Current DFT Methods The Kohn-Sham Approach

The relationship (7.2) means that E0 is afunctional of p0(x, y, z). A function is a rule that transforms a number into another (or the same) number  

Afunctional is a rule that transforms a function into a number  

The functional J f(x)dx transforms the function x3 into the number four. We designate the fact that the integral is a functional of/(x) by writing 

A functional is a function of a definite (cf. the definite integral above) function. 

The first Hohenberg-Kohn theorem, then, says that any ground state property of a molecule is a functional of the ground state electron density function, e.g. for the energy 

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