Editing Molecular dynamics (section)

=== Hybrid QM/MM ===
{{Main|QM/MM}}
QM (quantum-mechanical) methods are very powerful. However, they are computationally expensive, while the MM (classical or molecular mechanics) methods are fast but suffer from several limits (require extensive parameterization; energy estimates obtained are not very accurate; cannot be used to simulate reactions where covalent bonds are broken/formed; and are limited in their abilities for providing accurate details regarding the chemical environment). A new class of method has emerged that combines the good points of QM (accuracy) and MM (speed) calculations. These methods are termed mixed or hybrid quantum-mechanical and molecular mechanics methods (hybrid QM/MM).<ref>The methodology for such methods was introduced by Warshel and coworkers. In the recent years have been pioneered by several groups including: [[Arieh Warshel]] ([[University of Southern California]]), Weitao Yang ([[Duke University]]), Sharon Hammes-Schiffer ([[The Pennsylvania State University]]), Donald Truhlar and Jiali Gao ([[University of Minnesota]]) and Kenneth Merz ([[University of Florida]]).</ref>

The most important advantage of hybrid QM/MM method is the speed. The cost of doing classical molecular dynamics (MM) in the most straightforward case scales O(n<sup>2</sup>), where n is the number of atoms in the system. This is mainly due to electrostatic interactions term (every particle interacts with every other particle). However, use of cutoff radius, periodic pair-list updates and more recently the variations of the particle-mesh Ewald's (PME) method has reduced this to between O(n) to O(n<sup>2</sup>). In other words, if a system with twice as many atoms is simulated then it would take between two and four times as much computing power. On the other hand, the simplest ''ab initio'' calculations typically scale O(n<sup>3</sup>) or worse (restricted [[Hartree–Fock]] calculations have been suggested to scale ~O(n<sup>2.7</sup>)). To overcome the limit, a small part of the system is treated quantum-mechanically (typically active-site of an enzyme) and the remaining system is treated classically.

In more sophisticated implementations, QM/MM methods exist to treat both light nuclei susceptible to quantum effects (such as hydrogens) and electronic states. This allows generating hydrogen wave-functions (similar to electronic wave-functions). This methodology has been useful in investigating phenomena such as hydrogen tunneling. One example where QM/MM methods have provided new discoveries is the calculation of hydride transfer in the enzyme liver [[alcohol dehydrogenase]]. In this case, [[quantum tunneling]] is important for the hydrogen, as it determines the reaction rate.<ref>{{cite journal | vauthors = Billeter SR, Webb SP, Agarwal PK, Iordanov T, Hammes-Schiffer S | title = Hydride transfer in liver alcohol dehydrogenase: quantum dynamics, kinetic isotope effects, and role of enzyme motion | journal = Journal of the American Chemical Society | volume = 123 | issue = 45 | pages = 11262–11272 | date = November 2001 | pmid = 11697969 | doi = 10.1021/ja011384b }}</ref>