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Resultant gradient information, kinetic energy and molecular virial theorem

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Variations of the BO total electronic energy
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Submitted   Mar 4, 2019
Published   Mar 25, 2019
Issue    Vol 1 No 1 (2019)
DOI   10.25082/CR.2019.01.003

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Roman F. Nalewajski corresponding author
Department of Theoretical Chemistry, Jagiellonian University, Gronostajowa 2, 30-387 Cracow, Poland

Abstract

Resultant gradient-information is introduced and applied to problems in chemical reactivity theory. This local measure of the structural information contained in (complex) wavefunctions of electronic states is related to the system overall kinetic energy combining the modulus (probability) and phase (current) contributions. The grand-ensemble representation of thermodynamic equilibria in open systems demonstrates the physical equivalence of the variational energetic and information principles. It is used and to relate the populational derivatives of ensemble-average functionals in both these representations, which represent reactivity criteria for diagnosing the charge-transfer (CT) phenomena. Their equivalence is demonstrated by using the in situ potential and hardness descriptors to predict the direction and optimum amount of CT. The virial theorem is generalized into thermodynamic quantities and used to extract the kinetic energy component from qualitative energy profiles in the bond-formation and (exo/endo)-ergic reactions. The role of electronic kinetic energy in such chemical processes is reexamined, the virial theorem implications for the Hammond postulate of reactivity theory are explored, and variations of the structural-information in chemical processes are addressed. The maximum thermodynamic information rule is formulated and “production” of the gradient- information in chemical reactions is addressed. The Hammond postulate is shown to be indexed by the geometric derivative of resultant gradient-information at transition-state complex.

Keywords
bond formation, chemical reactivity, grand ensemble, information theory, resultant information, virial theorem

Article Details

How to Cite
Nalewajski, R. (2019). Resultant gradient information, kinetic energy and molecular virial theorem. Chemical Reports, 1(1), 22-35. https://doi.org/10.25082/CR.2019.01.003
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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

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