Bridging the gap between accurate ab initio many-body theory and simple density-functionals

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Density-functional theory is at the forefront of today's quantum mechanical approaches for the description of the molecules and materials that are the building blocks for a diverse range of technologies. The key to the predictive power and accuracy of the approach is the treatment of the quantum mechanical exchange and correlation interactions of the electrons. Present-day approximations for these contributions are limited to a narrow comfort zone of applicability - the work in this proposal will develop new approximations to significantly expand the range of viable applications. Methods to describe the exchange and correlation contributions to the energy are often relatively simple models based on the electronic density distribution and its gradient. Higher accuracy can be obtained using first-principles techniques based on the many-electron wave function. In this work we construct a common framework for the comparison of these expensive high accuracy approaches with simple density-functional approximations. This framework gives new insight into the development of new simple models - in particular the higher derivatives of the density are highlighted as a key variables for the description of electronic correlation. Functionals based on this quantity will be developed in this work, opening the way to more accurate and robust correlation treatments - removing error cancellations that plague present-day approximations.