The adaptive buffered force QM/MM method in the CP2K and AMBER software packages

The implementation and validation of the adaptive buffered force (AdBF) quantum‐mechanics/molecular‐mechanics (QM/MM) method in two popular packages, CP2K and AMBER are presented. The implementations build on the existing QM/MM functionality in each code, extending it to allow for redefinition of the QM and MM regions during the simulation and reducing QM‐MM interface errors by discarding forces near the boundary according to the buffered force‐mixing approach. New adaptive thermostats, needed by force‐mixing methods, are also implemented. Different variants of the method are benchmarked by simulating the structure of bulk water, water autoprotolysis in the presence of zinc and dimethyl‐phosphate hydrolysis using various semiempirical Hamiltonians and density functional theory as the QM model. It is shown that with suitable parameters, based on force convergence tests, the AdBF QM/MM scheme can provide an accurate approximation of the structure in the dynamical QM region matching the corresponding fully QM simulations, as well as reproducing the correct energetics in all cases. Adaptive unbuffered force‐mixing and adaptive conventional QM/MM methods also provide reasonable results for some systems, but are more likely to suffer from instabilities and inaccuracies. © 2015 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

Interactions between phosphate and water in solution: a natural bond orbital based analysis in a QM/MM framework

The natural bond orbital (NBO) and natural energy decomposition analysis (NEDA) calculations are used to analyze the interaction between mono-methyl phosphate-ester (MMP) and its solvation environment in a combined quantum mechanical/molecular mechanical (QM/MM) framework. The solute-solvent configurations are generated using a specific parametrization of the self-consistent-charge density functional tight-binding (SCC-DFTB) model for the MMP and TIP3P for water. The NBO and NEDA calculations are done with several QM/MM partitioning schemes with HF/6-31+G** as the QM level. Regardless of the size of the QM region, a notable amount of charge transfer is observed between MMP and the neighboring water molecules and the charge-transfer interactions are, in the NEDA framework, as important as the electric (electrostatic and polarization) components. This work illustrates that NBO based analyses are effective tools for probing intermolecular interactions in condensed phase systems.     

Development of massive multilevel molecular dynamics simulation program,platypus (PLATform for dYnamic protein unified simulation), for the elucidation of protein functions

A massively parallel program for quantum mechanical‐molecular mechanical (QM/MM) molecular dynamics simulation, called Platypus (PLATform for dYnamic Protein Unified Simulation), was developed to elucidate protein functions. The speedup and the parallelization ratio of Platypus in the QM and QM/MM calculations were assessed for a bacteriochlorophyll dimer in the photosynthetic reaction center (DIMER) on the K computer, a massively parallel computer achieving 10 PetaFLOPs with 705,024 cores. Platypus exhibited the increase in speedup up to 20,000 core processors at the HF/cc‐pVDZ and B3LYP/cc‐pVDZ, and up to 10,000 core processors by the CASCI(16,16)/6‐31G** calculations. We also performed excited QM/MM‐MD simulations on the chromophore of Sirius (SIRIUS) in water. Sirius is a pH‐insensitive and photo‐stable ultramarine fluorescent protein. Platypus accelerated on‐the‐fly excited‐state QM/MM‐MD simulations for SIRIUS in water, using over 4000 core processors. In addition, it also succeeded in 50‐ps (200,000‐step) on‐the‐fly excited‐state QM/MM‐MD simulations for the SIRIUS in water. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

Developing adaptive QM/MM computer simulations for electrochemistry

We report the development of adaptive QM/MM computer simulations for electrochemistry, providing public access to all sources via the free and open source software development model. We present a modular workflow‐based MD simulation code as a platform for algorithms for partitioning space into different regions, which can be treated at different levels of theory on a per‐timestep basis. Currently implemented algorithms focus on targeting molecules and their solvation layers relevant to electrochemistry. Instead of using built‐in forcefields and quantum mechanical methods, the code features a universal interface, which allows for extension to a range of external forcefield programs and programs for quantum mechanical calculations, thus enabling the user to readily implement interfaces to those programs. The purpose of this article is to describe our codes and illustrate its usage. © 2016 Wiley Periodicals, Inc.     

