Hybrid QM/MM methods

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. 

Illingworth CJR, Gooding SR, Winn PJ, Jones GA, Ferenczy GG, Reynolds CA (2006) Classical polarization in hybrid QM/MM methods. J Phys Chem A 110(20) 6487-6497... 

In 1976 Warshel and Levitt introduced the idea of a hybrid QM/MM method [23] that treated a small part of a system (e.g., the solute) using a quantum mechanical representation, while the rest of the system, which did not need such a detailed description (e.g., the solvent) was represented by an empirical force field. These hybrid methods, in particular the empirical valence bond approach, were then used to study a wide variety of reactions in solution. The combined QM/MM methods use the MM method with the potential calculated ab initio [24]. 

The approaches based on explicit representations of the environment molecules include full quantum mechanical (QM) and hybrid QM/MM methods. In the former, the supramolecular system that is the object of the calculations cannot be very large for instance, it can be composed of the chromophore and a few solvent molecules ( cluster or microsolvation approach). A full QM calculation can be combined with PCM to take into account the bulk of the medium [5,13], which is also a way to test the accuracy of the PCM and of its parameterization, by comparing PCM only and PCM+microsolvation results. The full QM microsolvation approach is recommended when dealing with chromophore-environment interactions that are not easily modelled in the standard ways, such as those involving Rydberg states. An example is the simulation of the absorption spectrum of liquid water, by calculations on water clusters (all QM), clusters + PCM, and a single molecule + PCM only the cluster approach (with or without PCM) yielded results in agreement with experiment [13] (but we note that this example does not conform to the above requirement for a clear distinction between chromophore and environment). 

With the above reservations we turn back to the interaction based classification of the hybrid QM/MM methods which allows us to distinguish the mechanical embedding, polarization embedding etc. We shall consider them subsequently. 

Analyzing the semiempirical QC methods in relation to their suitability for developing the hybrid QM/MM methods reveals certain problems. Using the HFR form of the electron trial wave function together with the ZDO type of parametrization results in the decomposition of the total energy of a molecular system into a sum of mono-and diatomic increments ... 

An important feature of the EHCF(L) theory is that it allows us to estimate the crystal field in terms of the local ESVs of the ligands. This can be done for arbitrary geometry of the complex, which is a prerequisite for developing a hybrid QM/MM method. 

Takahashi, H., Hori T., Hashimoto H. and Nitta T., A hybrid QM/MM method employing real space grids for QM water in the TIP4P water solvents. J.Comput.Chem. (2001) 22 1252-1261. 

This chapter is intended for an audience of computational organometallic chemists interested in the practical use of hybrid QM/MM methods. Because of this the description of the methodological details will be kept to a minimum, condensed in the second section. Similarly, the chapter is not intended to be a review of published applications, which can be found in another recent review... 

Good general discussions on hybrid QM/MM methods can be found in presentations of methodological novelties (8,34,37) and also in recent reviews of these methods (1,38 1). Because of this, the discussion here will be very brief. 

The main difference between the current implementations of IMOMM, IM-OMO, and ONIOM and the majority of other available QM/MM methods is related to the handling of the interaction between the QM and the MM regions. In principle, in any hybrid QM/MM method the total energy of the whole system can in all generality be expressed as ... 

The energy expression in a general hybrid QM/MM method thus has four components. Two of them correspond simply to the pure QM and MM calculations of the corresponding regions. And the other two correspond to the evaluation of the interaction between both regions, in principle at both computational levels. Different computational schemes are defined by the choice of the method to compute the gM(QM/MM) and E mmCQM/MM) terms. 

The presence of chemical bonds between the QM and MM regions poses a problem to the use of hybrid QM/MM methods, with different approaches taking different solutions. The particular method applied by IMQMM and derived methods, the introduction of additional link atoms to saturate the dangling bonds, will be discussed in more detail in Section 3.4 of this chapter. 

Hybrid QM/MM methods have been developed essentially as a tool for the calculation of reliable geometries and energies at a reasonable computational cost. However, the results of their application can also be analyzed in a way that can provide further insight into the properties of chemical systems. 

The two examples described in this subsection show how the use of hybrid QM/MM methods gives access to analysis tools that are absent in pure QM calculations, even if those are more accurate. They also show how the particular chemical problem under study can require slightly different handling of the QM/MM results. 

Before delving into the techniques, a semantic excursion seems necessary. First, computational quantum chemistry as used in this chapter reflects the broader definition, referring to any technique that uses computers to model a chemical system via the Schrodinger equation or some approximation thereof this is a catch-all for every ab initio method, semiempirical scheme, and theoretical model chemistry. (Density functional theory also is included, although it does not stringently satisfy this definition, because it enjoys widespread identification with the ab initio methods.) Molecular mechanics, therefore, is not computational quantum chemistry, but its application to hybrid QM/MM methods will be discussed regardless. 

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