Inexpensive modeling of quantum dynamics using path integral generalized Langevin equation thermostats

Abstract

The properties of molecules and materials containing light nuclei are affected by their quantum mechanical nature. Modelling these quantum nuclear effects accurately requires computationally demanding path integral techniques. Considerable success has been achieved in reducing the cost of such simulations by using generalized Langevin dynamics to induce frequency-dependent fluctuations. Path integral generalized Langevin equation methods, however, have this far been limited to the study of static, thermodynamic properties due to the large perturbation to the system's dynamics induced by the aggressive thermostatting. Here we introduce a post-processing scheme, based on analytical estimates of the dynamical perturbation induced by the generalized Langevin dynamics, that makes it possible to recover meaningful time correlation properties from a thermostatted trajectory. We show that this approach yields spectroscopic observables for model and realistic systems which have an accuracy comparable to much more demanding approximate quantum dynamics techniques based on full path integral simulations.Vibrational spectroscopic techniques -from conventional infrared (IR) and Raman to advanced femtosecond pump-probe [1, 2], sum-frequency generation, second harmonic scattering [3, 4], and multi-dimensional vibrational spectroscopy [5] -are a cornerstone of chemistry [6]. These techniques have a multitude of applications such as the characterization of functional groups in chemical systems [7], the determination of the atomistic mechanisms of phase transitions through insight into chemical environments [8], and identification of unique structural fingerprints of molecular crystals [9]. The use of atomistic simulations for the computation of spectroscopic properties facilitates the interpretation of these experiments and provides support to the characterization of novel materials.Even neglecting effects that go beyond the Born-Oppenheimer (BO) decoupling of electronic and nuclear degrees of freedom, accurate calculations of the vibrational spectra of materials require an explicit treatment of the quantum dynamics of the nuclear degrees of freedom [10] on the electronic ground state potential energy surface. Quantum dynamics is in principle exactly obtained from the solution of the time dependent Schrödinger equation for the nuclei, but this is only practical for systems containing a handful of degrees of freedom [11,12]. Condensed phase systems can be studied [13] either by an exact treatment of the quantum dynamics of a subset of the nuclear degrees of freedom [14], or through classical dynamics on the quantum free energy surface of the nuclei [15,16]. Among the methods in the latter class, several of the most popular ones are based on the imaginary time path integral framework -such as (thermostatted) ring polymer molecular dynamics [17,18] ((T)RPMD), centroid molec- * venkat.kapil@epfl.ch ular dynamics [19,20] (CMD) and the recently developed quasi-centroid molecular dynamics [21] (QCMD). These methods ignore real time cohe...

Path-integral approximations to quantum dynamics

“…Another potential efficiency saving is the use of Cayley propagators [111,112], which also avoid possible nonergodicity artifacts. Closely related to TRPMD, the PIGLET approach [113] uses a strong quantum thermostat to reduce the number of polymer beads to just a few; it was previously used to compute static properties, but a post-processing approach has recently been developed which extracts dynamical properties from PIGLET, using an iterative image-space reconstruction algorithm [114]. The PIGLET vibrational density of states for liquid water is in reasonable agreement with the TRPMD result (see Fig.…”

“…Adapted from Ref. [114], with the permission of AIP Publishing lations of diffusion in quantum glasses [118], and in flexible q-TIP4P/F liquid water [117] (which revealed the importance of cancellation between competing intraand inter-molecular quantum effects). Recently, CMD has also been used to compute the thermal heat conductivity of liquid hydrogen and helium [123], using a reformulation of this observable that avoids non-linear Gibbs-Kubo relations [124].…”

Gaussian Process Regression for Materials and Molecules

“…The theoretical calculation of light scattering also requires tensor properties; for example, second-harmonic scattering (SHS) is determined by the first hyperpolarizability tensor, β . 83 , 396 This strategy has been applied to the IR and Raman spectra of molecules 84 and condensed phases 86 , 203 , 394 and even to incorporate the effects of the quantum-mechanical behavior of light nuclei on the spectroscopic properties of complex molecules and condensed phases 85 , 397 —a remarkable feat that would have been all but impossible without ML models that are capable to accurately reproduce all of the properties that are accessible to electronic-structure calculations.…”

Machine learning-accelerated quantum mechanics-based atomistic simulations for industrial applications

“…A symmetry-adapted GPR version (SA-GPR) [178] was found to be most suitable for describing tensorial properties such as polarizabilities. The SA-GPR approach has been also successfully applied to the prediction of Raman and IR spectra for liquid water and ice based on path integral MD simulations that include nuclear quantum effects [179]. Using an ensemble of 16 ML models to estimate uncertainties, Raimbault et al applied their approach to calculate the Raman spectrum of two crystal forms of paracetamol (see Fig.…”