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The hybrid QM/MM (quantum mechanics/molecular mechanics) approach is a molecular simulation method that combines the strengths of the QM (accuracy) and MM (speed) approaches, thus allowing for the study of chemical processes in solution and in proteins. The QM/MM approach was introduced in the 1976 paper of Warshel and Levitt.[1] They, along with Martin Karplus, won the 2013 Nobel Prize in Chemistry for "the development of multiscale models for complex chemical systems".[2][3]

An important advantage of QM/MM methods is their efficiency. The cost of doing classical molecular mechanics (MM) simulations in the most straight forward case scales O(N2), where N is the number of atoms in the system. This is mainly due to electrostatic interactions term (every particle interacts with everything else). However, use of cutoff radius, periodic pair-list updates and more recently the variations of the particle mesh Ewald (PME) method has reduced this between O(N) to O(N2). In other words, if a system with twice many atoms is simulated then it would take between twice to four times as much computing power. On the other hand the simplest ab-initio calculations formally scale as O(N3) or worse (Restricted Hartree–Fock calculations have been suggested to scale ~O(N2.7)). Here in the ab initio calculations, N stands for the number of basis functions (It is not the number of atoms). Each atom has at least as many basis functions as is the number of electrons (e.g., with the STO-3G basis set). To overcome the limitation, a small part of the system that is of major interest is treated quantum-mechanically (for instance, the active-site of an enzyme) and the remaining system is treated classically.

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  1. ^ Warshel, A; Levitt, M (1976). "Theoretical studies of enzymic reactions: Dielectric, electrostatic and steric stabilization of the carbonium ion in the reaction of lysozyme". Journal of Molecular Biology 103 (2): 227–49. doi:10.1016/0022-2836(76)90311-9. PMID 985660. 
  2. ^ "The Nobel Prize in Chemistry 2013" (PDF) (Press release). Royal Swedish Academy of Sciences. October 9, 2013. Retrieved October 9, 2013. 
  3. ^ Chang, Kenneth (October 9, 2013). "3 Researchers Win Nobel Prize in Chemistry". New York Times. Retrieved October 9, 2013.