Abstract
The combined quantum mechanical (QM) and molecular mechanical (MM) approach (QM/MM) is a popular method to study reactions in biochemical macromolecules. Even if the general procedure of using QM for a small, but interesting part of the system and MM for the rest is common to all approaches, the details of the implementations vary extensively, especially the treatment of the interface between the two systems. For example, QM/MM can use either additive or subtractive schemes, of which the former is often said to be preferable, although the two schemes are often mixed up with mechanical and electrostatic embedding. In this article, we clarify the similarities and differences of the two approaches. We show that inherently, the two approaches should be identical and in practice require the same sets of parameters. However, the subtractive scheme provides an opportunity to correct errors introduced by the truncation of the QM system, i.e., the link atoms, but such corrections require additional MM parameters for the QM system. We describe and test three types of link-atom correction, viz. for van der Waals, electrostatic, and bonded interactions. The calculations show that electrostatic and bonded link-atom corrections often give rise to problems in the geometries and energies. The van der Waals link-atom corrections are quite small and give results similar to a pure additive QM/MM scheme. Therefore, both approaches can be recommended.
Highlights
We study six different approaches: the additive scheme (Add, i.e., without any link-atom corrections), the subtractive scheme with van der Waals (VLAC), electrostatic (ELAC), and bonded link-atom corrections (BLAC), the latter in two variants (BLAC1 or BLAC2 and BLAC2J) and mechanical embedding (ME, using a subtractive scheme and van der Waals link-atom correction (VLAC))
As for sulfite oxidase, we used the quantum mechanical (QM)/molecular mechanical (MM) calculations with the full OXF ligand as the reference and study how the various quantum mechanics and molecular mechanics (QM/MM) calculations with OXT reproduce these calculations in terms of the root-mean-squared deviation (RMSD) deviation for the entire QM system, key distances and energies
The primary difference is that the subtractive scheme allows for an attempt to correct for errors introduced by the link atoms
Summary
Combined quantum mechanics and molecular mechanics (QM/MM) is a popular method to study biological macromolecules, as well as homogeneous catalysis and nanostructures, with computational methods (Balcells and Maseras, 2007; Lin and Truhlar, 2007; Ramos and Fernandes, 2008; Stoyanov et al, 2008; Senn and Thiel, 2009; Keal et al, 2011; Chung et al, 2015; Jover and Maseras, 2016; Ryde, 2016). One QM calculation with the QM region (system 1; E1QM) and two MM calculations, one for the entire system (systems 1 and 2; E1M2M) and one for the QM region (E1MM) (Maseras and Morokuma, 1995; Ryde, 1996b; Svensson et al, 1996): EsQuMb /MM = EQ1 M + EM12M − EM1 M (1) The advantage with this approach is the simplicity: It automatically ensures that no interactions are double-counted and it can be set up for any QM and MM software (provided that they can write out energies and forces), without the need of any modification of the code. We prefer the definition in Equations (1, 2), emphasizing that the subtractive scheme employs two MM calculations with an external MM program, whereas the additive scheme employs a single MM calculation with an internal MM program, allowing the developer to cherry-pick the MM terms needed Both additive and subtractive schemes may use either mechanical or electrostatic (or even polarized) embedding. The subtractive scheme may be tuned to correct errors introduced by the link atoms and additional parameters are needed
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