Deformations of density functions in molecular quantum chemistry

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Abstract
We generalize the use of the local scaling transformation developed by E. S. Kryachko and E. V. Ludeña to molecules in order to deform density functions. The connection with the Jacobian problem is clearly made, and we solve that problem using a formalism introduced by J. Moser. As a consequence, we can control the density information contained in a wave function, in some sense, at the same time as we keep particular regularity and behavior assumptions in the wave function (in particular concerning the symmetries of the wave function). The principal aim of the paper is to develop a correct mathematical background for further utilization in connection with density functional theory. Theoretical implications and numerical aspects are also discussed.