An extensible interface for QM/MM molecular dynamics simulations with AMBER

We present an extensible interface between the AMBER molecular dynamics (MD) software package and electronic structure software packages for quantum mechanical (QM) and mixed QM and classical molecular mechanical (MM) MD simulations within both mechanical and electronic embedding schemes. With this interface, ab initio wave function theory and density functional theory methods, as available in the supported electronic structure software packages, become available for QM/MM MD simulations with AMBER. The interface has been written in a modular fashion that allows straight forward extensions to support additional QM software packages and can easily be ported to other MD software. Data exchange between the MD and QM software is implemented by means of files and system calls or the message passing interface standard. Based on extensive tests, default settings for the supported QM packages are provided such that energy is conserved for typical QM/MM MD simulations in the microcanonical ensemble. Results for the free energy of binding of calcium ions to aspartate in aqueous solution comparing semiempirical and density functional Hamiltonians are shown to demonstrate features of this interface. © 2013 Wiley Periodicals, Inc.     

QuanPol: A full spectrum and seamless QM/MM program

The quantum chemistry polarizable force field program (QuanPol) is implemented to perform combined quantum mechanical and molecular mechanical (QM/MM) calculations with induced dipole polarizable force fields and induced surface charge continuum solvation models. The QM methods include Hartree–Fock method, density functional theory method (DFT), generalized valence bond theory method, multiconfiguration self‐consistent field method, Møller–Plesset perturbation theory method, and time‐dependent DFT method. The induced dipoles of the MM atoms and the induced surface charges of the continuum solvation model are self‐consistently and variationally determined together with the QM wavefunction. The MM force field methods can be user specified, or a standard force field such as MMFF94, Chemistry at Harvard Molecular Mechanics (CHARMM), Assisted Model Building with Energy Refinement (AMBER), and Optimized Potentials for Liquid Simulations‐All Atom (OPLS‐AA). Analytic gradients for all of these methods are implemented so geometry optimization and molecular dynamics (MD) simulation can be performed. MD free energy perturbation and umbrella sampling methods are also implemented. © 2013 Wiley Periodicals, Inc.     

Quantum supercharger library: Hyper‐parallel integral derivatives algorithms for ab initio QM/MM dynamics

This article describes an extension of the quantum supercharger library (QSL) to perform quantum mechanical (QM) gradient and optimization calculations as well as hybrid QM and molecular mechanical (QM/MM) molecular dynamics simulations. The integral derivatives are, after the two‐electron integrals, the most computationally expensive part of the aforementioned calculations/simulations. Algorithms are presented for accelerating the one‐ and two‐electron integral derivatives on a graphical processing unit (GPU). It is shown that a Hartree–Fock ab initio gradient calculation is up to 9.3X faster on a single GPU compared with a single central processing unit running an optimized serial version of GAMESS‐UK, which uses the efficient Schlegel method for ‐ and ‐orbitals. Benchmark QM and QM/MM molecular dynamics simulations are performed on cellobiose in vacuo and in a 39 Å water sphere (45 QM atoms and 24843 point charges, respectively) using the 6‐31G basis set. The QSL can perform 9.7 ps/day of ab initio QM dynamics and 6.4 ps/day of QM/MM dynamics on a single GPU in full double precision. © 2015 Wiley Periodicals, Inc.     

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.     

Optimizing efficiency of perturbative Monte Carlo method

We introduce error weighting functions into the perturbative Monte Carlo method for use with a hybrid ab initio quantum mechanics/molecular mechanics (QM/MM) potential. The perturbative Monte Carlo approach introduced earlier provides a means to reduce the number of full SCF calculations in simulations using a QM/MM potential by evoking perturbation theory to calculate energy changes due to displacements of an MM molecule. The use of weighting functions, introduced here, allows an optimal number of MM molecule displacements to occur between the performance of the full self-consistent field calculations. This will allow the ab initio QM/MM approach to be applied to systems that require more accurate treatment of the QM and/or MM regions. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1632–1638, 1998     

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.     

