QM/MM

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 straightforward 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 to 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.[4][5]

The electrostatic QM-MM interaction

Electrostatic interactions between the QM and MM region may be considered at different levels of sophistication. These methods can be classified as either mechanical embedding, electrostatic embedding or polarized embedding.

Mechanical embedding

Mechanical embedding treats the electrostatic interactions at the MM level, though simpler than the other methods, certain issues may occur, in part due to the extra difficulty in assigning appropriate MM properties such as atom centered point charges to the QM region. The QM region being simulated is the site of the reaction thus it is likely that during the course of the reaction the charge distribution will change resulting in a high level of error if a single set of MM electrostatic parameters is used to describe it. Another problem is the fact that mechanical embedding will not consider the effects of electrostatic interactions with the MM system on the electronic structure of the QM system.[6]

Electrostatic embedding

Electrostatic embedding does not require the MM electrostatic parameters for the QM. This is due to it considering the effects of the electrostatic interactions by including certain one electron terms in the QM regions Hamiltonian. This means that polarization of the QM system by the electrostatic interactions with the MM system will now be accounted for. Though an improvement on the mechanical embedding scheme it comes at the cost of increased complexity hence requiring more computational effort. Another issue is it neglects the effects of the QM system on the MM system whereas in reality both systems would polarize each other until an equilibrium is met.

In order to construct the required one electron terms for the MM region it is possible to utilize the partial charges described by the MM calculation. This is the most popular method for constructing the QM Hamiltonian however it may not be suitable for all systems.[6]

Problems involved with QM/MM

Even though QM/MM methods are often very efficient, they are still rather tricky to handle. A researcher has to limit the regions (atomic sites) which are simulated by QM. Moving the limitation borders can both affect the results and the time computing the results. The way the QM and MM systems are coupled can differ substantially depending on the arrangement of particles in the system and their deviations from equilibrium positions in time. Usually limits are set at carbon-carbon bonds and avoided in regions that are associated with charged groups, since such an electronically variant limit can influence the quality of the model.[7]

Covalent bonds across the QM-MM boundary

Directly connected atoms, where one is described by QM and the other by MM are referred to as Junction atoms. Having the boundary between the QM region and MM region pass through a covalent bond may prove problematic however this is sometimes unavoidable. When it does occur it is important that the bond of the QM atom be capped in order to prevent the appearance of bond cleavage in the QM system.[7]

See also

References

  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.
  4. ↑ Brunk, Elizabeth; Rothlisberger, Ursula. "Mixed Quantum Mechanical/Molecular Mechanical Molecular Dynamics Simulations of Biological Systems in Ground and Electronically Excited States". Chemical Reviews. 115 (12): 6217–6263. doi:10.1021/cr500628b. PMID 25880693.
  5. ↑ Morzan, Uriel N.; Alonso de Armiño, Diego J.; Foglia, Nicolas; Ramirez, Francisco; Gonzalez Lebrero, Mariano C.; Scherlis, Damian A.; Estrin, Dario A. "Spectroscopy in Complex Environments from QM–MM Simulations". Chemical Reviews. 118 (7): 4071–4113. doi:10.1021/acs.chemrev.8b00026. PMID 29561145.
  6. 1 2 Lin, Hai; Truhlar, Donald G. "QM/MM: what have we learned, where are we, and where do we go from here?". Theoretical Chemistry Accounts. 117 (2): 185–199. doi:10.1007/s00214-006-0143-z. ISSN 1432-881X.
  7. 1 2 Hans Martin Senn, Walter Thiel (2009). "QM/MM Methods for Biomolecular Systems". Angew Chem Int Ed Engl. 48: 1198–1229. doi:10.1002/anie.200802019.
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