Structure and Dynamics of Liquid Water from ab Initio Molecular Dynamics—Comparison of BLYP, PBE, and revPBE Density Functionals with and without van der Waals Corrections

A Systematic Study of DFT Performance for Geometry Optimizations of Ionic Liquid Clusters

Clusters of two ion pairs of imidazolium-based ionic liquids were optimized with 43 different levels of theory, including DFT functionals and MP2-based methods combined with varying Dunning's basis sets, and added dispersion corrections. Better preforming DFT functionals were then applied to clusters consisting of four ion pairs. Excellent performance of some DFT functionals for the two ion pair clusters did not always match that of the four ion-paired clusters despite interionic distances remaining constant between the optimized two and four ion-paired clusters of the same ionic liquid. Combinations of DFT functional and basis set such as ωB97X-D/cc-pVDZ, M06-2X/aug-cc-pVDZ, B3LYP-D3/cc-pVTZ, and TPSS-D3/cc-pVTZ gave excellent results for geometry optimization of two ion-paired clusters of imidazolium ionic liquids but gave larger deviations when applied to the four ion-paired clusters of varying ionic liquids. Empirical dispersion corrections were seen to be crucial in correctly capturing correlation effects in the studied ionic liquid clusters, becoming more important in larger clusters. Dunning's double-ζ basis set, cc-pVDZ, is associated with the smallest root mean squared deviations for geometries; however, it also produces the largest deviations in total electronic energies. ωB97X-D and M06-2X produced the best performance with the augmented version of this basis set. The triple-ζ basis set, cc-pVTZ, leads to the best performance of most of the DFT functionals (especially the dispersion-corrected ones) used, whereas its augmented version, aug-cc-pVTZ, was not seen to improve results. The combinations of functional and basis set that gave the best geometry and energetics in both two and four ion-paired clusters were PBE-D3/cc-pVTZ, ωB97X-D/aug-cc-pVDZ, and BLYP-D3/cc-pVTZ. All three combinations are recommended for geometry optimizations of larger clusters of ionic liquids. PBE-D3/cc-pVTZ performed the best with an average deviation of 2.3 kJ mol^-1 and a standard deviation of 3.4 kJ mol^-1 for total electronic energy when applied to four ion-paired clusters. Geometries optimized with FMO2-SRS-MP2/cc-pVTZ produced total energy within 2.0 kJ mol^-1 off the benchmark in two ion-paired clusters, with the cc-pVDZ basis set performing unsurprisingly poorly with the same method. The error increased to 4.8 kJ mol^-1 on average in four ion-paired clusters, with the smallest RMSD deviations in geometries when compared to the benchmark ones. This study is the first report that investigated the performance of DFT functionals for two and four ion-paired clusters of a wide range of ionic liquids consisting of commonly used cations such as pyrrolidinium, imidazolium, pyridinium, and ammonium. It also identified the importance of assessing the performance of quantum chemical methods for ionic liquids on a variety of cation-anion combinations.

Quadrupolar NMR Relaxation of Aqueous 127I-, 131Xe, and 133Cs+: A First-Principles Approach from Dynamics to Properties

Quadrupolar NMR relaxation rates were computed for aqueous ¹³³Cs⁺, ¹³¹Xe, and ¹²⁷I^- via Kohn-Sham (KS) density functional theory-based ab initio molecular dynamics and KS calculations of the electric field gradient (EFG) tensors along the trajectories. The resulting rates are within a factor of 1-3 of the experimental values and can be compared to available results from classical dynamics and EFGs from electrostatic models with corrections via Sternheimer antishielding factors. Relativistic effects are shown to have an enhancing effect on the magnitude of the EFGs. An analysis of the EFGs was carried out in terms of localized molecular orbitals to elucidate contributions from the solvent versus solute polarization and assess the validity of the Sternheimer approximation for these systems.

Ab Initio Molecular Dynamics Study of Methanol-Water Mixtures under External Electric Fields

Intense electric fields applied on H-bonded systems are able to induce molecular dissociations, proton transfers, and complex chemical reactions. Nevertheless, the effects induced in heterogeneous molecular systems such as methanol-water mixtures are still elusive. Here we report on a series of state-of-the-art ab initio molecular dynamics simulations of liquid methanol-water mixtures at different molar ratios exposed to static electric fields. If, on the one hand, the presence of water increases the proton conductivity of methanol-water mixtures, on the other, it hinders the typical enhancement of the chemical reactivity induced by electric fields. In particular, a sudden increase of the protonic conductivity is recorded when the amount of water exceeds that of methanol in the mixtures, suggesting that important structural changes of the H-bond network occur. By contrast, the field-induced multifaceted chemistry leading to the synthesis of e.g., hydrogen, dimethyl ether, formaldehyde, and methane observed in neat methanol, in 75:25, and equimolar methanol-water mixtures, completely disappears in samples containing an excess of water and in pure water. The presence of water strongly inhibits the chemical reactivity of methanol.

