An efficient water force field calibrated against intermolecular THz and Raman spectra

Effects of polarizability and charge transfer on water dynamics and the underlying activation energies

A large number of force fields have been proposed for describing the behavior of liquid water within classical atomistic simulations, particularly molecular dynamics. In the past two decades, models that incorporate molecular polarizability and even charge transfer have become more prevalent, in attempts to develop more accurate descriptions. These are frequently parameterized to reproduce the measured thermodynamics, phase behavior, and structure of water. On the other hand, the dynamics of water is rarely considered in the construction of these models, despite its importance in their ultimate applications. In this paper, we explore the structure and dynamics of polarizable and charge-transfer water models, with a focus on timescales that directly or indirectly relate to hydrogen bond (H-bond) making and breaking. Moreover, we use the recently developed fluctuation theory for dynamics to determine the temperature dependence of these properties to shed light on the driving forces. This approach provides key insight into the timescale activation energies through a rigorous decomposition into contributions from the different interactions, including polarization and charge transfer. The results show that charge transfer effects have a negligible effect on the activation energies. Furthermore, the same tension between electrostatic and van der Waals interactions that is found in fixed-charge water models also governs the behavior of polarizable models. The models are found to involve significant energy-entropy compensation, pointing to the importance of developing water models that accurately describe the temperature dependence of water structure and dynamics.

Incorporating Polarization and Charge Transfer into a Point-Charge Model for Water Using Machine Learning

Rigid nonpolarizable water models with fixed point charges have been widely employed in molecular dynamics simulations due to their efficiency and reasonable accuracy for the potential energy surface. However, the dipole moment surface of water is not necessarily well-described by the same fixed charges, leading to failure in reproducing dipole-related properties. Here, we developed a machine-learning model trained against electronic structure data to assign point charges for water, and the resulting dipole moment surface significantly improved the predictions of the dielectric constant and the low-frequency IR spectrum of liquid water. Our analysis reveals that within our atom-centered point-charge description of the dipole moment surface, the intermolecular charge transfer is the major source of the peak intensity at 200 cm^-1, whereas the intramolecular polarization controls the enhancement of the dielectric constant. The effects of exact Hartree-Fock exchange in the hybrid density functional on these properties are also discussed.

Two-dimensional infrared-Raman spectroscopy as a probe of water's tetrahedrality

Two-dimensional spectroscopic techniques combining terahertz (THz), infrared (IR), and visible pulses offer a wealth of information about coupling among vibrational modes in molecular liquids, thus providing a promising probe of their local structure. However, the capabilities of these spectroscopies are still largely unexplored due to experimental limitations and inherently weak nonlinear signals. Here, through a combination of equilibrium-nonequilibrium molecular dynamics (MD) and a tailored spectrum decomposition scheme, we identify a relationship between the tetrahedral order of liquid water and its two-dimensional IR-IR-Raman (IIR) spectrum. The structure-spectrum relationship can explain the temperature dependence of the spectral features corresponding to the anharmonic coupling between low-frequency intermolecular and high-frequency intramolecular vibrational modes of water. In light of these results, we propose new experiments and discuss the implications for the study of tetrahedrality of liquid water.

Double proton transfer in hydrated formic acid dimer: Interplay of spatial symmetry and solvent-generated force on reactivity

The double proton transfer (DPT) reaction in the hydrated formic acid dimer (FAD) is investigated at molecular-level detail. For this, a global and reactive machine learned (ML) potential energy surface (PES) is developed to run extensive (more than 100 ns) mixed ML/MM molecular dynamics (MD) simulations in explicit molecular mechanics (MM) solvent at MP2-quality for the solute. Simulations with fixed – as in a conventional empirical force field – and conformationally fluctuating – as available from the ML-based PES – charge models for FAD show a significant impact on the competition between DPT and dissociation of FAD into two formic acid monomers. With increasing temperature the barrier height for DPT in solution changes by about 10% (∼1 kcal mol⁻¹) between 300 K and 600 K. The rate for DPT is largest, ∼1 ns⁻¹, at 350 K and decreases for higher temperatures due to destabilisation and increased probability for dissociation of FAD. The water solvent is found to promote the first proton transfer by exerting a favourable solvent-induced Coulomb force along the O–H⋯O hydrogen bond whereas the second proton transfer is significantly controlled by the O–O separation and other conformational degrees of freedom. Double proton transfer in hydrated FAD is found to involve a subtle interplay and balance between structural and electrostatic factors.

