Negative Temperature of Electronic Motion in Atoms and Molecules

Shu-Kun Lin

Molecular Diversity Preservation International (MDPI), Saengergasse 25, CH-4054 Basel, Switzerland; Institute for Organic Chemistry, University of Basel, CH-4056 Basel, Switzerland (lin@ubaclu.unibas.ch)

By definition both energy E and entropy S are positive functions. They are related to temperature T by [1]. The model of local thermodynamics of electronic motion by Ghosh, Berkowitz and Parr [2] is of great interest. Following virial theorem and the von Neumann-Shannon entropy formula, locally E and S vary in a way that the E reduces while its S increases [2]. Consequently, relative to the conventional thermodynamic temperature of the surroundings, the local thermodynamic temperature T of electronic motion in atoms and molecules must be negative. Locally both kinetic energy K and S increase with the increase of the absolute value of the local thermodynamic temperature, , or when T becomes more negative and when the system approaches the ground state. The typical quantum effects are characterized by such a local negative T. A local informational temperature ( ) of an electronic configuration in atoms and molecules is also defined, which is of the opposite sign (i.e., positive) of its local thermodynamic temperature, T. can be used to predict the relative stabilities of the excited states, where the local temperature T approaches zero at the excited states. The local thermodynamic temperature and the local informational temperature have been used as convenient concepts to characterize structural stability and process spontaneity of electronic systems.

[1] Ramsey, N. F. Phys. Rev. 1956, 103, 20-28; Kittel, C.; Kroemer, H. Thermal Physics, W. H. Freeman and Company, San Francisco, 1980, p. 42.

[2] Ghosh, S. W.; Berkowitz, M. Parr, R. G. Proc. Natl. Acad. Sci. USA 1984, 81, 8028-8031.