Fine Tuning Classical and Quantum Molecular Dynamics using a Generalized Langevin Equation

Generalized Langevin Equation (GLE) thermostats have been used very effectively as a tool to manipulate and optimize the sampling of thermodynamic ensembles and the associated static properties. Here we show that a similar, exquisite level of control can be achieved for the dynamical properties computed from thermostatted trajectories. By developing quantitative measures of the disturbance induced by the GLE to the Hamiltonian dynamics of a harmonic oscillator, we show that these analytical results accurately predict the behavior of strongly anharmonic systems. We also show that it is possible to correct, to a significant extent, the effects of the GLE term onto the corresponding microcanonical dynamics, which puts on more solid grounds the use of non-equilibrium Langevin dynamics to approximate quantum nuclear effects and could help improve the prediction of dynamical quantities from techniques that use a Langevin term to stabilize dynamics. Finally we address the use of thermostats in the context of approximate path-integral-based models of quantum nuclear dynamics. We demonstrate that a custom-tailored GLE can alleviate some of the artifacts associated with these techniques, improving the quality of results for the modelling of vibrational dynamics of molecules, liquids and solids

Sampling Free Energy Surfaces as Slices by Combining Umbrella Sampling and Metadynamics

Metadynamics (MTD) is a very powerful technique to sample high-dimensional free energy landscapes, and due to its self-guiding property, the method has been successful in studying complex reactions and conformational changes. MTD sampling is based on filling the free energy basins by biasing potentials and thus for cases with flat, broad and unbound free energy wells, the computational time to sample them becomes very large. To alleviate this problem, we combine the standard Umbrella Sampling (US) technique with MTD to sample orthogonal collective variables (CVs) in a simultaneous way. Within this scheme, we construct the equilibrium distribution of CVs from biased distributions obtained from independent MTD simulations with umbrella potentials. Reweighting is carried out by a procedure that combines US reweighting and Tiwary-Parrinello MTD reweighting within the Weighted Histogram Analysis Method (WHAM). The approach is ideal for a controlled sampling of a CV in a MTD simulation, making it computationally efficient in sampling flat, broad and unbound free energy surfaces. This technique also allows for a distributed sampling of a high-dimensional free energy surface, further increasing the computational efficiency in sampling. We demonstrate the application of this technique in sampling high-dimensional surface for various chemical reactions using ab initio and QM/MM hybrid molecular dynamics simulations. Further, in order to carry out MTD bias reweighting for computing forward reaction barriers in ab initio or QM/MM simulations, we propose a computationally affordable approach that does not require recrossing trajectories

The importance of nuclear quantum effects for NMR crystallography

The resolving power of solid-state nuclear magnetic resonance (NMR) crystallography depends heavily on the accuracy of the computational prediction of NMR chemical shieldings of candidate structures, which are usually taken to be local minima in the potential energy surface. To test the limits of this approximation, we perform a systematic study of the role of finite-temperature and quantum nuclear fluctuations on $^1$H, $^{13}$C, and $^{15}$N chemical shieldings in molecular crystals -- considering the paradigmatic examples of the different polymorphs of benzene, glycine, and succinic acid. We find the effect of quantum fluctuations to be comparable in size to the typical errors of predictions of chemical shieldings for static nuclei with respect to experimental measurements, and to improve the match between experiments and theoretical predictions, translating to more reliable assignment of the NMR spectra to the correct candidate structure. Thanks to the use of integrated machine-learning models trained on both first-principles configurational energies and chemical shieldings, the accurate sampling of thermal and quantum fluctuations of the structures can be achieved at an affordable cost, setting a new standard for the calculations that underlie solid-state structural determination by NMR

Quantum dynamics using path integral coarse-graining

Vibrational spectra of condensed and gas-phase systems containing light nuclei are influenced by their quantum-mechanical behaviour. The quantum dynamics of light nuclei can be approximated by the imaginary time path integral (PI) formulation, but still at a large computational cost that increases sharply with decreasing temperature. By leveraging advances in machine-learned coarse-graining, we develop a PI method with the reduced computational cost of a classical simulation. We also propose a simple temperature elevation scheme to significantly attenuate the artefacts of standard PI approaches and also eliminate the unfavourable temperature scaling of the computational cost.We illustrate the approach, by calculating vibrational spectra using standard models of water molecules and bulk water, demonstrating significant computational savings and dramatically improved accuracy compared to more expensive reference approaches. We believe that our simple, efficient and accurate method could enable routine calculations of vibrational spectra including nuclear quantum effects for a wide range of molecular systems.Comment: 9 pages; 4 figure

