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Ab initio molecular dynamics (AIMD) is an important simulation method applied to understand systems encountered in chemistry and biochemistry, as well as in physics and materials science. It provides means to study complex systems undergoing chemical reactions or phase transitions, as occurring in systems under extreme conditions, or previously unknown compositions. We introduce the basic concepts and methods of AIMD when used together with density functional theory approaches. The connection between the currently most widely used methods, Born–Oppenheimer MD and 2 n d Generation Car–Parrinello MD is derived. Important parameters for efficient and accurate simulation protocols are discussed with the focus on the implementations in the CP2K software. Step by step procedures to correctly set up simulations are provided. Sample applications from literature are presented with a special emphasis on the simulation system parameters and protocols used.

The Random-Phase approximation (RPA) provides an appealing framework for semi-local density functional theory. In its Resolution-of-the-Identity (RI) approach, it is a very accurate and more cost-effective method than most other wavefunction-based correlation methods. For widespread applications, efficient implementations of nuclear gradients for structure optimizations and data sampling of machine learning approaches are required. We report a well scaling implementation of RI-RPA nuclear gradients on massively parallel computers. The approach is applied to two polymorphs of the benzene crystal obtaining very good cohesive and relative energies. Different correction and extrapolation schemes are investigated for further improvement of the results and estimations of error bars.

Water adsorption and dissociation processes on pristine low-index TiO$_{2}$ interfaces are important but poorly understood outside the well-studied anatase (101) and rutile (110). To understand these, we construct three sets of machine learning potentials that are simultaneously applicable to various TiO$_{2}$ surfaces, based on three density-functional-theory approximations. Here we show the water dissociation free energies on seven pristine TiO$_{2}$ surfaces, and predict that anatase (100), anatase (110), rutile (001), and rutile (011) favor water dissociation, anatase (101) and rutile (100) have mostly molecular adsorption, while the simulations of rutile (110) sensitively depend on the slab thickness and molecular adsorption is preferred with thick slabs. Moreover, using an automated algorithm, we reveal that these surfaces follow different types of atomistic mechanisms for proton transfer and water dissociation: one-step, two-step, or both. These mechanisms can be rationalized based on the arrangements of water molecules on the different surfaces. Our finding thus demonstrates that the different pristine TiO$_{2}$ surfaces react with water in distinct ways, and cannot be represented using just the low-energy anatase (101) and rutile (110) surfaces.

Micropollutants have become a serious environmental problem by threatening ecosystems and the quality of drinking water. This account investigates if advanced AI can be used to find solutions for this problem. We review background, the challenges involved, and the current state-of-the-art of quantitative structure-biodegradation relationships (QSBR). We report on recent progress combining experiment, quantum chemistry (QC) and chemoinformatics, and provide a perspective on potential future uses of AI technology to help improve water quality.

We study self-interaction effects in solvated and strongly-correlated cationic molecular clusters, with a focus on the solvated hydroxyl radical. To address the self-interaction issue, we apply the DC-r2SCAN method, with the auxiliary density matrix approach. Validating our method through simulations of bulk liquid water, we demonstrate that DC-r2SCAN maintains the structural accuracy of r2SCAN while effectively addressing spin density localization issues. Extending our analysis to solvated cationic molecular clusters, we find that the hemibonded motif in the [CH3S∴CH3SH]+ cluster is disrupted in the DC-r2SCAN simulation, in contrast to r2SCAN that preserves the (three-electron-two-center)-bonded motif. Similarly, for the [SH∴SH2]+ cluster, r2SCAN restores the hemibonded motif through spin leakage, while DC-r2SCAN predicts a weaker hemibond formation influenced by solvent-solute interactions. Our findings demonstrate the potential of DC-r2SCAN combined with the auxiliary density matrix method to improve electronic structure calculations, providing insights into the properties of solvated cationic molecular clusters. This work contributes to the advancement of self-interaction corrected electronic structure theory and offers a computational framework for modeling condensed phase systems with intricate correlation effects.

