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Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density

Why this mattered

Lee, Yang, and Parr’s 1988 paper mattered because it helped turn density-functional theory from a formally powerful framework into a practical computational chemistry method. The key move was to recast the Colle-Salvetti correlation-energy expression, originally tied to Hartree-Fock pair-density information, into a usable functional of the electron density and its derivatives. That made electron correlation accessible in the same local, density-based language as exchange-correlation approximations already being developed in DFT, while retaining an empirical connection to accurate atomic and molecular correlation energies.

The resulting LYP correlation functional gave chemists a correlation model that worked across atoms, ions, and molecules, including both closed-shell and open-shell systems, with errors reported in the paper as typically only a few percent for the tested cases. This was important not because it solved correlation exactly, but because it showed that chemically useful correlation energies could be obtained without explicit many-electron wavefunctions. It helped shift routine quantum chemistry toward functionals that were fast enough for larger molecules yet accurate enough to compete with more expensive post-Hartree-Fock methods for many applications.

Its broader impact came through combination. LYP correlation was soon paired with Becke’s gradient-corrected exchange to form BLYP, and then incorporated into hybrid functionals such as B3LYP, which became one of the most widely used electronic-structure methods in chemistry. In that lineage, the paper was a bridge between earlier wavefunction-based insight into electron correlation and the later dominance of practical exchange-correlation functional design. It made a specific idea newly possible: that a compact, density-based approximation could encode enough correlation physics to support predictive molecular calculations at scale.

Abstract

A correlation-energy formula due to Colle and Salvetti [Theor. Chim. Acta 37, 329 (1975)], in which the correlation energy density is expressed in terms of the electron density and a Laplacian of the second-order Hartree-Fock density matrix, is restated as a formula involving the density and local kinetic-energy density. On insertion of gradient expansions for the local kinetic-energy density, density-functional formulas for the correlation energy and correlation potential are then obtained. Through numerical calculations on a number of atoms, positive ions, and molecules, of both open- and closed-shell type, it is demonstrated that these formulas, like the original Colle-Salvetti formulas, give correlation energies within a few percent.

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