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Atomic and Molecular Complexities: Their Physical and Chemical Interpretations

  • Chapter
Statistical Complexity

Abstract

Within the present work on the meaning, interpretation and applications of the complexity measures, different order-uncertainty planes embodying relevant information-theoretical magnitudes are studied in order to analyse the information content of the position and momentum electron densities of several atomic (neutrals, singly-charged ions, isoelectronic series) and molecular (closed shells, radicals, isomers) systems. The quantities substaining those planes are the exponential and the power Shannon entropies, the disequilibrium, the Fisher information and the variance. Each plane gives rise to a measure of complexity, determined by the product of its components. In the present work, the values of the so-called López-Ruiz, Mancini and Calbet (LMC), Fisher-Shannon (FS) and Cramér-Rao (CR) complexities will be provided in both conjugated spaces and interpreted from physical and chemical points of view. Computations for atoms were carried out within a Hartree-Fock framework, while for molecules by means of CISD(T)/6-311++G(3df, 2p) wave functions. In order to have a complete information-theoretical description of these systems, it appears relevant to consider simultaneously the results in both spaces.

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Acknowledgements

We wish to thank Nelson Flores-Gallegos and Sheila López-Rosa for their kind help in the preparation of this chapter, and to Professor K.D. Sen for helpful discussions. This work was supported in part by the Spanish grants FIS-2008-02380 and FIS-2005-06237 (MICINN), FQM-1735 and P06-FQM-2445 (Junta de Andalucía), and the Mexican grants 08266 CONACyT, PIFI 3.3 PROMEP-SEP. We belong to the Andalusian research group FQM-0207.

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Authors and Affiliations

  1. Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071, Granada, Spain

    J. C. Angulo

  2. Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071, Granada, Spain

    J. C. Angulo, J. Antolín & R. O. Esquivel

  3. Departamento de Física Aplicada, EUITIZ, Universidad de Zaragoza, 50018, Zaragoza, Spain

    J. Antolín

  4. Departamento de Química, Universidad Autónoma Metropolitana, 09340, México D.F., México

    R. O. Esquivel

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Correspondence to J. C. Angulo .

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  1. School of Chemistry, University of Hyderabad, Hyderabad, 500046, India

    K.D. Sen

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Angulo, J.C., Antolín, J., Esquivel, R.O. (2011). Atomic and Molecular Complexities: Their Physical and Chemical Interpretations. In: Sen, K. (eds) Statistical Complexity. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3890-6_6

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