An Improved Isotropic Periodic Sum Method That Uses Linear Combinations of Basis Potentials

Analytic Gradients for the Electrostatic Embedding QM/MM Model in Periodic Boundary Conditions Using Particle-Mesh Ewald Sums and Electrostatic Potential Fitted Charge Operators

Long-range electrostatic effects are fundamental for describing chemical reactivity in the condensed phase. Here, we present the methodology of an efficient quantum mechanical/molecular mechanical (QM/MM) model in periodic boundary conditions (PBC) compatible with QM/MM boundaries at chemical bonds. The method combines electrostatic potential fitted charge operators and electrostatic potentials derived from the smooth particle-mesh Ewald (PME) sum approach. The total energy and its analytic first derivatives with respect to QM, MM, and lattice vectors allow QM/MM molecular dynamics (MD) in the most common thermodynamic ensembles. We demonstrate the robustness of the method by performing a QM/MM MD equilibration of methanol in water. We simulate the cis/trans isomerization free-energy profiles in water of proline amino acid and a proline-containing oligopeptide, showing a correct description of the reaction barrier. Our PBC-compatible QM/MM model can efficiently be used to study the chemical reactivity in the condensed phase and enzymatic catalysis.

Analytical Hessians for Ewald and particle mesh Ewald electrostatics

The particle mesh Ewald (PME) method has become ubiquitous in the molecular simulation community due to its ability to deliver long range electrostatics accurately with ON  ⁡log(N) complexity. Despite this widespread use, spanning more than two decades, second derivatives (Hessians) have not been available. In this work, we describe the theory and implementation of PME Hessians, which have applications in normal mode analysis, characterization of stationary points, phonon dispersion curve calculation, crystal structure prediction, and efficient geometry optimization. We outline an exact strategy that requires O(1) effort for each Hessian element; after discussing the excessive memory requirements of such an approach, we develop an accurate, efficient approximation that is far more tractable on commodity hardware.

Reaction-field electrostatics in molecular dynamics simulations: development of a conservative scheme compatible with an atomic cutoff

Shifting and switching schemes are developed to enable strict energy conservation in molecular dynamics simulations relying on reaction-field electrostatic (as well as Lennard-Jones) interactions with an atom-based cutoff truncation.

A fast and accurate computational method for the linear-combination-based isotropic periodic sum

An isotropic periodic sum (IPS) is a powerful technique to reasonably calculate intermolecular interactions for wide range of molecular systems under periodic boundary conditions. A linear-combination-based IPS (LIPS) has been developed to attain computational accuracy close to an exact lattice sum, such as the Ewald sum. The algorithm of the original LIPS method has a high computational cost because it needs long-range interaction calculations in real space. This becomes a performance bottleneck for long-time molecular simulations. In this work, the combination of an LIPS and fast Fourier transform (FFT) was developed, and evaluated on homogeneous and heterogeneous molecular systems. This combinational approach of LIPS/FFT attained computational efficiency close to that of a smooth particle mesh Ewald while maintaining the same high accuracy as the original LIPS. We concluded that LIPS/FFT has great potential to extend the capability of IPS techniques for the fast and accurate computation of many types of molecular systems.

Critical test of isotropic periodic sum techniques with group-based cut-off schemes

Truncation is still chosen for many long-range intermolecular interaction calculations to efficiently compute free-boundary systems, macromolecular systems and net-charge molecular systems, for example. Advanced truncation methods have been developed for long-range intermolecular interactions. Every truncation method can be implemented as one of two basic cut-off schemes, namely either an atom-based or a group-based cut-off scheme. The former computes interactions of “atoms” inside the cut-off radius, whereas the latter computes interactions of “molecules” inside the cut-off radius. In this work, the effect of group-based cut-off is investigated for isotropic periodic sum (IPS) techniques, which are promising cut-off treatments to attain advanced accuracy for many types of molecular system. The effect of group-based cut-off is clearly different from that of atom-based cut-off, and severe artefacts are observed in some cases. However, no severe discrepancy from the Ewald sum is observed with the extended IPS techniques.

Comparison of the accuracy of periodic reaction field methods in molecular dynamics simulations of a model liquid crystal system

A periodic reaction field (PRF) method is a technique to estimate long-range interactions. The method has the potential to effectively reduce the computational cost while maintaining adequate accuracy. We performed molecular dynamics (MD) simulations of a model liquid-crystal system to assess the accuracy of some variations of the PRF method in low-charge-density systems. All the methods had adequate accuracy compared with the results of the particle mesh Ewald (PME) method, except for a few simulation conditions. Furthermore, in all of the simulation conditions, one of the PRF methods had the same accuracy as the PME method.