Simulation of double proton transfer in formic acid dimer by reactive ML potential in explicit molecular mechanics water solvent.

Equilibrium-nonequilibrium ring-polymer molecular dynamics for nonlinear spectroscopy

Two-dimensional Raman and hybrid terahertz-Raman spectroscopic techniques provide invaluable insight into molecular structures and dynamics of condensed-phase systems. However, corroborating experimental results with theory is difficult due to the high computational cost of incorporating quantum-mechanical effects in the simulations. Here, we present the equilibrium-nonequilibrium ring-polymer molecular dynamics (RPMD), a practical computational method that can account for nuclear quantum effects on the two-time response function of nonlinear optical spectroscopy. Unlike a recently developed approach based on the double Kubo transformed (DKT) correlation function, our method is exact in the classical limit, where it reduces to the established equilibrium-nonequilibrium classical molecular dynamics method. Using benchmark model calculations, we demonstrate the advantages of the equilibrium-nonequilibrium RPMD over classical and DKT-based approaches. Importantly, its derivation, which is based on the nonequilibrium RPMD, obviates the need for identifying an appropriate Kubo transformed correlation function and paves the way for applying real-time path-integral techniques to multidimensional spectroscopy.

Singular value decomposition analysis of the electron density changes occurring upon electrostatic polarization of water

In-depth elucidation of how molecules are electrically polarized would be one key factor for understanding the properties of those molecules under various thermodynamic and/or spatial conditions. Here this problem is tackled for the case of hydrogen-bonded water by conducting singular value decomposition of the electron density changes that occur upon electrostatic polarization. It is shown that all those electron density changes are approximately described as linear combinations of ten orthonormal basis “vectors”. One main component is the interatomic charge transfer through each OH bond, while some others are characterized as the atomic dipolar polarizations, meaning that both of these components are important for the electrostatic polarization of water. The interaction parameters that reasonably well reproduce the induced dipole moments are derived, which indicate the extent of mixing of the two components in electrostatic polarization.

The main features of the electron density changes that occur upon electrostatic polarization of water are elucidated by conducting singular value decomposition analysis of those changes.

The necessity of periodic boundary conditions for the accurate calculation of crystalline terahertz spectra

Terahertz vibrational spectroscopy has emerged as a powerful spectroscopic technique, providing valuable information regarding long-range interactions - and associated collective dynamics - occurring in solids. However, the terahertz sciences are relatively nascent, and there have been significant advances over the last several decades that have profoundly influenced the interpretation and assignment of experimental terahertz spectra. Specifically, because there do not exist any functional group or material-specific terahertz transitions, it is not possible to interpret experimental spectra without additional analysis, specifically, computational simulations. Over the years simulations utilizing periodic boundary conditions have proven to be most successful for reproducing experimental terahertz dynamics, due to the ability of the calculations to accurately take long-range forces into account. On the other hand, there are numerous reports in the literature that utilize gas phase cluster geometries, to varying levels of apparent success. This perspective will provide a concise introduction into the terahertz sciences, specifically terahertz spectroscopy, followed by an evaluation of gas phase and periodic simulations for the assignment of crystalline terahertz spectra, highlighting potential pitfalls and good practice for future endeavors.

Dynamical Collectivity and Nuclear Quantum Effects on the Intermolecular Stretching Mode of Liquid Water

This study investigated the broadband terahertz and low-frequency Raman spectroscopy of liquid water (H₂O, D₂O, and H₂¹⁸O) over 2 decades of frequency to address long-standing challenges regarding the interpretation of the intermolecular stretching mode at around 5 THz. We experimentally demonstrated that the intermolecular stretching mode of liquid water obtained via terahertz spectroscopy is significantly redshifted and broadened compared with that via Raman. This result was rationalized by the enhanced dynamical collectivity probed by terahertz spectroscopy, although both have a common origin in the kinetic motion. Their temperature and isotope dependences emphasize the significance of oscillation mass in determining the intermolecular stretching lineshape, while quantum effects cannot be overlooked in both terahertz and low-frequency Raman spectra.

