# Van der Waals' density gradient theory

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This can be considered as the first density-functional theory.

The grand potential of an interface is expressed as

- ,

where a local approximation is employed in
the first term ( being the grand potential density of the
bulk system), and the variation in the density profile enters in the second term.
This second term is the integral of the square of the density gradient, with
a proportionality constant that is termed the **influence parameter**.

## References

- J.S. Rowlinson and B. Widom "Molecular Theory of Capillarity". Dover 2002 (originally: Oxford University Press 1982.)