Comparison of path integral molecular dynamics methods for the infrared absorption spectrum of liquid water

Multi-time formulation of Matsubara dynamics

Matsubara dynamics has recently emerged as the most general form of a quantum-Boltzmann-conserving classical dynamics theory for the calculation of single-time correlation functions. Here, we present a generalization of Matsubara dynamics for the evaluation of multitime correlation functions. We first show that the Matsubara approximation can also be used to approximate the two-time symmetrized double Kubo transformed correlation function. By a straightforward extension of these ideas to the multitime realm, a multitime Matsubara dynamics approximation can be obtained for the multitime fully symmetrized Kubo transformed correlation function. Although not a practical method, due to the presence of a phase-term, this multitime formulation of Matsubara dynamics represents a benchmark theory for future development of Boltzmann preserving semiclassical approximations to general higher order multitime correlation functions. It also reveals a connection between imaginary time-ordering in the path integral and the classical dynamics of multitime correlation functions.

Probing photodissociation dynamics using ring polymer molecular dynamics

The performance of the ring polymer molecular dynamics (RPMD) approach to simulate typical photodissociation processes is assessed. The correct description of photodissociation requires the calculation of correlation functions or expectation values associated with non-equilibrium initial conditions, which was shown to be possible with RPMD very recently [J. Chem. Phys. 145, 204118 (2016)]. This approach is combined with treatment of the nonadiabatic dynamics employing the ring polymer surface hopping approach (RPSH), which is based on Tully's fewest switches surface hopping (FSSH) approach. The performance is tested using one-dimensional photodissociation models. It is found that RPSH with non-equilibrium initial conditions can well reproduce the time-dependent dissociation probability, and adiabatic and diabatic populations for cases where the crossing point is below and above the Franck-Condon point, respectively, while standard FSSH fails to reproduce the exact quantum dynamics in the latter case. Thus, it is shown that RPSH is an efficient and accurate alternative to standard FSSH, which is one of the most widely employed approaches to study photochemistry.

Path Integral Energy Landscapes for Water Clusters

The energy landscapes for a discretized path integral representation of the water dimer, trimer and pentamer are characterized in terms of the localized (classical) and delocalized minima and transition states. The transition states are finite-temperature approximations to the exact instanton path, and they are typically used to calculate the tunneling splittings or reaction rates. The features of the path integral landscape are explored, thus elucidating procedures that could usefully be automated when searching for instantons in larger systems. Our work not only clarifies the role of minima and transition states in path integral calculations but also enables us to analyze the quantum-to-classical transition.

Quantum approaches to vibrational dynamics and spectroscopy: is ease of interpretation sacrificed as rigor increases?

The subject of this Perspective is quantum approaches, beyond the harmonic approximation, to vibrational dynamics and IR spectroscopy.

Using a monomer potential energy surface to perform approximate path integral molecular dynamics simulation of ab initio water at near-zero added cost

It is now established that nuclear quantum motion plays an important role in determining water's hydrogen bonding, structure, and dynamics. Such effects are important to include in density functional theory (DFT) based molecular dynamics simulation of water. The standard way of treating nuclear quantum effects, path integral molecular dynamics (PIMD), multiplies the number of energy/force calculations by the number of beads required. In this work we introduce a method whereby PIMD can be incorporated into a DFT simulation with little extra cost and little loss in accuracy. The method is based on the many body expansion of the energy and has the benefit of including a monomer level correction to the DFT energy. Our method calculates intramolecular forces using the highly accurate monomer potential energy surface developed by Partridge-Schwenke, which is cheap to evaluate. Intermolecular forces and energies are calculated with DFT only once per timestep using the centroid positions. We show how our method may be used in conjunction with a multiple time step algorithm for an additional speedup and how it relates to ring polymer contraction and other schemes that have been introduced recently to speed up PIMD simulations. We show that our method, which we call "monomer PIMD", correctly captures changes in the structure of water found in a full PIMD simulation but at much lower computational cost.