Determining Partial Atomic Charges for Liquid Water: Assessing Electronic Structure and Charge Models

Partial atomic charges provide an intuitive and efficient way to describe the charge distribution and the resulting intermolecular electrostatic interactions in liquid water. Many charge models exist and it is unclear which model provides the best assignment of partial atomic charges in response to the local molecular environment. In this work, we systematically scrutinize various electronic structure methods and charge models (Mulliken, natural population analysis, CHelpG, RESP, Hirshfeld, Iterative Hirshfeld, and Bader) by evaluating their performance in predicting the dipole moments of isolated water, water clusters, and liquid water as well as charge transfer in the water dimer and liquid water. Although none of the seven charge models is capable of fully capturing the dipole moment increase from isolated water (1.85 D) to liquid water (about 2.9 D), the Iterative Hirshfeld method performs best for liquid water, reproducing its experimental average molecular dipole moment, yielding a reasonable amount of intermolecular charge transfer, and showing modest sensitivity to the local water environment. The performance of the charge model is dependent on the choice of the density functional and the quantum treatment of the environment. The computed molecular dipole moment of water generally increases with the percentage of the exact Hartree-Fock exchange in the functional, whereas the amount of charge transfer between molecules decreases. For liquid water, including two full solvation shells of surrounding water molecules (within about 5.5 Å of the central water) in the quantum chemical calculation converges the charges of the central water molecule. Our final pragmatic quantum chemical charge-assigning protocol for liquid water is the Iterative Hirshfeld method with M06-HF/aug-cc-pVDZ and a quantum region cutoff radius of 5.5 Å.

A Feynman diagram description of the 2D-Raman-THz response of amorphous ice

The 2D-Raman-THz response in all possible time-orderings (Raman-THz-THz, THz-Raman-THz, and THz-THz-Raman) of amorphous water ice is calculated in two ways: from atomistic molecular dynamics simulations and with the help of a Feynman diagram model, the latter of which power-expands the potential energy surface and the dipole and polarizability surfaces up to leading order. Comparing both results allows one to dissect the 2D-Raman-THz response into contributions from mechanical anharmonicity, as well as electrical dipole and polarizability anharmonicities. Mechanical anharmonicity dominates the 2D-Raman-THz response of the hydrogen-bond stretching and hydrogen-bond bending bands of water, and dipole anharmonicity dominates that of the librational band, while the contribution of polarizability anharmonicity is comparably weak. A distinct echo of the hydrogen-bond stretching band is observed for the THz-Raman-THz pulse sequence, again dominated by mechanical anharmonicity. A peculiar mechanism is discussed, which is based on the coupling between the many normal modes within the hydrogen-bond stretching band and which will inevitably generate such an echo for an amorphous structure.

Polarizable MD simulations of ionic liquids: How does additional charge transfer change the dynamics?

A new model for treating charge transfer in ionic liquids is developed and applied to 1-ethyl-3-methylimidazolium tetrafluoroborate. The model allows for us to examine the roles of charge transfer, polarizability, and charge scaling effects on the dynamics of ionic liquids.

Multistate Reactive Molecular Dynamics Simulations of Proton Diffusion in Water Clusters and in the Bulk

The molecular mechanics with proton transfer (MMPT) force field is combined with multistate adiabatic reactive molecular dynamics (MS-ARMD) to describe proton transport in the condensed phase. Parametrization for small protonated water clusters based on electronic structure calculations at the MP2/6-311+G(2d,2p) level of theory and refinement by comparing with infrared spectra for a protonated water tetramer yields a force field which faithfully describes the minimum energy structures of small protonated water clusters. In protonated water clusters up to (H₂O)₁₀₀H⁺, the proton hopping rate is around 100 hops/ns. This rate converges for 21 ≤ n ≤ 31, and no further speedup in bulk water is found. This indicates that bulklike behavior requires the solvation of a Zundel motif by ∼25 water molecules, which corresponds to the second solvation sphere. For smaller cluster sizes, the number of available states (i.e., the number of proton acceptors) is too small and slows down proton-transfer rates. The cluster simulations confirm that the excess proton is typically located on the surface. The free-energy surface as a function of the weights of the two lowest states and a configurational parameter suggests that the "special pair" plays a central role in rapid proton transport. The barriers between this minimum-energy structure and the Zundel and Eigen minima are sufficiently low (∼1 kcal/mol, consistent with recent experiments and commensurate with a hopping rate of ∼100/ns or 1 every 10 ps), leading to a highly dynamic environment. These findings are also consistent with recent experiments which find that Zundel-type hydration geometries are prevalent in bulk water.