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

Abstract

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

Insights in quantum dynamical effects in the infrared spectroscopy of liquid water from a semiclassical study with an ab initio-based flexible and polarizable force field

“…Vari-ous applications of the LSC-IVR method have also verified the LSC-IVR correlation function is most reliable for times on the order of the thermal time¯β for condensed phase systems. 4,13,14 This implies ∼25.78 fs at 300 K, which covers the first periods of the bending band. This suggests a value of ∼3275 cm −1 for the peak position of the O-H stretching band of the quantum IR spectrum for the TTM3-F model while using the time scale of the thermal time (25.78 fs) as t half for the damping Gaussian approach [Eq.…”

“…approaches 4 are needed for this-but it does describe a number of aspects of the dynamics very well. [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] For instance, the LSC-IVR has been shown to describe reactive flux correlation functions for chemical reaction rates quite well, including strong tunneling regimes, 5,7,22 and correlation functions [10][11][12][13][14][15][16][17][18][19][20][21] in systems with enough degrees of freedom for quantum rephasing to be unimportant. More recently, Liu and Miller have proposed a local Gaussian approximation (LGA) for treating imaginary frequencies 7 with the LSC-IVR, which provides a practical tool to study quantum effects in large/complex molecular systems whose interactions are often too difficult to be parameterized by Gaussians or polynomials and where ab initio dynamics is called for.…”

A simple model for the treatment of imaginary frequencies in chemical reaction rates and molecular liquids

“…III D describes the application of the LSC-IVR with the LGA to liquid para-hydrogen and compares the results with those obtained using other trajectory-based methods which were shown in our previous work. 13 Section IV summarizes and concludes. ͓In Appendix A, we also show how a similar LGA can be obtained from a simple modification of the Feynman-Kleinert approximation 16,[20][21][22] ͑FKA͒.͔ With the LGA, which extends LHAs for the Wigner function to be able to handle regions of imaginary frequencies even at low temperature, the LSC-IVR is now applicable to essentially any molecular system for which ordinary classical MD simulations are possible, providing a useful description of the quantum effects ͑other than true coherence͒ therein.…”

Path integral Liouville dynamics for thermal equilibrium systems

“…2-9), PILD can accurately capture the most important short time dephasing behavior and extend the accuracy of correlation functions of both linear and nonlinear operators to longer time (comparing with LSC-IVR and other comparable methods). Because comparison of LSC-IVR to experiment has demonstrated that the physical decay often dominates in many condensed phase systems, [9][10][11][12][13][62][63][64][65][66][67][68][69][70][71][72][73][74][75] Figs. 4 and 8 imply that the PILD correlation function will converge much faster for these systems as the adiabatic parameter γ ad decreases.…”

“…[9][10][11][12][13][62][63][64][65][66][67][68][69][70][71][72][73][74][75] It would also certainly be of interest to compare PILD to other imaginary time path integral based methods such as CMD and RPMD for realistic molecular systems. Note added in proof: In the reviewing process, we became aware of the work by Martyna and Cao 55, 56 on the adiabatic Wigner PIMD.…”