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Interpolation of diabatic potential-energy surfaces: Quantum dynamics on ab initio surfaces
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10.1063/1.2047569
/content/aip/journal/jcp/123/13/10.1063/1.2047569
http://aip.metastore.ingenta.com/content/aip/journal/jcp/123/13/10.1063/1.2047569
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

The reaction probability on the analytic surface is shown as a function of the initial translational energy for ground-state adiabatic dynamics, —, and two-state diabatic dynamics ----. The translational energies used throughout the paper to monitor convergence are marked with vertical lines (10, 20, 30, 60, and ).

Image of FIG. 2.
FIG. 2.

The probability of exchange for quantum diabatic dynamics is shown at translational energies of 20, 30, 60, and as a function of the size of the data set; analytic result ---- and the average of the five interpolated potentials —. The error bars indicate the variation in the reaction probability for the five interpolated diabatic potentials to one standard deviation.

Image of FIG. 3.
FIG. 3.

The reaction probability is shown as a function of the translational energy for one of the ab initio surfaces with 800 data points: single-surface adiabatic dynamics, — and two-state diabatic dynamics ----. The inset figure shows an enlarged view of the reaction probability at low energy.

Image of FIG. 4.
FIG. 4.

The single-surface (adiabatic) probability of exchange is shown as a function of the data set size at translational energies of 20, 30, 60, and (reaction probability increases with translational energy). The average of the five potentials is shown (—) with error bars that indicate variation between the potentials to one standard deviation.

Image of FIG. 5.
FIG. 5.

The probability of exchange is shown as a function of the data set size at translational energies of 10, 20, 30, 60, and (reaction probability increases with translational energy) for the ab initio diabatic surfaces. The adiabatic values, derived from Fig. 4 (----) are shown for comparison. The average of the values from the five diabatic potentials (—) are shown with error bars which indicate variation between the potentials to one standard deviation.

Image of FIG. 6.
FIG. 6.

The correlation between the magnitude of the actual derivative coupling vector and the magnitude of the corresponding interpolated vector is shown for a sample of 1600 molecular configurations for the (a) analytic surface and (b) ab initio surface.

Image of FIG. 7.
FIG. 7.

The ADT angle (a) and the magnitude of the derivative coupling vector (b) are shown as functions of a H–H bond length. The three HH bond lengths are given by for from . Interpolation —, ab initio values ----.

Image of FIG. 8.
FIG. 8.

The correlation between the magnitude of the ab initio derivative coupling vector and the magnitude of the corresponding interpolated vector, from Eq. (45), is shown for a sample of 1600 molecular configurations for the (a) analytic surface and (b) ab initio surface.

Image of FIG. 9.
FIG. 9.

The reaction probability is shown as a function of translational energy for one of the ab initio surfaces. The result for two-state diabatic dynamics is shown for (—⋯—), 1 (— – —), 3 (---), 10 (– – –), and 30 (—). The reaction probability for adiabatic dynamics is indistinguishable from the value for .

Image of FIG. 10.
FIG. 10.

(a) The probability of exchange is shown as a function of the size of the data set at 20, 30, 60, and of translational energy on the analytic surface (reaction probability increases with translational energy). The probability for two-state diabatic dynamics performed on the analytic surface (----) is compared to the average of five smoothed interpolations for the analytic potential (—). The error bars indicate the variation between results for the five potentials to one standard deviation. (b) The probability of exchange is shown as a function of the size of the data set at 10, 20, 30, 60, and of translational energy (reaction probability increases with translational energy). The probability for ground-state adiabatic dynamics (----), derived from Fig. 4, is compared to the average probability for five smoothed interpolations for the ab initio potential (—). The error bars indicate variation between the potentials to one standard deviation.

Image of FIG. 11.
FIG. 11.

The derivative couplings, ∎, and the residual couplings, ∎, for the interpolation of the ab initio surface are shown as a function of the energy difference between the two states for (a) the interpolated residual coupling and (b) the smoothed interpolated residual couplings.

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/content/aip/journal/jcp/123/13/10.1063/1.2047569
2005-10-04
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Interpolation of diabatic potential-energy surfaces: Quantum dynamics on ab initio surfaces
http://aip.metastore.ingenta.com/content/aip/journal/jcp/123/13/10.1063/1.2047569
10.1063/1.2047569
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