Quantum dynamics using path integral coarse-graining

The vibrational spectra of condensed and gas-phase systems are influenced by thequantum-mechanical behavior of light nuclei. Full-dimensional simulations of approximate quantum dynamics are possible thanks to the imaginary time path-integral (PI) formulation of quantum statistical mechanics, albeit at a high computational cost which increases sharply with decreasing temperature. By leveraging advances in machine-learned coarse-graining, we develop a PI method with the reduced computational cost of a classical simulation. We also propose a simple temperature elevation scheme to significantly attenuate the artifacts of standard PI approaches as well as eliminate the unfavorable temperature scaling of the computational cost. We illustrate the approach, by calculating vibrational spectra using standard models of water molecules and bulk water, demonstrating significant computational savings and dramatically improved accuracy compared to more expensive reference approaches. Our simple, efficient, and accurate method has prospects for routine calculations of vibrational spectra for a wide range of molecular systems - with an explicit treatment of the quantum nature of nuclei

Hands-On Projects and Exercises to Strengthen Understanding of Basic Computer Engineering Concepts

The Introduction to Computer Engineering course at the University of Missouri-Rolla provides a thorough understanding of basic digital logic analysis and design. The course covers: digital numbering systems, Boolean algebra, function minimization using Karnaugh maps (K-maps), memory elements, and sequential logic design. Students\u27 grades are determined by their performance on homework assignments, quizzes, and in-class examinations. A laboratory course (optional for all but EE and CpE majors) supplements the lecture by providing experiments that include analysis and design using Mentor Graphics and FPGAs. While the laboratory is a very useful supplement to the lecture, almost half the students taking the lecture are not required to take the laboratory and there is not sufficient time in the laboratory schedule to introduce significant design elements. In Fall 2004, hands-on group projects, for all students, were introduced to the lecture course. The goal was for students to develop a more practical understanding and appreciation of hardware design and to improve motivation. Two projects were introduced that involve design of simple digital systems (based on practical applications), design optimization, and physical realization of the system using logic gates and/or memory elements. Two surveys, conducted during the semester, show the benefit of hands-on projects in gaining experience on basic digital hardware design

MACE-OFF23: Transferable Machine Learning Force Fields for Organic Molecules

Classical empirical force fields have dominated biomolecular simulation for over 50 years. Although widely used in drug discovery, crystal structure prediction, and biomolecular dynamics, they generally lack the accuracy and transferability required for predictive modelling. In this paper, we introduce MACE-OFF23, a transferable force field for organic molecules created using state-of-the-art machine learning technology and first-principles reference data computed with a high level of quantum mechanical theory. MACE-OFF23 demonstrates the remarkable capabilities of local, short-range models by accurately predicting a wide variety of gas and condensed phase properties of molecular systems. It produces accurate, easy-to-converge dihedral torsion scans of unseen molecules, as well as reliable descriptions of molecular crystals and liquids, including quantum nuclear effects. We further demonstrate the capabilities of MACE-OFF23 by determining free energy surfaces in explicit solvent, as well as the folding dynamics of peptides. Finally, we simulate a fully solvated small protein, observing accurate secondary structure and vibrational spectrum. These developments enable first-principles simulations of molecular systems for the broader chemistry community at high accuracy and low computational cost

i-PI 2.0: A Universal Force Engine for Advanced Molecular Simulations

Progress in the atomic-scale modeling of matter over the past decade has been tremendous. This progress has been brought about by improvements in methods for evaluating interatomic forces that work by either solving the electronic structure problem explicitly, or by computing accurate approximations of the solution and by the development of techniques that use the Born–Oppenheimer (BO) forces to move the atoms on the BO potential energy surface. As a consequence of these developments it is now possible to identify stable or metastable states, to sample configurations consistent with the appropriate thermodynamic ensemble, and to estimate the kinetics of reactions and phase transitions. All too often, however, progress is slowed down by the bottleneck associated with implementing new optimization algorithms and/or sampling techniques into the many existing electronic-structure and empirical-potential codes. To address this problem, we are thus releasing a new version of the i-PI software. This piece of software is an easily extensible framework for implementing advanced atomistic simulation techniques using interatomic potentials and forces calculated by an external driver code. While the original version of the code (Ceriotti et al., 2014) was developed with a focus on path integral molecular dynamics techniques, this second release of i-PI not only includes several new advanced path integral methods, but also offers other classes of algorithms. In other words, i-PI is moving towards becoming a universal force engine that is both modular and tightly coupled to the driver codes that evaluate the potential energy surface and its derivatives