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A simple model for the treatment of imaginary frequencies in chemical reaction rates and molecular liquids
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10.1063/1.3202438
/content/aip/journal/jcp/131/7/10.1063/1.3202438
http://aip.metastore.ingenta.com/content/aip/journal/jcp/131/7/10.1063/1.3202438

Figures

Image of FIG. 1.
FIG. 1.

(a) Eckart barrier [given by Eq. (2.4)]. (b) Second derivative of the Eckart barrier.

Image of FIG. 2.
FIG. 2.

Off-diagonal elements at the top of the Eckart barrier for the Eckart barrier at (a) and (b) . The Fourier transform of produces the local momentum distribution . (c) Normalized local momentum distribution at . [Solid line: Exact results. Dotted-dashed line: LGA results.] (d) Same as (c) but at a lower temperature .

Image of FIG. 3.
FIG. 3.

Quantum correction factor . As in the conventional way, imaginary frequencies are shown as on the negative axis (i.e., shown as ). Solid line: LHA. Dashed line: LGA. Note that the imaginary frequency for is where the LHA breaks down.

Image of FIG. 4.
FIG. 4.

Gaussian width parameters of the local momentum distribution generated from the Fourier transform of . Imaginary frequencies are plotted on the negative axis. Solid line: Exact results. Solid circles: LGA results. Dashed line with hollow squares: LHA results. Note that for the imaginary frequency is where the LHA breaks down.

Image of FIG. 5.
FIG. 5.

(a) An Arrhenius plot of the thermal rate constant for the 1D Eckart barrier. Solid line: Exact quantum results. Dotted line with solid circles: LSC-IVR results using the LGA. Dashed line: Classical results. Hollow squares: LSC-IVR results using the LHA. (b) Tunneling correction factors for the 1D Eckart barrier. Solid line: Exact quantum results. Solid circles: LSC-IVR results with the LGA. Hollow squares: LSC-IVR results with the LHA. Solid triangles: LSC-IVR results with the exact Wigner function (from Ref. 8). (c) Relative errors of tunneling correction factors or thermal rate constants. Solid line with solid circles: LSC-IVR results with the LGA. Dotted line with hollow triangles: LSC-IVR results with the exact Wigner function (from Ref. 8). [Since most LSC-IVR results with the LHA deviate from the exact results by a few orders as shown in (a) and (b), their relative errors are not demonstrated here.]

Image of FIG. 6.
FIG. 6.

(a) Asymmetric Eckart barrier [given by Eq. (3.15)]. (b) Second derivative of the asymmetric Eckart barrier.

Image of FIG. 7.
FIG. 7.

Tunneling correction factors for the 1D asymmetric Eckart barrier with respect to different dividing surfaces. (a) Temperature . (b) Temperature . (c) Temperature .

Image of FIG. 8.
FIG. 8.

Comparison between LSC-IVR (LGA) and its QTST counterpart for tunneling correction factors for the 1D asymmetric Eckart barrier with respect to different dividing surfaces. (a) Temperature . (b) Temperature . (c) Temperature .

Image of FIG. 9.
FIG. 9.

(a) Tunneling correction factors for the 1D asymmetric Eckart barrier at different temperatures. Solid line: Exact quantum results. Solid circles: LSC-IVR results with the LGA. (b) Relative errors of tunneling correction factors or thermal rate constants.

Image of FIG. 10.
FIG. 10.

Normalized density of local frequencies from the path integral calculations for the liquid para- at the state points (a) and and (b) and . Dotted lines indicate the imaginary frequency .

Image of FIG. 11.
FIG. 11.

Kubo-transformed momentum autocorrelation functions (divided by ) based on the LSC-IVR formulation for the liquid para- at the state points (a) and and (b) and . Comparisons between the LHA and the LGA. LHA2 represents the LHA with only real frequencies.

Image of FIG. 12.
FIG. 12.

Kubo-transformed momentum autocorrelation functions (divided by ) based on the LSC-IVR formulation for the liquid para- at the state points (a) and and (b) and . Comparisons between the TGA (and its MEAC-corrected version) to the LGA (and its MEAC-corrected version).

Image of FIG. 13.
FIG. 13.

Probability distribution functions of path integral beads with the centroid fixed at the top of the 1D Eckart barrier . (a) and (b) . Comparisons between the FKA and the PIMC.

Tables

Generic image for table
Table I.

Information entropies in the MEAC procedure for different priors for liquid para-hydrogen at and and and under nearly zero extent pressure.

Generic image for table
Table II.

Diffusion contants for liquid para-hydrogen at and under nearly zero extent pressure.

Generic image for table
Table III.

Diffusion contants for liquid para-hydrogen at and under nearly zero extent pressure.

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/content/aip/journal/jcp/131/7/10.1063/1.3202438
2009-08-21
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A simple model for the treatment of imaginary frequencies in chemical reaction rates and molecular liquids
http://aip.metastore.ingenta.com/content/aip/journal/jcp/131/7/10.1063/1.3202438
10.1063/1.3202438
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