Complex-time velocity autocorrelation functions for Lennard-Jones fluids with quantum pair-product propagators

Kegerreis, Jeb S.; Nakayama, Akira; Makri, Nancy

doi:10.1063/1.2911925

Cited by 12 publications

(12 citation statements)

References 46 publications

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“…89 In addition, accurate quantum mechanical calculations have been performed at short times on the symmetrized version of the velocity autocorrelation function 46 using a single-bead PPP treatment. 90,91 The FBSD results are very similar to those of the linearized semiclassical approximation (which is based on the same physical assumption) and were found to be in excellent agreement with the quantum PPP calculations.…”

Section: (E) Fbsd For Neat Liquidssupporting

confidence: 68%

Forward–backward semiclassical and quantum trajectory methods for time correlation functions

Makri

2011

Phys. Chem. Chem. Phys.

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Forward-backward trajectory formulations of time correlation functions are reviewed. Combination of the forward and reverse time evolution operators within the time-dependent semiclassical approximation minimizes phase cancellation, giving rise to an efficient methodology for simulating the dynamics of low-temperature fluids. A quantum mechanical version of the forward-backward formulation, based on the hydrodynamic formulation of time-dependent quantum mechanics, is also available but is practical only for small systems.

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Section: (E) Fbsd For Neat Liquidssupporting

confidence: 68%

Forward–backward semiclassical and quantum trajectory methods for time correlation functions

Makri

2011

Phys. Chem. Chem. Phys.

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“…This is in agreement with previous simulations of this system at the same temperature and density, and with the same size. 29,30 Figure 4 shows the Kubo-transformed quantum velocity autocorrelation function as obtained via RPMD and the numerical convergence with time of the integral constraints on the right-hand side of eqs 29a−29c. The value of the It is clear that the first constraint integrates to the value of G v⃗ v⃗ (0) in ∼0.2 ps, showing that the correlation function is correctly described over this range of time.…”

Section: ■ Examplesmentioning

confidence: 99%

Sum Rule Constraints and the Quality of Approximate Kubo-Transformed Correlation Functions

Peña

2016

J. Phys. Chem. B

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In this work, a general protocol for evaluating the quality of approximate Kubo correlation functions of nontrivial systems in many dimensions is discussed. We first note that the generalized deconvolution of the Kubo transformed correlation function onto a time correlation function at a given value τ in imaginary time, such that 0 < τ < βℏ, leads to a series of sum rules applicable to the nth derivative of the Kubo function and whose iterative extension allows us to link derivatives of different order in the corresponding correlation functions. We focus on the case when τ = βℏ/2, for which all deconvolution kernels become real valued functions and their asymptotic behavior at long times exhibits a polynomial divergence. It is then shown that thermally symmetrized static averages, and the averages of the corresponding time derivatives, are ideally suited to investigate the quality of approximate Kubo correlation functions at successively larger (and up to arbitrarily long) times. This overall strategy is illustrated analytically for a harmonic system and numerically for a multidimensional double-well potential and a Lennard-Jones fluid. The analysis includes an assessment of RPMD position autocorrelation results as a function of the number of dimensions in a double-well potential and of the RPMD velocity autocorrelation function of liquid neon at 30 K.

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“…The classical Wigner model is an old idea, but it is important to realize that it is contained within the SC-IVR approach, as a well-defined approximation to it 39,40 . There are other ways to derive the classical Wigner model (or one may simply postulate it) 6,44,49,50 , and we also note that the 'forward-backward semiclassical dynamics' (FBSD) approximation of Makri et al 24,[28][29][30][51][52][53][54][55][56][57][58][59][60][61][62] is very similar to it. The LSC-IVR/classical Wigner model cannot describe true quantum coherence effects in time correlation functions-more accurate SC-IVR approaches, such as the Fourier transform forward-backward IVR (FB-IVR) approach 22,63 , or the still more accurate generalized FB-IVR 64 and exact FB-IVR 5 of Miller et al , are needed for this-but it does describe some aspects of the quantum dynamics very well [24][25][26][34][35][36][37][38]41,42,[65][66][67] .…”

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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Complex-time velocity autocorrelation functions for Lennard-Jones fluids with quantum pair-product propagators

Cited by 12 publications

References 46 publications

Forward–backward semiclassical and quantum trajectory methods for time correlation functions

Forward–backward semiclassical and quantum trajectory methods for time correlation functions

Sum Rule Constraints and the Quality of Approximate Kubo-Transformed Correlation Functions

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

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