Extending the QM region

In this section, we shall briefly review recent progress that has been made in designing algorithms that allow QM methods to be applied to larger and larger systems. While these methods are general, and not restricted for use with hybrid potentials, they could improve significantly the precision and applicability of hybrid potential techniques. 

In most QM algorithms, there will be two or more steps in a calculation with unfavourable scaling behaviour. This means that for an algorithm which scales linearly overall with system size, each separate step in the calculation must be made to scale linearly as well. Owing to the variety of different QM calculations no attempt will be made here to comprehensively list the many alternative linear-scaling approaches. Instead, we confine ourselves to a number of general remarks. 

One important linear-scaling problem concerns the summation of the Coulomb pairwise interactions in a system which is formally a O(n ) process. Of course, this is a crucial step when MM potentials are being used too, although there 

While the method of Yang has been the most widely used so far for biological 

In the past several years, hybrid QM/MM potentials have been used to investigate the mechanism of about twenty or so different enzymatic reactions. Table 1 gives details of these studies by listing the QM method, the MM force field, the treatment of the QM/MM interface and the type of simulation employed. We shall discuss some of them in greater detail below. Warshel has also applied his EVB (see section 2) method to a wide range of enzyme systems, including the serine proteases, carbonic anhydrase and lactate dehydrogenase, but we will not mention any of these results here. Instead, readers should refer to the appropriate references [20,21,62]. 

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