Inclusion of nuclear quantum effects for simulations of nonlinear spectroscopy

The computation and interpretation of nonlinear vibrational spectroscopy is of vital importance for understanding a wide range of dynamical processes in molecular systems. Here, we introduce an approach to evaluate multi-time response functions in terms of multi-time double symmetrized Kubo transformed thermal correlation functions. Furthermore, we introduce a multi-time extension of ring polymer molecular dynamics to evaluate these Kubo transforms. Benchmark calculations show that the approximations are useful for short times even for nonlinear operators, providing a consistent improvement over classical simulations of multi-time correlation functions. The introduced methodology thus provides a practical way of including nuclear quantum effects in multi-time response functions of non-linear optical spectroscopy.

Approximating Matsubara dynamics using the planetary model: Tests on liquid water and ice

Matsubara dynamics is the quantum-Boltzmann-conserving classical dynamics which remains when real-time coherences are taken out of the exact quantum Liouvillian [T. J. H. Hele et al., J. Chem. Phys. 142, 134103 (2015)]; because of a phase-term, it cannot be used as a practical method without further approximation. Recently, Smith et al. [J. Chem. Phys. 142, 244112 (2015)] developed a "planetary" model dynamics which conserves the Feynman-Kleinert (FK) approximation to the quantum-Boltzmann distribution. Here, we show that for moderately anharmonic potentials, the planetary dynamics gives a good approximation to Matsubara trajectories on the FK potential surface by decoupling the centroid trajectory from the locally harmonic Matsubara fluctuations, which reduce to a single phase-less fluctuation particle (the "planet"). We also show that the FK effective frequency can be approximated by a direct integral over these fluctuations, obviating the need to solve iterative equations. This modification, together with use of thermostatted ring-polymer molecular dynamics, allows us to test the planetary model on water (gas-phase, liquid, and ice) using the q-TIP4P/F potential surface. The "planetary" fluctuations give a poor approximation to the rotational/librational bands in the infrared spectrum, but a good approximation to the bend and stretch bands, where the fluctuation lineshape is found to be motionally narrowed by the vibrations of the centroid.

First-Principles Simulations of Liquid Water Using a Dielectric-Dependent Hybrid Functional

We carried out first-principles simulations of liquid water under ambient conditions using a dielectric-dependent hybrid functional, where the fraction of exact exchange is set equal to the inverse of the high-frequency dielectric constant of the liquid. We found excellent agreement with experiment for the oxygen-oxygen partial correlation function at the experimental equilibrium density and 311 ± 3 K. Other structural and dynamical properties, such as the diffusion coefficient, molecular dipole moments, and vibrational spectra, are also in good agreement with experiment. Our results, together with previous findings on electronic properties of the liquid with the same functional, show that the dielectric-dependent hybrid functional accurately describes both the structural and electronic properties of liquid water.

Harmonic-phase path-integral approximation of thermal quantum correlation functions

We present an approximation to the thermal symmetric form of the quantum time-correlation function in the standard position path-integral representation. By transforming to a sum-and-difference position representation and then Taylor-expanding the potential energy surface of the system to second order, the resulting expression provides a harmonic weighting function that approximately recovers the contribution of the phase to the time-correlation function. This method is readily implemented in a Monte Carlo sampling scheme and provides exact results for harmonic potentials (for both linear and non-linear operators) and near-quantitative results for anharmonic systems for low temperatures and times that are likely to be relevant to condensed phase experiments. This article focuses on one-dimensional examples to provide insights into convergence and sampling properties, and we also discuss how this approximation method may be extended to many-dimensional systems.

Nuclear quantum effects on the vibrational dynamics of liquid water

Based on quantum-mechanical path-integral molecular dynamics simulations, the impact of nuclear quantum effects on the vibrational and hydrogen bond dynamics in liquid water is investigated. The instantaneous fluctuations in the frequencies of the O-H stretch modes are calculated using the wavelet method of time-series analysis, while the time scales of the vibrational spectral diffusion are determined from frequency-time correlation functions, joint probability distributions, and the slope of three-pulse photon echo. We find that the inclusion of nuclear quantum effects leads not only to a redshift of the vibrational frequency distribution by around 130 cm^-1 but also to an acceleration of the vibrational dynamics by as much as 30%. In addition, quantum fluctuations also entail a significantly faster decay of correlation in the initial diffusive regime, which is in agreement with recent vibrational echo experiments.

