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On the analytical representation of free energy profiles with a Morse/long-range model: Application to the water dimer
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10.1063/1.4810006
/content/aip/journal/jcp/138/23/10.1063/1.4810006
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/23/10.1063/1.4810006

Figures

Image of FIG. 1.
FIG. 1.

Behaviour of the radial variable () for various integer values of .

Image of FIG. 2.
FIG. 2.

GS pmf values, represented as solid circles, and MLR fitted pmf for the water dimer at 230 K. (a) MLR fits with = 3, = 2, and = 2 − 12. The inset shows the difference between the fitted pmf and the GS: Δ = () − (). (b) Same as (a) with = 4, = 2, and = 2 − 9.

Image of FIG. 3.
FIG. 3.

Water dimer −()/ at 230 K. The labelling is the same as in Fig. 2 . The insets represent a magnification near the minima of the curves. The ideal gas result, labelled IG, is also presented.

Image of FIG. 4.
FIG. 4.

versus T calculated from MLR fits with = 3 − 4, = 2, and = 2 − 12. The labelling is the same as in Fig. 2 . (a) = 230 K, (b) = 243 K, (c) = 273 K, and (d) = 303 K.

Image of FIG. 5.
FIG. 5.

GS, represented as solid circles, MLR fitted pmf for the water dimer and −()/ at 243 K. (a) MLR fits with = 3 − 4, = 2, and = 4 − 6. The inset shows a magnification of the fitted pmf and the GS in the region from 5.4 to 5.8 Å. (b) The labelling is the same as in (a). The insets represent a magnification near the minima of the curves from 5.2 to 5.8 Å. The ideal gas result, labelled IG, is also presented.

Image of FIG. 6.
FIG. 6.

GS, represented as solid circles, MLR fitted pmf for the water dimer and −()/ at 273 K. (a) MLR fits with = 3 − 4, = 2, and = 4 − 6. The inset shows a magnification of the fitted pmf and the GS in the region from 5.4 to 5.8 Å. (b) The labelling is same as in (a). The insets represent a magnification near the minima of the curves from 5.1 to 5.5 Å. The ideal gas result, labelled IG, is also presented.

Image of FIG. 7.
FIG. 7.

GS, represented as solid circles, MLR fitted pmf for the water dimer and −()/ at 303 K. (a) MLR fits with = 3 − 4, = 2, and = 4 − 6. The inset shows a magnification of the fitted pmf and the GS in the region from 5.4 to 5.6 Å. (b) The labelling is same as in (a). The insets represent a magnification near the minima of the curves from 5.0 to 5.5 Å. The ideal gas result, labelled IG, is also presented.

Image of FIG. 8.
FIG. 8.

GS, represented as solid circles, MLR fitted pmf for the GS, pmf from metadynamics (metaD), MLR fit of the metaD data and −()/ at 243 K, (a) metaD MLR fit with = 2, MLR fits to the GS with = 3 and = 4. = 2 and = 6 for all the fits. (b) The labeling is the same as in (a) but only the −()/ of the MLR fits are represented. The insets represent a magnification near the minima of the curves from 5.2 to 5.8 Å.

Image of FIG. 9.
FIG. 9.

Uncertainties in the GS data points at 230 K, 243 K, 273 K, and 303 K. (a) Absolute uncertainties in the GS points (). (b) Relative uncertainties in the GS points ()/(). (c) “Average” relative uncertainties in the GS points. The average was calculated using the values of the relative uncertainties in the , the predecessor and the successor .

Image of FIG. 10.
FIG. 10.

GS, represented as solid circles, MLR fitted pmf for the GS, pmf from metaD, MLR fit of the metaD data and −()/ at 273 K, (a) metaD MLR fit with = 2, MLR fits to the GS with = 3 and = 4. = 2 and = 6 for all the fits. (b) The labeling is the same as in (a) but only the −()/ of the MLR fits are represented. The insets represent a magnification near the minima of the curves from 5.1 to 5.5 Å.

Image of FIG. 11.
FIG. 11.

GS, represented as solid circles, MLR fitted pmf for the GS, pmf from metaD, MLR fit of the metaD data and −()/ at 303 K, (a) metaD MLR fit with = 2, MLR fits to the GS with = 3 and = 4. = 2 and = 6 for all the fits. (b) The labeling is the same as in (a) but only the −()/ of the MLR fits are represented. The insets represent a magnification near the minima of the curves from 5.0 to 5.5 Å.

Image of FIG. 12.
FIG. 12.

Values ( ) versus 1/ calculated for the GS, an MLR fitted model of GS with N = 4, q = 6, and an MLR fitted model of the metadynamics calculation with N = 2 and q = 6.

Tables

Generic image for table
Table I.

MLR parameters of a fit to the GS at = 230 K. Numbers in parentheses represent uncertainties in the last digits shown.

Generic image for table
Table II.

MLR parameters of a fit to the GS at 230 K. Numbers in parentheses represent uncertainties in the last digits shown.

Generic image for table
Table III.

MLR parameters of a fit to the metadynamics data at 243 K. Numbers in parentheses represent uncertainties in the last digits shown.

Generic image for table
Table IV.

Values of the variational rate constant for different models at different temperatures.

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/content/aip/journal/jcp/138/23/10.1063/1.4810006
2013-06-18
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: On the analytical representation of free energy profiles with a Morse/long-range model: Application to the water dimer
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/23/10.1063/1.4810006
10.1063/1.4810006
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