Hydration Properties of HnPO4n-3 (n = 0-3) From Ab Initio Molecular Dynamics Simulations

For a comprehensive and detailed microscopic understanding of the hydration properties of primary aqueous phosphorus species of valence states V (viz., H₃PO₄, H₂PO₄^-, HPO₄^2-, and PO₄^3-), a series of extensive ab initio molecular dynamics simulations is conducted at ambient temperature. In each of these cases, the spatially resolved, three-dimensional hydration shells are computed, allowing for a direct microscopic visual understanding of the hydration shells around the species. Since these species are excellent agents for the formation of hydrogen bonds (H-bonds) in water, which determine a wide range of their structural, dynamic, and spectroscopic features, a detailed analysis of the qualitative and quantitative aspects of the H-bonds, including their lifetime calculations, is performed. Vibrational density of states (VDOS) is calculated for each of the species in solute phases, resolved for each H-bonding site, and compared against the gas-phase normal modes of H₃PO₄ for the purpose of understanding the signatures of the peaks in VDOS plots and, in particular, the effects of solvation and H-bonding mechanisms. The results are well in line with available experimental data and other recent computer-aided studies in the literature.

Carbon dioxide, bicarbonate and carbonate ions in aqueous solutions under deep Earth conditions

We investigate the effect of pressure, temperature and acidity on the composition of water-rich carbon-bearing fluids under thermodynamic conditions that correspond to the Earth's deep crust and upper mantle. Our first-principles molecular dynamics simulations provide mechanistic insight into the hydration shell of carbon dioxide, bicarbonate and carbonate ions, and into the pathways of the acid/base reactions that convert these carbon species into one another in aqueous solutions. At temperatures of 1000 K and higher, our simulations can sample the chemical equilibrium of these acid/base reactions, thus allowing us to estimate the chemical composition of diluted carbon dioxide and (bi)carbonate ions as a function of acidity and thermodynamic conditions. We find that, especially at the highest temperature, the acidity of the solution is essential to determine the stability domain of CO₂vs. HCO₃^-vs. CO₃^2-.

Vibrational mode frequency correction of liquid water in density functional theory molecular dynamics simulations with van der Waals correction

We develop a frequency correction scheme for the stretch and bending modes of liquid water, which substantially improves the prediction of the vibrational spectra.

Dynamic Interplay between Defective UiO-66 and Protic Solvents in Activated Processes

UiO‐66, composed by Zr‐oxide inorganic bricks [Zr₆(μ₃‐O)₄(μ₃‐OH)₄] and organic terephthalate linkers, is one of the most studied metal–organic frameworks (MOFs) due to its exceptional thermal, chemical, and mechanical stability. Thanks to its high connectivity, the material can withstand structural deformations during activation processes such as linker exchange, dehydration, and defect formation. These processes do alter the zirconium coordination number in a dynamic way, creating open metal sites for catalysis and thus are able to tune the catalytic properties. In this work, it is shown, by means of first‐principle molecular‐dynamics simulations at operating conditions, how protic solvents may facilitate such changes in the metal coordination. Solvent can induce structural rearrangements in the material that can lead to undercoordinated but also overcoordinated metal sites. This is demonstrated by simulating activation processes along well‐chosen collective variables. Such enhanced MD simulations are able to track the intrinsic dynamics of the framework at realistic conditions.

Ab initio spectroscopy of water under electric fields

Whereas a broad range of literature exists on the spectroscopy of water in disparate conditions, infrared (IR) and Raman spectra of water subjected to electric fields have never extensively been investigated so far. Based on ab initio molecular dynamics simulations, here we present IR and Raman spectra of bulk liquid water under the effect of static electric fields. A contraction of the entire frequency range is recorded upon increasing the field intensity both in the IR and in the Raman spectra. Whilst the OH stretching band is progressively shifted toward lower frequencies - indicating a field-induced strengthening of the H-bond network - all the other bands are up-shifted by the field. Furthermore, an evident modification of the librational mode band appears in all the spectra. Finally, the order-maker action of the field emerges also from the increase of the water orientational tetrahedral order. Upon field exposure, the water structure becomes more "ice like".

