On the use of Laplace's equation for global predictions of internuclear separation and dissociation energy |
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Authors: | Ray Hefferlin Jonathan Knoll |
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Institution: | (1) Physics Department, Southern Adventist University, Collegedale, TN 37315, USA |
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Abstract: | Properties of target species can be estimated by various means including interpolations in periodic charts. Interpolation is equivalent to numerical solution of the Laplace equation. A test of this equivalence, within some confidence level, for any N-atomic molecule surrounded by 4N nearest neighbors: the sum of the second differences of the data in all directions must be zero. Since very few molecules have 4N neighbors with known data, the test becomes: the sum of the averages of the second differences must be zero. The validity of these tests is explored. For radii of main-group atoms, and for internuclear separations of their diatomic combinations, the averages are different from zero and the sums of the averages are zero to within one if second-nearest neighbors are used. Dissociation potentials pass the tests but with larger scatter. Predictions for dissociation potentials, using iterative interpolation within boundaries on which there are known data, are reviewed. |
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Keywords: | Laplace equation internuclear distance dissociation potential periodic systems diatomic molecules |
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