Jacob’s Ladder

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The Jacob’s ladder analogy serves to describe the hierarchal relationship between major XC functional approximations. Starting from the bottom of the ladder and move up, you introduce more and more complexity to the approximation, requiring more computation and information but increasing physical accuracy. For example, at the bottom of the ladder lies the LDA (being just a functional of the density), and then next comes the GGA (a functional of density AND density gradient), and then meta-GGA (density, density gradient, and kinetic energy density). An important facet of Jacob’s ladder is that each higher approximation builds upon and refines the lower approximations, incorporating compatible new approaches rather than using entirely dissimilar ones.

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