Publication of the first paper (Carbó, Leyda, & Arnau, 1980), where our laboratory introduced some seminal quantum similarity (QS) concepts, lead the way of defining and refining this quantum chemical line of work (Bultinck, Gironés, & Carbó-Dorca, 2005; Bultinck, Van Damme, & Carbó-Dorca, 2009; Carbó, Besalú, Amat, & Fradera, 1996; Carbó, Calabuig, Vera, & Besalú, 1994; Carbó & Besalú, 1995; Carbó & Calabuig, 1990; Carbó & Domingo, 1987; Carbó-Dorca, Besalú, & Mercado, 2011; Carbó-Dorca & Besalú, 1998; Carbó-Dorca, 2013d). The applications of the theoretical tools provided by this quantum chemical branch have been focused in three directions.
The Three Directions of Quantum Similarity
In a first place was developed the possibility that QS could be used to find out order within molecular sets, this could be seen in the already cited work (Carbó, Leyda, & Arnau, 1980) and certainly in subsequent publications like (Carbó & Domingo, 1987), even in one of the last publications (Carbó-Dorca, Besalú, & Mercado, 2011) on the subject.
A second topic related to QS was the systematic description of molecular sets. It started from the definition of the so-called molecular point clouds (Carbó & Calabuig, 1990, 1992a, 1992b), evolved into the definition of tagged sets and quantum object sets (QOS) (Carbó-Dorca, 1998), and finally nowadays emerged the definitions of quantum (multi)molecular polyhedra (QMP) (Carbó-Dorca & Barragán, n. d.; Carbó-Dorca & Besalú, 2012a; Carbó-Dorca & González, 2016; Carbó-Dorca, 2015d, 2012, 2013b, 2014a, 2014b, 2015a, 2015c; Mercado & Carbó-Dorca, 2011). Everyone of this issues has opened the way to multiple characterizations of molecular sets, via the construction of QMP collective parameters and condensed molecular indices (Carbó-Dorca & Barragán, n. d., 2015; Carbó-Dorca, 2013b), which not only are useful to describe from multiple points of view molecular sets, but can be also a source of order within QMP.
However, the development of QS third branch, plausibly the most important for application purposes, has to be associated to the discussion about structure-properties relations (QSPR). In this application track, QS development has been active from the earlier stages, both in a comparable way as the Hansch (Hansch & Leo, 1979) analysis (Amat, Carbó-Dorca, Cooper, Allan, & Ponec, 2003; Amat, Carbó-Dorca, & Ponec, 1999; Carbó-Dorca & Gallegos, 2009; Gironés, Carbó-Dorca, & Ponec, 2003; Ponec, Amat, & Carbó-Dorca, 1999a, 1999b) or using similarity integrals as classical molecular descriptors (Besalú, Gironés, Amat, & Carbó-Dorca, 2002; Carbó-Dorca, Amat, Besalú, Gironés, & Robert, 2000, 2001; Carbó-Dorca & Besalú, 2000, 2002; Carbó-Dorca & Gironés, 2005; Carbó-Dorca & Van Damme, 2007b, 2008, 2007a; Carbó-Dorca, 2004, 2007, 2013c, 2015b; Fradera, Amat, Besalú, & Carbó-Dorca, 1997), within an empirical or classical QSPR (CQSPR) statistically bound working frame.