Absorption and emission spectra of fluorescent silica nanoparticles from TD-DFT/MM/PCM calculations

A multi-scale computational protocol, which combines Quantum Mechanics and Molecular Mechanics (QM/MM) calculations with the polarisable continuum model (PCM), has been used to study the tetramethylrhodamine isothiocyanate (TRITC) fluorophore, embedded in three different environments, namely in water, on an amorphous silica surface and covalently encapsulated in a silica nanoparticle (C dot). Absorption and emission spectra have been simulated by using TD-B3LYP/PCM calculations, performed on the TRITC ground and excited state geometries, optimized at the QM/MM level. The results are in good agreement with experimental data confirming the caging effect played by the silica shell on the mobility of the TRITC molecule when covalently encapsulated in silica nanoparticles. This could result in a decrease of the nonradiative decay rate and thus an increase of the quantum yield of the molecule.     

Energy decomposition in molecular complexes: implications for the treatment of polarization in molecular simulations

This study examines the contribution of electrostatic and polarization to the interaction energy in a variety of molecular complexes. The results obtained from the Kitaura-Morokuma (KM) energy decomposition analysis at the HF/6-31G(d) level indicate that, for intermolecular distances around the equilibrium geometries, the polarization energy can be determined as the addition of the polarization energies of interacting blocks, as the mixed polarization term is typically negligible. Comparison of KM and QM/MM results shows that the electrostatic energy determined in the KM method is underestimated (in absolute value) by QM/MM methods. The reason of such underestimation can be attributed to the simplified representation of treating the interaction between overlapping charge distribution by the interaction of a QM molecule with a set of point charges. Nevertheless, the polarization energies calculated by KM and QM/MM methods are in close agreement. Finally, a consistent, automated strategy to derive charge distributions that include implicitly polarization effects in pairwise, additive force fields is presented. The strategy relies in the simultaneous fitting of electrostatic and polarization energies computed by placing a suitable perturbing particle at selected points around the molecule. The suitability of these charges to describe molecular interactions is discussed.     

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.     

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.     

The implementation of a fast and accurate QM/MM potential method in Amber

Version 9 of the Amber simulation programs includes a new semi-empirical hybrid QM/MM functionality. This includes support for implicit solvent (generalized Born) and for periodic explicit solvent simulations using a newly developed QM/MM implementation of the particle mesh Ewald (PME) method. The code provides sufficiently accurate gradients to run constant energy QM/MM MD simulations for many nanoseconds. The link atom approach used for treating the QM/MM boundary shows improved performance, and the user interface has been rewritten to bring the format into line with classical MD simulations. Support is provided for the PM3, PDDG/PM3, PM3CARB1, AM1, MNDO, and PDDG/MNDO semi-empirical Hamiltonians as well as the self-consistent charge density functional tight binding (SCC-DFTB) method. Performance has been improved to the point where using QM/MM, for a QM system of 71 atoms within an explicitly solvated protein using periodic boundaries and PME requires less than twice the cpu time of the corresponding classical simulation.     

Convergence in the QM‐only and QM/MM modeling of enzymatic reactions: A case study for acetylene hydratase

We report systematic quantum mechanics‐only (QM‐only) and QM/molecular mechanics (MM) calculations on an enzyme‐catalyzed reaction to assess the convergence behavior of QM‐only and QM/MM energies with respect to the size of the chosen QM region. The QM and MM parts are described by density functional theory (typically B3LYP/def2‐SVP) and the CHARMM force field, respectively. Extending our previous work on acetylene hydratase with QM regions up to 157 atoms (Liao and Thiel, J. Chem. Theory Comput. 2012, 8, 3793), we performed QM/MM geometry optimizations with a QM region M4 composed of 408 atoms, as well as further QM/MM single‐point calculations with even larger QM regions up to 657 atoms. A charge deletion analysis was conducted for the previously used QM/MM model ( M3a , with a QM region of 157 atoms) to identify all MM residues with strong electrostatic contributions to the reaction energetics (typically more than 2 kcal/mol), which were then included in M4 . QM/MM calculations with this large QM region M4 lead to the same overall mechanism as the previous QM/MM calculations with M3a , but there are some variations in the relative energies of the stationary points, with a mean absolute deviation (MAD) of 2.7 kcal/mol. The energies of the two relevant transition states are close to each other at all levels applied (typically within 2 kcal/mol), with the first (second) one being rate‐limiting in the QM/MM calculations with M3a ( M4 ). QM‐only gas‐phase calculations give a very similar energy profile for QM region M4 (MAD of 1.7 kcal/mol), contrary to the situation for M3a where we had previously found significant discrepancies between the QM‐only and QM/MM results (MAD of 7.9 kcal/mol). Extension of the QM region beyond M4 up to M7 (657 atoms) leads to only rather small variations in the relative energies from single‐point QM‐only and QM/MM calculations (MAD typically about 1–2 kcal/mol). In the case of acetylene hydratase, a model with 408 QM atoms thus seems sufficient to achieve convergence in the computed relative energies to within 1–2 kcal/mol.Copyright © 2013 Wiley Periodicals, Inc.     

