QM/MM model

However, the active site is only a conceptual tool and the assignment of the active-site atoms is more or less arbitrary. It is not possible to know beforehand which residues and protein interactions that will turn out to be important for the studied reaction. Hybrid QM/MM methods have been used to extend the active site only models by incorporating larger parts of the protein matrix in studies of enzymatic reactions [19-22], The problem to select active-site residues appears both for active-site and QM/MM models, but in the latter, explicit effects of the surrounding protein (i.e. atoms outside the active-site selection) can at least be approximately evaluated. As this and several other contributions in this volume show, this is in many cases highly desirable. 

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. 

Figure 2-14. Illustration of the different hydrogen bonding patterns for an iron-bound peroxide in IPNS using an active-site model (left) and an ONIOM QM MM model (right)...

Our studies on the three enzymes have involved the use of semi-empirical methods, using published and also SRP parameter sets. For both LADH and MADH (Figures 5-3a and b) hybrid QM/MM models were employed [8, 9, 88-90], In LADH the PES surface was calculated at the AMI level [20] but scaled by data from the HF/3-21G surface [91]. The results of the CVT calculation with the SCT correction show quite modest yet contributory degrees of tunnelling, an RTE... 

This section describes the main methodological advances that will be used in subsequent selected applications, including (1) Development of fast semiempirical methods for multiscale quantum simulations, (2) Directions for development of next-generation QM/MM models, and (3) Linear-scaling electrostatic and generalized solvent boundary methods. 

The combined QM/MM model can be used along with Statistical Perturbation Theory to carry out a Monte Carlo simulation of a chemical reaction in solution, with the advantage of allowing solute electronic structure relaxation in solution. Particularly, the combined AM1/TIP3P force field has recently been applied to simulate several chemical processes in solution. We will refer here briefly to the Claisen rearrangement and to the Menshutkin reaction. 

Figure 3. Structural representation of the computational models A-F. Models B, D, and E are combined QM/MM models where the regions enclosed in the dotted polygons represent the QM region. The regions outside the polygons are treated by a molecular mechanics force field. For the electronic structure calculation of the QM region, the covalent bonds that traverse the QM/MM boundary (the dotted polygon), have been capped with hydrogen atoms. In model A the atoms labelled 1 through 4 are the atoms that have been fixed in the calculations of models A through E.

Next let us examine a QM/MM model system of complex 3 where the steric influence of the phenyl substituents and of the ferrocene is accounted for but the electronic effects have been largely eliminated (model B). In other words, the peripheral groups have been delegated to the MM region, while keeping the molecular system used for electronic structure calculation identical to that in model A. 

Finally, we have constructed a QM/MM model of complex 3 whereby the phenyl phosphine groups are contained in the QM region, while the ferrocenyl and phenyl substituents on the pyrazole is accounted for on a steric basis only (model E). The agreement between the X-ray structure of 3 and model E is remarkable. For example, both the Pd-P distance and the twist of the coordination plane of the Pd center, 0, are virtually identical to those of the X-ray structure. In fact, the selected parameters displayed in Table 2 are generally better than those of the full QM calculation. The good agreement between the calculated and experimental structures is important for the detailed mechanistic study of the hydrosilylation that is presented in later sections of this chapter. 

In the X-ray structures of both 3 and 4, the tetrahedral distortion is greater than that found in model A. Since there is an electronic preference for a square planar coordination, the pendant phenyl substituents in 3 and 4 likely result in further steric crowding and therefore in more distorted structures compared to model A. In the QM/MM model B an optimized 0 angle of 30° is found, close to the 34° angle of the X-ray structure. Since the phenyl and trimethyl phenyl groups are accounted for on a steric basis only in model B, the result supports the notion that the severely distorted coordination of the Pd center in 3 is due to a steric effect. 

Figure 12. Calculated reaction profile with QM/MM model B of the catalytic cycle for the most favoured pathway.

In this section we focused our attention to a rationalization of the factors determining the stereoselectivity through ab initio mixed quantum/classical (QM/MM) Car-Parrinello molecular dynamic simulations. We have used the same basic computational approach used in Section 3 to explore the potential energy surface of the reaction. Since the catalyst system, 1, is relatively large, we have used the combined QM/MM model system B as shown in Figure 3 and described in subsections 2.1 and 3.1. 

Fig. 11.13 QM/MM model used in calculations of the chlorine KIE on DhlA catalyzed reaction (Devi-Kesavan, L.S. and Gao, J., J. Am. Chem. Soc. 125, 4550 (2003))...

All of the QM/MM models discussed this far, much like continuum models, envision partitioning a chemical system into (at least) two distinct regions, where the boundary between these regions is everywhere characterized by a very low level of electron density. That is, no atoms on one side of the boundary are bonded to atoms on the other side. As a result, the //qm/mm term in the Hamiltonian of Eq. (13.1) is restricted to non-bonded interactions. 

Alhambra and co-workers adopted a QM/MM strategy to better understand quantum mechanical effects, and particularly the influence of tunneling, on the observed primary kinetic isotope effect of 3.3 in this system (that is, the reaction proceeds 3.3 times more slowly when the hydrogen isotope at C-2 is deuterium instead of protium). In order to carry out their analysis they combined fully classical MD trajectories with QM/MM modeling and analysis using variational transition-state theory. Kinetic isotope effects (KIEs), tunneling, and variational transition state theory are discussed in detail in Chapter 15 - we will not explore these topics in any particular depth in this case study, but will focus primarily on the QM/MM protocol. 

Waller MP, Biihl M, Geethalakshmi KR, Wang D, Thiel W (2007) 51V NMR Chemical Shifts Calculated from QM/MM Models of Vanadium Chloroperoxidase. Chem Eur J 13 4723... 

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