Derivation and Implementation of the Gradient of the R–7 Dispersion Interaction in the Effective Fragment Potential Method

The Effective Fragment Molecular Orbital Method: Achieving High Scalability and Accuracy for Large Systems

The effective fragment molecular orbital (EFMO) method has been developed to predict the total energy of a very large molecular system accurately (with respect to the underlying quantum mechanical method) and efficiently by taking advantage of the locality of strong chemical interactions and employing a two-level hierarchical parallelism. The accuracy of the EFMO method is partly attributed to the accurate and robust intermolecular interaction prediction between distant fragments, in particular, the many-body polarization and dispersion effects, which require the generation of static and dynamic polarizability tensors by solving the coupled perturbed Hartree-Fock (CPHF) and time-dependent HF (TDHF) equations, respectively. Solving the CPHF and TDHF equations is the main EFMO computational bottleneck due to the inefficient (serial) and I/O-intensive implementation of the CPHF and TDHF solvers. In this work, the efficiency and scalability of the EFMO method are significantly improved with a new CPU memory-based implementation for solving the CPHF and TDHF equations that are parallelized by either message passing interface (MPI) or hybrid MPI/OpenMP. The accuracy of the EFMO method is demonstrated for both covalently bonded systems and noncovalently bound molecular clusters by systematically examining the effects of basis sets and a key distance-related cutoff parameter, Rcut. Rcut determines whether a fragment pair (dimer) is treated by the chosen ab initio method or calculated using the effective fragment potential (EFP) method (separated dimers). Decreasing the value of Rcut increases the number of separated (EFP) dimers, thereby decreasing the computational effort. It is demonstrated that excellent accuracy (<1 kcal/mol error per fragment) can be achieved when using a sufficiently large basis set with diffuse functions coupled with a small Rcut value. With the new parallel implementation, the total EFMO wall time is substantially reduced, especially with a high number of MPI ranks. Given a sufficient workload, nearly ideal strong scaling is achieved for the CPHF and TDHF parts of the calculation. For the first time, EFMO calculations with the inclusion of long-range polarization and dispersion interactions on a hydrated mesoporous silica nanoparticle with explicit water solvent molecules (more than 15k atoms) are achieved on a massively parallel supercomputer using nearly 1000 physical nodes. In addition, EFMO calculations on the carbinolamine formation step of an amine-catalyzed aldol reaction at the nanoscale with explicit solvent effects are presented.

R-8 Dispersion Interaction: Derivation and Application to the Effective Fragment Potential Method

The anisotropic and isotropic R-8 dispersion contributions (disp8) are derived and implemented within the framework of the effective fragment potential (EFP) method formulated with imaginary frequency-dependent Cartesian polarizability tensors distributed at the centroids of the localized molecular orbitals (LMOs). Two forms of damping functions, intermolecular overlap-based and Tang-Toennies, are extended for disp8. To obtain LMO polarizability tensors centered at LMO centroids, an origin-shifting transformation is derived and implemented for the dipole-octopole polarizability tensor and the quadrupole-quadrupole polarizability tensor. The analytic gradient is derived and implemented for the isotropic disp8 contribution. Relative to the previously implemented empirical EFP disp8 energy, the isotropic disp8 component of the interaction energy improves the overall agreement of the EFP dispersion energies with the symmetry-adapted perturbation theory (SAPT) benchmarks, reducing the mean absolute errors (MAEs) and mean absolute percentage errors for most of the databases examined in this work. While the anisotropic disp8 can further enhance the accuracy of the EFP dispersion energy and yield smaller MAEs, significantly overbound dispersion energies are predicted by the anisotropic disp8 when the maximum element in the intermolecular overlap matrix is greater than 0.1, possibly due to the breakdown of the approximations made in the EFP dispersion derivation at a short range. For potential energy scan databases, the newly developed EFP dispersion model with isotropic disp8 yields the overall correct curvature and good agreement with SAPT benchmarks around equilibrium and longer but overestimates the dispersion interactions at a short range. While the overlap-based dispersion-damping functions produce better MAEs than Tang-Toennies damping functions, further improvement is needed to better screen the large attractive dispersion energies at a short range (overlap >0.1).

The General Atomic and Molecular Electronic Structure System (GAMESS): Novel Methods on Novel Architectures

The primary focus of GAMESS over the last 5 years has been the development of new high-performance codes that are able to take effective and efficient advantage of the most advanced computer architectures, both CPU and accelerators. These efforts include employing density fitting and fragmentation methods to reduce the high scaling of well-correlated (e.g., coupled-cluster) methods as well as developing novel codes that can take optimal advantage of graphical processing units and other modern accelerators. Because accurate wave functions can be very complex, an important new functionality in GAMESS is the quasi-atomic orbital analysis, an unbiased approach to the understanding of covalent bonds embedded in the wave function. Best practices for the maintenance and distribution of GAMESS are also discussed.