Comment on “a minimal implementation of the AMBER–GAUSSIAN interface for Ab Initio QM/MM‐MD simulation”

We comment upon the recent critique of use of the Program for User Package Interfacing and Linking (PUPIL) system for linking AMBER and GAUSSIAN in a multiscale quantum mechanical/molecular mechanics (QM/MM) simulation (Okamoto et al., J. Comput. Chem. 2011 , 32, 932). Specifically, their method for computing forces on the MM particles from the QM region via the GAUSSIAN‐03 electrical field was already implemented in PUPIL version 1.3, publicly available beginning December 2009. Some other doubtful characterizations of PUPIL are discussed briefly in the context of current awareness of open‐source codes more generally. © 2012 Wiley Periodicals, Inc.     

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.     

The CHARMM–TURBOMOLE interface for efficient and accurate QM/MM molecular dynamics,free energies,and excited state properties

The quantum mechanical (QM)/molecular mechanical (MM) interface between Chemistry at HARvard Molecular Mechanics (CHARMM) and TURBOMOLE is described. CHARMM provides an extensive set of simulation algorithms, like molecular dynamics (MD) and free energy perturbation, and support for mature nonpolarizable and Drude polarizable force fields. TURBOMOLE provides fast QM calculations using density functional theory or wave function methods and excited state properties. CHARMM–TURBOMOLE is well‐suited for extended QM/MM MD simulations using first principles methods with large (triple‐ζ) basis sets. We demonstrate these capabilities with a QM/MM simulation of Mg²⁺(aq), where the MM outer sphere water molecules are represented using the SWM4‐NDP Drude polarizable force field and the ion and inner coordination sphere are represented using QM PBE, PBE0, and MP2 methods. The relative solvation free energies of Mg²⁺ and Zn²⁺ were calculated using thermodynamic integration. We also demonstrate the features for excited state properties. We calculate the time‐averaged solution absorption spectrum of indole, the emission spectrum of the indole excited state, and the electronic circular dichroism spectrum of an oxacepham. © 2014 Wiley Periodicals, Inc.     

CPMD/GULP QM/MM interface for modeling periodic solids: Implementation and its application in the study of Y‐zeolite supported Rhn clusters

We report here the development of hybrid quantum mechanics/molecular mechanics (QM/MM) interface between the plane‐wave density functional theory based CPMD code and the empirical force‐field based GULP code for modeling periodic solids and surfaces. The hybrid QM/MM interface is based on the electrostatic coupling between QM and MM regions. The interface is designed for carrying out full relaxation of all the QM and MM atoms during geometry optimizations and molecular dynamics simulations, including the boundary atoms. Both Born–Oppenheimer and Car–Parrinello molecular dynamics schemes are enabled for the QM part during the QM/MM calculations. This interface has the advantage of parallelization of both the programs such that the QM and MM force evaluations can be carried out in parallel to model large systems. The interface program is first validated for total energy conservation and parallel scaling performance is benchmarked. Oxygen vacancy in α‐cristobalite is then studied in detail and the results are compared with a fully QM calculation and experimental data. Subsequently, we use our implementation to investigate the structure of rhodium cluster (Rh_n; n = 2 to 6) formed from Rh(C₂H₄)₂ complex adsorbed within a cavity of Y‐zeolite in a reducible atmosphere of H₂ gas. © 2016 Wiley Periodicals, Inc.     

Molecular insight into the interaction mechanisms of amino‐2H‐imidazole derivatives with BACE1 protease: A QM/MM and QTAIM study

In this study, we described quantitatively the interactions between two new amino‐2H‐imidazole inhibitors ((R)‐1t and (S)‐1m) and BACE1 using a hybrid quantum mechanics‐molecular mechanical (QM/MM) method together with a quantum theory of atoms In Molecules (QTAIM) analysis. Our computational calculations revealed that the binding affinity of these compounds is mostly related to the amino‐2H‐imidazole core, which interact tightly with the aspartate dyad of the active site. The interactions were stronger when the inhibitors presented a bulky substituent with a hydrogen bond acceptor motif pointing toward Trp76, such as the 3,5‐dimethyl‐4‐methoxyphenyl group of compound (S)‐1m. Furthermore, the QTAIM analysis revealed that many hydrophobic interactions complement cooperatively the hydrogen bond which is not present when compound (R)‐1t is bound to the enzyme. The combined QM/MM‐QTAIM analysis allows identifying the interactions that account for the activity difference between compounds, even at a nanomolar range.     

