Hybrid QM/MM molecular dynamics simulations for an ionic SN2 reaction in the supercritical water: OH- + CH3Cl --> CH3OH + Cl-

A hybrid real space quantum mechanical/molecular mechanical (RS-QM/MM) method has been applied to an ionic S(N)2 reaction (OH- + CH3Cl --> CH3OH + Cl-) in water solution to investigate dynamic solvation effects of the supercritical water (SCW) on the reaction. It has been demonstrated that the approaching process of OH- to methyl group is prevented by water molecules in the ambient water (AW), while the reaction takes place easily in the gas phase. Almost the same solvation effect on the dynamics of OH- is observed in the SCW, though the bulk density of water is substantially reduced compared with that of the AW. It has been shown that the solvation of the SCW around the OH anion is locally identical to that of the AW due to the strong ion-dipole interactions between OH- and water molecules. At the transition state, the QM/MM simulations have revealed that the excess electron is quite flexible, and the charge volume, as well as the fractional charges on atoms, vary seriously depending on the instantaneous solvent configurations. However, it has been found that the solvation energy in the SCW can be qualitatively related to the HOMO volume of the system by Born's equation.     

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.     

Polarization and charge-transfer effects in aqueous solution via ab initio QM/MM simulations

Combined ab initio quantum mechanical and molecular mechanical (QM/MM) simulations coupled with the block-localized wave function energy decomposition (BLW-ED) method have been conducted to study the solvation of two prototypical ionic systems, acetate and methylammonium ions in aqueous solution. Calculations reveal that the electronic polarization between the targeted solutes and water is the primary many-body effect, whereas the charge-transfer term only makes a small fraction of the total solute-solvent interaction energy. In particular, the polarization effect is dominated by the solvent (water) polarization.     

Coupled semiempirical quantum mechanics and molecular mechanics (QM/MM) calculations on the aqueous solvation free energies of ionized molecules

The aqueous solvation free energies of ionized molecules were computed using a coupled quantum mechanical and molecular mechanical (QM/MM) model based on the AM1, MNDO, and PM3 semiempirical molecular orbital methods for the solute molecule and the TIP3P molecular mechanics model for liquid water. The present work is an extension of our model for neutral solutes where we assumed that the total free energy is the sum of components derived from the electrostatic/polarization terms in the Hamiltonian plus an empirical “nonpolar” term. The electrostatic/polarization contributions to the solvation free energies were computed using molecular dynamics (MD) simulation and thermodynamic integration techniques, while the nonpolar contributions were taken from the literature. The contribution to the electrostatic/polarization component of the free energy due to nonbonded interactions outside the cutoff radii used in the MD simulations was approximated by a Born solvation term. The experimental free energies were reproduced satisfactorily using variational parameters from the vdW terms as in the original model, in addition to a parameter from the one-electron integral terms. The new one-electron parameter was required to account for the short-range effects of overlapping atomic charge densities. The radial distribution functions obtained from the MD simulations showed the expected H-bonded structures between the ionized solute molecule and solvent molecules. We also obtained satisfactory results by neglecting both the empirical nonpolar term and the electronic polarization of the solute, i.e., by implementing a nonpolarization model. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1028–1038, 1999     

Toward a consistent treatment of polarization in model QM/MM calculations

The concept of model chemistries within hybrid QM/MM calculations has been addressed through analysis of the polarization energy determined by two distinct approaches based on (i) induced charges and (ii) induced dipoles. The quantum mechanical polarization energy for four configurations of the water dimer has been determined for a range of basis sets using Morokuma energy decomposition analysis. This benchmark value has been compared to the fully classical polarization energy determined using the induced dipole approach, and the molecular mechanics polarization energy calculated using induced charges within the MM region of hybrid QM/MM calculations. From the water dimer calculations, it is concluded that the induced charge approach is consistent with medium sized basis set calculations whereas the induced dipole approach is consistent with large basis set calculations. This result is highly relevant to the concept of QM/MM model chemistries.     

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.     

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.     

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.     

Reduction potentials and acidity constants of Mn superoxide dismutase calculated by QM/MM free-energy methods

We used two theoretical methods to estimate reduction potentials and acidity constants in Mn superoxide dismutase (MnSOD), namely combined quantum mechanical and molecular mechanics (QM/MM) thermodynamic cycle perturbation (QTCP) and the QM/MM-PBSA approach. In the latter, QM/MM energies are combined with continuum solvation energies calculated by solving the Poisson-Boltzmann equation (PB) or by the generalised Born approach (GB) and non-polar solvation energies calculated from the solvent-exposed surface area. We show that using the QTCP method, we can obtain accurate and precise estimates of the proton-coupled reduction potential for MnSOD, 0.30±0.01 V, which compares favourably with experimental estimates of 0.26-0.40 V. However, the calculated potentials depend strongly on the DFT functional used: The B3LYP functional gives 0.6 V more positive potentials than the PBE functional. The QM/MM-PBSA approach leads to somewhat too high reduction potentials for the coupled reaction and the results depend on the solvation model used. For reactions involving a change in the net charge of the metal site, the corresponding results differ by up to 1.3 V or 24 pK(a) units, rendering the QM/MM-PBSA method useless to determine absolute potentials. However, it may still be useful to estimate relative shifts, although the QTCP method is expected to be more accurate.     

