Quantum mechanical force fields for condensed phase molecular simulations

Amber free energy tools: Interoperable software for free energy simulations using generalized quantum mechanical/molecular mechanical and machine learning potentials

We report the development and testing of new integrated cyberinfrastructure for performing free energy simulations with generalized hybrid quantum mechanical/molecular mechanical (QM/MM) and machine learning potentials (MLPs) in Amber. The Sander molecular dynamics program has been extended to leverage fast, density-functional tight-binding models implemented in the DFTB+ and xTB packages, and an interface to the DeePMD-kit software enables the use of MLPs. The software is integrated through application program interfaces that circumvent the need to perform "system calls" and enable the incorporation of long-range Ewald electrostatics into the external software's self-consistent field procedure. The infrastructure provides access to QM/MM models that may serve as the foundation for QM/MM-ΔMLP potentials, which supplement the semiempirical QM/MM model with a MLP correction trained to reproduce ab initio QM/MM energies and forces. Efficient optimization of minimum free energy pathways is enabled through a new surface-accelerated finite-temperature string method implemented in the FE-ToolKit package. Furthermore, we interfaced Sander with the i-PI software by implementing the socket communication protocol used in the i-PI client-server model. The new interface with i-PI allows for the treatment of nuclear quantum effects with semiempirical QM/MM-ΔMLP models. The modular interoperable software is demonstrated on proton transfer reactions in guanine-thymine mispairs in a B-form deoxyribonucleic acid helix. The current work represents a considerable advance in the development of modular software for performing free energy simulations of chemical reactions that are important in a wide range of applications.

Electronic and Nuclear Quantum Effects on Proton Transfer Reactions of Guanine-Thymine (G-T) Mispairs Using Combined Quantum Mechanical/Molecular Mechanical and Machine Learning Potentials

Rare tautomeric forms of nucleobases can lead to Watson-Crick-like (WC-like) mispairs in DNA, but the process of proton transfer is fast and difficult to detect experimentally. NMR studies show evidence for the existence of short-time WC-like guanine-thymine (G-T) mispairs; however, the mechanism of proton transfer and the degree to which nuclear quantum effects play a role are unclear. We use a B-DNA helix exhibiting a wGT mispair as a model system to study tautomerization reactions. We perform ab initio (PBE0/6-31G*) quantum mechanical/molecular mechanical (QM/MM) simulations to examine the free energy surface for tautomerization. We demonstrate that while the ab initio QM/MM simulations are accurate, considerable sampling is required to achieve high precision in the free energy barriers. To address this problem, we develop a QM/MM machine learning potential correction (QM/MM-ΔMLP) that is able to improve the computational efficiency, greatly extend the accessible time scales of the simulations, and enable practical application of path integral molecular dynamics to examine nuclear quantum effects. We find that the inclusion of nuclear quantum effects has only a modest effect on the mechanistic pathway but leads to a considerable lowering of the free energy barrier for the GT*⇌G*T equilibrium. Our results enable a rationalization of observed experimental data and the prediction of populations of rare tautomeric forms of nucleobases and rates of their interconversion in B-DNA.

Seamless integration of GEM, a density based-force field, for QM/MM simulations via LICHEM, Psi4, and Tinker-HP

Hybrid quantum mechanics/molecular mechanics (QM/MM) simulations have become an essential tool in computational chemistry, particularly for analyzing complex biological and condensed phase systems. Building on this foundation, our work presents a novel implementation of the Gaussian Electrostatic Model (GEM), a polarizable density-based force field, within the QM/MM framework. This advancement provides seamless integration, enabling efficient and optimized QM/GEM calculations in a single step using the LICHEM Code. We have successfully applied our implementation to water dimers and hexamers, demonstrating the ability to handle water systems with varying numbers of water molecules. Moreover, we have extended the application to describe the double proton transfer of the aspartic acid dimer in a box of water, which highlights the method's proficiency in investigating heterogeneous systems. Our implementation offers the flexibility to perform on-the-fly density fitting or to utilize pre-fitted coefficients to estimate exchange and Coulomb contributions. This flexibility enhances efficiency and accuracy in modeling molecular interactions, especially in systems where polarization effects are significant.

