QM:QM electronic embedding using Mulliken atomic charges: energies and analytic gradients in an ONIOM framework

An accurate first-principles treatment of chemical reactions for large systems remains a significant challenge facing electronic structure theory. Hybrid models, such as quantum mechanics:molecular mechanics (QM:MM) and quantum mechanics:quantum mechanics (QM:QM) schemes, provide a promising avenue for such studies. For many chemistries, including important reactions in materials science, molecular mechanics or semiempirical methods may not be appropriate, or parameters may not be available (e.g., surface chemistry of compound semiconductors such as indium phosphide or catalytic chemistry of transition metal oxides). In such cases, QM:QM schemes are of particular interest. In this work, a QM:QM electronic embedding model within the ONIOM (our own N-layer integrated molecular orbital molecular mechanics) extrapolation framework is presented. To define the embedding potential, we choose the real-system low-level Mulliken atomic charges. This results in a set of well-defined and unique embedding charges. However, the parametric dependence of the charges on molecular geometry complicates the energy gradient that is necessary for the efficient exploration of potential energy surfaces. We derive an efficient form for the forces where a single set of self-consistent field response equations is solved. Initial tests of the method and key algorithmic issues are discussed.     

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.     

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.     

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.     

Simulations of liquid ammonia based on the combined quantum mechanical/molecular mechanical (QM/MM) approach

Two combined quantum mechanics/molecular mechanics (QM/MM) molecular dynamics simulations, namely, HF/MM and B3LYP/MM, have been performed to investigate the local structure and dynamics of liquid ammonia. The most interesting region, a sphere containing a central reference molecule and all its nearest surrounding molecules (first coordination shell), was treated by the Hartree-Fock (HF) and hybrid density functional B3LYP methods, whereas the rest of the system was described by the classical pair potentials. On the basis of both HF and B3LYP methods, it is observed that the hydrogen bonding in this peculiar liquid is weak. The structure and dynamics of this liquid are suggested to be determined by the steric packing effects, rather than by the directional hydrogen bonding interactions. Compared to previous empirical as well as Car-Parrinello (CP) molecular dynamics studies, our QM/MM simulations provide detailed information that is in better agreement with experimental data.     

The structure of the enzyme-substrate complex of the phosphodiesterase catalytic domain with cyclic diguanosine monophosphate

A three-dimensional, all-atom structure of the enzyme-substrate complex of the phosphodiesterase catalytic domain with diguanosine monophosphate was constructed based on the results of hybrid quantum mechanics/molecular mechanics (QM/MM) calculations.     

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.     

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     

Reaction path potential for complex systems derived from combined ab initio quantum mechanical and molecular mechanical calculations

Combined ab initio quantum mechanical and molecular mechanical calculations have been widely used for modeling chemical reactions in complex systems such as enzymes, with most applications being based on the determination of a minimum energy path connecting the reactant through the transition state to the product in the enzyme environment. However, statistical mechanics sampling and reaction dynamics calculations with a combined ab initio quantum mechanical (QM) and molecular mechanical (MM) potential are still not feasible because of the computational costs associated mainly with the ab initio quantum mechanical calculations for the QM subsystem. To address this issue, a reaction path potential energy surface is developed here for statistical mechanics and dynamics simulation of chemical reactions in enzymes and other complex systems. The reaction path potential follows the ideas from the reaction path Hamiltonian of Miller, Handy and Adams for gas phase chemical reactions but is designed specifically for large systems that are described with combined ab initio quantum mechanical and molecular mechanical methods. The reaction path potential is an analytical energy expression of the combined quantum mechanical and molecular mechanical potential energy along the minimum energy path. An expansion around the minimum energy path is made in both the nuclear and the electronic degrees of freedom for the QM subsystem internal energy, while the energy of the subsystem described with MM remains unchanged from that in the combined quantum mechanical and molecular mechanical expression and the electrostatic interaction between the QM and MM subsystems is described as the interaction of the MM charges with the QM charges. The QM charges are polarizable in response to the changes in both the MM and the QM degrees of freedom through a new response kernel developed in the present work. The input data for constructing the reaction path potential are energies, vibrational frequencies, and electron density response properties of the QM subsystem along the minimum energy path, all of which can be obtained from the combined quantum mechanical and molecular mechanical calculations. Once constructed, it costs much less for its evaluation. Thus, the reaction path potential provides a potential energy surface for rigorous statistical mechanics and reaction dynamics calculations of complex systems. As an example, the method is applied to the statistical mechanical calculations for the potential of mean force of the chemical reaction in triosephosphate isomerase.     

A Molecular Mechanics Energy Partitioning Software for Biomolecular Systems

The partitioning of the molecular mechanics (MM) energy in calculations involving biomolecular systems is important to identify the source of major stabilizing interactions, e.g., in ligand–protein interactions, or to identify residues with considerable contributions in hybrid multiscale calculations, i.e., quantum mechanics/molecular mechanics (QM/MM). Here, we describe Energy Split, a software program to calculate MM energy partitioning considering the AMBER Hamiltonian and parameters. Energy Split includes a graphical interface plugin for VMD to facilitate the selection of atoms and molecules belonging to each part of the system. Energy Split is freely available at or can be easily installed through the VMD Store.     

量子力学和分子力学组合方法

量子力学和分子力学(QM/MM)组合方法结合了量子力学的精确性和分子力学的高效性,在研究凝聚态中的化学反应及生物大分子的结构和活性等方面发挥着重要作用。本文主要介绍了QM/MM组合方法的基本原理及国内外有关QM/MM组合方法的研究进展。