Toward a new approach for determination of solute's charge distribution to analyze interatomic electrostatic interactions in quantum mechanical/molecular mechanical simulations

We present an alternative approach to determine "density-dependent property"-derived charges for molecules in the condensed phase. In the case of a solution, it is essential to take into consideration the electron polarization of molecules in the active site of this system. The solute and solvent molecules in this site have to be described by a quantum mechanical technique and the others are allowed to be treated by a molecular mechanical method (QM/MM scheme). For calculations based on this scheme, using the forces and interaction energy as density-dependent property our charges from interaction energy and forces (CHIEF) approach can provide the atom-centered charges on the solute atoms. These charges reproduce well the electrostatic potentials around the solvent molecules and present properly the picture of the electron density of the QM subsystem in the solution system. Thus, the CHIEF charges can be considered as the atomic charges under the conditions of the QM/MM simulation, and then enable one to analyze electrostatic interactions between atoms in the QM and MM regions. This approach would give a view of the QM nuclei and electrons different from the conventional methods.     

Interfacing the GROMOS (bio)molecular simulation software to quantum‐chemical program packages

The newly implemented quantum‐chemical/molecular‐mechanical (QM/MM) functionality of the Groningen molecular simulation (GROMOS) software for (bio)molecular simulation is described. The implementation scheme is based on direct coupling of the GROMOS C++ software to executables of the quantum‐chemical program packages MNDO and TURBOMOLE, allowing for an independent further development of these packages. The new functions are validated for different test systems using program and model testing techniques. The effect of truncating the QM/MM electrostatic interactions at various QM/MM cutoff radii is discussed and the application of semiempirical versus density‐functional Hamiltonians for a solute molecule in aqueous solution is compared. © 2012 Wiley Periodicals, Inc.     

Incorporation of a QM/MM buffer zone in the variational double self-consistent field method

The explicit polarization (X-Pol) potential is an electronic-structure-based polarization force field, designed for molecular dynamics simulations and modeling of biopolymers. In this approach, molecular polarization and charge transfer effects are explicitly treated by a combined quantum mechanical and molecular mechanical (QM/MM) scheme, and the wave function of the entire system is variationally optimized by a double self-consistent field (DSCF) method. In the present article, we introduce a QM buffer zone for a smooth transition from a QM region to an MM region. Instead of using the Mulliken charge approximation for all QM/MM interactions, the Coulombic interactions between the adjacent fragments are determined directly by electronic structure theory. The present method is designed to accelerate the speed of convergence of the total energy and charge density of the system.     

Contributions of pauli repulsions to the energetics and physical properties computed in QM/MM methods

Conventional combined quantum mechanical/molecular mechanical (QM/MM) methods lack explicit treatment of Pauli repulsions between the quantum‐mechanical and molecular‐mechanical subsystems. Instead, classical Lennard‐Jones (LJ) potentials between QM and MM nuclei are used to model electronic Pauli repulsion and long‐range London dispersion, despite the fact that the latter two are inherently of quantum nature. Use of the simple LJ potential in QM/MM methods can reproduce minimal geometries and energies of many molecular clusters reasonably well, as compared to full QM calculations. However, we show here that the LJ potential cannot correctly describe subtle details of the electron density of the QM subsystem because of the neglect of Pauli repulsions between the QM and MM subsystems. The inaccurate electron density subsequently affects the calculation of electronic and magnetic properties of the QM subsystem. To explicitly consider Pauli interactions with QM/MM methods, we propose a method to use empirical effective potentials on the MM atoms. The test case of the binding energy and magnetic properties of a water dimer shows promising results for the general application of effective potentials to mimic Pauli repulsions in QM/MM calculations. © 2013 Wiley Periodicals, Inc.     

Converging ligand‐binding free energies obtained with free‐energy perturbations at the quantum mechanical level

In this article, the convergence of quantum mechanical (QM) free‐energy simulations based on molecular dynamics simulations at the molecular mechanics (MM) level has been investigated. We have estimated relative free energies for the binding of nine cyclic carboxylate ligands to the octa‐acid deep‐cavity host, including the host, the ligand, and all water molecules within 4.5 Å of the ligand in the QM calculations (158–224 atoms). We use single‐step exponential averaging (ssEA) and the non‐Boltzmann Bennett acceptance ratio (NBB) methods to estimate QM/MM free energy with the semi‐empirical PM6‐DH2X method, both based on interaction energies. We show that ssEA with cumulant expansion gives a better convergence and uses half as many QM calculations as NBB, although the two methods give consistent results. With 720,000 QM calculations per transformation, QM/MM free‐energy estimates with a precision of 1 kJ/mol can be obtained for all eight relative energies with ssEA, showing that this approach can be used to calculate converged QM/MM binding free energies for realistic systems and large QM partitions. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