Ab Initio Molecular Dynamics Simulations of the Influence of Lithium Bromide Salt on the Deprotonation of Formic Acid in Aqueous Solution

The deprotonation of formic acid is investigated using metadynamics in tandem with Born-Oppenheimer molecular dynamics simulations. We compare our findings for formic acid in pure water with previous studies before examining formic acid in aqueous solutions of lithium bromide. We carefully consider different definitions for the collective variable(s) used to drive the metadynamics, emphasizing that the variables used must include all of the possible reactive atoms in the system, in this case carboxylate oxygens and water hydrogens. This ensures that all the various possible proton exchange events can be accommodated and the collective variable(s) can distinguish the protonated and deprotonated states, even over rather long ab initio simulation runs (ca. 200-300 ps). Our findings show that the formic acid deprotonation barrier and the free energy of the deprotonated state are higher in concentrated lithium bromide, in agreement with the available experimental data for acids in salt solution. We show that the presence of Br^- in proximity to the formic acid hydroxyl group effectively inhibits deprotonation. Our study extends previous work on acid deprotonation in pure water and at air-water interfaces to more complex multicomponent systems of importance in atmospheric and marine chemistry.

An ab initio molecular dynamics study of benzene in water at supercritical conditions: Structure, dynamics, and polarity of hydration shell water and the solute

Anisotropic structure and dynamics of the hydration shell of a benzene solute in supercritical water are investigated by means of ab initio molecular dynamics simulations. The polarity and structural distortion of the benzene solute in supercritical water are also investigated in this study. Calculations are done at 673 K for three different densities of the solvent. The simulations are carried out using the Becke-Lee-Yang-Parr (BLYP) and also the Becke-Lee-Yang-Parr functional including dispersion corrections of Grimme (BYLP-D). The structural anisotropy is found to exist even at supercritical conditions as elucidated by the radial distribution functions of different conical regions and also by angular and spatial distribution functions. The benzene-water πH-bond and also the water-water hydrogen bonds are found to exist even at the supercritical temperature of 673 K. However, the numbers of these hydrogen bonds are reduced substantially with a decrease in water density. The water molecules in the axial region of benzene are found to be preferably oriented with one OH vector pointing toward the benzene ring, whereas the water molecules located in the equatorial region are found to orient their dipoles mostly parallel to the ring plane. The orientational distributions, however, are found to be rather broad at the supercritical temperature due to thermal fluctuations. Although the water molecules have faster dynamics at these supercritical conditions, a slight difference is observed in the dynamics of the solvation shell and bulk molecules. The conformational flexibility of the ring is found to be enhanced which causes an increase in polarity of the benzene solute in water under supercritical conditions.

Structure and Dynamics of Water at the Water-Air Interface Using First-Principles Molecular Dynamics Simulations. II. NonLocal vs Empirical van der Waals Corrections

van der Waals (vdW) correction schemes have been recognized to be essential for an accurate description of liquid water in first-principles molecular dynamics simulation. The description of the structure and dynamics of water is governed by the type of the vdW corrections. So far, two vdW correction schemes have been often used: empirical vdW corrections and nonlocal vdW corrections. In this paper, we assess the influence of the empirical vs nonlocal vdW correction schemes on the structure and dynamics of water at the water–air interface. Since the structure of water at the water–air interface is established by a delicate balance of hydrogen bond formation and breaking, the simulation at the water–air interface provides a unique platform to testify as to the heterogeneous interaction of water. We used the metrics [Ohto et al. J. Chem. Theory Comput., 2019, 15, 595−60230468702] which are directly connected with the sum-frequency generation spectroscopic measurement. We find that the overall performance of nonlocal vdW methods is either similar or worse compared to the empirical vdW methods. We also investigated the performance of the optB88-DRSLL functional, which showed slightly less accuracy than the revPBE-D3 method. We conclude that the revPBE-D3 method shows the best performance for describing the interfacial water.

Heterogeneous Occupancy and Vibrational Dynamics of Spatially Patterned Water Molecules

We performed first-principles molecular dynamics simulations of relatively dilute aqueous solutions of sulfate and thiosulfate dianions to analyze the structure, dynamics, and vibrational spectral properties of water molecules around the solute, especially the spatially patterned solvent molecules in the first solvation layer and the extended layers. This study also involves the investigation of dynamics of dangling OH groups in these layers and their role in patterning the water molecules around the dianions. Structural evaluation of the systems is carried out by radial distribution functions, number integrals, and spatial distribution functions. The lifetime of dangling OH groups inside the solvation shell is compared more to that of the bulk. By constructing the O-H groups in three ensembles (S1, S2, and S3) around the anion, we show that the frequency distribution of OH modes in the S1 ensemble show red-shifting for both sulfate and thiosulfate. The O-H groups in the S2 ensemble of the sulfate-water system show red-shifting by 10 cm^-1, while in the case of thiosulfate-water, these O-H groups show blue-shifting by 8 cm^-1. The water molecules in S1 and S2 subensembles have slower dynamics compared to those in the bulk (S3). The dynamics of various kinds of hydrogen bonds were characterized by hydrogen bond population correlation functions. The spectral diffusion of solvation shell O-H modes was performed through a frequency-time correlation function. We find a significant amount of orientational retardation of water molecules in the S1 layer and moderate retardation in the S2 layer as compared to that in the bulk, S3 layer. All these findings, the red shift of the OH stretching frequency in S1 and S2 layers, slowing down of the orientational dynamics of OH vectors in S1 and S2 layers, and less diffusivity of water in S1 and S2 layers, show the long-range kosmotropic effect of multivalent sulfate and thiosulfate oxyanions. Due to the long-range effect, heterogeneous occupancy of water molecules is observed, and the water molecules are found to arrange in a patterned manner in the vicinity of anions with varied local density.