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.     

Cope elimination: elucidation of solvent effects from QM/MM simulations

The Cope elimination reactions for threo- and erythro-N,N-dimethyl-3-phenyl-2-butylamine oxide have been investigated using QM/MM calculations in water, THF, and DMSO. The aprotic solvents provide up to million-fold rate accelerations. The effects of solvation on the reactants, transition structures, and rates of reaction are elucidated here using two-dimensional potentials of mean force (PMF) derived from free-energy perturbation calculations in Monte Carlo simulations (MC/FEP). The resultant free energies of activation in solution are in close agreement with experiment. Ab initio calculations at the MP2/6-311+G-(2d,p) level using the PCM continuum solvent model were also carried out; however, only the QM/MM methodology was able to reproduce the large rate increases in proceeding from water to the dipolar aprotic solvents. Solute-solvent interaction energies and radial distribution functions are also analyzed and show that poorer solvation of the reactant in the aprotic solvents is primarily responsible for the observed rate enhancements. It is found that the amine oxide oxygen is the acceptor of three hydrogen bonds from water molecules for the reactant but only one to two weaker ones at the transition state. The overall quantitative success of the computations supports the present QM/MM/MC approach, featuring PDDG/PM3 as the QM method.     

Structure and dynamics of hydrated NH(4) (+): an ab initio QM/MM molecular dynamics simulation

A combined ab initio quantum mechanical/molecular mechanical (QM/MM) molecular dynamics simulation has been performed to investigate solvation structure and dynamics of NH(4) (+) in water. The most interesting region, the sphere includes an ammonium ion and its first hydration shell, was treated at the Hartree-Fock level using DZV basis set, while the rest of the system was described by classical pair potentials. On the basis of detailed QM/MM simulation results, the solvation structure of NH(4) (+) is rather flexible, in which many water molecules are cooperatively involved in the solvation shell of the ion. Of particular interest, the QM/MM results show fast translation and rotation of NH(4) (+) in water. This phenomenon has resulted from multiple coordination, which drives the NH(4) (+) to translate and rotate quite freely within its surrounding water molecules. In addition, a "structure-breaking" behavior of the NH(4) (+) is well reflected by the detailed analysis on the water exchange process and the mean residence times of water molecules surrounding the ion.     

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.     

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.     

A novel quantum mechanical/molecular mechanical approach to the free energy calculation for isomerization of glycine in aqueous solution

The free energy change associated with the isomerization reaction of glycine in water solution has been studied by a hybrid quantum mechanical/molecular mechanical (QM/MM) approach combined with the theory of energy representation (QM/MM-ER) recently developed. The solvation free energies for both neutral and zwitterionic form of glycine have been determined by means of the QM/MM-ER simulation. The contributions of the electronic polarization and the fluctuation of the QM solute to the solvation free energy have been investigated. It has been found that the contribution of the density fluctuation of the zwitterionic solute is estimated as -4.2 kcal/mol in the total solvation free energy of -46.1 kcal/mol, while that of the neutral form is computed as -3.0 kcal/mol in the solvation free energy of -15.6 kcal/mol. The resultant free energy change associated with the isomerization of glycine in water has been obtained as -7.8 kcal/mol, in excellent agreement with the experimental data of -7.3 or -7.7 kcal/mol, implying the accuracy of the QM/MM-ER approach. The results have also been compared with those computed by other methodologies such as the polarizable continuum model and the classical molecular simulation. The efficiency and advantage of the QM/MM-ER method has been discussed.     

Water solvent effects using continuum and discrete models: The nitromethane molecule,CH3NO2

The first three valence transitions of the two nitromethane conformers (CH₃NO₂) are two dark n → π* transitions and a very intense π → π* transition. In this work, these transitions in gas‐phase and solvated in water of both conformers were investigated theoretically. The polarizable continuum model (PCM), two conductor‐like screening (COSMO) models, and the discrete sequential quantum mechanics/molecular mechanics (S‐QM/MM) method were used to describe the solvation effect on the electronic spectra. Time dependent density functional theory (TDDFT), configuration interaction including all single substitutions and perturbed double excitations (CIS(D)), the symmetry‐adapted‐cluster CI (SAC‐CI), the multistate complete active space second order perturbation theory (CASPT2), and the algebraic‐diagrammatic construction (ADC(2)) electronic structure methods were used. Gas‐phase CASPT2, SAC‐CI, and ADC(2) results are in very good agreement with published experimental and theoretical spectra. Among the continuum models, PCM combined either with CASPT2, SAC‐CI, or B3LYP provided good agreement with available experimental data. COSMO combined with ADC(2) described the overall trends of the transition energy shifts. The effect of increasing the number of explicit water molecules in the S‐QM/MM approach was discussed and the formation of hydrogen bonds was clearly established. By including explicitly 24 water molecules corresponding to the complete first solvation shell in the S‐QM/MM approach, the ADC(2) method gives more accurate results as compared to the TDDFT approach and with similar computational demands. The ADC(2) with S‐QM/MM model is, therefore, the best compromise for accurate solvent calculations in a polar environment. © 2015 Wiley Periodicals, Inc.