The QM‐MM interface for CHARMM‐deMon

We present a new QM/MM interface for fast and efficient simulations of organic and biological molecules. The CHARMM/deMon interface has been developed and tested to perform minimization and atomistic simulations for multi‐particle systems. The current features of this QM/MM interface include readability for molecular dynamics, tested compatibility with Free Energy Perturbation simulations (FEP) using the dual topology/single coordinate method. The current coupling scheme uses link atoms, but further extensions of the code to incorporate other available schemes are planned. We report the performance of different levels of theory for the treatment of the QM region, while the MM region was represented by a classical force‐field (CHARMM27) or a polarizable force‐field based on a simple Drude model. The current QM/MM implementation can be coupled to the dual‐thermostat method and the VV2 integrator to run molecular dynamics simulations. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Assessment of weak intermolecular interactions across QM/MM noncovalent boundaries

An assessment of a number of quantum mechanical/molecular mechanical (QM/MM) combinations was performed for weak intermolecular interactions across noncovalent QM/MM 'boundaries'. The popular S22 data set, comprising of a number of weak hydrogen-bonded, dispersion-bound and complexes with mixed interactions was used for the assessment. A range of QM methods was combined with a number of popular MM force fields. The single-point interaction energies, at reference geometries, are presented as deviations to accurate CCSD(T)/CBS reference values. This investigation employed both additive and subtractive QM/MM schemes. The density functional has only a negligible effect; the choice of basis set was also negligible in terms of accuracy. The importance of selecting the most appropriate MM force field for accurately describing interactions at the noncovalent 'boundary' region has a dramatic effect on the accuracy.     

Geometry optimization using tuned and balanced redistributed charge schemes for combined quantum mechanical and molecular mechanical calculations

We performed geometry optimizations using the tuned and balanced redistributed charge algorithms to treat the QM-MM boundary in combined quantum mechanical and molecular mechanical (QM/MM) methods. In the tuned and balanced redistributed charge (TBRC) scheme, the QM boundary atom is terminated by a tuned F link atom, and the charge of the MM boundary atom is properly adjusted to conserve the total charge of the entire QM/MM system; then the adjusted MM boundary charge is moved evenly to the midpoints of the bonds between the MM boundary atom and its neighboring MM atoms. In the tuned and balanced redistributed charge-2 (TBRC2) scheme, the adjusted MM boundary charge is moved evenly to all MM atoms that are attached to the MM boundary atom. A new option, namely charge smearing, has been added to the TBRC scheme, yielding the tuned and balanced smeared redistributed charge (TBSRC) scheme. In the new scheme, the redistributed charges near the QM-MM boundary are smeared to make the electrostatic interactions between the QM region and the redistributed charges more realistic. The TBRC2 scheme and new TBSRC scheme have been tested for various kinds of bonds at a QM-MM boundary, including C-C, C-N, C-O, O-C, N-C, C-S, S-S, S-C, C-Si, and O-N bonds. Charge smearing is necessary if the redistributed charges are close to the QM region, as in the TBSRC scheme, but not if the redistributed charge is farther from the QM region, as in the TBRC2 scheme. We found that QM/MM results using either the TBRC2 scheme or the TBSRC scheme agree well with full QM results; the mean unsigned error (MUE) of the QM/MM deprotonation energy is 1.6 kcal/mol in both cases, and the MUE of QM/MM optimized bond lengths over the three bonds closest to the QM-MM boundary, with errors averaged over the protonated forms and unprotonated forms, is 0.015 ? for TBRC2 and 0.021 ? for TBSRC. The improvements in the new scheme are essential for QM-MM boundaries that pass through a polar bond, but even for boundaries that pass through C-C bonds, the improvement can be quite significant.     

Structures of the Peptide–Water Complexes Studied by the Hybrid Quantum Mechanical—Molecular Mechanical (QM/MM) Technique

Applications of a new approach to the hybrid quantum mechanical and molecular mechanical (QM/MM) theory based on the effective fragment potential technique to calculations of the structures of the peptide—water complexes are described. Our approach assumes that the MM subsystem is viewed as a flexible composition of effective fragments, while fragment–fragment interactions are replaced by MM force fields. In this work, the QM subsystem is composed of water molecules and the MM part refers to peptides. Different isomers of the hydrogen-bonded complex of the dipeptide N-acetyl-L-alanine N-methylamide (AAMA) with four water molecules are considered, and the results of QM/MM calculations are compared to experimental data and to the results of the density functional theory (DFT) treatment. The properties of water chains inside polypeptide tubes, modeling proton wires inside ionic channels, are described.     

