Quantum diffusion in liquid water from ring polymer molecular dynamics

Miller, Thomas F.; Manolopoulos, David E.

doi:10.1063/1.2074967

Cited by 201 publications

(199 citation statements)

References 55 publications

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“…Two widely used methods based on imaginary-time path integrals are centroid molecular dynamics (CMD) [24][25][26][27][28] and ring-polymer molecular dynamics (RPMD). [29][30][31][32] Although both methods have known artifacts, such as the spurious-mode effect in RPMD [33][34][35] and the curvature problem 35,36 in CMD, they have proven effective for a vast range of chemical applications including the calculation of thermal rate constants, 30,[37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55] diffusion coefficients, 31,[56][57][58][59][60][61] and vibrational spectra. [33][34][35][36][62][63][64]…”

Section: Introductionmentioning

confidence: 99%

Non-equilibrium dynamics from RPMD and CMD

Welsch

Song

Shi

et al. 2016

The Journal of Chemical Physics

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We investigate the calculation of approximate non-equilibrium quantum time correlation functions (TCFs) using two popular path-integral-based molecular dynamics methods, ring-polymer molecular dynamics (RPMD) and centroid molecular dynamics (CMD). It is shown that for the cases of a sudden vertical excitation and an initial momentum impulse, both RPMD and CMD yield non-equilibrium TCFs for linear operators that are exact for high temperatures, in the t = 0 limit, and for harmonic potentials; the subset of these conditions that are preserved for non-equilibrium TCFs of non-linear operators is also discussed. Furthermore, it is shown that for these non-equilibrium initial conditions, both methods retain the connection to Matsubara dynamics that has previously been established for equilibrium initial conditions. Comparison of non-equilibrium TCFs from RPMD and CMD to Matsubara dynamics at short times reveals the orders in time to which the methods agree. Specifically, for the position-autocorrelation function associated with sudden vertical excitation, RPMD and CMD agree with Matsubara dynamics up to O(t4) and O(t1), respectively; for the position-autocorrelation function associated with an initial momentum impulse, RPMD and CMD agree with Matsubara dynamics up to O(t5) and O(t2), respectively. Numerical tests using model potentials for a wide range of non-equilibrium initial conditions show that RPMD and CMD yield non-equilibrium TCFs with an accuracy that is comparable to that for equilibrium TCFs. RPMD is also used to investigate excited-state proton transfer in a system-bath model, and it is compared to numerically exact calculations performed using a recently developed version of the Liouville space hierarchical equation of motion approach; again, similar accuracy is observed for non-equilibrium and equilibrium initial conditions.

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Section: Introductionmentioning

confidence: 99%

Non-equilibrium dynamics from RPMD and CMD

Welsch

Song

Shi

et al. 2016

The Journal of Chemical Physics

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“…Static properties can be calculated exactly using this mapping while RPMD uses the classical evolution of the polymers to provide an approximation to quantum dynamics. This approach has been previously shown to give accurate dynamical properties for systems ranging from nearly classical to those where tunnelling is dominant 21,22 .…”

