Relationships among derivatives of the integrals in the calculation of the gradient of the electronic energy with respect to the nuclear coordinates

1981 ◽  
Vol 75 (8) ◽  
pp. 3962-3966 ◽  
Author(s):  
Luis R. Kahn
Keyword(s):  
Electronic Energy ◽  
Derivatives Of

scholarly journals Resultant Information Descriptors, Equilibrium States and Ensemble Entropy †

Entropy ◽  
2021 ◽  
Vol 23 (4) ◽  
pp. 483
Author(s):  
Roman F. Nalewajski
Keyword(s):  
Equilibrium Phase ◽  
Electronic Energy ◽  
Local Source ◽  
Sources Of Information ◽  
Gradient Information ◽  
Entropy Information ◽  
Current Densities ◽  
Stationary Quantum ◽  
Thermodynamic Phase ◽  
Derivatives Of

In this article, sources of information in electronic states are reexamined and a need for the resultant measures of the entropy/information content, combining contributions due to probability and phase/current densities, is emphasized. Probability distribution reflects the wavefunction modulus and generates classical contributions to Shannon’s global entropy and Fisher’s gradient information. The phase component of molecular states similarly determines their nonclassical supplements, due to probability “convection”. The local-energy concept is used to examine the phase equalization in the equilibrium, phase-transformed states. Continuity relations for the wavefunction modulus and phase components are reexamined, the convectional character of the local source of the resultant gradient information is stressed, and latent probability currents in the equilibrium (stationary) quantum states are related to the horizontal (“thermodynamic”) phase. The equivalence of the energy and resultant gradient information (kinetic energy) descriptors of chemical processes is stressed. In the grand-ensemble description, the reactivity criteria are defined by the populational derivatives of the system average electronic energy. Their entropic analogs, given by the associated derivatives of the overall gradient information, are shown to provide an equivalent set of reactivity indices for describing the charge transfer phenomena.

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