Surface-Accelerated String Method for Locating Minimum Free Energy Paths

We present a surface-accelerated string method (SASM) to efficiently optimize low-dimensional reaction pathways from the sampling performed with expensive quantum mechanical/molecular mechanical (QM/MM) Hamiltonians. The SASM accelerates the convergence of the path using the aggregate sampling obtained from the current and previous string iterations, whereas approaches like the string method in collective variables (SMCV) or the modified string method in collective variables (MSMCV) update the path only from the sampling obtained from the current iteration. Furthermore, the SASM decouples the number of images used to perform sampling from the number of synthetic images used to represent the path. The path is optimized on the current best estimate of the free energy surface obtained from all available sampling, and the proposed set of new simulations is not restricted to being located along the optimized path. Instead, the umbrella potential placement is chosen to extend the range of the free energy surface and improve the quality of the free energy estimates near the path. In this manner, the SASM is shown to improve the exploration for a minimum free energy pathway in regions where the free energy surface is relatively flat. Furthermore, it improves the quality of the free energy profile when the string is discretized with too few images. We compare the SASM, SMCV, and MSMCV using 3 QM/MM applications: a ribozyme methyltransferase reaction using 2 reaction coordinates, the 2'-O-transphosphorylation reaction of Hammerhead ribozyme using 3 reaction coordinates, and a tautomeric reaction in B-DNA using 5 reaction coordinates. We show that SASM converges the paths using roughly 3 times less sampling than the SMCV and MSMCV methods. All three algorithms have been implemented in the FE-ToolKit package made freely available.

Modelling local and general quantum mechanical properties with attention-based pooling

Atom-centred neural networks represent the state-of-the-art for approximating the quantum chemical properties of molecules, such as internal energies. While the design of machine learning architectures that respect chemical principles has continued to advance, the final atom pooling operation that is necessary to convert from atomic to molecular representations in most models remains relatively undeveloped. The most common choices, sum and average pooling, compute molecular representations that are naturally a good fit for many physical properties, while satisfying properties such as permutation invariance which are desirable from a geometric deep learning perspective. However, there are growing concerns that such simplistic functions might have limited representational power, while also being suboptimal for physical properties that are highly localised or intensive. Based on recent advances in graph representation learning, we investigate the use of a learnable pooling function that leverages an attention mechanism to model interactions between atom representations. The proposed pooling operation is a drop-in replacement requiring no changes to any of the other architectural components. Using SchNet and DimeNet++ as starting models, we demonstrate consistent uplifts in performance compared to sum and mean pooling and a recent physics-aware pooling operation designed specifically for orbital energies, on several datasets, properties, and levels of theory, with up to 85% improvements depending on the specific task.

Automated Fragmentation Quantum Mechanical Calculation of 15N and 13C Chemical Shifts in a Membrane Protein

In this work, we developed an accurate and cost-effective automated fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) method to calculate the chemical shifts of 15N and 13C of membrane proteins. The convergence of the AF-QM/MM method was tested using Krokinobacter eikastus rhodopsin 2 as a test case. When the distance threshold of the QM region is equal to or larger than 4.0 Å, the results of the AF-QM/MM calculations are close to convergence. In addition, the effects of selected density functionals, basis sets, and local chemical environment of target atoms on the chemical shift calculations were systematically investigated. Our results demonstrate that the predicted chemical shifts are more accurate when important environmental factors including cross-protomer interactions, lipid molecules, and solvent molecules are taken into consideration, especially for the 15N chemical shift prediction. Furthermore, with the presence of sodium ions in the environment, the chemical shift of residues, retinal, and retinal Schiff base are affected, which is consistent with the results of the solid-state nuclear magnetic resonance (NMR) experiment. Upon comparing the performance of various density functionals (namely, B3LYP, B3PW91, M06-2X, M06-L, mPW1PW91, OB95, and OPBE), the results show that mPW1PW91 is a suitable functional for the 15N and 13C chemical shift prediction of the membrane proteins. Meanwhile, we find that the improved accuracy of the 13Cβ chemical shift calculations can be achieved by the employment of the triple-ζ basis set. However, the employment of the triple-ζ basis set does not improve the accuracy of the 15N and 13Cα chemical shift calculations nor does the addition of a diffuse function improve the overall prediction accuracy of the chemical shifts. Our study also underscores that the AF-QM/MM method has significant advantages in predicting the chemical shifts of key ligands and nonstandard residues in membrane proteins than most widely used empirical models; therefore, it could be an accurate computational tool for chemical shift calculations on various types of biological systems.