Quantum mechanical/molecular mechanical study on the mechanism of the enzymatic Baeyer-Villiger reaction

We report a combined quantum mechanical/molecular mechanical (QM/MM) study on the mechanism of the enzymatic Baeyer-Villiger reaction catalyzed by cyclohexanone monooxygenase (CHMO). In QM/MM geometry optimizations and reaction path calculations, density functional theory (B3LYP/TZVP) is used to describe the QM region consisting of the substrate (cyclohexanone), the isoalloxazine ring of C4a-peroxyflavin, the side chain of Arg-329, and the nicotinamide ring and the adjacent ribose of NADP(+), while the remainder of the enzyme is represented by the CHARMM force field. QM/MM molecular dynamics simulations and free energy calculations at the semiempirical OM3/CHARMM level employ the same QM/MM partitioning. According to the QM/MM calculations, the enzyme-reactant complex contains an anionic deprotonated C4a-peroxyflavin that is stabilized by strong hydrogen bonds with the Arg-329 residue and the NADP(+) cofactor. The CHMO-catalyzed reaction proceeds via a Criegee intermediate having pronounced anionic character. The initial addition reaction has to overcome an energy barrier of about 9 kcal/mol. The formed Criegee intermediate occupies a shallow minimum on the QM/MM potential energy surface and can undergo fragmentation to the lactone product by surmounting a second energy barrier of about 7 kcal/mol. The transition state for the latter migration step is the highest point on the QM/MM energy profile. Gas-phase reoptimizations of the QM region lead to higher barriers and confirm the crucial role of the Arg-329 residue and the NADP(+) cofactor for the catalytic efficiency of CHMO. QM/MM calculations for the CHMO-catalyzed oxidation of 4-methylcyclohexanone reproduce and rationalize the experimentally observed (S)-enantioselectivity for this substrate, which is governed by the conformational preferences of the corresponding Criegee intermediate and the subsequent transition state for the migration step.     

Importance of van der Waals Interactions in QM/MM Simulations

The importance of accurately treating van der Waals interactions between the quantum mechanical (QM) and molecular mechanical (MM) atoms in hybrid QM/MM simulations has been investigated systematically. First, a set of van der Waals (vdW) parameters was optimized for an approximate density functional method, the self-consistent charge-tight binding density functional (SCC-DFTB) approach, based on small hydrogen-bonding clusters. The sensitivity of condensed phase observables to the SCC-DFTB vdW parameters was then quantitatively investigated by SCC-DFTB/MM simulations of several model systems using the optimized set and two sets of extreme vdW parameters selected from the CHARMM22 forcefield. The model systems include a model FAD molecule in solution and a solvated enediolate, and the properties studied include the radial distribution functions of water molecules around the solute (model FAD and enediolate), the reduction potential of the model FAD and the potential of mean force for an intramolecular proton transfer in the enediolate. Although there are noticeable differences between parameter sets for gas-phase clusters and solvent structures around the solute, thermodynamic quantities in the condensed phase (e.g., reduction potential and potential of mean force) were found to be less sensitive to the numerical values of vdW parameters. The differences between SCC-DFTB/MM results with the three vdW parameter sets for SCC-DFTB atoms were explained in terms of the effects of the parameter set on solvation. The current study has made it clear that efforts in improving the reliability of QM/MM methods for energetical properties in the condensed phase should focus on components other than van der Waals interactions between QM and MM atoms.     

An application of the novel quantum mechanical/molecular mechanical method combined with the theory of energy representation: An ionic dissociation of a water molecule in the supercritical water

A novel quantum chemical approach recently developed has been applied to an ionic dissociation of a water molecule (2H(2)O-->H(3)O(+)+OH(-)) in ambient and supercritical water. The method is based on the quantum mechanical/molecular mechanical (QM/MM) simulations combined with the theory of energy representation (QM/MM-ER), where the energy distribution function of MM solvent molecules around a QM solute serves as a fundamental variable to determine the hydration free energy of the solute according to the rigorous framework of the theory of energy representation. The density dependence of the dissociation free energy in the supercritical water has been investigated for the density range from 0.1 to 0.6 g/cm(3) with the temperature fixed at a constant. It has been found that the product ionic species significantly stabilizes in the high density region as compared with the low density. Consequently, the dissociation free energy decreases monotonically as the density increases. The decomposition of the hydration free energy has revealed that the entropic term (-TDeltaS) strongly depends on the density of the solution and dominates the behavior of the dissociation free energy with respect to the variation of the density. The increase in the entropic term in the low density region can be attributed to the decrease in the translational degrees of freedom brought about by the aggregation of solvent water molecules around the ionic solute.