High order path integrals made easy

Kapil, Venkat; Behler, Jörg; Ceriotti, Michele

doi:10.1063/1.4971438

Cited by 60 publications

(79 citation statements)

References 57 publications

(92 reference statements)

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“…The only major discrepancy in the spectra is the oversoftening of the bending band, which is an artefact that was already observed in Ref. [39] and linked to a shortcoming of the neural network potential. As shown in the middle panel of Fig.…”

Section: ( )mentioning

confidence: 72%

“…We first generate 100 ps long trajectories with opt(V) PIGLET parameters, using 12 replicas for hexagonal ice at 200 K and 6 replicas for liquid water at 300 K. In order to assess the comparative importance of the underlying potential energy surface and that of the approximations to quantum dynamics, we ran simulations with two ML potentials based on a Behler-Parrinello neural network framework [53] -the one introduced in Ref. 39 based on B3LYP+D3 reference calculations, and the one introduced in Ref. 54, based revPB0+D3.…”

Section: ( )mentioning

confidence: 99%

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

Kapil

Wilkins

Lan

et al. 2020

The Journal of Chemical Physics

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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...

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confidence: 72%

Section: ( )mentioning

confidence: 99%

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

Kapil

Wilkins

Lan

et al. 2020

The Journal of Chemical Physics

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“…60,61 Techniques developed for increasing the efficiency of path-integral molecular dynamics could conceivably also be employed in instanton calculations. In particular, the use of higher-order discretization schemes 62 and ring-polymer contraction 63,64 has not yet been fully explored.…”

Section: B Implementation Of Ab Initio Instanton Theorymentioning

confidence: 99%

Perspective: Ring-polymer instanton theory

Richardson

2018

The Journal of Chemical Physics

124

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Since the earliest explorations of quantum mechanics, it has been a topic of great interest that quantum tunneling allows particles to penetrate classically insurmountable barriers. Instanton theory provides a simple description of these processes in terms of dominant tunneling pathways. Using a ring-polymer discretization, an efficient computational method is obtained for applying this theory to compute reaction rates and tunneling splittings in molecular systems. Unlike other quantum-dynamics approaches, the method scales well with the number of degrees of freedom, and for many polyatomic systems, the method may provide the most accurate predictions which can be practically computed. Instanton theory thus has the capability to produce useful data for many fields of low-temperature chemistry including spectroscopy, atmospheric and astrochemistry, as well as surface science. There is however still room for improvement in the efficiency of the numerical algorithms, and new theories are under development for describing tunneling in nonadiabatic transitions.

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“…17,31 While algorithms for performing path integral simulations at constant pressure conditions exist, 32,33 an accurate evaluation of the thermophysical properties requires a very large number of replicas for convergence. In this article, we introduce a method, based on a recently developed implementation of high order path integral factorizations, 26 to greatly accelerate the convergence of these simulations.…”

Section: Introductionmentioning

confidence: 99%

Modeling the Structural and Thermal Properties of Loaded Metal–Organic Frameworks. An Interplay of Quantum and Anharmonic Fluctuations

Kapil

Wieme

Vandenbrande

et al. 2019

J. Chem. Theory Comput.

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Metal-organic frameworks show both fundamental interest and great promise for applications in adsorption-based technologies, such as the separation and storage of gases. The flexibility and complexity of the molecular scaffold poses a considerable challenge to atomistic modeling, especially when also considering the presence of guest molecules. We investigate the role played by quantum and anharmonic fluctuations in the archetypical case of MOF-5, comparing the material at various levels of methane loading. Accurate path integral simulations of such effects are made affordable by the introduction of an accelerated simulation scheme and the use of an optimized force 1 arXiv:1901.03770v1 [cond-mat.mtrl-sci] 11 Jan 2019field based on first-principles reference calculations. We find that the level of statistical treatment that is required for predictive modeling depends significantly on the property of interest. The thermal properties of the lattice are generally well described by a quantum harmonic treatment, with the adsorbate behaving in a classical but strongly anharmonic manner. The heat capacity of the loaded framework -which plays an important role in the characterization of the framework and in determining its stability to thermal fluctuations during adsorption/desorption cycles -requires, however, a full quantum and anharmonic treatment, either by path integral methods or by a simple but approximate scheme. We also present molecular-level insight into the nanoscopic interactions contributing to the material's properties and suggest design principles to optimize them.

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High order path integrals made easy

Cited by 60 publications

References 57 publications

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

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

Perspective: Ring-polymer instanton theory

Modeling the Structural and Thermal Properties of Loaded Metal–Organic Frameworks. An Interplay of Quantum and Anharmonic Fluctuations

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