The name is absent

functional now applies to spatial distribution of the molecules of the fluid. The first
application of DFT as a general methodology to classical systems was introduced by
Ebner et. al. [97] for modeling the interfacial properties of a Lennard-Jones fluid.

The underlying basis of all DFTs is that the Helmholtz free energy of an open
system can be expressed as a unique functional of the density profiles of the con-
stituent molecules, independent of the external potential. This free energy (A[p(R)])
is referred to as the intrinsic Helmholtz free energy. The equilibrium density profile of
the system can be obtained from this free energy using the energy minimum principle.
The partition function of an open system at fixed V, T, and μ in an external field
(F^exi(R)) can be related to the grand potential of the system as,

Ω = -kβTlnΞ.                          (3.1)

Legendre transformation of Ω yields the intrinsic Helmholtz free energy,

A[p(R)] = Ω[p(R)] + ʃ dR>(R')(μ - V^exi (R')),            (3.2)

or grand potential can be written as

Ω[p(R)] = A[p(R)] - [dR'p(R')(μ - V^ext(R')).            (3.3)

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