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The Journal of Chemical Physics

Comment on “Legendre-transform functionals for spin-density-functional theory” [J. Chem. Phys. 124, 224108 (2006)]

A. Holas, Robert Balawender

Published Dec 26, 2006• 16 citations
Publisher

Abstract

In this Comment the authors propose an alternative formulation of the starting point to the analysis performed in the commented paper [P. W. Ayers and W. Yang, J. Chem. Phys.124, 224108 (2006)]. An important role of the z component of the vector of the total spin angular momentum operator for the considered many-electron system is indicated. The authors believe their approach to be mathematically cleaner and conceptually easier than the original treatment.

DOI
10.1063/1.2423002

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In this Comment the authors propose an alternative formulation of the starting point to the analysis performed in the commented paper [P. W. Ayers and W. Yang, J. Chem. Phys.124, 224108 (2006)]. An important role of the z component of the vector of the total spin angular momentum operator for the considered many-electron system is indicated. The authors believe their approach to be mathematically cleaner and conceptually easier than the original treatment.
The argument presented makes two points about Snider’s [J. Chem. Phys. 76, 3543 (1982)] transformation between ‘‘unit position’’ states ‖r̂〉 and ‘‘unit momentum’’ states ‖p〉 for the motion of a structureless particle in three space: Snider’s transformation (1) implicitly defines an operator p̂ that has a classical limit a unit vector that is perpendicular to both r̂ and l=r×p, while on a classical scattering trajectory for r→∞, the physical unit vector p/p≊±r̂, and (2) attempts, inconsistent with the kinematics of states and observables of the system, to pass from r̂ to p̂ amplitudes of a state vector without any reference to the scalar r or p dependence of the wave functions.
We comment on a recent paper by Yuen-Zhou et al. [ Phys. Chem. Chem. Phys. 2009, 11, 4509 ] which extends some of the results of Time-Dependent Current Density Functional Theory applied to open quantum systems. Besides pointing out some incorrect statements in the theorems, we show that in the proof of the main result of the paper an arbitrary condition is introduced. Moreover, we argue that, since this condition has not a physical origin, one can find two systems with different vector potentials that lead to the same dynamics of the physical quantities of interest, the current and particle densities.