PhD position in Time-Dependent Kohn-Sham Theory, in the group of Dr NI Gidopoulos, at Durham University

Ground state density functional theory (DFT), based on the Hohenberg-Kohn theorem [1], has changed the way we study electronic structure by focusing on the density of the electronic system rather than its wave function. Especially the concept of the virtual Kohn-Sham (KS) system of noninteracting electrons with the same density as the interacting one has proven invaluable in simplifying the many-electron problem, giving computational access to large systems and providing new conceptual tools to analyse and understand the results of the calculations.

Time-dependent density functional theory (TDDFT), based on the Runge-Gross theorem [2], is the extension of the ground state theory to the time-dependent case. It allows the study of time dependent phenomena and, in linear response, of electronic excited states [3]; The increasing popularity of the latter application resembles the explosion in the use of ground state DFT in chemistry and physics. However, time dependence and electronic excitations are considerably harder to study accurately than the electronic ground state.

Recently, the ground state KS potential was obtained from a straightforward optimisation of an appropriately chosen energy difference [4]. This fact allows the employment of techniques from wave function theory and many-body perturbation theory in DFT, prompting the development of novel sophisticated approximations for the exchange and correlation energy functional. This line of research is currently pursued in the group of Dr NI Gidopoulos at Durham.

The ground state variational principle can be extended in the time dependent case, in order to yield the time-dependent KS potential by making stationary an appropriate difference of actions. As in the ground state case, this allows the use of wave function and many body techniques to develop accurate approximations for the exchange and correlation potential and its derivative with respect to the density, keeping for the first time the dependence of these quantities on the density at previous times and on the initial wave function.

The PhD work will involve analytical work in order to develop and investigate mathematically the sophisticated approximations for the effective KS potential (exchange and correlation potential) and its derivative (exchange and correlation kernel). It will also involve computational work to implement and apply these developments in electronic structure codes, in particular the plane wave electronic structure code CASTEP, co-authored by Prof. S. Clark, who is the head of Condensed Matter Theory at Durham and a collaborator in the project.

The project will develop in close collaboration with Prof. EKU Gross, director of the Max Planck Institute (MPI) for microstructure physics at Halle in Germany. It is anticipated that the Durham based PhD student, will visit frequently the MPI benefitting from and forming a part of the link between the two groups at Halle and Durham.

We seek a student from the UK or from the rest of the European Union, with a strong background in theoretical physics or chemistry, keen to be involved in analytical and computational work and eager to interact with two separate groups and to spend long visits at the MPI in Germany. For information and to apply contact Dr NI Gidopoulos at [email protected]. Tel: +44 (0) 191 3343633.

It is possible that two more PhD positions will become available in the same group, with earliest starting date in January 2016. Prospective students are encouraged to contact Dr NI Gidopoulos to register their interest.

[1] P. Hohenberg, W. Kohn, "Inhomogeneous electron gas". Phys. Rev. 136, B864 (1964); doi:10.1103/PhysRev.136.B864.

[2] E. Runge, E.K.U. Gross, "Density-Functional Theory for Time-Dependent Systems". Phys. Rev. Lett. 52, 997 (1984); doi:10.1103/PhysRevLett.52.997.

[3] M. Petersilka, U. J. Gossmann, and E.K.U. Gross, "Excitation Energies from Time-Dependent Density-Functional Theory". Phys. Rev. Lett. 76 (8): 1212–1215 (1996); doi:10.1103/PhysRevLett.76.1212.

[4] N.I. Gidopoulos, "Progress at the interface of wave-function and density-functional theories", Phys. Rev. A 83, 040502(R) (2011); DOI: 10.1103/PhysRevA.83.040502