Increasing the time step with mass scaling in Born‐Oppenheimer ab initio QM/MM molecular dynamics simulations

Born‐Oppenheimer ab initio QM/MM molecular dynamics simulation with umbrella sampling is a state‐of‐the‐art approach to calculate free energy profiles of chemical reactions in complex systems. To further improve its computational efficiency, a mass‐scaling method with the increased time step in MD simulations has been explored and tested. It is found that by increasing the hydrogen mass to 10 amu, a time step of 3 fs can be employed in ab initio QM/MM MD simulations. In all our three test cases, including two solution reactions and one enzyme reaction, the resulted reaction free energy profiles with 3 fs time step and mass scaling are found to be in excellent agreement with the corresponding simulation results using 1 fs time step and the normal mass. These results indicate that for Born‐Oppenheimer ab initio QM/MM molecular dynamics simulations with umbrella sampling, the mass‐scaling method can significantly reduce its computational cost while has little effect on the calculated free energy profiles. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

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.     

Revealing the Absolute Configuration of the CO and CN− Ligands at the Active Site of a [NiFe] Hydrogenase

Combined molecular dynamics (MD) and quantum mechanical/molecular mechanical (QM/MM) calculations were performed on the crystal structure of the reduced membrane‐bound [NiFe] hydrogenase (MBH) from Ralstonia eutropha to determine the absolute configuration of the CO and the two CN^? ligands bound to the active‐site iron of the enzyme. For three models that include the CO ligand at different positions, often indistinguishable on the basis of the crystallographic data, we optimized the structures and calculated the ligand stretching frequencies. Comparison with the experimental IR data reveals that the CO ligand is in trans position to the substrate‐binding site of the bimetallic [NiFe] cluster.     

A QM/MM study of the binding of RAPTA ligands to cathepsin B

We have carried out quantum mechanical (QM) and QM/MM (combined QM and molecular mechanics) calculations, as well as molecular dynamics (MD) simulations to study the binding of a series of six RAPTA (Ru(II)-arene-1,3,5-triaza-7-phosphatricyclo-[3.3.1.1] decane) complexes with different arene substituents to cathepsin B. The recently developed QM/MM-PBSA approach (QM/MM combined with Poisson–Boltzmann solvent-accessible surface area solvation) has been used to estimate binding affinities. The QM calculations reproduce the antitumour activities of the complexes with a correlation coefficient (r ²) of 0.35–0.86 after a conformational search. The QM/MM-PBSA method gave a better correlation (r ² = 0.59) when the protein was fixed to the crystal structure, but more reasonable ligand structures and absolute binding energies were obtained if the protein was allowed to relax, indicating that the ligands are strained when the protein is kept fixed. In addition, the best correlation (r ² = 0.80) was obtained when only the QM energies were used, which suggests that the MM and continuum solvation energies are not accurate enough to predict the binding of a charged metal complex to a charged protein. Taking into account the protein flexibility by means of MD simulations slightly improves the correlation (r ² = 0.91), but the absolute energies are still too large and the results are sensitive to the details in the calculations, illustrating that it is hard to obtain stable predictions when full flexible protein is included in the calculations.     

