in However, no exchange of A and B electrons is permitted in Va° b°- zeroth iteration of the SCF procedure yields an energy which differs from the total energy of the pair of isolated subunits by an amount taken to be ,.5 since it permits the field of each monomer to interact with the electron density, v /.°, of the partner, without perturbing that density. 

The exchange energy is extracted by again beginning the SCF procedure but this time permitting interchange of electrons between A and B, indicated by the operator below. 

The energy associated with differs from that of v / by an amount defined here as the exchange energy, owing to the electron exchange within the yj wave function. 

One of the problems of this technique lies in the mixing term which provides no physical insights. Furthermore, this term grows to uncomfortably large proportions when the interaction strengthens. It was also found that the various components of the interaction energy are even more sensitive to basis set choice than is the total interaction energy. The 

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Despite the fact that the Kitaura Morokuma approach allows insight into the nature of interaction to be obtained, it has also a lot of limitations. One of the most important is that the binding energy and its components are not free of the basis set superposition error [39]. Another variation-perturbation scheme of the decomposition of the interaction energy was previously proposed [40]. The starting wave functions of the subsystems are obtained in this approach in the dimer-centered basis set (DCBS) hence, the following interaction energy components free of BSSE can be obtained ... 

Kitaura K, Morokuma K (1976) A new energy decomposition scheme for molecular interactions within the Hartree-Fock approximation. Int J Quantum Chem 10 325... 

K. Kitaura and K. Morokuma, Int.. Quantum Chem., 10, 325 (1976). A New Energy Decomposition Scheme for Molecular Interactions Within the Hartree-Fock Approximation. 

Some of these points can be illustrated with simple examples. Table 1.4 lists the components of the interaction energy of the water dimer computed by the Morokuma-Kitaura scheme for the water dimer, taken in its experimental geometry, with an interoxygen separation of 2.98 The electrostatic term is clearly highly sensitive to the basis set chosen. 

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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