Using Machine Learning to Greatly Accelerate Path Integral Ab Initio Molecular Dynamics

Performant automatic differentiation of local coupled cluster theories: Response properties and ab initio molecular dynamics

In this work, we introduce a differentiable implementation of the local natural orbital coupled cluster (LNO-CC) method within the automatic differentiation framework of the PySCFAD package. The implementation is comprehensively tuned for enhanced performance, which enables the calculation of first-order static response properties on medium-sized molecular systems using coupled cluster theory with single, double, and perturbative triple excitations [CCSD(T)]. We evaluate the accuracy of our method by benchmarking it against the canonical CCSD(T) reference for nuclear gradients, dipole moments, and geometry optimizations. In addition, we demonstrate the possibility of property calculations for chemically interesting systems through the computation of bond orders and Mössbauer spectroscopy parameters for a [NiFe]-hydrogenase active site model, along with the simulation of infrared spectra via ab initio LNO-CC molecular dynamics for a protonated water hexamer.

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.

Multiple-time scale integration method based on an interpolated potential energy surface for ab initio path integral molecular dynamics

A new multiple-time scale integration method is presented that propagates ab initio path integral molecular dynamics (PIMD). This method uses a large time step to generate an approximate geometrical configuration whose energy and gradient are evaluated at the level of an ab initio method, and then, a more precise integration scheme, e.g., the Bulirsch-Stoer method or velocity Verlet integration with a smaller time step, is used to integrate from the previous step using the computationally efficient interpolated potential energy surface constructed from two consecutive points. This method makes the integration of PIMD more efficient and accurate compared with the velocity Verlet integration. A Nosé-Hoover chain thermostat combined with this new multiple-time scale method has good energy conservation even with a large time step, which is usually challenging in velocity Verlet integration for PIMD due to the very small chain mass when a large number of beads are used. The new method is used to calculate infrared spectra and free energy profiles to demonstrate its accuracy and capabilities.

Coarse-Graining with Equivariant Neural Networks: A Path Toward Accurate and Data-Efficient Models

Machine learning has recently entered into the mainstream of coarse-grained (CG) molecular modeling and simulation. While a variety of methods for incorporating deep learning into these models exist, many of them involve training neural networks to act directly as the CG force field. This has several benefits of which the most significant is accuracy. Neural networks can inherently incorporate multibody effects during the calculation of CG forces, and a well-trained neural network force field outperforms pairwise basis sets generated from essentially any methodology. However, this comes at a significant cost. First, these models are typically slower than pairwise force fields, even when accounting for specialized hardware, which accelerates the training and integration of such networks. The second and the focus of this paper is the need for a considerable amount of data to train such force fields. It is common to use 10s of microseconds of molecular dynamics data to train a single CG model, which approaches the point of eliminating the CG model's usefulness in the first place. As we investigate in this work, this "data-hunger" trap from neural networks for predicting molecular energies and forces can be remediated in part by incorporating equivariant convolutional operations. We demonstrate that, for CG water, networks that incorporate equivariant convolutional operations can produce functional models using data sets as small as a single frame of reference data, while networks without these operations cannot.

Nuclear quantum effects on zeolite proton hopping kinetics explored with machine learning potentials and path integral molecular dynamics

Proton hopping is a key reactive process within zeolite catalysis. However, the accurate determination of its kinetics poses major challenges both for theoreticians and experimentalists. Nuclear quantum effects (NQEs) are known to influence the structure and dynamics of protons, but their rigorous inclusion through the path integral molecular dynamics (PIMD) formalism was so far beyond reach for zeolite catalyzed processes due to the excessive computational cost of evaluating all forces and energies at the Density Functional Theory (DFT) level. Herein, we overcome this limitation by training first a reactive machine learning potential (MLP) that can reproduce with high fidelity the DFT potential energy surface of proton hopping around the first Al coordination sphere in the H-CHA zeolite. The MLP offers an immense computational speedup, enabling us to derive accurate reaction kinetics beyond standard transition state theory for the proton hopping reaction. Overall, more than 0.6 μs of simulation time was needed, which is far beyond reach of any standard DFT approach. NQEs are found to significantly impact the proton hopping kinetics up to ~473 K. Moreover, PIMD simulations with deuterium can be performed without any additional training to compute kinetic isotope effects over a broad range of temperatures.

Quantum Free Energy Profiles for Molecular Proton Transfers

Although many molecular dynamics simulations treat the atomic nuclei as classical particles, an adequate description of nuclear quantum effects (NQEs) is indispensable when studying proton transfer reactions. Herein, quantum free energy profiles are constructed for three typical proton transfers, which properly take NQEs into account using the path integral formalism. The computational cost of the simulations is kept tractable by deriving machine learning potentials. It is shown that the classical and quasi-classical centroid free energy profiles of the proton transfers deviate substantially from the exact quantum free energy profile.

