Evaluating Boundary Dependent Errors in QM/MM Simulations

Abstract

Hybrid quantum mechanics/molecular mechanics (QM/MM) simulations provide a powerful tool for studying chemical reactions, especially in complex biochemical systems. In most works to date, the quantum region is kept fixed throughout the simulation and is defined in an ad hoc way based on chemical intuition and available computational resources. The simulation errors associated with a given choice of the quantum region are, however, rarely assessed in a systematic manner. Here we study the dependence of two relevant quantities on the QM region size: the force error at the center of the QM region and the free energy of a proton transfer reaction. Taking lysozyme as our model system, we find that in an apolar region the average force error rapidly decreases with increasing QM region size. In contrast, the average force error at the polar active site is considerably higher, exhibits large oscillations and decreases more slowly, and may not fall below acceptable limits even for a quantum region radius of 9.0 A. Although computation of free energies could only be afforded until 6.0 A, results were found to change considerably within these limits. These errors demonstrate that the results of QM/MM calculations are heavily affected by the definition of the QM region (not only its size), and a convergence test is proposed to be a part of setting up QM/MM simulations.

On the Convergence of QM/MM Energies

“…QTCP 0 in set 2). The reason why previous investigations have given better results with electrostatic embedding 15,19,22,23 is that the results depends on the tested system, i.e. the relative importance of polarisation and the junction errors, but also that we have in this investigation developed new variants of mechanical embedding (ME dir and ME scal ) that give the best results.…”

“…This is appreciably more than in previous studies. 15,24,12,19,20,21,22,23 By systematically adding different components and corrections, we can estimate the size of the various terms and the accuracy of the various corrections. We have arrived at several interesting conclusions.…”

“…For example, it has been shown that the error in QM/MM forces are sizeable for QM regions with a radius of up to 9 Å and that QM/MM free energies change by 12 kJ/mol when increasing the size of the QM system from 3 to 5 Å. 15 In this paper, we supplement our QM-only study by an investigation of the corresponding convergence of the QM/MM approach. Thus, we use a 446-atom model of [Ni,Fe] hydrogenase from our previous investigation 14 as a reference and investigate how the QM/MM energy converges towards the QM energy of the full system as the QM system in the QM/MM treatment is enlarged.…”

Large-Scale Density Functional Theory Transition State Searching in Enzymes

“…16,17 The resulting NBOs may then be categorized into chemically-intuitive Lewis-type bonding and lone pair orbitals, as well as their anti-bonding counterparts. Electronic delocalization from filled to vacant NBOs causes a variational lowering of the total energy, which can be estimated from second order perturbation theory (∆E (2) , see SI). This stabilization energy is strongly correlated with the strengths of hydrogen bonds in simple systems, 17,18 and we can therefore use it as a qualitative estimate of the importance of activesite residues in the catalytic rate enhancement in CM.…”

Quantitative Assessment of Electrostatic Embedding in Density Functional Theory Calculations of Biomolecular Systems

“…A similar study was carried out by Solt et al 12 in a full QM/MM framework where they attempt to assess in a systematic manner simulation errors at the center of the QM region as a function of the size of that region. They showed that even with a full MM coupling, there are significant errors in the forces affecting atoms near the edge of the QM region By reducing the secondary subsystem to a simple electrostatic environment, the interaction between primary and secondary subsystems is greatly simplified.…”