Quantitative Prediction of Aggregation‐Induced Emission: A Full Quantum Mechanical Approach to the Optical Spectra

Full quantum mechanical (FQM) calculation of the excited state of aggregation‐induced‐emission (AIE) materials is highly sought but still a challenging task. Herein, we employed the recently developed electrostatically embedded generalized molecular fractionation (EE‐GMF) method, a method based on the systematic fragmentation approach, to predict, for the first time, the spectra of a prototype AIE fluorophore: di(p‐methoxylphenyl)dibenzofulvene (FTPE). Compared to the single molecular or QM/MM calculations, the EE‐GMF method shows significantly improved accuracy, nearly reproducing the experimental optical spectra of FTPE in both condensed phases. Importantly, we show that the conventional restriction of the intramolecular rotation mechanism cannot fully account for AIE, whereas the two‐body intermolecular quantum mechanical interaction plays a crucial role in AIE.     

Comparison of radii sets,entropy, QM methods,and sampling on MM‐PBSA,MM‐GBSA,and QM/MM‐GBSA ligand binding energies of F. tularensis enoyl‐ACP reductase (FabI)

To validate a method for predicting the binding affinities of FabI inhibitors, three implicit solvent methods, MM‐PBSA, MM‐GBSA, and QM/MM‐GBSA were carefully compared using 16 benzimidazole inhibitors in complex with Francisella tularensis FabI. The data suggests that the prediction results are sensitive to radii sets, GB methods, QM Hamiltonians, sampling protocols, and simulation length, if only one simulation trajectory is used for each ligand. In this case, QM/MM‐GBSA using 6 ns MD simulation trajectories together with GB^neck2, PM3, and the mbondi2 radii set, generate the closest agreement with experimental values (r² = 0.88). However, if the three implicit solvent methods are averaged from six 1 ns MD simulations for each ligand (called “multiple independent sampling”), the prediction results are relatively insensitive to all the tested parameters. Moreover, MM/GBSA together with GB^HCT and mbondi, using 600 frames extracted evenly from six 0.25 ns MD simulations, can also provide accurate prediction to experimental values (r² = 0.84). Therefore, the multiple independent sampling method can be more efficient than a single, long simulation method. Since future scaffold expansions may significantly change the benzimidazole's physiochemical properties (charges, etc.) and possibly binding modes, which may affect the sensitivities of various parameters, the relatively insensitive “multiple independent sampling method” may avoid the need of an entirely new validation study. Moreover, due to large fluctuating entropy values, (QM/)MM‐P(G)BSA were limited to inhibitors’ relative affinity prediction, but not the absolute affinity. The developed protocol will support an ongoing benzimidazole lead optimization program. © 2015 Wiley Periodicals, Inc.     

Calculation of wave‐functions with frozen orbitals in mixed quantum mechanics/molecular mechanics methods. II. Application of the local basis equation

The application of the local basis equation (Ferenczy and Adams, J. Chem. Phys. 2009 , 130, 134108) in mixed quantum mechanics/molecular mechanics (QM/MM) and quantum mechanics/quantum mechanics (QM/QM) methods is investigated. This equation is suitable to derive local basis nonorthogonal orbitals that minimize the energy of the system and it exhibits good convergence properties in a self‐consistent field solution. These features make the equation appropriate to be used in mixed QM/MM and QM/QM methods to optimize orbitals in the field of frozen localized orbitals connecting the subsystems. Calculations performed for several properties in divers systems show that the method is robust with various choices of the frozen orbitals and frontier atom properties. With appropriate basis set assignment, it gives results equivalent with those of a related approach [G. G. Ferenczy previous paper in this issue] using the Huzinaga equation. Thus, the local basis equation can be used in mixed QM/MM methods with small size quantum subsystems to calculate properties in good agreement with reference Hartree–Fock–Roothaan results. It is shown that bond charges are not necessary when the local basis equation is applied, although they are required for the self‐consistent field solution of the Huzinaga equation based method. Conversely, the deformation of the wave‐function near to the boundary is observed without bond charges and this has a significant effect on deprotonation energies but a less pronounced effect when the total charge of the system is conserved. The local basis equation can also be used to define a two layer quantum system with nonorthogonal localized orbitals surrounding the central delocalized quantum subsystem. © 2013 Wiley Periodicals, Inc.