DeePMD-kit v2: A software package for deep potential models

DeePMD-kit is a powerful open-source software package that facilitates molecular dynamics simulations using machine learning potentials known as Deep Potential (DP) models. This package, which was released in 2017, has been widely used in the fields of physics, chemistry, biology, and material science for studying atomistic systems. The current version of DeePMD-kit offers numerous advanced features, such as DeepPot-SE, attention-based and hybrid descriptors, the ability to fit tensile properties, type embedding, model deviation, DP-range correction, DP long range, graphics processing unit support for customized operators, model compression, non-von Neumann molecular dynamics, and improved usability, including documentation, compiled binary packages, graphical user interfaces, and application programming interfaces. This article presents an overview of the current major version of the DeePMD-kit package, highlighting its features and technical details. Additionally, this article presents a comprehensive procedure for conducting molecular dynamics as a representative application, benchmarks the accuracy and efficiency of different models, and discusses ongoing developments.

A specific MNDO parameterization for water

A modified neglect of differential overlap has been parameterized specifically for water and its oligomers with the addition of polarization functions on both hydrogen and oxygen, Feynman dispersion, and a slight modification of the treatment of the hydrogen nucleus. The results show that it is possible to easily obtain good geometries and energies for hydrogen-bonded water aggregates. Data from the Benchmark Energy and Geometry Database water-cluster database were used to parameterize the new Hamiltonian for water clusters from the dimer to the decamer using MP2/aug-cc-pVDZ optimized geometries and CCSD(T)/CBS oligomerization energies. Seventy five oligomerization and rearrangement energies derived from the parameterization data are reproduced with a root mean-square error (RMSE) of 0.79 kcal mol^-1 and the geometries of 38 oligomers with an RMSE of 0.17 Å. Interestingly, the Feynman dispersion term adopts a role different from that intended and tunes the atomic polarizability. The implications of these results in terms of future dedicated neglect of diatomic differential overlap Hamiltonians and those that use force-field-like atom types are discussed.

Development of Range-Corrected Deep Learning Potentials for Fast, Accurate Quantum Mechanical/Molecular Mechanical Simulations of Chemical Reactions in Solution

We develop a new deep potential─range correction (DPRc) machine learning potential for combined quantum mechanical/molecular mechanical (QM/MM) simulations of chemical reactions in the condensed phase. The new range correction enables short-ranged QM/MM interactions to be tuned for higher accuracy, and the correction smoothly vanishes within a specified cutoff. We further develop an active learning procedure for robust neural network training. We test the DPRc model and training procedure against a series of six nonenzymatic phosphoryl transfer reactions in solution that are important in mechanistic studies of RNA-cleaving enzymes. Specifically, we apply DPRc corrections to a base QM model and test its ability to reproduce free-energy profiles generated from a target QM model. We perform these comparisons using the MNDO/d and DFTB2 semiempirical models because they differ in the way they treat orbital orthogonalization and electrostatics and produce free-energy profiles which differ significantly from each other, thereby providing us a rigorous stress test for the DPRc model and training procedure. The comparisons show that accurate reproduction of the free-energy profiles requires correction of the QM/MM interactions out to 6 Å. We further find that the model's initial training benefits from generating data from temperature replica exchange simulations and including high-temperature configurations into the fitting procedure, so the resulting models are trained to properly avoid high-energy regions. A single DPRc model was trained to reproduce four different reactions and yielded good agreement with the free-energy profiles made from the target QM/MM simulations. The DPRc model was further demonstrated to be transferable to 2D free-energy surfaces and 1D free-energy profiles that were not explicitly considered in the training. Examination of the computational performance of the DPRc model showed that it was fairly slow when run on CPUs but was sped up almost 100-fold when using NVIDIA V100 GPUs, resulting in almost negligible overhead. The new DPRc model and training procedure provide a potentially powerful new tool for the creation of next-generation QM/MM potentials for a wide spectrum of free-energy applications ranging from drug discovery to enzyme design.

Development and application of quantum mechanics/molecular mechanics methods with advanced polarizable potentials

Quantum mechanics/molecular mechanics (QM/MM) simulations are a popular approach to study various features of large systems. A common application of QM/MM calculations is in the investigation of reaction mechanisms in condensed-phase and biological systems. The combination of QM and MM methods to represent a system gives rise to several challenges that need to be addressed. The increase in computational speed has allowed the expanded use of more complicated and accurate methods for both QM and MM simulations. Here, we review some approaches that address several common challenges encountered in QM/MM simulations with advanced polarizable potentials, from methods to account for boundary across covalent bonds and long-range effects, to polarization and advanced embedding potentials.

