DFT is certainly the best inexpensive first principles approach to calculating the energies of solids, liquids and large molecules, but its lack of consistent accuracy is a major shortcoming. This project is therefore aimed at constructing better density functionals using results and insights from accurate many-body calculations. One of the most common methods used in developing new functionals has been the fitting of a chosen functional form containing variable parameters to the total energies of a `training set' of small molecules. This idea has been successful to some extent, but the number of systems included in the fits has been small and each system is characterized by a single number, the total energy. The methodology proposed here is fundamentally different. It involves constructing functionals by fitting to results obtained from accurate many-body calculations using not only total energies but also information about the exchange-correlation (XC) hole and XC energy density in inhomogeneous systems. Until recently the problem with such an approach has been the difficulty of obtaining data of sufficient quality.

The basic idea of Kohn-Sham DFT is to replace the calculation of the full many-body wave function with that of a single Slater determinant which represents a non-interacting model system yet yields the same ground state density. The central quantity is the difference between the true ground state energy and the energy of the non-interacting system, the XC energy functional ; the LDA and GGA functionals are approximations to the quantity , known as the XC energy density. An explicit expression for E_xc can be written down in terms of the interaction between the electronic charge density and a non-local XC hole surrounding each electron, using an adiabatic connection between the interacting and non-interacting systems. can be calculated as an integral at constant charge density involving the coupling-constant-dependent pair-correlation function, . Calculating and is a time consuming and complicated business, as accurate correlated wave functions giving the same density for a range of different values of the coupling constant are required. We have calculated the XC energy density for bulk silicon in this way using QMC techniques. QMC calculations have also been performed for the model sine-wave jellium system at different densities and with a range of amplitudes and wavevectors (in collaboration with M. Nekovee and M. Foulkes of Imperial College). These have produced considerable information about the behaviour of the XC hole and the XC energy density, from which important insights into constructing new functionals can be gained. In particular, it appears the XC energy density can be described to high accuracy using three variables to describe the charge density in the neighbourhood of a point , i.e., , , and , although the fitted coefficients differ from those of the standard gradient expansion.

Our suggested approach to constructing new functionals is to use QMC to calculate the changes in the XC hole and XC energy density due to the real inhomogeneous density in a small local region, and then to define a mapping from the shape of the charge density in the neighbourhood of a point onto a correction to E_xc^LDA. The relative merits of various methods of doing this are currently being evaluated.

• A quantum Monte Carlo approach to the adiabatic connection method, M. Nekovee, W.M.C. Foulkes, A.J. Williamson, G. Rajagopal and R.J. Needs, Advances in Quantum Chemistry', 343, 189 (1999) [PDF]
• Exchange and correlation in silicon, R.Q. Hood, M.-Y. Chou, A.J. Williamson, G. Rajagopal and R.J. Needs, Phys. Rev. B 57, 8972 (1998), [PDF]
• Quantum Monte Carlo investigation of exchange and correlation in silicon , R.Q. Hood, M.-Y. Chou, A.J. Williamson, G. Rajagopal, R.J. Needs and W.M.C. Foulkes, Phys. Rev. Lett. 78, 3350 (1997), [PDF]