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A refined ring polymer molecular dynamics theory of chemical reaction rates
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10.1063/1.1954769
/content/aip/journal/jcp/123/3/10.1063/1.1954769
http://aip.metastore.ingenta.com/content/aip/journal/jcp/123/3/10.1063/1.1954769

Figures

Image of FIG. 1.
FIG. 1.

Schematic illustration of the original RPMD method in Eq. (20) for calculating a reaction rate. At time zero, the first bead of the ring-polymer necklace is pinned to the transition state dividing surface and contributes a velocity factor of to the flux-side correlation function . The polymer then evolves under the classical equations of motion in Eqs. (17) and (18) and contributes a side factor of to the correlation function at time .

Image of FIG. 2.
FIG. 2.

Schematic illustration of the new RPMD method in Eq. (24) for calculating a reaction rate. At time zero, the centroid of the ring-polymer necklace is pinned to the transition state dividing surface and contributes a velocity factor of to the flux-side correlation function . The polymer then evolves under the classical equations of motion in Eqs. (17) and (18) and contributes a side factor of [ or 1] to the correlation function at time .

Image of FIG. 3.
FIG. 3.

Comparison of the flux-side correlation function in Eq. (24) (solid line) with that in Eq. (20) (dashed line) for the symmetric Eckart barrier at 300 and 1000 K.

Image of FIG. 4.
FIG. 4.

Histograms of the factors in Eq. (27) and in Eq. (28) for the symmetric Eckart barrier at 300 K.

Image of FIG. 5.
FIG. 5.

(a) An Arrhenius plot of the rate coefficient for the symmetric Eckart barrier. The solid line is the RPMD result obtained from Eq. (24) and the filled circles indicate the exact quantum-mechanical rate. (b) Percentage error in the RPMD result over the same temperature range as in (a).

Image of FIG. 6.
FIG. 6.

Top panel: the location of five different dividing surfaces on the symmetric Eckart barrier. Middle panel: the computed RPMD flux-side correlation functions at 300 K for each of these dividing surfaces. (Note that the dividing surfaces at and give the same correlation functions by symmetry.) Bottom panel: dependence of the QTST and RPMD rate coefficients on the location of the dividing surface.

Image of FIG. 7.
FIG. 7.

Computed QTST (dashed line) and RPMD (solid line) transmission coefficients for the asymmetric Eckart barrier at three different temperatures as a function of the location of the dividing surface .

Image of FIG. 8.
FIG. 8.

Time-dependent RPMD transmission coefficients for the asymmetric Eckart barrier at the three different temperatures considered in Fig. 7.

Tables

Generic image for table
Table I.

Transmission coefficients for the asymmetric Eckart barrier.

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/content/aip/journal/jcp/123/3/10.1063/1.1954769
2005-07-22
2014-04-23
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A refined ring polymer molecular dynamics theory of chemical reaction rates
http://aip.metastore.ingenta.com/content/aip/journal/jcp/123/3/10.1063/1.1954769
10.1063/1.1954769
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