Automated fragmentation quantum mechanical calculation of 13C and 1H chemical shifts in molecular crystals

In this work, the automated fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) approach was applied to calculate the ¹³C and ¹H nuclear magnetic resonance (NMR) chemical shifts in molecular crystals. Two benchmark sets of molecular crystals were selected to calculate the NMR chemical shifts. Systematic investigation was conducted to examine the convergence of AF-QM/MM calculations and the impact of various density functionals with different basis sets on the NMR chemical shift prediction. The result demonstrates that the calculated NMR chemical shifts are close to convergence when the distance threshold for the QM region is larger than 3.5 Å. For ¹³C chemical shift calculations, the mPW1PW91 functional is the best density functional among the functionals chosen in this study (namely, B3LYP, B3PW91, M06-2X, M06-L, mPW1PW91, OB98, and OPBE), while the OB98 functional is more suitable for the ¹H NMR chemical shift prediction of molecular crystals. Moreover, with the B3LYP functional, at least a triple-ζ basis set should be utilized to accurately reproduce the experimental ¹³C and ¹H chemical shifts. The employment of diffuse basis functions will further improve the accuracy for ¹³C chemical shift calculations, but not for the ¹H chemical shift prediction. We further proposed a fragmentation scheme of dividing the central molecule into smaller fragments. By comparing with the results of the fragmentation scheme using the entire central molecule as the core region, the AF-QM/MM calculations with the fragmented central molecule can not only achieve accurate results but also reduce the computational cost. Therefore, the AF-QM/MM approach is capable of predicting the ¹³C and ¹H NMR chemical shifts for molecular crystals accurately and effectively, and could be utilized for dealing with more complex periodic systems such as macromolecular polymers and biomacromolecules. The AF-QM/MM program for molecular crystals is available at https://github.com/shiman1995/NMR.

Alchemical Binding Free Energy Calculations in AMBER20: Advances and Best Practices for Drug Discovery

Predicting protein-ligand binding affinities and the associated thermodynamics of biomolecular recognition is a primary objective of structure-based drug design. Alchemical free energy simulations offer a highly accurate and computationally efficient route to achieving this goal. While the AMBER molecular dynamics package has successfully been used for alchemical free energy simulations in academic research groups for decades, widespread impact in industrial drug discovery settings has been minimal because of the previous limitations within the AMBER alchemical code, coupled with challenges in system setup and postprocessing workflows. Through a close academia-industry collaboration we have addressed many of the previous limitations with an aim to improve accuracy, efficiency, and robustness of alchemical binding free energy simulations in industrial drug discovery applications. Here, we highlight some of the recent advances in AMBER20 with a focus on alchemical binding free energy (BFE) calculations, which are less computationally intensive than alternative binding free energy methods where full binding/unbinding paths are explored. In addition to scientific and technical advances in AMBER20, we also describe the essential practical aspects associated with running relative alchemical BFE calculations, along with recommendations for best practices, highlighting the importance not only of the alchemical simulation code but also the auxiliary functionalities and expertise required to obtain accurate and reliable results. This work is intended to provide a contemporary overview of the scientific, technical, and practical issues associated with running relative BFE simulations in AMBER20, with a focus on real-world drug discovery applications.

Fast Evaluation of Two-Center Integrals over Gaussian Charge Distributions and Gaussian Orbitals with General Interaction Kernels

We present efficient algorithms for computing two-center integrals and integral derivatives, with general interaction kernels K(r₁₂), over Gaussian charge distributions of general angular momenta l. While formulated in terms of traditional ab initio integration techniques, full derivations and required secondary information, as well as a reference implementation, are provided to make the content accessible to other fields. Concretely, the presented algorithms are based on an adaption of the McMurchie-Davidson Recurrence Relation (MDRR) combined with analytical properties of the solid harmonic transformation; this obviates all intermediate recurrences except the adapted MDRR itself, and allows it to be applied to fully contracted auxiliary kernel integrals. The technique is particularly well-suited for semiempirical molecular orbital methods, where it can serve as a more general and efficient replacement of Slater-Koster tables, and for first-principles quantum chemistry methods employing density fitting. But the formalism's high efficiency and ability of handling general interaction kernels K(r₁₂) and multipolar Gaussian charge distributions may also be of interest for modeling electrostatic interactions and short-range exchange and charge penetration effects in classical force fields and model potentials. With the presented technique, a 4894 × 4894 univ-JKFIT Coulomb matrix J_AB = (A|1/r₁₂|B) (183 MiB) can be computed in 50 ms on a Q2'2018 notebook CPU, without any screening or approximations.

