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<p>We examine the concept of basis sets consisting of functions whose products have exact linear dependencies. The structure and properties of such linearly dependent product (LDP) basis sets are shown to be interrelated with those of the better known linearly independent product (LIP) basis sets. In particular, we suggest the possibility of constructing LIP basis sets by factorizing suitable linear combinations of given basis functions. Such factorization is always possible for an LDP basis set consisting of three functions. Construction methods and potential applications of LDP basis sets are also discussed.</p>

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Properties and applications of basis sets with linearly dependent products

  • 期刊论文

  • 发表日期：

    2025年3月13日

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  • Georgii N. Sizov,
  • Viktor N. Staroverov

摘要

We examine the concept of basis sets consisting of functions whose products have exact linear dependencies. The structure and properties of such linearly dependent product (LDP) basis sets are shown to be interrelated with those of the better known linearly independent product (LIP) basis sets. In particular, we suggest the possibility of constructing LIP basis sets by factorizing suitable linear combinations of given basis functions. Such factorization is always possible for an LDP basis set consisting of three functions. Construction methods and potential applications of LDP basis sets are also discussed.