Effect of Functional and Electron Correlation on the Structure and Spectroscopy of the Al2O3(001)-H2O Interface

Oxide-water interfaces are ubiquitous, with many applications in industry and the environment, yet there is a great deal of controversy over their properties and microscopic structure. This controversy stems, in part, from the unique H-bond networks formed at different surface terminations and mineral compositions. Density functional theory simulations of these interfaces require an accurate description of both the oxide mineral and water in diverse H-bond environments. Thus, herein we simulate the Al₂O₃(001)-H₂O interface using the PBE, PBE-TS, RPBE, SCAN, and HSE06-TS functionals to determine how calculated interfacial properties depend on the choice of functional. We find that the structure of the first few layers of water at the surface is determined by electron correlation in a way that cannot be approximated using semiemipirical van der Waals corrections. Of the functionals investigated, we find that SCAN yields the most accurate interfacial structure, dynamics, and sum frequency generation spectrum. Furthermore, SCAN leads to a reduction in the order of the 2D H-bond network of water at the alumina surface predicted by GGA functionals, leading to a significant decrease in the anisotropy of the diffusion coefficient at the surface. We emphasize the importance of using a functional which accurately describes electron correlation for more complex oxides, such as transition-metal oxides, where electron correlation may play an even greater role in determining the structure and dynamics of the oxide-water interface.

Importance of van der Waals effects on the hydration of metal ions from the Hofmeister series

The van der Waals (vdW) interaction plays a crucial role in the description of liquid water. Based on ab initio molecular dynamics simulations, including the non-local and fully self-consistent density-dependent implementation of the Tkatchenko-Scheffler dispersion correction, we systematically studied the aqueous solutions of metal ions (K⁺, Na⁺, and Ca²⁺) from the Hofmeister series. Similar to liquid water, the vdW interactions strengthen the attractions among water molecules in the long-range, leading to the hydrogen bond networks softened in all the ion solutions. However, the degree that the hydration structure is revised by the vdW interactions is distinct for different ions, depending on the strength of short-range interactions between the hydrated ion and surrounding water molecules. Such revisions by the vdW interactions are important for the understanding of biological functionalities of ion channels.

Vibration Spectral Dynamics of Weakly Coordinating Water Molecules near an Anion: FPMD Simulations of an Aqueous Solution of Tetrafluoroborate

The extent to which the ions affect the nearby water molecules will decide the structure-making or breaking nature of those ions in aqueous solutions. The effects of a weakly coordinating anion on the structure, dynamics, and vibrational properties of water molecules are not so significant as compared to an anion capable of making strong ion-water hydrogen bonds. The present work deals with the first-principles molecular dynamics study of an aqueous solution of such a weakly coordinating anion, tetrafluoroborate (BF₄^-), using dispersion-corrected DFT-based first-principles molecular dynamics (FPMD) simulations. Various structural, dynamical, and spectral properties, such as radial distribution functions (RDFs), rotational dynamics, vibrational density of states (VDOS), hydrogen bond as well as dangling OH autocorrelation functions, and residence dynamics, were calculated to investigate the effects of the anion on nearby water molecules. The process of spectral diffusion was assessed through a time series wavelet transformation of trajectories obtained from FPMD simulations. The first ion-water solvation shell extends up to 5.5 Å, containing around 20 water molecules. The lifetime of the ion-water hydrogen bond is found to be 1.19 ps, whereas the water-water hydrogen bond lifetime is found to be 1.13 ps. Inside the solvation shell, the persistence time of dangling OH chromophores and the average frequency of OH modes inside the solvation shell are found to be more compared to bulk. Three time scales are found for solvation shell OH modes from the frequency-frequency correlation function. A very short time scale is found for the intact ion-water interaction; the short time scale is for the ion-water hydrogen bond, and the long time scale is for escape dynamics of water molecules from the ion solvation shell. From the mean squared displacement, it is found that solvation water molecules diffuse slower than the bulk. However, solvation shell water molecules show faster relaxation from the analysis of rotational anisotropy. Within the longer time scale of spectral diffusion, this process (which is related to various dynamics of the molecules) is not yet complete, as compared to fast anisotropic decay. This fact is similar to the experimental finding of spectral diffusion and anisotropy time scales in the aqueous solution of borohydride anion. The calculated results are also compared with available experimental data wherever possible.