Molecular modeling study of checkpoint kinase 1 inhibitors by multiple docking strategies and prime/MM-GBSA calculation

Developing chemicals that inhibit checkpoint kinase 1 (Chk1) is a promising adjuvant therapeutic to improve the efficacy and selectivity of DNA-targeting agents. Reliable prediction of binding-free energy and binding affinity of Chk1 inhibitors can provide a guide for rational drug design. In this study, multiple docking strategies and Prime/Molecular Mechanics Generalized Born Surface Area (Prime/MM-GBSA) calculation were applied to predict the binding mode and free energy for a series of benzoisoquinolinones as Chk1 inhibitors. Reliable docking results were obtained using induced-fit docking and quantum mechanics/molecular mechanics (QM/MM) docking, which showed superior performance on both ligand binding pose and docking score accuracy to the rigid-receptor docking. Then, the Prime/MM-GBSA method based on the docking complex was used to predict the binding-free energy. The combined use of QM/MM docking and Prime/MM-GBSA method could give a high correlation between the predicted binding-free energy and experimentally determined pIC(50) . The molecular docking combined with Prime/MM-GBSA simulation can not only be used to rapidly and accurately predict the binding-free energy of novel Chk1 inhibitors but also provide a novel strategy for lead discovery and optimization targeting Chk1.     

Role of structural water molecule in HIV protease-inhibitor complexes: a QM/MM study

Structural water molecule 301 found at the interface of HIV protease-inhibitor complexes function as a hydrogen bond (H-bond) donor to carbonyl groups of the inhibitor as well as H-bond acceptor to amide/amine groups of the flap region of the protease. In this study, six systems of HIV protease-inhibitor complexes were analyzed, which have the presence of this "conserved" structural water molecule using a two-layer QM/MM ONIOM method. The combination of QM/MM and QM method enabled the calculation of strain energies of the bound ligands as well as the determination of their binding energies in the ligand-water and ligand-water-protease complexes. Although the ligand experiences considerable strain in the protein bound structure, the H-bond interactions through the structural water overcomes this strain effect to give a net stability in the range of 16-24 kcal/mol. For instance, in 1HIV system, the strain energy of the ligand was 12.2 kcal/mol, whereas the binding energy associated with the structural water molecule was 20.8 kcal/mol. In most of the cases, the calculated binding energy of structural water molecule showed the same trend as that of the experimental binding free energy values. Further, the classical MD simulations carried out on 1HVL system with and without structural water 301 showed that this conserved water molecule enhances the H-bond dynamics occurring at the Asp-bound active site region of the protease-inhibitor system, and therefore it will have a direct influence on the mechanism of drug action.     

Chaperoned alchemical free energy simulations: a general method for QM, MM, and QM/MM potentials

A general method for alchemical free energy simulations using QM, MM, and QM/MM potential is developed by introducing "chaperones" to restrain the structures, particularly near the end points. A calculation of the free energy difference between two triazole tautomers in aqueous solution is used to illustrate the method.     

An efficient method for the calculation of quantum mechanics/molecular mechanics free energies

The combination of quantum mechanics (QM) with molecular mechanics (MM) offers a route to improved accuracy in the study of biological systems, and there is now significant research effort being spent to develop QM/MM methods that can be applied to the calculation of relative free energies. Currently, the computational expense of the QM part of the calculation means that there is no single method that achieves both efficiency and rigor; either the QM/MM free energy method is rigorous and computationally expensive, or the method introduces efficiency-led assumptions that can lead to errors in the result, or a lack of generality of application. In this paper we demonstrate a combined approach to form a single, efficient, and, in principle, exact QM/MM free energy method. We demonstrate the application of this method by using it to explore the difference in hydration of water and methane. We demonstrate that it is possible to calculate highly converged QM/MM relative free energies at the MP2/aug-cc-pVDZ/OPLS level within just two days of computation, using commodity processors, and show how the method allows consistent, high-quality sampling of complex solvent configurational change, both when perturbing hydrophilic water into hydrophobic methane, and also when moving from a MM Hamiltonian to a QM/MM Hamiltonian. The results demonstrate the validity and power of this methodology, and raise important questions regarding the compatibility of MM and QM/MM forcefields, and offer a potential route to improved compatibility.     

Uptake of phenol on aerosol particles

We present a study of the interaction between a phenol molecule and an aerosol particle. The aerosol particle is represented by a cluster of 128 water molecules. Using a classical approach, we present interaction energy surfaces for different relative distances and for three orientations of phenol relative to the particle. From the energy surfaces we find the reaction pathways with the largest interaction between the molecule and the particle. We use a quantum mechanics/molecular mechanics (QM/MM) method to calculate a potential energy curve for each reaction path. Coupled cluster methods are used for the part of the system described by quantum mechanics, while the part described by molecular mechanics is represented by a polarizable force field. We compare results obtained from the classical approach with the QM/MM results. Furthermore, we use the QM/MM results to calculate mass accommodation coefficients using a quantum-statistical (QM-ST) model and show how the mass accommodation coefficient depends on the relative orientation of phenol with respect to the aerosol particle.     

