Quantum ONIOM

In the ONIOM(QM MM) scheme as described in Section 2.2, the protein is divided into two subsystems. The QM region (or model system ) contains the active-site selection and is treated by quantum mechanics (here most commonly the density functional B3LYP [31-34]). The MM region (referred to as the real system ) is treated with an empirical force field (here most commonly Amber 96 [35]). The real system contains the surrounding protein (or selected parts of it) and some solvent molecules. To analyze the effects of the protein on the catalytic reactions, we have in general compared the results from ONIOM QM MM models with active-site QM-only calculations. Such comparisons make it possible to isolate catalytic effects originating from e.g. the metal center itself from effects of the surrounding protein matrix. 

Despite the availability of fast computers and efficient codes for accurate quantum chemistry calculations, it is not likely in the near future that we will be able to study chemical reactions in proteins taking all the proteins atoms into quantum mechanical calculations. Hybrid methods in which different parts of large molecular systems are treated by different theoretical levels of methods are likely to play a key role in such studies for the coming decade or more. The ONIOM method we have developed is a versatile hybrid method that allows combining different quantum mechanical methods as well as molecular mechanics method in multiple layers, some features of... 

The isotope effect was first modeled using the ONIOM multi layer approach developed by Morokuma and coworkers (reading list). In this method a part of the whole system is selected for detailed quantum mechanical modeling and designated model while the whole system is called real . The total energy of (Eoniom) is given by Equation 11.87... 

T. Vreven, K. S. Byun, I. Komaromi, S. Dapprich, J. A. Montgomery Jr., K. Morokuma and M. J. Frisch, Combining quantum mechanics methods with molecular mechanics methods in ONIOM, J. Chem. Theory Comput., 2 (2006) 815-826. 

The two-layered ONIOM(B3LYP HF) method describing the whole system at quantum mechanical level, without the support of a molecular mechanics method, was employed by Landis and Uddin to explore the hydroformylation of 1-alkenes by a Rh-xantphos complex [119]. The authors state that their results dispel the assumption that only phosphine diequatorial isomers... 

The performance of the cluster approach can be improved dramatically if it is combined with the recently developed ONIOM methodology43 which is an n-layered integrated molecular orbital and molecular mechanics approach. A threelayered version of the ONIOM approximation allows a quantum-mechanical study of systems which are normally considered with molecular mechanics methods to be performed. The three-layered total energy expression for the ONIOM scheme is defined as... 

An ONIOM study of the adsorption of Sarin on dickite (a 1 1 dioctahedral clay mineral of the kaolinite group)85 was recently published. For the calculations of the studied systems, the two-layered ONIOM method using combinations of quantum-mechanical methods was applied.43,86,87 The investigated systems of... 

As mentioned, the reference compound for 170 NMR is TTO. There are several values of the absolute CS for water in the literature.22-25 For example, Wasylishen et al.22 reported a value of 307.9 ppm. The theoretical prediction of the 170 CS tensors is one of the challenging topics for theoretical chemists. So far, traditional quantum chemical calculations or solid-state physical approaches with periodic boundary conditions26 have been applied to the calculations of 170 CS tensors. Very recently, Nakajima27 has demonstrated the superiority of the ONIOM method28,29 for 170 NMR calculations, which will be given in a later section. 

K. Frisch, M. J. Combining quantum mechanics methods with molecular mechanics methods in ONIOM, 7. Chem. Theory Comput. 2006,2, 815-826. 

Although most computational studies of organotin systems employ ECPs, other methods can be used to describe tin. These methods include semi-empirical methods, all-electron relativistic methods, and hybrid energy methods, such as Morokuma s ONIOM method and hybrid quantum mechanical and molecular mechanics methods (QM/MM). 

Combined quantum mechanical/molecular mechanical methods are not, of course, restricted to studies of reactions but can also be used to study association processes and conformational transitions. Most implementations use a two-zone model as described above, but Morokuma and colleagues have described a multilayered approach called ONIOM [Svensson et al. 1996]. ONIOM is a particularly apt name given that a typical calculation is constructed from a series of layers For example, a three-layer ONIOM calculation on the Diels-Alder reaction involved an inner core treated with the B3LYP density functional approach, the intermediate layer with a Hartree-Fock level of theory and the outer layer with MM3. A particular feature of ONIOM and its related methods is that they provide rigorous gradients and second derivatives, so enabling properties such as vibrational frequencies to be calculated [Dapprich et al. 1999]... 

Quantum mechanical study of the photoisomerization reaction of PYP began with calculations of the adiabatic potential energy surfaces of small model compounds of the chromophore (Yamada et al. 2001). However, to fully describe the protein-chromophore interaction, we had to include the entire protein molecule in the photoisomerization reaction. Recently, QM/MM (Hayashi and Ohmine 2000) and the ONIOM (Yamada et al. 2002 Vreven and Morokuma 2003), both of which are hybrid methods of high- and low-level calculations, have been used for large molecular systems. We performed the ONIOM (IMOMM) calculations on PYP to elucidate the role of the protein enviroiunent (Yamada etal. 2004a,b). We also investigated the origin of the force that drives photoisomerization. 

Hybrid (usually referred to as QM/MM, but other combinations, such as QM/QM are possible) methods treat the most important part of a system with a higher level of theory than the remainder of the system (in the ONIOM method up to three layers are allowed) (56, 57, 58). Often the inq)ortant part is treated with some level of quantum mechanics and the remainder with molecular mechanics. Molecular mechanics treats a molecule in a ball-and-spring fashion (albeit a very sophisticated spring) in classical fields, but does not explicitly treat electrons in the Hamiltonian, and hence is incapable of treating problems where electronic phenomena are key. Disadvantages of these methods include the proper treatment of the interface between the QM and MM portions, the quantum portion still scales as the parent technique, and an unsatisfactory treatment of electron transport and optical properties. Along these lines, Sauer has introduced a combined quantum mechanics-interatomic potential function approach QM-Pot (59). 

Excited-states simulations were mainly limited to small and medium-sized molecules before the 90s. However, many important photophysical processes, as for example, the photoisomerization of rhodopsin, take place in a biological environment, seldom not without the presence of an enzyme. To study photochemical processes in the large-size systems, alternative methods are required. One such method, the QM/MM method," was developed by Warshel and Levitt in 1976. This approach combines the accuracy of quantum chemical models with the speed of molecular mechanics. An alternative method to combine different quantum chemical approaches, the ONIOM method, was developed by Morokuma and co-workers." These methods were initially used in the context of ground-state reactions. Early applications of the QM/MM hybrid method to photochemical processes can be found as early as 1982," however, it was not until at the beginning of this century that the method started to be used extensively for photochemical and photophysical dynamics. To find representative investigations of that time consult the reference list." " ... 

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