Information theoretical statistical discrimination measures for electronic densities. (English) Zbl 1500.81085
Summary: Information theoretical measures are examined as methodologies for optimizing linear and non-linear parameters to obtain the best densities for particular classes of functions. We focus on the use of Gaussian type functions to represent the hydrogen atom, and examine combinations of these functions which have been used in the STO-\(n\)G basis sets. The densities obtained from these procedures are compared and contrasted to those obtained from energy optimization, and from least-squares fitting to the wave function and to the density, by evaluation of density expectation values and comparisons to their exact values. We show how densities obtained from the optimization of Kullback-Leibler (KL) measures yield better results in general, as compared to the ones obtained from energy optimization or least-squares fitting procedures. Furthermore, these types of densities are observed to provide exact results in the case of two expectation values, for all the studied classes of functions. The densities obtained from optimization of the cumulative residual KL measures, based on survival densities, provide the most accurate tail behaviour of the densities and hence the most accurate higher-order moments.
MSC:
| 81V45 | Atomic physics |
| 62B10 | Statistical aspects of information-theoretic topics |
| 94A15 | Information theory (general) |
| 94A17 | Measures of information, entropy |
| 28C20 | Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) |
| 93E24 | Least squares and related methods for stochastic control systems |
| 37A10 | Dynamical systems involving one-parameter continuous families of measure-preserving transformations |
Keywords:
Kullback-Leibler minimization; cumulative residual Kullback-Leibler minimization; variational principle; STO-3G basis set; information theoryReferences:
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