Molecular interactions in diffusion-controlled aldol condensation with mesoporous silica nanoparticles

The aldol reaction of p-nitrobenzaldehyde in amino-catalyzed mesoporous silica nanoparticles (MSN) has revealed varying catalytic activity with the size of the pores of MSN. The pore size dependence related to the reactivity indicates that the diffusion process is important. A detailed molecular-level analysis for understanding diffusion requires assessment of the noncovalent interactions of the molecular species involved in the aldol reaction with each other, with the solvent, and with key functional groups on the pore surface. Such an analysis is presented here based upon the effective fragment potential (EFP). The EFP method can calculate the intermolecular interactions, decomposed into Coulomb, polarization, dispersion, exchange-repulsion, and charge-transfer interactions. In this study, the potential energy surfaces corresponding to each intermolecular interaction are analyzed for homo- and hetero-dimers with various configurations. The monomers that compose dimers are five molecules such as p-nitrobenzaldehyde, acetone, n-hexane, propylamine, and silanol. The results illustrate that the dispersion interaction is crucial in most dimers.

Rotational and translational diffusion of liquid n-hexane: EFP-based molecular dynamics analysis

Molecular Dynamics (MD) simulations based on the Effective Fragment Potential (EFP) method are utilized to provide a comprehensive assessment of diffusion in liquid n-hexane. We decompose translational diffusion into components along and orthogonal to the long axis of the molecule. Rotational diffusion is decomposed into tumbling and spinning motions about this axis. Our analysis yields four corresponding diffusion coefficients which are related to diagonal entries in the complete 6 × 6 diffusion tensor accounting for the three rotational and three translational degrees of freedom and for the potential coupling between them. However, coupling between different degrees of freedom is expected to be minimal for a natural choice of the molecular body-fixed axis, so then off-diagonal entries in the tensor are negligible. This expectation is supported by a hydrodynamic analysis of the diffusion tensor which treats the liquid surrounding the molecule being tracked as a viscous continuum. Thus, the EFP MD analysis provides a comprehensive characterization of diffusion and also reveals expected shortcomings of the hydrodynamic treatment, particularly for rotational diffusion, when applied to neat liquids.

Effective Fragment Potential-Based Molecular Dynamics Studies of Diffusion in Acetone and Hexane

To facilitate more reliable descriptions of transport properties in liquids, molecular dynamics (MD) simulations are performed based on the effective fragment potential (EFP) method derived from first-principles quantum mechanics (in contrast to MD based upon empirically fitted potentials). The EFP method describes molecular interactions in terms of Coulomb, polarization/induction, dispersion, exchange-repulsion, and charge-transfer interactions. The EFP MD simulations described in this paper, performed on hexane and acetone, are able to track the mean-square displacement of molecules for sufficient time to reliably extract translational diffusion coefficients. The results reported here are in reasonable agreement with experiment.

Recent developments in the general atomic and molecular electronic structure system

A discussion of many of the recently implemented features of GAMESS (General Atomic and Molecular Electronic Structure System) and LibCChem (the C++ CPU/GPU library associated with GAMESS) is presented. These features include fragmentation methods such as the fragment molecular orbital, effective fragment potential and effective fragment molecular orbital methods, hybrid MPI/OpenMP approaches to Hartree-Fock, and resolution of the identity second order perturbation theory. Many new coupled cluster theory methods have been implemented in GAMESS, as have multiple levels of density functional/tight binding theory. The role of accelerators, especially graphical processing units, is discussed in the context of the new features of LibCChem, as it is the associated problem of power consumption as the power of computers increases dramatically. The process by which a complex program suite such as GAMESS is maintained and developed is considered. Future developments are briefly summarized.

Quantum Mechanical Modeling of the Interactions between Noble Metal (Ag and Au) Nanoclusters and Water with the Effective Fragment Potential Method

Explicit solvent interactions can significantly alter the physical and chemical properties of noble metal (e.g., gold and silver) nanoclusters. In order to compute these solvent interactions at a reasonable computational cost, a quantum mechanical (QM)/molecular mechanics (MM) approach, where the metal nanocluster is treated with full QM and the water molecules are treated with a MM force field, can be used. However, classical MM force fields were typically parameterized using molecules containing main group elements as the reference. The accuracy of noble metal-solvent interactions obtained with these force fields therefore remains unpredictable. The effective fragment potential (EFP) force field, designed to model explicitly solvated systems, represents an attractive method to simulate solvated noble metal nanoclusters because it is derived from first principles and contains few or no fitted parameters, depending on implementation. At the density functional theory-optimized geometries, good correlation is obtained between the nanocluster-water interaction energies computed with EFP and those computed with the reference coupled cluster singles, doubles, and perturbative triples method. It is shown that the EFP method gives qualitatively accurate interaction energies at medium-large intermolecular distances for various molecular configurations. In order to achieve higher quantitative accuracy, the first solvation shell should be treated with full QM, if possible. EFP is therefore a promising method for the QM modeling of explicitly solvated silver and gold nanoclusters.