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confidence: 99%

Quantum fluctuations can promote or inhibit glass formation

et al. 2011

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Glasses are dynamically arrested states of matter that do not exhibit the long-range periodic structure of crystals 1-4 . Here we develop new insights from theory and simulation into the impact of quantum fluctuations on glass formation. As intuition may suggest, we observe that large quantum fluctuations serve to inhibit glass formation as tunnelling and zero-point energy allow particles to traverse barriers facilitating movement. However, as the classical limit is approached a regime is observed in which quantum effects slow down relaxation making the quantum system more glassy than the classical system. This dynamical 'reentrance' occurs in the absence of obvious structural changes and has no counterpart in the phenomenology of classical glass-forming systems.Although a wide variety of glassy systems ranging from metallic to colloidal can be accurately described using classical theory, quantum systems ranging from molecular, to electronic and magnetic form glassy states 5,6 . Perhaps the most intriguing of these is the coexistence of superfluidity and dynamical arrest, namely the 'superglass' state suggested by recent numerical, theoretical and experimental work [7][8][9] . Although such intriguing examples exist, at present there is no unifying framework to treat the interplay between quantum and glassy fluctuations in the liquid state.To attempt to formulate a theory for a quantum liquid to glass transition, we may first appeal to the classical case for guidance. Here, a microscopic theory exists in the form of mode-coupling theory (MCT), which requires only simple static structural information as input and produces a full range of dynamical predictions for time correlation functions associated with single-particle and collective fluctuations 10 . Although MCT has a propensity to overestimate a liquid's tendency to form a glass, it has been shown to account for the emergence of the non-trivial growing dynamical length scales associated with vitrification 11 . Perhaps more importantly, MCT has made numerous non-trivial predictions ranging from logarithmic temporal decay of density fluctuations and reentrant dynamics in adhesive colloidal systems to various predictions concerning the effect of compositional mixing on glassy behaviour 12,13 . These have been confirmed by both simulation and experiment [14][15][16] .A fully microscopic quantum version of MCT (QMCT) that requires only the observable static structure factor as input may be developed along the same lines as the classical version. Indeed, a zero-temperature version of such a theory has been developed and successfully describes the wave-vector-dependent dispersion in superfluid helium 17 . In the Supplementary Information, we outline the derivation of a full temperature-dependent QMCT. In the limit of high temperatures, our theory reduces to the hard-sphere fluid. φ is the volume fraction, Λ * = (βh 2 /mσ 2 ) 1/2 is the thermal wavelength in units of inter-particle separation σ , and β = 1/k B T is the inverse temperature. The approach by which the...

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“…Habershon et al 84 showed that the ring polymer molecular dynamics (RPMD) model [85][86][87][88][89][90][91]92 could provide a good 'prior' for the MEAC. LSC-IVR, RPMD, and the centroid molecular dynamics [93][94][95][96][97][98][99][100][101][102][103][104][105] (CMD) are all approximate ways for adding some quantum effects to classical MD simulations, though none of them incorporate 'true' quantum coherence effects.…”

Section: ˆ/ Iht E −mentioning

confidence: 99%

Linearized semiclassical initial value time correlation functions with maximum entropy analytic continuation

Liu

Miller

2008

The Journal of Chemical Physics

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The maximum entropy analytic continuation (MEAC) method is used to extend the range of accuracy of the linearized semiclassical initial value representation (LSC-IVR)/classical Wigner approximation for real time correlation functions. The LSC-IVR provides a very effective 'prior' for the MEAC procedure since it is very good for short times, exact for all time and temperature for harmonic potentials (even for correlation functions of nonlinear operators), and becomes exact in the classical high temperature limit. This combined MEAC+LSC/IVR approach is applied here to two highly nonlinear dynamical systems, a pure quartic potential in one dimensional and liquid para-hydrogen at two thermal state points (25K and 14K under nearly zero external pressure). The former example shows the MEAC procedure to be a very significant enhancement of the LSC-IVR, for correlation functions of both linear and nonlinear operators, and especially at low temperature where semiclassical approximations are least accurate. For liquid para-hydrogen, the LSC-IVR is seen already to be excellent at T = 25K, but the MEAC procedure produces a significant correction at the lower temperature (T = 14K). Comparisons are also made to how the MEAC procedure is able to provide corrections for other trajectory-based dynamical approximations when used as priors.2

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Quantum diffusion in liquid water from ring polymer molecular dynamics

Cited by 201 publications

References 55 publications

Non-equilibrium dynamics from RPMD and CMD

Non-equilibrium dynamics from RPMD and CMD

Quantum fluctuations can promote or inhibit glass formation

Linearized semiclassical initial value time correlation functions with maximum entropy analytic continuation

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