Basis set dependence of molecular information channels and their entropic bond descriptors

Abstract

Information channels from SCF MO calculations using different basis sets and their entropic bond descriptors are compared within the orbital communication theory. In this information-theoretic (IT) treatment of communications between basis functions the overall covalency and ionicity bond components reflect the average communication noise and information flow, respectively, in the resolution level specified by the adopted set of basis functions. The basis-set dependence of the orbital conditional probabilities and their entropic descriptors of the information covalency/ionicity content is explored. Compared to the minimum set \({{\bf \chi}}\) of the occupied atomic orbitals of the separated constituent atoms, the extended basis sets of Gaussian orbitals and/or their formal contractions generally give rise to a higher IT-covalency and lower IT-ionicity descriptors of the system chemical bonds. In the augmented set case, \({{\bf \chi}^{aug.} = ({\bf \chi},{\bf \psi})}\) , containing the polarization function complement \({{\bf \psi}}\) of \({{\bf \chi}}\) , the use of only \({{\bf \chi} \rightarrow {\bf \chi}}\) communications is advocated in a semi-quantitative chemical interpretation of the IT bond indices. The maximum-overlap criterion is used to transform the general (orthonormal) extended basis \({{\bf \xi}}\) to its semi-augmented form \({\widetilde{\bf \chi}^{aug.} = \widetilde{\bf \xi}=(\widetilde{\bf \chi}, \widetilde{\bf \psi}),}\) in which \({\widetilde {\bf \chi} \approx {\bf \chi}}\) and \({\widetilde {\bf \psi} \approx{\bf \psi}}\), which facilitates the near minimum basis set interpretation of bond descriptors and extraction of communications involving the polarization functions \({{\widetilde {\mathbf \psi}}}\) . A similar transformation using the minimum information distance criterion can be also envisaged. The effect of the atomic reduction of the molecular channels, which misses the effect of the “internal” communications (bonds) on constituent atoms, is also examined. As intuitively expected, the IT descriptors of such reduced channels are found to be less sensitive to the basis set enlargement.

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Correspondence to Roman F. Nalewajski.

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Throughout the paper A, A and A denote the scalar quantity, row-vector and square/rectangular matrix, respectively.

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Nalewajski, R.F., Szczepanik, D. & Mrozek, J. Basis set dependence of molecular information channels and their entropic bond descriptors. J Math Chem 50, 1437–1457 (2012). https://doi.org/10.1007/s10910-012-9982-0

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Keywords

  • Basis set dependence
  • Bond covalency/ionicity
  • Chemical bond multiplicities
  • Entropic bond descriptors
  • Information theory
  • Maximum overlap criterion
  • Minimum information distance rule
  • Molecular information channels
  • Orbital communication theory