ABSTRACT
Since the publication of what can be considered as the rst reference on quantum similarity (QS) in 1980,1 there has been a steady increasing amount of devoted papers,2-4 where an up-to-date bibliographic account on relevant QS contributions is given. In this 1980 original work, the initial idea was planned to emphasize the dissimilarity or, what is the same, the Euclidean distance between two quantum mechanical density functions (DFs) instead of their similarity or cosine of the subtended angle, although both possibilities were indeed open for practical use in reference 1 as a rst instance. It was decided afterward to put more emphasis on similarity than on dissimilarity parameters, however; nevertheless, the importance of the Euclidean
17.1 Quantum Similarity Indices and Measures .................................................. 349 17.2 Similarity Measures ...................................................................................... 350
17.2.1 Generalized Similarity Measures ..................................................... 351 17.2.2 QS Geometric Point of View ............................................................ 351
17.3 QS Similarity-Dissimilarity Indices ............................................................ 352 17.3.1 Origin Shift of Two DFs ................................................................... 352 17.3.2 Quantum Object Sets and Quantum Point Clouds ........................... 353 17.3.3 Discrete Representations of Quantum Point Clouds ........................ 354
17.4 Illustrative Example: QS Analysis of Three p-Type Functions .................... 355 17.4.1 Discrete QS Representation of n-Fold Degenerate
Wavefunctions .................................................................................. 357 17.4.2 QS of Binary States .......................................................................... 357
17.5 Stereoisomer Particular Case of Quantum Mechanical Expectation Values and Quantum QSPR .......................................................................... 358 17.5.1 Setting Up QQSPR Operator ............................................................ 358 17.5.2 Assorted Molecular Structure-Specic Polarization
Angle QQSPR................................................................................... 359 17.5.3 QQSPR for Amino Acids ................................................................. 359 17.5.4 QQSPR for Heterogeneous Optically Active Molecules .................. 361
17.6 Hyperbolic Sine Relation .............................................................................. 362 17.7 Computation Details ..................................................................................... 363 17.8 Final Discussion ............................................................................................ 363 Acknowledgment ...................................................................................................364 References ..............................................................................................................364
