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

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.

This proposal will introduce a paradigm shift in the way density-functional approximations are constructed. The proposed models differ significantly from widely used approximations based on the gradient of the electronic density and are informed and inspired by the use of highly accurate ab initio quantum chemical techniques. To allow for this cross-fertilization a common language and computational framework is introduced for the representation of density-functional and wave function based models, giving a unified treatment in an easily visualizable real space representation.

The impacts of density-functional theory have been far reaching in many areas of modern science, a fact reflected in the number of citations acquired by key papers in the area. The paper describing the Hohenberg-Kohn theorems, which give a foundation to the theory, has been cited more than 22000 times. The paper describing the Kohn-Sham equations, which represents the most common practical implementation of the theory, has been cited more than 23000 times. Popular functionals have also amassed considerable citations: BLYP (26998), PBE (37070), B3LYP (47243). These reflect the widespread usage desnity-functional theory has enjoyed, as a relatively simple, essentially black box, approach that can be utilized by theorists and experimentalists alike.

This proposal aims to construct models for the exchange-correlation energy that maintain this simplicity whilst offering a significant shift in performance. Preliminary work using high accuracy ab initio approaches suggests that a key ingredient to enable a higher accuracy description of the correlation energy is the Laplacian of the density. This quantity is often overlooked in functional construction. However, this proposal aims to utilize this simple quantity more directly and effectively in new models. The simplicity of these models means that they will be easily implementable in a huge range of density-functional software used in molecular and solid state simulations.

To ensure the proposed research in this project reaches the broadest possible audience we will

- Implement the new methodology in the widely used and freely available quantum chemistry program DALTON, providing a route to disseminate the results of this work to a wide user base
- Provide open source library routines for key evaluations, making it easy to implement the work in third party programs
- Offer collaborative support to implement the new methods in other codes
- Promote the results of this research at leading national and international conferences

Be ensuring the developed methodology is widely available in a range of software packages the outputs of this research should impact wide of users drawn from many areas of science and industry.