Robert van Leeuwen

Self-consistent solution of the Dyson equation for atoms and molecules within a conserving approximation

We have calculated the self-consistent Greens function for a number of atoms and diatomic molecules. This Greens function is obtained from a conserving self-energy approximation, which implies that the observables calculated from the Greens functions agree with the macroscopic conservation laws for particle number, momentum, and energy. As a further consequence, the kinetic and potential energies agree with the virial theorem, and the many possible methods for calculating the total energy all give the same result. In these calculations we use the finite temperature formalism and calculate the Greens function on the imaginary time axis. This allows for a simple extension to nonequilibrium systems. We have compared the energies from self-consistent Greens functions to those of nonselfconsistent schemes and also calculated ionization potentials from the Greens functions by using the extended Koopmans theorem.

Violation of the zero-force theorem in the time-dependent Krieger-Li-Iafrate approximation

We demonstrate that the time-dependent Krieger-Li-Iafrate approximation in combination with the exchange-only functional violates the zero-force theorem. By analyzing the time-dependent dipole moment of Na-5 and Na-9(+), we furthermore show that this can lead to an unphysical self-excitation of the system depending on the system properties and the excitation strength. Analytical aspects, especially the connection between the zero-force theorem and the generalized-translation invariance of the potential, are discussed.

Nonequilibrium Green function theory for excitation and transport in atoms and molecules

In this work we discuss the application of nonequilibrium Green functions theory to atomic and molecular systems with the aim to study charge and energy transport in these systems. We apply the Kadanoff-Baym equations to atoms and diatomic molecules initially in the ground state. The results obtained for the correlated initial states are used to analyze variational energy functionals of the Green function which are shown to perform very well. We further show an application of the Kadanoff-Baym equations to a molecule exposed to an external laser field. Finally we discuss the connection between nonequilibrium Green function theory and time-dependent density-functional theory with the aim to develop better density functionals in order to treat larger systems than those attainable with the nonequilibrium Green function method.

Propagating the Kadanoff-Baym equations for atoms and molecules

While the use of Greens function techniques has a long tradition in quantum chemistry, the possibility of propagating the Kadanoff-Baym equations has remained largely unexplored. We have implemented the time-propagation for atoms and diatomic molecules, starting from a system in the groundstate. The initial stage of the calculation requires solving the Dyson equation self-consistently for the equilibrium Greens function. This Greens function contains a huge amount of information, and we have found it particularly interesting to compare the self-consistent total energies to the results of variational energy functionals of the Greens function. We also use time-propagation for calculating linear response functions, as a means for obtaining the excitation energies of the system. We have presently implemented the propagation for the second Born approximation, while the GW approximation has now been implemented for the ground state calculations.

NONEQUILIBRIUM GREEN FUNCTIONS IN TIME-DEPENDENT CURRENT-DENSITY-FUNCTIONAL THEORY

We give an overview of the underlying concepts of time-dependent current-densityfunctional theory (TDCDFT). We show how the basic equations of TDCDFT can be elegantly derived using the time contour method of nonequilibrium Green function theory. We further demonstrate how the formalism can be used to derive explicit equations for the exchange-correlation vector potentials and integral kernels for the Kohn-Sham equations and their linearized form.

The Keldysh Formalism Applied to Time-Dependent Current-Density-Functional Theory

In this work we demonstrate how to derive the Kohn-Sham equations of time-dependent current-density functional theory from a generating action functional defined on a Keldysh time contour. These Kohn-Sham equations contain an exchange-correlation contribution to the vector potential. For this quantity we derive an integral equation. We further derive an integral equation for its functional derivative, the exchangecorrelation kernel, which plays an essential role in response theory. The exchange-only limits of the latter equation is studied in detail for the electron gas and future applications are discussed.