Mixed ab initio QM/MM modeling using frozen orbitals and tests with alanine dipeptide and tetrapeptide

Methodology is discussed for mixed ab initio quantum mechanics/molecular mechanics modeling of systems where the quantum mechanics (QM) and molecular mechanics (MM) regions are within the same molecule. The ab initio QM calculations are at the restricted Hartree–Fock level using the pseudospectral method of the Jaguar program while the MM part is treated with the OPLS force fields implemented in the IMPACT program. The interface between the QM and MM regions, in particular, is elaborated upon, as it is dealt with by “breaking” bonds at the boundaries and using Boys-localized orbitals found from model molecules in place of the bonds. These orbitals are kept frozen during QM calculations. Results from tests of the method to find relative conformational energies and geometries of alanine dipeptides and alanine tetrapeptides are presented along with comparisons to pure QM and pure MM calculations. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1468–1494, 1999     

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     

A test of ligand field molecular mechanics as an efficient alternative to QM/MM for modelling metalloproteins: the structures of oxidised type I copper centres

Ligand Field Molecular Mechanics based on homoleptic model systems delivers accurate, unbiased geometries of complete mononuclear blue copper proteins about four orders of magnitude faster than comparable QM/MM calculations.     

Quantum mechanics/molecular mechanics minimum free-energy path for accurate reaction energetics in solution and enzymes: sequential sampling and optimization on the potential of mean force surface

To accurately determine the reaction path and its energetics for enzymatic and solution-phase reactions, we present a sequential sampling and optimization approach that greatly enhances the efficiency of the ab initio quantum mechanics/molecular mechanics minimum free-energy path (QM/MM-MFEP) method. In the QM/MM-MFEP method, the thermodynamics of a complex reaction system is described by the potential of mean force (PMF) surface of the quantum mechanical (QM) subsystem with a small number of degrees of freedom, somewhat like describing a reaction process in the gas phase. The main computational cost of the QM/MM-MFEP method comes from the statistical sampling of conformations of the molecular mechanical (MM) subsystem required for the calculation of the QM PMF and its gradient. In our new sequential sampling and optimization approach, we aim to reduce the amount of MM sampling while still retaining the accuracy of the results by first carrying out MM phase-space sampling and then optimizing the QM subsystem in the fixed-size ensemble of MM conformations. The resulting QM optimized structures are then used to obtain more accurate sampling of the MM subsystem. This process of sequential MM sampling and QM optimization is iterated until convergence. The use of a fixed-size, finite MM conformational ensemble enables the precise evaluation of the QM potential of mean force and its gradient within the ensemble, thus circumventing the challenges associated with statistical averaging and significantly speeding up the convergence of the optimization process. To further improve the accuracy of the QM/MM-MFEP method, the reaction path potential method developed by Lu and Yang [Z. Lu and W. Yang, J. Chem. Phys. 121, 89 (2004)] is employed to describe the QM/MM electrostatic interactions in an approximate yet accurate way with a computational cost that is comparable to classical MM simulations. The new method was successfully applied to two example reaction processes, the classical SN2 reaction of Cl-+CH3Cl in solution and the second proton transfer step of the reaction catalyzed by the enzyme 4-oxalocrotonate tautomerase. The activation free energies calculated with this new sequential sampling and optimization approach to the QM/MM-MFEP method agree well with results from other simulation approaches such as the umbrella sampling technique with direct QM/MM dynamics sampling, demonstrating the accuracy of the iterative QM/MM-MFEP method.     

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.     

On the effect of a variation of the force field, spatial boundary condition and size of the QM region in QM/MM MD simulations

During the past years, the use of combined quantum-classical, QM/MM, methods for the study of complex biomolecular processes, such as enzymatic reactions and photocycles, has increased considerably. The quality of the results obtained from QM/MM calculations is largely dependent on five aspects to be considered when setting up a molecular model: the QM Hamiltonian, the MM Hamiltonian or force field, the boundary and coupling between the QM and MM regions, the size of the QM region and the boundary condition for the MM region. In this study, we systematically investigate the influence of a variation of the molecular mechanics force field and the size of the QM region in QM/MM MD simulations on properties of the photoactive part of the blue light photoreceptor protein AppA. For comparison, we additionally performed classical MD simulations and studied the effect of a variation of the type of spatial boundary condition. The classical boundary conditions and the force field used in a QM/MM MD simulation are shown to have non-neglegible effects upon the structural and energetic properties of the protein which makes it advisable to minimize computational artifacts in QM/MM MD simulations by application of periodic boundary conditions and a thermodynamically calibrated force field. A comparison of the structural and energetic properties of MD simulations starting from two alternative, different X-ray structures for the blue light utilizing flavin protein in its dark state indicates a slight preference of the two force fields used for the so-called Anderson structure over the Jung structure.