The hybrid QM/MM (quantum mechanics/molecular mechanics) approach is a molecular simulation method that combines the strength of both QM (accuracy) and MM (speed) calculations, 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].
An important advantage of QM/MM methods is the 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)). 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.