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

The Journal of Physical Chemistry. B
Lisandro Hernandez de la Pena

Abstract

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 o...Continue Reading

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Citations

Dec 6, 2016·Micron : the International Research and Review Journal for Microscopy·Franz-Philipp SchmidtJoachim R Krenn
Jun 25, 2020·Physical Review. E·Ubaldo BafileEleonora Guarini

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