IMOMM-ONIOM

The Integrated Molecular Orbital Molecular Mechanics (IMOMM) method [108] is relatively young compared to the Warshel and Levitt work in 1976. It was designed to study organometallic reactions where bulky ligands were important but too expensive to employ the same ab initio method that the metal requires. Since these big ligands usually only play a steric role, in the IMOMM hybrid method the polarization of the MM charges to the one-electron Hamiltonian is not included and only van der Waals interactions are considered between the two regions. As any other hybrid method the energy expression can be defined as

$$E_{TOT}=E_{QM} + E_{MM} + E_{QM/MM}$$ (2.65)

Where the third term is only the van der Waals between the two zones

$$E_{QM/MM}=V^{van der Waals}_{QM/MM}$$

Or in a very simplified expression

$$E_{TOT} = E^{low}_{real} - E^{low}_{model} + E^{high}_{model}$$ (2.66)

The formulation of equation 1.66 is too simplified because does not indicate explicitly the crossed terms between the model (core) and the environment (real - model) region. In the original publication by Maseras and Morokuma [108] there is a discussion referring to the topic of double counting the interaction at the low and high level and how the frontier is treated.

The "Our-own N-layered Integrated molecular Orbital and Molecular mechanics" (ONIOM) strategy [109] is essentially an extension to the usage of more than two layers of theory and the consideration that the low level can be a quantum mechanical method such as semiempirical (IMOMO). This possibility involves that the low level energy cannot be decomposed in energy terms like molecular mechanics. In this case the expressions in equations 1.65 and 1.66 are not equivalent, and the total energy is an addition-subtraction of energy as displayed in equation 1.66. The problems and solutions of this issue will be found in the original papers [109].

Some authors think that IMOMM-ONIOM are not properly hybrids methods because they do not include explicitly the polarization that the environment provokes on the core region. My personal opinion is that a hybrid method is any strategy that combines two methods in two regions of a system avoiding the full high-level treatment. So IMOMM-like methods should belong to this hybrid family as a full member.

Besides, this method that was designed to study organometallic chemistry it has been used in enzymatic systems with successful results [110,111].