Facilitating ab initio QM/MM free energy simulations by Gaussian process regression with derivative observations

In combined quantum mechanical and molecular mechanical (QM/MM) free energy simulations, how to synthesize the accuracy of ab initio (AI) methods with the speed of semiempirical (SE) methods for a cost-effective QM treatment remains a long-standing challenge. In this work, we present a machine-learning-facilitated method for obtaining AI/MM-quality free energy profiles through efficient SE/MM simulations. In particular, we use Gaussian process regression (GPR) to learn the energy and force corrections needed for SE/MM to match with AI/MM results during molecular dynamics simulations. Force matching is enabled in our model by including energy derivatives into the observational targets through the extended-kernel formalism. We demonstrate the effectiveness of this method on the solution-phase SN2 Menshutkin reaction using AM1/MM and B3LYP/6-31+G(d,p)/MM as the base and target levels, respectively. Trained on only 80 configurations sampled along the minimum free energy path (MFEP), the resulting GPR model reduces the average energy error in AM1/MM from 18.2 to 5.8 kcal mol-1 for the 4000-sample testing set with the average force error on the QM atoms decreased from 14.6 to 3.7 kcal mol-1 Å-1. Free energy sampling with the GPR corrections applied (AM1-GPR/MM) produces a free energy barrier of 14.4 kcal mol-1 and a reaction free energy of -34.1 kcal mol-1, in closer agreement with the AI/MM benchmarks and experimental results.

Centroid Molecular Dynamics Can Be Greatly Accelerated through Neural Network Learned Centroid Forces Derived from Path Integral Molecular Dynamics

For nearly the past 30 years, centroid molecular dynamics (CMD) has proven to be a viable classical-like phase space formulation for the calculation of quantum dynamical properties. However, calculation of the centroid effective force remains a significant computational cost and limits the ability of CMD to be an efficient approach to study condensed phase quantum dynamics. In this paper, we introduce a neural network-based methodology for first learning the centroid effective force from path integral molecular dynamics data, which is subsequently used as an effective force field to evolve the centroids directly with the CMD algorithm. This method, called machine-learned centroid molecular dynamics (ML-CMD), is faster and far less costly than both standard "on the fly" CMD and ring polymer molecular dynamics (RPMD). The training aspect of ML-CMD is also straightforwardly implemented utilizing the DeepMD software kit. ML-CMD is then applied to two model systems to illustrate the approach: liquid para-hydrogen and water. The results show comparable accuracy to both CMD and RPMD in the estimation of quantum dynamical properties, including the self-diffusion constant and velocity time correlation function, but with significantly reduced overall computational cost.

Coupled Multiphysics Modelling of Sensors for Chemical, Biomedical, and Environmental Applications with Focus on Smart Materials and Low-Dimensional Nanostructures

Low-dimensional nanostructures have many advantages when used in sensors compared to the traditional bulk materials, in particular in their sensitivity and specificity. In such nanostructures, the motion of carriers can be confined from one, two, or all three spatial dimensions, leading to their unique properties. New advancements in nanosensors, based on low-dimensional nanostructures, permit their functioning at scales comparable with biological processes and natural systems, allowing their efficient functionalization with chemical and biological molecules. In this article, we provide details of such sensors, focusing on their several important classes, as well as the issues of their designs based on mathematical and computational models covering a range of scales. Such multiscale models require state-of-the-art techniques for their solutions, and we provide an overview of the associated numerical methodologies and approaches in this context. We emphasize the importance of accounting for coupling between different physical fields such as thermal, electromechanical, and magnetic, as well as of additional nonlinear and nonlocal effects which can be salient features of new applications and sensor designs. Our special attention is given to nanowires and nanotubes which are well suited for nanosensor designs and applications, being able to carry a double functionality, as transducers and the media to transmit the signal. One of the key properties of these nanostructures is an enhancement in sensitivity resulting from their high surface-to-volume ratio, which leads to their geometry-dependant properties. This dependency requires careful consideration at the modelling stage, and we provide further details on this issue. Another important class of sensors analyzed here is pertinent to sensor and actuator technologies based on smart materials. The modelling of such materials in their dynamics-enabled applications represents a significant challenge as we have to deal with strongly nonlinear coupled problems, accounting for dynamic interactions between different physical fields and microstructure evolution. Among other classes, important in novel sensor applications, we have given our special attention to heterostructures and nucleic acid based nanostructures. In terms of the application areas, we have focused on chemical and biomedical fields, as well as on green energy and environmentally-friendly technologies where the efficient designs and opportune deployments of sensors are both urgent and compelling.