Recent Advances toward a General Purpose Linear-Scaling Quantum Force Field

Abstract

ConspectusThere is need in the molecular simulation community to develop new quantum mechanical (QM) methods that can be routinely applied to the simulation of large molecular systems in complex, heterogeneous condensed phase environments. Although conventional methods, such as the hybrid quantum mechanical/molecular mechanical (QM/MM) method, are adequate for many problems, there remain other applications that demand a fully quantum mechanical approach. QM methods are generally required in applications that involve changes in electronic structure, such as when chemical bond formation or cleavage occurs, when molecules respond to one another through polarization or charge transfer, or when matter interacts with electromagnetic fields. A full QM treatment, rather than QM/MM, is necessary when these features present themselves over a wide spatial range that, in some cases, may span the entire system. Specific examples include the study of catalytic events that involve delocalized changes in chemical bonds, charge transfer, or extensive polarization of the macromolecular environment; drug discovery applications, where the wide range of nonstandard residues and protonation states are challenging to model with purely empirical MM force fields; and the interpretation of spectroscopic observables. Unfortunately, the enormous computational cost of conventional QM methods limit their practical application to small systems. Linear-scaling electronic structure methods (LSQMs) make possible the calculation of large systems but are still too computationally intensive to be applied with the degree of configurational sampling often required to make meaningful comparison with experiment.In this work, we present advances in the development of a quantum mechanical force field (QMFF) suitable for application to biological macromolecules and condensed phase simulations. QMFFs leverage the benefits provided by the LSQM and QM/MM approaches to produce a fully QM method that is able to simultaneously achieve very high accuracy and efficiency. The efficiency of the QMFF is made possible by partitioning the system into fragments and self-consistently solving for the fragment-localized molecular orbitals in the presence of the other fragment’s electron densities. Unlike a LSQM, the QMFF introduces empirical parameters that are tuned to obtain very accurate intermolecular forces. The speed and accuracy of our QMFF is demonstrated through a series of examples ranging from small molecule clusters to condensed phase simulation, and applications to drug docking and protein–protein interactions. In these examples, comparisons are made to conventional molecular mechanical models, semiempirical methods, ab initio Hamiltonians, and a hybrid QM/MM method. The comparisons demonstrate the superior accuracy of our QMFF relative to the other models; nonetheless, we stress that the overarching role of QMFFs is not to supplant these established computational methods for problems where their use is appropriate. The role of QMFFs within the toolbox of mult...

Quantum mechanical force fields for condensed phase molecular simulations

“…21,22,82–84,84–92 In this section, we emphasize the differences between fragment algorithms through the discussion of four types of methods: The “Divide-and-Conquer” (DC) LSQM method.The Fragment Molecular Orbital (FMO) LSQM method.Force fields founded upon underlying QM calculations, such as the Effective Fragment Potential (EFP), the Sum of Interactions between Fragments Ab initio (SIBFA), and Gaussian Electrostatic Model (GEM) methods.The eXplicit Polarization (X-Pol) and modified Divide-and-Conquer (mDC) QMFF methods.…”

“…Consequently, it has been shown that water clusters lose their hydrogen bond angles, instead choosing to adopt TIP3P-like, 133 planar hydrogen bonding motifs. 21,59,61 To correct for this deficiency, the mDC method concocts a new, auxiliary atomic multipole representation of the fragment density that is solely used for the inter-fragment Coulomb interactions.…”

“…For example, applications of the mDC method found that the inclusion of atomic dipoles and quadrupoles were paramount for obtaining proper hydrogen bond angles in water clusters. 21,59,61 Furthermore, condensed phase simulations of QMFFs require a treatment for the long-range electrostatic interactions, such as Ewald’s method. 155 Ewald’s method has seen widespread adoption within standard MM software packages after the development of Particle Mesh Ewald (PME) 156–159 because electrostatic cutoff methods have been found to produce structural artifacts in biomolecules 160–162 and in the simulations of thermodynamic properties of water.…”

“…The first QMFF suited for condensed phase simulation applications was Gao’s “molecular orbital derived empirical potential for liquid simulations” (MODEL) method; 24 however, the term “quantum mechanical force field” has been used to describe this type of method only recently. 21,22 Within the current context, QMFFs are fundamentally built on a QM framework rather than simply using quantum mechanical results to fit an empirical molecular mechanical potential, as has been used successfully in the derivation of class II 25 and other classical 26,27 force fields. It should be pointed out that strategies for developing quantum methods for large molecular systems differ in some ways from those for solid state systems owing to the need to address distinct challenges.…”

Multiscale Methods for Computational RNA Enzymology

“…Most enzyme systems are far too large to treat with a fully quantum mechanical method, although recently advances in so-called linear-scaling quantum force fields may alter that paradigm (Giese, Chen, Huang, & York, 2014; Giese, Huang, Chen, & York, 2014). An attractive alternative that has been widely applied is to use so-called combined quantum mechanical/molecular mechanical (QM/MM) models (QMMM, enzyme reactions, electrostatic and steric stabilzation, 1976; QMMM, molecular dynamics, 1990).…”