The collective and quantum nature of proton transfer in the cyclic water tetramer on NaCl(001)

Proton tunneling is an elementary process in the dynamics of hydrogen-bonded systems. Collective tunneling is known to exist for a long time. Atomistic investigations of this mechanism in realistic systems, however, are scarce. Using a combination of ab initio theoretical and high-resolution experimental methods, we investigate the role played by the protons on the chirality switching of a water tetramer on NaCl(001). Our scanning tunneling spectroscopies show that partial deuteration of the H₂O tetramer with only one D₂O leads to a significant suppression of the chirality switching rate at a cryogenic temperature (T), indicating that the chirality switches by tunneling in a concerted manner. Theoretical simulations, in the meantime, support this picture by presenting a much smaller free-energy barrier for the translational collective proton tunneling mode than other chirality switching modes at low T. During this analysis, the virial energy provides a reasonable estimator for the description of the nuclear quantum effects when a traditional thermodynamic integration method cannot be used, which could be employed in future studies of similar problems. Given the high-dimensional nature of realistic systems and the topology of the hydrogen-bonded network, collective proton tunneling may exist more ubiquitously than expected. Systems of this kind can serve as ideal platforms for studies of this mechanism, easily accessible to high-resolution experimental measurements.

Water Librations in the Hydration Shell of Phospholipids

The hydrophilic phosphate moiety in the headgroup of phospholipids forms strong hydrogen bonds with water molecules in the first hydration layer. Time-domain terahertz spectroscopy in a range from 100 to 1000 cm^-1 reveals the influence of such interactions on rotations of water molecules. We determine librational absorption spectra of water nanopools in phospholipid reverse micelles for a range from w₀ = 2 to 16 waters per phospholipid molecule. A pronounced absorption feature with maximum at 830 cm^-1 is superimposed on a broad absorption band between 300 and 1000 cm^-1. Molecular dynamics simulations of water in the reverse micelles suggest that the feature at 830 cm^-1 arises from water molecules forming one or two strong hydrogen bonds with phosphate groups, while the broad component comes from bulk-like environments. This behavior is markedly different from water interacting with less polar surfaces.

Vibrational Spectroscopy and Proton Transfer Dynamics in Protonated Oxalate

The dynamics and infrared spectroscopic signatures of proton transfer in protonated oxalate (p-Oxa) are studied using classical and quantum dynamics. The intermolecular interactions are described by a force field suitable to follow proton transfer. This allows to carry out multiple extended classical molecular dynamics (MD) and ring polymer MD simulations from which the infrared spectrum is determined. Simulations at 600 K sample the quantum mechanical ground state probability distribution and best reproduce the experimentally observed maximum absorption wavelength and part of the line shape. Comparison with the experimentally measured spectrum provides an estimate for the barrier height for proton transfer which can not be determined directly from experiment. A barrier of 4.2 kcal/mol is found to best reproduce the position and width of the infrared absorption of the transferring proton in p-Oxa and also leads to an infrared (IR) spectrum in good agreement with experiment for the deuterated species d-Oxa. A novel means to capture the two resonance forms of oxalate depending on the localization of the excess proton on either CO moiety is found to yield improved results for the spectroscopy in the framework region between 1000 and 2000 cm^-1.

Quantum Dynamics and Spectroscopy of Ab Initio Liquid Water: The Interplay of Nuclear and Electronic Quantum Effects

Understanding the reactivity and spectroscopy of aqueous solutions at the atomistic level is crucial for the elucidation and design of chemical processes. However, the simulation of these systems requires addressing the formidable challenges of treating the quantum nature of both the electrons and nuclei. Exploiting our recently developed methods that provide acceleration by up to 2 orders of magnitude, we combine path integral simulations with on-the-fly evaluation of the electronic structure at the hybrid density functional theory level to capture the interplay between nuclear quantum effects and the electronic surface. Here we show that this combination provides accurate structure and dynamics, including the full infrared and Raman spectra of liquid water. This allows us to demonstrate and explain the failings of lower-level density functionals for dynamics and vibrational spectroscopy when the nuclei are treated quantum mechanically. These insights thus provide a foundation for the reliable investigation of spectroscopy and reactivity in aqueous environments.