Mutually polarizable QM/MM model with in situ optimized localized basis functions

We extend our recently developed quantum-mechanical/molecular mechanics (QM/MM) approach [Dziedzic et al., J. Chem. Phys. 145, 124106 (2016)] to enable in situ optimization of the localized orbitals. The quantum subsystem is described with onetep linear-scaling density functional theory and the classical subsystem - with the AMOEBA polarizable force field. The two subsystems interact via multipolar electrostatics and are fully mutually polarizable. A total energy minimization scheme is employed for the Hamiltonian of the coupled QM/MM system. We demonstrate that, compared to simpler models using fixed basis sets, the additional flexibility offered by in situ optimized basis functions improves the accuracy of the QM/MM interface, but also poses new challenges, making the QM subsystem more prone to overpolarization and unphysical charge transfer due to increased charge penetration. We show how these issues can be efficiently solved by replacing the classical repulsive van der Waals term for QM/MM interactions with an interaction of the electronic density with a fixed, repulsive MM potential that mimics Pauli repulsion, together with a modest increase in the damping of QM/MM polarization. We validate our method, with particular attention paid to the hydrogen bond, in tests on water-ion pairs, the water dimer, first solvation shells of neutral and charged species, and solute-solvent interaction energies. As a proof of principle, we determine suitable repulsive potential parameters for water, K⁺, and Cl^-. The mechanisms we employed to counteract the unphysical overpolarization of the QM subsystem are demonstrated to be adequate, and our approach is robust. We find that the inclusion of explicit polarization in the MM part of QM/MM improves agreement with fully QM calculations. Our model permits the use of minimal size QM regions and, remarkably, yields good energetics across the well-balanced QM/MM interface.

Simulated XUV photoelectron spectra of THz-pumped liquid water

Highly intense, sub-picosecond terahertz (THz) pulses can be used to induce ultrafast temperature jumps (T-jumps) in liquid water. A supercritical state of gas-like water with liquid density is established, and the accompanying structural changes are expected to give rise to time-dependent chemical shifts. We investigate the possibility of using extreme ultraviolet photoelectron spectroscopy as a probe for ultrafast dynamics induced by sub-picosecond THz pulses of varying intensities and frequencies. To this end, we use ab initio methods to calculate photoionization cross sections and photoelectron energies of (H₂O)₂₀ clusters embedded in an aqueous environment represented by point charges. The cluster geometries are sampled from ab initio molecular dynamics simulations modeling the THz-water interactions. We find that the peaks in the valence photoelectron spectrum are shifted by up to 0.4 eV after the pump pulse and that they are broadened with respect to unheated water. The shifts can be connected to structural changes caused by the heating, but due to saturation effects they are not sensitive enough to serve as a thermometer for T-jumped water.

Ab Initio Molecular Dynamics Simulations of the Influence of Lithium Bromide on the Structure of the Aqueous Solution-Air Interface

We present the results of ab initio molecular dynamics simulations of the solution–air interface of aqueous lithium bromide (LiBr). We find that, in agreement with the experimental data and previous simulation results with empirical polarizable force field models, Br^– anions prefer to accumulate just below the first molecular water layer near the interface, whereas Li⁺ cations remain deeply buried several molecular layers from the interface, even at very high concentration. The separation of ions has a profound effect on the average orientation of water molecules in the vicinity of the interface. We also find that the hydration number of Li⁺ cations in the center of the slab N_{c,Li⁺–H2O} ≈ 4.7 ± 0.3, regardless of the salt concentration. This estimate is consistent with the recent experimental neutron scattering data, confirming that results from nonpolarizable empirical models, which consistently predict tetrahedral coordination of Li⁺ to four solvent molecules, are incorrect. Consequently, disruption of the hydrogen bond network caused by Li⁺ may be overestimated in nonpolarizable empirical models. Overall, our results suggest that empirical models, in particular nonpolarizable models, may not capture all of the properties of the solution–air interface necessary to fully understand the interfacial chemistry.

Proton NMR relaxation from molecular dynamics: intramolecular and intermolecular contributions in water and acetonitrile

Accurate ¹H NMR relaxation rates for protons in pure water and acetonitrile are computed via ab initio and force field molecular dynamics. Dipole–dipole and spin-rotation mechanisms are considered.

