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Empirical valence bond models for reactive potential energy surfaces: A parallel multilevel genetic program approach
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10.1063/1.3610907
/content/aip/journal/jcp/135/4/10.1063/1.3610907
http://aip.metastore.ingenta.com/content/aip/journal/jcp/135/4/10.1063/1.3610907

Figures

Image of FIG. 1.
FIG. 1.

Tree representation of various functions.

Image of FIG. 2.
FIG. 2.

General overview of the PMLGP algorithm.

Image of FIG. 3.
FIG. 3.

(a) Average relative errors of Morse functions. (b) Average relative errors of Gaussian functions. (c) Average relative errors of double well functions.

Image of FIG. 4.
FIG. 4.

(a) Number of evolutionary cycles to reach an average relative error of 0.05 for Morse functions. (b) Number of evolutionary cycles to reach an average relative error of 0.05 for Gaussian functions. (c) Number of evolutionary cycles to reach an average relative error of 0.05 for double well functions.

Image of FIG. 5.
FIG. 5.

Molecular structures of the normal (enol) reactant state (left) and the tautomer (keto) product state (right) of 3-hydroxy-gamma-pyrone.

Image of FIG. 6.
FIG. 6.

(a) Contour plot of the ground state DFT data of 3-hydroxy-gamma-pyrone with the intrinsic reaction path overlaid (white-light dots). (b) Contour plot of the EVB ground state of 3-hydroxy-gamma-pyrone with the DFT intrinsic reaction path (white-light dots) and EVB intrinsic reaction path (blue-dark dots) overlaid.

Image of FIG. 7.
FIG. 7.

Contour plot of the readjusted EVB ground state of 3-hydroxy-gamma-pyrone with the DFT intrinsic reaction path (white-light dots) and EVB intrinsic reaction path (blue-dark dots) overlaid.

Image of FIG. 8.
FIG. 8.

Probability, P(t) for back proton transfer to the ground state normal form as a function of time after fluorescence from the equilibrated excited state tautomer minimum. The red-rapidly decaying curve gives the gas phase results at T = 300 K and green-slowly decaying curve gives results for back proton transfer in methanol solution at T = 300 K.

Image of FIG. 9.
FIG. 9.

Trajectories of various bond distances between the transferring proton on 3HGP and (1) the O-atom on the blocking methanol to which it is initially intermolecularly H-bonded (red curve that jumps up at 5 ps); (2) the O-atom on the mediator methanol molecule that approaches from solution and disrupts the blocking H-bond (green curve that fluctuates around a mean value of 4 Angstrom throughout); and (3) the normal form intramolecular O-atom on 3HGP to which the transferring proton first H-bonds (at 5 ps) and then transfers to (beyond 6 ps) (blue curve that jumps down at 5 ps).

Image of FIG. 10.
FIG. 10.

(a) One-dimensional best fit function for O 2 Morse function. (b) One-dimensional best fit function for Gaussian test case 5. (c) One-dimensional best fit function for double well test case 5.

Tables

Generic image for table
Table I.

Group mean, standard deviation, t value, confidence level, and effect size of the average relative errors and number of evolutionary cycles to obtain an average relative error of 0.05.

Generic image for table
Table II.

Relative barrier heights of the DFT ground state and EVB ground state of 3-hydroxy-gamma-pyrone.

Generic image for table
Table III.

Parameters used for (a) one-dimensional Gaussian test functions and (b) one-dimensional double well test functions.

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/content/aip/journal/jcp/135/4/10.1063/1.3610907
2011-07-27
2014-04-24
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Empirical valence bond models for reactive potential energy surfaces: A parallel multilevel genetic program approach
http://aip.metastore.ingenta.com/content/aip/journal/jcp/135/4/10.1063/1.3610907
10.1063/1.3610907
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