Embedding Methods for Quantum Chemistry: Applications from Materials to Life Sciences

Quantum mechanical embedding methods hold the promise to transform not just the way calculations are performed, but to significantly reduce computational costs and improve scaling for macro-molecular systems containing hundreds if not thousands of atoms. The field of embedding has grown increasingly broad with many approaches of different intersecting flavors. In this perspective, we lay out the methods into two streams: QM:MM and QM:QM, showcasing the advantages and disadvantages of both. We provide a review of the literature, the underpinning theories including our contributions, and we highlight current applications with select examples spanning both materials and life sciences. We conclude with prospects and future outlook on embedding, and our view on the use of universal test case scenarios for cross-comparisons of the many available (and future) embedding theories.

Hydration of Closely Related Manganese and Magnesium Porphyrins in Aqueous Solutions: Ab Initio Quantum Mechanical Charge Field Molecular Dynamics Simulation Study

To the best of our knowledge, the current study based on ab initio quantum mechanical charge field molecular dynamics (QMCF-MD) is the first to explore the difference in the hydration behavior between Mn(II)- and Mg(II)-associated porphyrins (Mn(II)-POR and Mg(II)-POR) in aqueous solution. The simulation study highlights similar and dissimilar characteristics of the structural, dynamical, and thermodynamical properties of these closely related metals bound to porphyrins in aqueous solution. The structural analysis is based on radial and angular distribution functions, coordination number distributions, and angular-radial distributions. Both hydrated systems demonstrate similar pentacoordinated structures formed via the axial coordination of one water molecule to the metal ion in addition to the four nitrogen atoms of the porphyrin ring. However, in the case of Mn(II)-POR, the formation of a distorted square pyramidal geometry was observed. It was envisaged as a weak coordination of the water molecule to the Mn(II) atom and thus higher atomic fluctuation for all atoms in contrast to that for the hydrated Mg(II)-POR. The dynamical data in terms of the mean residence times, velocity autocorrelation function, free energy, and other parameters revealed the difference in the metal binding effect because the Mn(II) atom was observed to inhibit H-bond formation more than the presence of Mg(II) atoms in the core of the porphyrin. The current study thus highlights the significant differences in the structural and dynamical properties of Mn(II)- and Mg(II)-associated porphyrin systems.

Prediction of Excited-State Properties of Oligoacene Crystals Using Fragment-Based Quantum Mechanical Method

A fundamental understanding of the excited-state properties of molecular crystals is of central importance for their optoelectronics applications. In this study, we developed the electrostatically embedded generalized molecular fractionation (EE-GMF) method for the quantitative characterization of the excited-state properties of locally excited molecular clusters. The accuracy of the EE-GMF method is systematically assessed for oligoacene crystals. Our result demonstrates that the EE-GMF method is capable of providing the lowest vertical singlet (S₁) and triplet excitation energies (T₁), in excellent agreement with the full-system quantum mechanical calculations. Using this method, we also investigated the performance of different density functionals in predicting the excited-state properties of the oligoacene crystals. Among the 13 tested functionals, B3LYP and MN15 give the two lowest overall mean unsigned errors with reference to the experimental S₁ and T₁ excitation energies. The EE-GMF approach can be readily utilized for studying the excited-state properties of large-scale organic solids at diverse ab initio levels.

A GPU-Accelerated Parameter Interpolation Thermodynamic Integration Free Energy Method

There has been a resurgence of interest in free energy methods motivated by the performance enhancements offered by molecular dynamics (MD) software written for specialized hardware, such as graphics processing units (GPUs). In this work, we exploit the properties of a parameter-interpolated thermodynamic integration (PI-TI) method to connect states by their molecular mechanical (MM) parameter values. This pathway is shown to be better behaved for Mg2+ → Ca2+ transformations than traditional linear alchemical pathways (with and without soft-core potentials). The PI-TI method has the practical advantage that no modification of the MD code is required to propagate the dynamics, and unlike with linear alchemical mixing, only one electrostatic evaluation is needed (e.g., single call to particle-mesh Ewald) leading to better performance. In the case of AMBER, this enables all the performance benefits of GPU-acceleration to be realized, in addition to unlocking the full spectrum of features available within the MD software, such as Hamiltonian replica exchange (HREM). The TI derivative evaluation can be accomplished efficiently in a post-processing step by reanalyzing the statistically independent trajectory frames in parallel for high throughput. We also show how one can evaluate the particle mesh Ewald contribution to the TI derivative evaluation without needing to perform two reciprocal space calculations. We apply the PI-TI method with HREM on GPUs in AMBER to predict p Ka values in double stranded RNA molecules and make comparison with experiments. Convergence to under 0.25 units for these systems required 100 ns or more of sampling per window and coupling of windows with HREM. We find that MM charges derived from ab initio QM/MM fragment calculations improve the agreement between calculation and experimental results.