Quadrupolar 14N NMR Relaxation from Force-Field and Ab Initio Molecular Dynamics in Different Solvents

Quadrupolar NMR spin relaxation rates and corresponding line widths were computed for the quadrupolar nucleus ¹⁴N for neat acetonitrile as well as for 1-methyl-1,3-imidazole and 1-methyl-1,3,4-triazole in different solvents. Molecular dynamics (MD) was performed with forces from the Kohn-Sham (KS) theory (ab initio MD) and force-field molecular mechanics (classical MD), followed by KS electric field gradient (EFG) calculations. For acetonitrile the agreement of the ¹⁴N line width with experiment is very good. Relative line widths for the azole nitrogens are improved over simpler approximations used previously in conjunction with single-point calculations at the multiconfigurational self-consistent field level. Overall, the NMR line widths are computed within a factor of 2 of the experimental values, giving access to reasonable estimates both of the dynamic EFG variance in the solvated systems as well as the associated correlation times that determine the relaxation rates.

A Comparison of QM/MM Simulations with and without the Drude Oscillator Model Based on Hydration Free Energies of Simple Solutes

Maintaining a proper balance between specific intermolecular interactions and non-specific solvent interactions is of critical importance in molecular simulations, especially when predicting binding affinities or reaction rates in the condensed phase. The most rigorous metric for characterizing solvent affinity are solvation free energies, which correspond to a transfer from the gas phase into solution. Due to the drastic change of the electrostatic environment during this process, it is also a stringent test of polarization response in the model. Here, we employ both the CHARMM fixed charge and polarizable force fields to predict hydration free energies of twelve simple solutes. The resulting classical ensembles are then reweighted to obtain QM/MM hydration free energies using a variety of QM methods, including MP2, Hartree⁻Fock, density functional methods (BLYP, B3LYP, M06-2X) and semi-empirical methods (OM2 and AM1 ). Our simulations test the compatibility of quantum-mechanical methods with molecular-mechanical water models and solute Lennard⁻Jones parameters. In all cases, the resulting QM/MM hydration free energies were inferior to purely classical results, with the QM/MM Drude force field predictions being only marginally better than the QM/MM fixed charge results. In addition, the QM/MM results for different quantum methods are highly divergent, with almost inverted trends for polarizable and fixed charge water models. While this does not necessarily imply deficiencies in the QM models themselves, it underscores the need to develop consistent and balanced QM/MM interactions. Both the QM and the MM component of a QM/MM simulation have to match, in order to avoid artifacts due to biased solute⁻solvent interactions. Finally, we discuss strategies to improve the convergence and efficiency of multi-scale free energy simulations by automatically adapting the molecular-mechanics force field to the target quantum method.

The Quest for Accurate Liquid Water Properties from First Principles

Developing accurate ab initio molecular dynamics (AIMD) models that capture both electronic reorganization and nuclear quantum effects associated with hydrogen bonding is key to quantitative understanding of bulk water and its anomalies as well as its role as a universal solvent. For condensed phase simulations, AIMD has typically relied on the generalized gradient approximation (GGA) of density functional theory (DFT) as the underlying model chemistry for the potential energy surface, with nuclear quantum effects (NQEs) sometimes modeled by performing classical molecular dynamics simulations at elevated temperatures. Here we show that the properties of liquid water obtained from the meta-GGA B97M-rV functional, when evaluated using accelerated path integral molecular dynamics simulations, display accuracy comparable to a computationally expensive dispersion-corrected hybrid functional, revPBE0-D3. We show that the meta-GGA DFT functional reproduces bulk water properties including radial distribution functions, self-diffusion coefficients, and infrared spectra with comparable accuracy of a much more expensive hybrid functional. This work demonstrates that the underlying quality of a good DFT functional requires evaluation with quantum nuclei and that high-temperature simulations are a poor proxy for properly treating NQEs.

A Microscopic Interpretation of Pump-Probe Vibrational Spectroscopy Using Ab Initio Molecular Dynamics

What happens when extra vibrational energy is added to water? Using nonequilibrium molecular dynamics simulations, also including the full electronic structure, and novel descriptors, based on projected vibrational density of states, we are able to follow the flow of excess vibrational energy from the excited stretching and bending modes. We find that the energy relaxation, mostly mediated by a stretching-stretching coupling in the first solvation shell, is highly heterogeneous and strongly depends on the local environment, where a strong hydrogen bond network can transport energy with a time scale of 200 fs, whereas a weaker network can slow down the transport by a factor 2-3.

