Quantum Information Measures and Their Use in Chemistry

Background: The resultant measures of the information content in molecular electronic states are revisited. In these overall measures the current-related terms complement the probability functionals of classical Information Theory. The nonclassical Shannon entropy reflects the average magnitude of the state phase distribution, while the related current term in the complementary Fisher measure accounts for the average phase-gradient. Method: These generalized Fisher and Shannon descriptors of the information content in complex electronic states are applied to determine the phase-equilibria in molecules. The vertical and horizontal equilibria in molecules, which mark the extrema of the nonclassical and resultant entropy/information descriptors, respectively, are explored. The requirement, that the resultant measures have common solutions of the associated extreme entropy/information principles, calls for the negative sign of the nonclassical gradient measure. Conclusion: These extrema imply the phase-transformation of molecular electronic states. A separation of the density (modulus) and current (phase) factors in many-electron states is effected using the Harriman-Zumbach-Maschke construction of complex antisymmetric states yielding the specified electron density. A combined description of molecular systems, which accounts for the density and current degrees-of-freedom of electronic states is summarized and continuity equations for the state phase and resultant entropy are discussed.