Abstract
Nuclear quantum effects have significant contributions to thermodynamic quantities and structural properties; furthermore, very expensive methods are necessary for their accurate computation. In most calculations, these effects, for instance, zero-point energies, are simply neglected or only taken into account within the quantum harmonic oscillator approximation. Herein, we present a new method, Generalized Smoothed Trajectory Analysis, to determine nuclear quantum effects from molecular dynamics simulations. The broad applicability is demonstrated with the examples of a harmonic oscillator and different states of water. Ab initio molecular dynamics simulations have been performed for ideal gas up to the temperature of 5000 K. Classical molecular dynamics have been carried out for hexagonal ice, liquid water, and vapor at atmospheric pressure. With respect to the experimental heat capacity, our method outperforms previous calculations in the literature in a wide temperature range at lower computational cost than other alternatives. Dynamic and structural nuclear quantum effects of water are also discussed.
Highlights
Calculations of reaction free energy profiles and activation barriers are routinely performed within the rigid-rotor and harmonic-oscillator approximation;[1] the more accurate computation of thermodynamic quantities or vibrational spectra is still a great challenge.[2−10] The inclusion of nuclear quantum effects (NQEs), such as zero-point energy (ZPE) or tunneling, is even more difficult.[11−13] Path-integral molecular dynamics (PIMD) and path integral Monte Carlo (PIMC) simulations are accurate, yet highly expensive methods to incorporate NQEs.[14,15]
We propose the Generalized Smoothed Trajectory Analysis (GSTA) method, which is numerically beneficial to the 1PT/2. Two-Phase Thermodynamics (2PT) methods and, addresses their limitations arising from the used approximations
A clear advance of GSTA compared to 1PT or 2PT methods is that the effect of anharmonicity can be determined rigorously using the work of smoothing defined by eq 53
Summary
Calculations of reaction free energy profiles and activation barriers are routinely performed within the rigid-rotor and harmonic-oscillator approximation;[1] the more accurate computation of thermodynamic quantities or vibrational spectra is still a great challenge.[2−10] The inclusion of nuclear quantum effects (NQEs), such as zero-point energy (ZPE) or tunneling, is even more difficult.[11−13] Path-integral molecular dynamics (PIMD) and path integral Monte Carlo (PIMC) simulations are accurate, yet highly expensive methods to incorporate NQEs.[14,15] The computational cost of PIMD simulations can be significantly reduced by advanced techniques.[16−18] Recently developed algorithms, such as a colored noise thermostat and quantum thermal bath, are more effective to add quantum effects to classical simulations,[19−21] but settings need to be chosen carefully to prevent zero-point energy leakage.[22,23]. When empirical water models were used in PIMD simulations, several properties deviated more from the experiments than in the classical simulations.[24−27] In these quantum simulations, the liquid water becomes less structured and less viscous This has been explained by double counting of quantum effects: once in the parameter optimization using experimental data, second in the quantum simulations. Recognizing the need to address this issue, more sophisticated approaches use slightly modified partition functions on optimized geometries.[37,38] There are a few methods which can estimate quantum corrections from classical MD trajectories, for example, one- and two-phase thermodynamics methods (1PT, 2PT).[39−41] In those cases the vibrational density of states (VDOS) is determined from molecular dynamics by the Fourier transformation of the velocity autocorrelation function.
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