An Accurate Quantum-Based Approach to Explicit Solvent Effects: Interfacing the General Effective Fragment Potential Method with Ab Initio Electronic Structure Theory

An interface between ab initio quantum mechanics (QM) methods and the general effective fragment potential (EFP2) method, QM-EFP2, is implemented in which the intermolecular interactions between a QM molecule and EFP fragments consist of Coulomb, polarization, exchange repulsion (exrep), and dispersion components. In order to ensure accuracy in the QM-EFP2 exrep interaction energy, the EFP2-EFP2 spherical Gaussian overlap (SGO) approximation is abandoned and replaced with the exact electron repulsion integrals (ERI) that are evaluated with a direct method to reduce disk usage. A Gaussian damping function for the QM-EFP2 Coulomb component damps both the EFP nuclear and electronic charges. A new overlap damping function has been implemented for the QM-EFP2 dispersion component. The current QM-EFP2 implementation has been benchmarked with the S22 and S66 data sets and demonstrates excellent agreement with symmetry-adapted perturbation theory (SAPT) for component energies and with coupled cluster theory [CCSD(T)] for the total interaction energies. Water clusters of various sizes (up to 256 water molecules) have been tested; it is shown that the QM-EFP2 method has an accuracy that is comparable to that of EFP2-EFP2. It has been shown previously that the accuracy of EFP2-EFP2 intermolecular interactions is comparable to that of second-order perturbation theory (MP2) or better. The implementation of the distributed data interface (DDI) parallelization scheme significantly improves the efficiency of QM-EFP2 calculations. The time to form the QM-EFP2 Fock operator per SCF iteration for water clusters scales linearly with the number EFP basis functions.

Ionic liquids from a fragmented perspective

The efficacy of using fragmentation methods, such as the effective fragment potential, the fragment molecular orbital and the effective fragment molecular orbital methods is discussed. The advantages and current limitations of these methods are considered, potential improvements are suggested, and a prognosis for the future is provided.

A physically grounded damped dispersion model with particle mesh Ewald summation

Accurate modeling of dispersion is critical to the goal of predictive biomolecular simulations. To achieve this accuracy, a model must be able to correctly capture both the short-range and asymptotic behavior of dispersion interactions. We present here a damped dispersion model based on the overlap of charge densities that correctly captures both regimes. The overlap damped dispersion model represents a classical physical interpretation of dispersion: the interaction between the instantaneous induced dipoles of two distinct charge distributions. This model is shown to be an excellent fit with symmetry adapted perturbation theory dispersion energy calculations, yielding an RMS error on the S101x7 database of 0.5 kcal/mol. Moreover, the damping function used in this model is wholly derived and parameterized from the electrostatic dipole-dipole interaction, making it not only physically grounded but transferable as well.

Benchmarking the Effective Fragment Potential Dispersion Correction on the S22 Test Set

The usual modeling of dispersion interactions in density functional theory (DFT) is often limited by the use of empirically fitted parameters. In this study, the accuracies of the popular empirical dispersion corrections and the first-principles derived effective fragment potential (EFP) dispersion correction are compared by computing the DFT-D and HF-D equilibria interaction energies and intermolecular distances of the S22 test set dimers. Functionals based on the local density approximation (LDA) and generalized gradient approximation (GGA), as well as hybrid functionals, are compared for the DFT-D calculations using coupled cluster CCSD(T) at the complete basis set (CBS) limit as the reference method. In general, the HF-D(EFP) method provides accurate equilibrium dimerization energies and intermolecular distances for hydrogen-bonded systems compared to the CCSD(T)/CBS reference data without using any empirical parameters. For dispersion-dominant and mixed systems, the structures and interaction energies obtained with the B3LYP-D(EFP) method are similar to or better than those obtained with the other DFT-D and HF-D methods. Overall, the first-principles derived -D(EFP) correction presents a robust alternative to the empirical -D corrections when used with the B3LYP functional for dispersion-dominant and mixed systems or with Hartree-Fock for hydrogen-bonded systems.