Density anomaly of water at negative pressures from first principles

Using molecular dynamics simulations based on ab initio trained high-dimensional neural network potentials, we study the equation of state of liquid water at negative pressures. From density isobars computed for various pressures down to p  =  -230 MPa we determine the line of density maxima for two potentials based on the BLYP and the RPBE functionals, respectively. In both cases, dispersion corrections are included to account for non-local long-range correlations that give rise to van der Waals forces. We have followed the density maximum down to negative pressures close to the spinodal instability. For both functionals, the temperature of maximum density increases with decreasing pressure under moderate stretching, but changes slope at [Formula: see text] MPa and [Formula: see text] MPa for BLYP and RPBE, respectively. Our calculations confirm qualitatively the retracing shape of the line of density maxima found for empirical water models, indicating that the spinodal line maintains a positive slope even at strongly negative pressures.

Diffusion and reaction pathways of water near fully hydrated TiO2 surfaces from ab initio molecular dynamics

Ab initio molecular dynamics simulations are reported for water-embedded TiO₂ surfaces to determine the diffusive and reactive behavior at full hydration. A three-domain model is developed for six surfaces [rutile (110), (100), and (001), and anatase (101), (100), and (001)] which describes waters as "hard" (irreversibly bound to the surface), "soft" (with reduced mobility but orientation freedom near the surface), or "bulk." The model explains previous experimental data and provides a detailed picture of water diffusion near TiO₂ surfaces. Water reactivity is analyzed with a graph-theoretic approach that reveals a number of reaction pathways on TiO₂ which occur at full hydration, in addition to direct water splitting. Hydronium (H₃O⁺) is identified to be a key intermediate state, which facilitates water dissociation by proton hopping between intact and dissociated waters near the surfaces. These discoveries significantly improve the understanding of nanoscale water dynamics and reactivity at TiO₂ interfaces under ambient conditions.

A Versatile Multiple Time Step Scheme for Efficient ab Initio Molecular Dynamics Simulations

We present here our implementation of a time-reversible, multiple time step (MTS) method for full QM and hybrid QM/MM Born-Oppenheimer molecular dynamics simulations. The method relies on a fully flexible combination of electronic structure methods, from density functional theory to wave function-based quantum chemistry methods, to evaluate the nuclear forces in the reference and in the correction steps. The possibility of combining different electronic structure methods is based on the observation that exchange and correlation terms only contribute to low frequency modes of nuclear forces. We show how a pair of low/high level electronic structure methods that individually would lead to very different system properties can be efficiently combined in the reference and correction steps of this MTS scheme. The current MTS implementation makes it possible to perform highly accurate ab initio molecular dynamics simulations at reduced computational cost. Stable and accurate trajectories were obtained with time steps of several femtoseconds, similar to and even exceeding the ones usually adopted in classical molecular dynamics, in particular when using a generalized Langevin stochastic thermostat. Compared to the standard Velocity Verlet integration, the present MTS scheme allows for a 5- to 6-fold overall speedup, at an unaltered level of accuracy.

Water under Supercritical Conditions: Hydrogen Bonds, Polarity, and Vibrational Frequency Fluctuations from Ab Initio Simulations with a Dispersion Corrected Density Functional

We have studied the effects of dispersion interactions on the dynamics of vibrational frequency fluctuations, hydrogen bonds, and free OD modes in supercritical heavy water at three different densities by means of ab initio molecular dynamics simulations. The vibrational spectral diffusion, as described by the frequency fluctuations, is studied through calculations of frequency time correlation of stretch modes of deuterated water, and its relations to the dynamics of hydrogen bonds and free OD modes are described. In addition, some of the other dynamical, structural, and electronic properties such as diffusion, rotational relaxation, radial distribution functions, hydrogen bond and coordination numbers, and dipole moments are also investigated from the perspectives of their variation with inclusion of dispersion interactions at varying density of the solvent. Although some changes in the structural properties are found on inclusion of dispersion corrections, no significant difference in the fluctuation dynamics of OD stretching frequencies and also in other dynamical quantities of supercritical water are found because of dispersion effects. The dynamics of water molecules under supercritical conditions is very fast compared to the corresponding dynamics under ambient conditions. The large thermal effects at such a high temperature seem to take over any relatively minor changes that might be introduced by weak dispersion interaction.

Interstitial Voids and Resultant Density of Liquid Water: A First-Principles Molecular Dynamics Study

Many anomalous properties of water can be explained on the basis of the coexistence of more than one density states: high-density water (HDW) and low-density water (LDW). We investigated these two phases of water molecules through first-principles molecular dynamics simulations using density functional theory (DFT) in conjunction with various van der Waals-corrected exchange and correlation functionals. Different density regions were found to exist due to the difference in short-range and long-range forces present in DFT potentials. These density regions were identified and analyzed on the basis of the distribution of molecules and voids present. We defined a local structure index to distinguish and find the probability of occurrence of these different states. HDW and LDW arise due to the presence of "interstitial water" molecules in between the first and second coordination shells. The population of interstitial water molecules is found to affect the overall dynamics of the system as they change the hydrogen bond pattern.

