Effective potential analytic continuation approach for real time quantum correlation functions involving nonlinear operators

Horikoshi, Atsushi; Kinugawa, Kenichi

doi:10.1063/1.1888576

Cited by 35 publications

(26 citation statements)

References 44 publications

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“…However, this argument assumed the odd time derivatives of the RPMD autocorrelation function to be continuous at t = 0, as they are in quantum mechanics. By considering the special case of a simple harmonic oscillator, for which the autocorrelation function can be worked out analytically, 50 Jang et al 51 have shown that the third derivative of the RPMD approximation toc q 2 q 2 (t) becomes discontinuous at t = 0 in the limit as n → ∞ (the correlation function contains a term proportional to |t| 3 in this limit 51 ). This implies that the error in the RPMD approximation to this non-linear autocorrelation function is O(t 3 ) rather than O(t 4 ).…”

Section: Braams and Manolopoulosmentioning

confidence: 99%

How to remove the spurious resonances from ring polymer molecular dynamics

Rossi

Ceriotti

Manolopoulos

2014

The Journal of Chemical Physics

245

347

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Two of the most successful methods that are presently available for simulating the quantum dynamics of condensed phase systems are centroid molecular dynamics (CMD) and ring polymer molecular dynamics (RPMD). Despite their conceptual differences, practical implementations of these methods differ in just two respects: the choice of the Parrinello-Rahman mass matrix and whether or not a thermostat is applied to the internal modes of the ring polymer during the dynamics. Here we explore a method which is halfway between the two approximations: we keep the path integral bead masses equal to the physical particle masses but attach a Langevin thermostat to the internal modes of the ring polymer during the dynamics. We justify this by showing analytically that the inclusion of an internal mode thermostat does not affect any of the desirable features of RPMD: thermostatted RPMD (TRPMD) is equally valid with respect to everything that has actually been proven about the method as RPMD itself. In particular, because of the choice of bead masses, the resulting method is still optimum in the short-time limit, and the transition state approximation to its reaction rate theory remains closely related to the semiclassical instanton approximation in the deep quantum tunneling regime. In effect, there is a continuous family of methods with these properties, parameterised by the strength of the Langevin friction. Here we explore numerically how the approximation to quantum dynamics depends on this friction, with a particular emphasis on vibrational spectroscopy. We find that a broad range of frictions approaching optimal damping give similar results, and that these results are immune to both the resonance problem of RPMD and the curvature problem of CMD.

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Section: Braams and Manolopoulosmentioning

confidence: 99%

How to remove the spurious resonances from ring polymer molecular dynamics

Rossi

Ceriotti

Manolopoulos

2014

The Journal of Chemical Physics

245

347

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“…First, the accuracy of the RPMD approximation is known to degrade for correlation functions involving nonlinear operators, 21,24,34 and ê i ͑t͒ is a highly nonlinear function of the coordinate operators r j ͑t͒. Second, the orientational motion of water molecules is predominantly a hydrogenatom motion and therefore inherently more quantum mechanical than the molecular center-of-mass motion that determines c v·v ͑t͒.…”

Section: B Orientational Correlation Functionsmentioning

confidence: 99%

“…͑10͒ and ͑15͒, it is not at all clear a priori that the approximation will be reliable at longer times. 21,24,34 A theoretical test of the accuracy of the RPMD approximations to c 1 ͑t͒ and c 2 ͑t͒ would therefore be very desirable.…”

Section: Moment "Sum Rule… Constraintsmentioning

confidence: 99%

Quantum diffusion in liquid water from ring polymer molecular dynamics

Miller

Manolopoulos²

2005

The Journal of Chemical Physics

205

190

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We have used the ring polymer molecular-dynamics method to study the translational and orientational motions in an extended simple point charge model of liquid water under ambient conditions. We find, in agreement with previous studies, that quantum-mechanical effects increase the self-diffusion coefficient D and decrease the relaxation times around the principal axes of the water molecule by a factor of around 1.5. These results are consistent with a simple Stokes-Einstein picture of the molecular motion and suggest that the main effect of the quantum fluctuations is to decrease the viscosity of the liquid by about a third. We then go on to consider the system-size scaling of the calculated self-diffusion coefficient and show that an appropriate extrapolation to the limit of infinite system size increases D by a further factor of around 1.3 over the value obtained from a simulation of a system containing 216 water molecules. These findings are discussed in light of the widespread use of classical molecular-dynamics simulations of this sort of size to model the dynamics of aqueous systems.

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“…Matsubara dynamics is therefore classical and conserves the distribution, but the phase factor in the distribution means that the correlation function is not amenable to computation in large systems. However, for the model systems for which it has been computed, it is more accurate than LSC-IVR, CMD or RPMD [32,57], and is exact for the position-squared correlation function in a harmonic potential [59] which is not the case for RPMD or CMD [60].…”

Section: Matsubara Dynamicsmentioning

confidence: 99%

Thermal quantum time-correlation functions from classical-like dynamics

Hele

2017

Molecular Physics

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Thermal quantum time-correlation functions are of fundamental importance in quantum dynamics, allowing experimentally-measurable properties such as reaction rates, diffusion constants and vibrational spectra to be computed from first principles. Since the exact quantum solution scales exponentially with system size, there has been considerable effort in formulating reliable linear-scaling methods involving exact quantum statistics and approximate quantum dynamics modelled with classical-like trajectories. Here we review recent progress in the field with the development of methods including Centroid Molecular Dynamics (CMD), Ring Polymer Molecular Dynamics (RPMD) and Thermostatted RPMD (TRPMD). We show how these methods have recently been obtained from 'Matsubara dynamics', a form of semiclassical dynamics which conserves the quantum Boltzmann distribution. We also rederive t → 0 + quantum transition-state theory (QTST) in the Matsubara dynamics formalism showing that Matsubara-TST, like RPMD-TST, is equivalent to QTST. We end by surveying areas for future progress. Submitted as a New View article to Molecular Physics (www.tandfonline.com/toc/tmph20/current) on 11th January 2017.

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Effective potential analytic continuation approach for real time quantum correlation functions involving nonlinear operators

Cited by 35 publications

References 44 publications

How to remove the spurious resonances from ring polymer molecular dynamics

How to remove the spurious resonances from ring polymer molecular dynamics

Quantum diffusion in liquid water from ring polymer molecular dynamics

Thermal quantum time-correlation functions from classical-like dynamics

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