Path integral-GC-AdResS simulation of a large hydrophobic solute in water: a tool to investigate the interplay between local microscopic structures and quantum delocalization of atoms in space

We perform large scale quantum (path integral) molecular dynamics simulations of a C₆₀ -like molecule in water.

Analysis of the Spectral Characteristics of Pure Moxa Stick Burning by Hyperspectral Imaging and Fourier Transform Infrared Spectroscopy

The objective of this study was to investigate the spectra characteristics (SC) at wavelengths of 400~1000 nm and 2.5~15.5 μm of pure moxa stick (MS) during its 25-minute burning process using new spectral imaging techniques. Spectral images were collected for the burning pure MS at 5, 10, 15, 20, and 25 min using hyperspectral imaging (HSI) and Fourier transform infrared spectroscopy (FTIR) for the first time. The results showed that, at wavelengths of 400~1000 nm, the spectral range of the cross section of MS burning was 750~980 nm; the peak position was 860 nm. At wavelengths of 2.5~15.5 μm, the spectral range of the cross section of MS burning was 3.0~4.0 μm; the peak position was approximately 3.5 μm. The radiation spectra of MS burning include litter red and amount of infrared (but mainly near infrared) wavelengths. The temperature, blood perfusion, and oxygen saturation increase of Shenshu (BL23) after moxibustion radiation were observed too. According to mechanism of photobiological effects and moxibustion biological effects, it was inferred that moxibustion effects should be linked with moxibustion SC. This study provided new data and means for physical properties of moxibustion research.

Quantum ring-polymer contraction method: Including nuclear quantum effects at no additional computational cost in comparison to ab initio molecular dynamics

We present a simple and accurate computational method which facilitates ab initio path-integral molecular dynamics simulations, where the quantum-mechanical nature of the nuclei is explicitly taken into account, at essentially no additional computational cost in comparison to the corresponding calculation using classical nuclei. The predictive power of the proposed quantum ring-polymer contraction method is demonstrated by computing various static and dynamic properties of liquid water at ambient conditions using density functional theory. This development will enable routine inclusion of nuclear quantum effects in ab initio molecular dynamics simulations of condensed-phase systems.

On the interplay of the potential energy and dipole moment surfaces in controlling the infrared activity of liquid water

Infrared vibrational spectroscopy is a valuable tool for probing molecular structure and dynamics. However, obtaining an unambiguous molecular-level interpretation of the spectral features is made difficult, in part, due to the complex interplay of the dipole moment with the underlying vibrational structure. Here, we disentangle the contributions of the potential energy surface (PES) and dipole moment surface (DMS) to the infrared spectrum of liquid water by examining three classes of models, ranging in complexity from simple point charge models to accurate representations of the many-body interactions. By decoupling the PES from the DMS in the calculation of the infrared spectra, we demonstrate that the PES, by directly modulating the vibrational structure, primarily controls the width and position of the spectroscopic features. Due to the dependence of the molecular dipole moment on the hydration environment, many-body electrostatic effects result in a ∼100 cm(-1) redshift in the peak of the OH stretch band. Interestingly, while an accurate description of many-body collective motion is required to generate the correct (vibrational) structure of the liquid, the infrared intensity in the OH stretching region appears to be a measure of the local structure due to the dominance of the one-body and short-ranged two-body contributions to the total dipole moment.

An adaptive quantum mechanics/molecular mechanics method for the infrared spectrum of water: incorporation of the quantum effect between solute and solvent

Quantum effects in solute–solvent interactions, such as the many-body effect and the dipole-induced dipole, are known to be critical factors influencing the infrared spectra of species in the liquid phase.