Effect of Basicity on the Hydrolysis of the Bi(III) Aqua Ion in Solution: An Ab Initio Molecular Dynamics Study

Hydrolysis of the Bi(III) aqua ion under a range of solution conditions has been studied by means of ab initio molecular dynamics simulations. While the Bi(III) aqua ion is stable in pure water, there is an increasing degree of hydrolysis with the number of hydroxide anions in the medium. This is accompanied by a monotonic decrease of the total coordination number to an asymptotic value of ∼6, reached under extreme basicity conditions. Comparison of the simulated Bi(III) hydrolyzed species with the experimental species distribution at different degrees of basicity suggests that, at the PBE/DFT level of theory here employed, liquid water shows an overly acidic character. Predictions of theoretical EXAFS and XANES spectra were generated from the AIMD trajectories for different Bi hydrolyzed species, [Bi(HO)_m(H₂O)_n]^3-m+, m = 0-3 and n = 7-2. Comparison with available experimental spectra is presented. Spectral features joined to the degree of hydrolysis and hydration are analyzed.

Structure of liquid water - a dynamical mixture of tetrahedral and 'ring-and-chain' like structures

The nature of the dynamical hydrogen-bond network of liquid water under ambient conditions has challenged both experimental and theoretical researchers for decades and remains a topic of intense debate. In this work, we addressed the structural issue of the hydrogen-bond network of liquid water based on an accurate ab initio molecular dynamics simulation. The present work showed clearly that liquid water is neither accurately described by a static picture of mostly tetrahedral water molecules nor dominated by "ring-and-chain" like structures. Instead, the structure of water is a dynamical mixture of tetrahedral and 'ring-and-chain' like structures with a slight bias toward the former. On average, each water molecule forms about three hydrogen bonds with the surrounding water molecules. The present accurate ab initio molecular dynamics simulation of liquid water was made possible by using a fragment-based second-order Møller-Plesset perturbation theory (MP2) with a large basis set to treat a large body of water molecules. This level of ab initio theory is sufficiently accurate for describing water interactions, and the simulated structural and dynamical properties of liquid water, including radial distribution functions, diffusion coefficient, dipole moment, etc., are uniformly in excellent agreement with experimental observations.

Development of Embedded and Performance of Density Functional Methods for Molecular Crystals

We report an alternative quantum mechanical:quantum mechanical (QM:QM) method to the currently used periodic density functional calculations including dispersion and investigate its performance with respect to main structural and energetic properties of the X23 set of molecular crystals. By setting the goal of reproducing reference periodic BLYP+D3 values and by embedding BLYP+D3 into DFTB, we obtain results similar to those of periodic BLYP+D3-typically within 1-2% in lattice energies and ∼0.4% in cell volumes. The accuracy of this QM:QM method in comparison to DFTB+D and DFT+D for the X23 set of molecular crystals is discussed.

Spin-state dependence of the structural and vibrational properties of solvated iron(ii) polypyridyl complexes from AIMD simulations: aqueous [Fe(bpy)3]Cl2, a case study

LS and HS IR spectra of aqueous [Fe(bpy)₃]²⁺ and corresponding HS–LS difference IR spectrum as obtained from state-of-the-art ab initio molecular dynamics simulations applied to the determination of the structural and vibrational properties of the solvated complex.

Grid-Based Projector Augmented Wave (GPAW) Implementation of Quantum Mechanics/Molecular Mechanics (QM/MM) Electrostatic Embedding and Application to a Solvated Diplatinum Complex

A multiscale density functional theory-quantum mechanics/molecular mechanics (DFT-QM/MM) scheme is presented, based on an efficient electrostatic coupling between the electronic density obtained from a grid-based projector augmented wave (GPAW) implementation of density functional theory and a classical potential energy function. The scheme is implemented in a general fashion and can be used with various choices for the descriptions of the QM or MM regions. Tests on H₂O clusters, ranging from dimer to decamer show that no systematic energy errors are introduced by the coupling that exceeds the differences in the QM and MM descriptions. Over 1 ns of liquid water, Born-Oppenheimer QM/MM molecular dynamics (MD) are sampled combining 10 parallel simulations, showing consistent liquid water structure over the QM/MM border. The method is applied in extensive parallel MD simulations of an aqueous solution of the diplatinum [Pt₂(P₂O₅H₂)₄]^4- complex (PtPOP), spanning a total time period of roughly half a nanosecond. An average Pt-Pt distance deviating only 0.01 Å from experimental results, and a ground-state Pt-Pt oscillation frequency deviating by <2% from experimental results were obtained. The simulations highlight a remarkable harmonicity of the Pt-Pt oscillation, while also showing clear signs of Pt-H hydrogen bonding and directional coordination of water molecules along the Pt-Pt axis of the complex.