The development of novel double-hybrid density functionals offers new levels of accuracy and is leading to fresh insights into the fundamental properties of matter. Hartree–Fock exact exchange and correlated wave function methods, such as second-order Møller–Plesset (MP2) and direct random phase approximation (dRPA), are usually required to build such functionals. Their high computational cost is a concern, and their application to large and periodic systems is, therefore, limited. In this work, low-scaling methods for Hartree–Fock exchange (HFX), SOS-MP2, and direct RPA energy gradients are developed and implemented in the CP2K software package. The use of the resolution-of-the-identity approximation with a short range metric and atom-centered basis functions leads to sparsity, allowing for sparse tensor contractions to take place. These operations are efficiently performed with the newly developed Distributed Block-sparse Tensors (DBT) and Distributed Block-sparse Matrices (DBM) libraries, which scale to hundreds of graphics processing unit (GPU) nodes. The resulting methods, resolution-of-the-identity (RI)-HFX, SOS-MP2, and dRPA, were benchmarked on large supercomputers. They exhibit favorable sub-cubic scaling with system size, good strong scaling performance, and GPU acceleration up to a factor of 3. These developments will allow for double-hybrid level calculations of large and periodic condensed phase systems to take place on a more regular basis.

Accurate descriptions of intermolecular interactions are of great importance in simulations of molecular liquids. We present an electronic structure method that combines the accuracy of the Harris functional approach with the computational efficiency of approximately linear-scaling density functional theory (DFT). The non-variational nature of the Harris functional has been addressed by constructing a Lagrangian energy functional, which restores the variational condition by imposing stationarity with respect to the reference density. The associated linear response equations may be treated with linear-scaling efficiency in an atomic orbital based scheme. Key ingredients to describe the structural and dynamical properties of molecular systems are the forces acting on the atoms and the stress tensor. These first-order derivatives of the Harris Lagrangian have been derived and implemented in consistence with the energy correction. The proposed method allows for simulations with accuracies close to the Kohn–Sham DFT reference. Embedded in the CP2K program package, the method is designed to enable ab initio molecular dynamics simulations of molecular solutions for system sizes of several thousand atoms. Available subsystem DFT methods may be used to provide the reference density required for the energy correction at near linear-scaling efficiency. As an example of production applications, we applied the method to molecular dynamics simulations of the binary mixtures cyclohexane-methanol and toluene-methanol, performed within the isobaric-isothermal ensemble, to investigate the hydrogen bonding network in these non-ideal mixtures.

We push the boundaries of electronic structure-based ab-initio molecular dynamics (AIMD) beyond 100 million atoms. This scale is otherwise barely reachable with classical force-field methods or novel neural network and machine learning potentials. We achieve this breakthrough by combining innovations in linear-scaling AIMD, efficient and approximate sparse linear algebra, low and mixed-precision floating-point computation on GPUs, and a compensation scheme for the errors introduced by numerical approximations. The core of our work is the non-orthogonalized local submatrix method (NOLSM), which scales very favorably to massively parallel computing systems and translates large sparse matrix operations into highly parallel, dense matrix operations that are ideally suited to hardware accelerators. We demonstrate that the NOLSM method, which is at the center point of each AIMD step, is able to achieve a sustained performance of 324 PFLOP/s in mixed FP16/FP32 precision corresponding to an efficiency of 67.7% when running on 1536 NVIDIA A100 GPUs.

Due to their improved accuracy, double-hybrid density functionals emerged as an important method for molecular electronic-structure calculations. The high computational costs of double-hybrid calculations in the condensed phase and the lack of efficient gradient implementations thereof inhibit a wide applicability for periodic systems. We present an implementation of forces and stress tensors for double-hybrid density functionals within the Gaussian and plane-waves electronic structure framework. The auxiliary density matrix method is used to reduce the overhead of the Hartree–Fock kernel providing an efficient and accurate methodology to tackle condensed phase systems. First applications to water systems of different densities and molecular crystals show the efficiency of the implementation and pave the way for advanced studies. Finally, we present large benchmark systems to discuss the performance of our implementation on modern large-scale computers.