Going clean: structure and dynamics of peptides in the gas phase and paths to solvation

The gas phase is an artificial environment for biomolecules that has gained much attention both experimentally and theoretically due to its unique characteristic of providing a clean room environment for the comparison between theory and experiment. In this review we give an overview mainly on first-principles simulations of isolated peptides and the initial steps of their interactions with ions and solvent molecules: a bottom up approach to the complexity of biological environments. We focus on the accuracy of different methods to explore the conformational space, the connections between theory and experiment regarding collision cross section evaluations and (anharmonic) vibrational spectra, and the challenges faced in this field.

First-Principles Framework to Compute Sum-Frequency Generation Vibrational Spectra of Semiconductors and Insulators

We present a first-principles framework to compute sum-frequency generation (SFG) vibrational spectra of semiconductors and insulators. The method is based on density functional theory and the use of maximally localized Wannier functions to compute the response to electric fields, and it includes the effect of electric field gradients at surfaces. In addition, it includes quadrupole contributions to SFG spectra, thus enabling the verification of the dipole approximation, whose validity determines the surface specificity of SFG spectroscopy. We compute the SFG spectra of ice I_{h} basal surfaces and identify which spectra components are affected by bulk contributions. Our results are in good agreement with experiments at low temperature.

Quantum calculations of the IR spectrum of liquid water using ab initio and model potential and dipole moment surfaces and comparison with experiment

The calculation and characterization of the IR spectrum of liquid water have remained a challenge for theory. In this paper, we address this challenge using a combination of ab initio approaches, namely, a quantum treatment of IR spectrum using the ab initio WHBB water potential energy surface and a refined ab initio dipole moment surface. The quantum treatment is based on the embedded local monomer method, in which the three intramolecular modes of each embedded H2O monomer are fully coupled and also coupled singly to each of six intermolecular modes. The new dipole moment surface consists of a previous spectroscopically accurate 1-body dipole moment surface and a newly fitted ab initio intrinsic 2-body dipole moment. A detailed analysis of the new dipole moment surface in terms of the coordinate dependence of the effective atomic charges is done along with tests of it for the water dimer and prism hexamer double-harmonic spectra against direct ab initio calculations. The liquid configurations are taken from previous molecular dynamics calculations of Skinner and co-workers, using the TIP4P plus E3B rigid monomer water potential. The IR spectrum of water at 300 K in the range of 0-4000 cm(-1) is calculated and compared with experiment, using the ab initio WHBB potential and new ab initio dipole moment, the q-TIP4P/F potential, which has a fixed-charged description of the dipole moment, and the TTM3-F potential and dipole moment surfaces. The newly calculated ab initio spectrum is in very good agreement with experiment throughout the above spectral range, both in band positions and intensities. This contrasts to results with the other potentials and dipole moments, especially the fixed-charge q-TIP4P/F model, which gives unrealistic intensities. The calculated ab initio spectrum is analyzed by examining the contribution of various transitions to each band.

Infrared and Raman Spectroscopy of Liquid Water through "First-Principles" Many-Body Molecular Dynamics

Vibrational spectroscopy is a powerful technique to probe the structure and dynamics of water. However, deriving an unambiguous molecular-level interpretation of the experimental spectral features remains a challenge due to the complexity of the underlying hydrogen-bonding network. In this contribution, we present an integrated theoretical and computational framework (named many-body molecular dynamics or MB-MD) that, by systematically removing uncertainties associated with existing approaches, enables a rigorous modeling of vibrational spectra of water from quantum dynamical simulations. Specifically, we extend approaches used to model the many-body expansion of interaction energies to develop many-body representations of the dipole moment and polarizability of water. The combination of these "first-principles" representations with centroid molecular dynamics simulations enables the simulation of infrared and Raman spectra of liquid water under ambient conditions that, without relying on any ad hoc parameters, are in good agreement with the corresponding experimental results. Importantly, since the many-body energy, dipole, and polarizability surfaces employed in the simulations are derived independently from accurate fits to correlated electronic structure data, MB-MD allows for a systematic analysis of the calculated spectra in terms of both electronic and dynamical contributions. The present analysis suggests that, while MB-MD correctly reproduces both the shifts and the shapes of the main spectroscopic features, an improved description of quantum dynamical effects possibly combined with a dissociable water potential may be necessary for a quantitative representation of the OH stretch band.