Linearly scaling and almost Hamiltonian dielectric continuum molecular dynamics simulations through fast multipole expansions

Hamiltonian Dielectric Solvent (HADES) is a recent method [S. Bauer et al., J. Chem. Phys. 140, 104103 (2014)] which enables atomistic Hamiltonian molecular dynamics (MD) simulations of peptides and proteins in dielectric solvent continua. Such simulations become rapidly impractical for large proteins, because the computational effort of HADES scales quadratically with the number N of atoms. If one tries to achieve linear scaling by applying a fast multipole method (FMM) to the computation of the HADES electrostatics, the Hamiltonian character (conservation of total energy, linear, and angular momenta) may get lost. Here, we show that the Hamiltonian character of HADES can be almost completely preserved, if the structure-adapted fast multipole method (SAMM) as recently redesigned by Lorenzen et al. [J. Chem. Theory Comput. 10, 3244-3259 (2014)] is suitably extended and is chosen as the FMM module. By this extension, the HADES/SAMM forces become exact gradients of the HADES/SAMM energy. Their translational and rotational invariance then guarantees (within the limits of numerical accuracy) the exact conservation of the linear and angular momenta. Also, the total energy is essentially conserved-up to residual algorithmic noise, which is caused by the periodically repeated SAMM interaction list updates. These updates entail very small temporal discontinuities of the force description, because the employed SAMM approximations represent deliberately balanced compromises between accuracy and efficiency. The energy-gradient corrected version of SAMM can also be applied, of course, to MD simulations of all-atom solvent-solute systems enclosed by periodic boundary conditions. However, as we demonstrate in passing, this choice does not offer any serious advantages.

Assessing the accuracy of the isotropic periodic sum method through Madelung energy computation

We tested the isotropic periodic sum (IPS) method for computing Madelung energies of ionic crystals. The performance of the method, both in its nonpolar (IPSn) and polar (IPSp) forms, was compared with that of the zero-charge and Wolf potentials [D. Wolf, P. Keblinski, S. R. Phillpot, and J. Eggebrecht, J. Chem. Phys. 110, 8254 (1999)]. The results show that the IPSn and IPSp methods converge the Madelung energy to its reference value with an average deviation of ∼10(-4) and ∼10(-7) energy units, respectively, for a cutoff range of 18-24a (a/2 being the nearest-neighbor ion separation). However, minor oscillations were detected for the IPS methods when deviations of the computed Madelung energies were plotted on a logarithmic scale as a function of the cutoff distance. To remove such oscillations, we introduced a modified IPSn potential in which both the local-region and long-range electrostatic terms are damped, in analogy to the Wolf potential. With the damped-IPSn potential, a smoother convergence was achieved. In addition, we observed a better agreement between the damped-IPSn and IPSp methods, which suggests that damping the IPSn potential is in effect similar to adding a screening potential in IPSp.

Design of a reaction field using a linear-combination-based isotropic periodic sum method

In our previous study (Takahashi et al., J. Chem. Theory Comput. 2012, 8, 4503), we developed the linear-combination-based isotropic periodic sum (LIPS) method. The LIPS method is based on the extended isotropic periodic sum theory that produces a ubiquitous interaction potential function to estimate homogeneous and heterogeneous systems. The LIPS theory also provides the procedure to design a periodic reaction field. To demonstrate this, in the present work, a novel reaction field of the LIPS method was developed. The novel reaction field was labeled LIPS-SW, because it provides an interaction potential function with a shape that resembles that of the switch function method. To evaluate the ability of the LIPS-SW method to describe in homogeneous and heterogeneous systems, we carried out molecular dynamics (MD) simulations of bulk water and water-vapor interfacial systems using the LIPS-SW method. The results of these simulations show that the LIPS-SW method gives higher accuracy than the conventional interaction potential function of the LIPS method. The accuracy of simulating water-vapor interfacial systems was greatly improved, while that of bulk water systems was maintained using the LIPS-SW method. We conclude that the LIPS-SW method shows great potential for high-accuracy, high-performance computing to allow large scale MD simulations. © 2014 Wiley Periodicals, Inc.

Isotropic Periodic Sum Treatment of Long-Range Electrostatic Interactions in Combined Quantum Mechanical and Molecular Mechanical Calculations

The isotropic periodic sum (IPS) method was extended to describe long-range electrostatic interactions in combined quantum mechanical and molecular mechanical (QM/MM) calculations. The resulting method, designated QM/MM-IPS, was tested for two ion association processes and a model SN2 reaction in aqueous solution. Potential of mean force (PMF) profiles and radial distribution functions computed from the QM/MM-IPS simulations were compared with those obtained by using the existing QM/MM-Ewald sum and cutoff (QM/MM-Cutoff) methods. In contrast to the QM/MM-Cutoff method, with which PMFs of ion separation tend to display a spurious linear drift, the QM/MM-IPS method successfully eliminates such artifacts, in excellent agreement with the QM/MM-Ewald results. The PMF obtained with the QM/MM-IPS method for the SN2 reaction that transfers an NH3 group between two chloride anions closely resembles that from the QM/MM-Ewald simulations. Compared with QM/MM-Ewald, the QM/MM-IPS method reduces the computational cost by 60-70% when a local region of 12 to 14 Å is used. These results suggest that the QM/MM-IPS method can be used as a reliable and efficient alternative to the QM/MM-Ewald method to incorporate long-range electrostatic effects in simulating solution-phase chemical reactions.