We push the boundaries of electronic structure-based \textit{ab-initio} molecular dynamics (AIMD) beyond 100 million atoms. This scale is otherwise barely reachable with classical force-field methods or novel neural network and machine learning potentials. We achieve this breakthrough by combining innovations in linear-scaling AIMD, efficient and approximate sparse linear algebra, low and mixed-precision floating-point computation on GPUs, and a compensation scheme for the errors introduced by numerical approximations. The core of our work is the non-orthogonalized local submatrix method (NOLSM), which scales very favorably to massively parallel computing systems and translates large sparse matrix operations into highly parallel, dense matrix operations that are ideally suited to hardware accelerators. We demonstrate that the NOLSM method, which is at the center point of each AIMD step, is able to achieve a sustained performance of 324 PFLOP/s in mixed FP16/FP32 precision corresponding to an efficiency of 67.7% when running on 1536 NVIDIA A100 GPUs., Comment: 12 pages, 11 figures

Linear-response time-dependent density functional theory (LR-TDDFT) for core level spectroscopy using standard local functionals suffers from self-interaction error and a lack of orbital relaxation upon creation of the core hole. As a result, LR-TDDFT calculated x-ray absorption near edge structure spectra needed to be shifted along the energy axis to match experimental data. We propose a correction scheme based on many-body perturbation theory to calculate the shift from first-principles. The ionization potential of the core donor state is first computed and then substituted for the corresponding Kohn–Sham orbital energy, thus emulating Koopmans’s condition. Both self-interaction error and orbital relaxation are taken into account. The method exploits the localized nature of core states for efficiency and integrates seamlessly in our previous implementation of core level LR-TDDFT, yielding corrected spectra in a single calculation. We benchmark the correction scheme on molecules at the K- and L-edges as well as for core binding energies and report accuracies comparable to higher order methods. We also demonstrate applicability in large and extended systems and discuss efficient approximations.

We discuss our implementation of linear-response time-dependent density functional theory (LR-TDDFT) for core level near-edge absorption spectroscopy. The method is based on established LR-TDDFT approaches to X-ray absorption spectroscopy (XAS) with additional accurate approximations for increased efficiency. We validate our implementation by reproducing benchmark results at the K-edge and showing that spin–orbit coupling effects at the L2,3-edge are well described. We also demonstrate that the method is suitable for extended systems in periodic boundary conditions and measure a favorable sub-cubic scaling of the calculation cost with system size. We finally show that GPUs can be efficiently exploited and report speedups of up to a factor 2.

The ability to reproduce the experimental structure of water around the sodium and potassium ions is a key test of the quality of interaction potentials due to the central importance of these ions in a wide range of important phenomena. Here, we simulate the Na+ and K+ ions in bulk water using three density functional theory functionals: (1) the generalized gradient approximation (GGA) based dispersion corrected revised Perdew, Burke, and Ernzerhof functional (revPBE-D3) (2) the recently developed strongly constrained and appropriately normed (SCAN) functional (3) the random phase approximation (RPA) functional for potassium. We compare with experimental X-ray diffraction (XRD) and X-ray absorption fine structure (EXAFS) measurements to demonstrate that SCAN accurately reproduces key structural details of the hydration structure around the sodium and potassium cations, whereas revPBE-D3 fails to do so. However, we show that SCAN provides a worse description of pure water in comparison with revPBE-D3. RPA also shows an improvement for K+, but slow convergence prevents rigorous comparison. Finally, we analyse cluster energetics to show SCAN and RPA have smaller fluctuations of the mean error of ion-water cluster binding energies compared with revPBE-D3.

Physical chemistry of electric double layers and ionic solutions plays a fundamental role in energy related applications such as electrocatalysis, super-capacitors, fuel cells, lithium/sodium ion batteries. A realistic representation of these electrochemical systems requires treating electronic, structural and dynamic properties on an equal footing. Density functional theory based molecular dynamics (DFTMD) is perhaps the only approach that can provide a consistent atomistic description. However, one of the challenges in DFTMD modelling of electrochemical systems is the slow convergence of the polarization $\mathbf{P}$, where $\mathbf{P}$ is the central quantity connecting to all electrical properties (the dielectric constant, the Helmholtz capacitance and the ionic conductivity). Here, we summarize our recent progress on developing finite field MD for computing electrical properties. Discussions on notable extensions and outlook for future works are also given.

CP2K is an open source electronic structure and molecular dynamics software package to perform atomistic simulations of solid-state, liquid,molecular, and biological systems. It is especially aimed at massively parallel and linear-scaling electronic structure methods and state-of-the-artab initiomolecular dynamics simulations. Excellent performance for electronic structure calculations is achieved using novel algorithmsimplemented for modern high-performance computing systems. This review revisits the main capabilities of CP2K to perform efficient andaccurate electronic structure simulations. The emphasis is put on density functional theory and multiple post–Hartree–Fock methods usingthe Gaussian and plane wave approach and its augmented all-electron extension.