R. M. Dreizler

From Explicit to Implicit Density Functionals

The concept of orbital‐ and eigenvalue‐dependent exchange‐correlation (xc) energy functionals is reviewed. We show how such functionals can be derived in a systematic fashion via a perturbation expansion, utilizing the Kohn–Sham system as a noninteracting reference system. We demonstrate that the second‐order contribution to this expansion of the xc‐energy functional includes the leading term of the van der Waals interaction. The optimized‐potential method (OPM), which allows the calculation of the multiplicative xc‐potential corresponding to an orbital‐ and eigenvalue‐dependent xc‐energy functional via an integral equation, is discussed in detail. We examine an approximate analytical solution of the OPM integral equation, pointing out that, for eigenvalue‐dependent functionals, the three paths used in the literature for the derivation of this approximation yield different results. Finally, a number of illustrative results, both for the exchange‐only limit and for the combination of the exact exchange with various correlation functionals, are given. © 1999 John Wiley & Sons, Inc. J Comput Chem 20: 31–50, 1999

Gradient expansion of the Coulomb exchange energy

With the aid of the gradient expansion technique of Kirzhnits we calculate the lowest order inhomogenity correction to the local approximation of the Coulomb exchange energy density.

Density functional approach to quantumhadrodynamics: Theoretical foundations and construction of extended thomas-fermi models

Abstract We outline the density functional approach to the strong interaction model of quantumhadrodynamics. In particular the extension of the Hohenberg-Kohn theorem to this situation is demonstrated. On the practical level we derive the gradient expansion of the noninteracting kinetic energy to second order in h 2 , including the effects of full four-vector meson exchange as well as vacuum contributions, and discuss the variational equations of the corresponding extended Thomas-Fermi model.

Accurate solution of the Thomas-Fermi-Dirac-Weizsäcker variational equations for the case of neutral atoms and positive ions

The numerical solution of the Thomas-Fermi-Dirac-Weizsäcker variational equations for atomic many electron systems is discussed in terms of a spline representation. Accurate values for groundstate energies are obtained for the full range of the central charge and all degrees of ionisation.

Exchange effects in low energy electron impact ionization of the inner and outer shells of argon

First order distorted wave Born approximation (DWBA) triple differential cross sections are reported for low-energy electron-impact ionization of the inner 3s and outer 3p shells of argon. Previous DWBA works have demonstrated that experiment and theory are not in accord for low energy ionization of inert gases and here we investigate the importance of exchange scattering. Different approximations for treating exchange scattering are investigated. It is shown that exchange scattering is particularly important for 3s ionization. Even with a proper treatment of exchange, the first order calculations are still not in satisfactory agreement with experiment. Consequently higher order effects will have to be included to achieve a satisfactory description of the low-energy ionization process. We also investigated both the Hartree-Fock and optimized potential methods for calculating atomic wavefunctions and static potentials and found that both methods produced almost the same cross sections.

The basis generator method: optimized dynamical representation of the solution of time-dependent quantum problems

The theoretical investigation of time-dependent quantum systems requires the solution of the time-dependent Schrodinger (Dirac) equation. The basis generator method presented here allows a systematic construction of dynamically adapted wavefunctions based on a decomposition of the Hilbert space into a hierarchical structure of finite subspaces. For the class of interactions obeying an inverse integer power law, e.g., Coulomb and polarization interactions, an explicit representation of the dynamically optimized basis set is given.

TDHF calculations for two-electron systems

TDHF calculations using a two-centre basis expansion technique are carried out for two-electron systems in the energy range of 5 to 40 keV/nucleon. Cross sections are calculated for one-electron capture of p+He(1s2) and for one- and two-electron capture of He2+ and Li3+ from He(1s2) and compared with other theoretical and experimental results. The influence of the exchange potential is briefly traced by considering the collision systems He+(2s)+He+(2s) and He+(2s)+H(1s) for the spin-singlet and spin-triplet cases.

Method for the calculation of global probabilities for many-electron systems

The question of extracting global transfer cross sections from determinantal wavefunctions as encountered in the impact parameter treatment of many-electron atomic collision systems is investigated. The authors demonstrate in particular a relation between two-electron and one-electron capture in the two-electron system He2++He and indicate the extension to N-electron situations.

Analysis of semiclassical approximations in the framework of quantumhadrodynamics

Abstract We examine the importance of gradient corrections to the Thomas-Fermi (TF) approximation for the description of semi-infinite nuclear matter and nuclei within the framework of quantumhadrodynamics. The discussion of semi-infinite nuclear matter exhibits most clearly how surface properties depend on the parametrisation of the effective interaction. In agreement with earlier studies it is found that for parametrisations with low effective mass the original extended TF (ETF) equations cannot be solved. We present a scheme to overcome this problem which is very much in the spirit of the semiclassical approach and allows for a solution in any situation. For the case of nuclei the results of the TF and ETF approximations are compared to those of Hartree calculations which serve as a standard in this context. In accordance with the sensitivity of semi-infinite nuclear matter results to the specific parametrisation, ETF does not yield a consistent improvement over TF for all parametrisations. However, by examining a larger number of parametrisations it is shown that those cases where TF results are closer to Hartree data have to be regarded as fortuitous and that on average the agreement between ETF and Hartree results is clearly better.

Direct and capture processes in proton-hydrogen scattering. II. Total cross sections for bombarding energies of 1 to 50 keV

The authors present total cross sections for direct and transfer processes in p-H scattering in the energy range between 1 and 50 keV. The results were obtained (as those of a previous pilot study at 2 and 8 keV) by numerical solution of the time-dependent Schrodinger equation in the impact parameter approximation by expansion in a pseudobasis set of the Hylleraas type. The authors discuss, in some detail, the properties of the coupled-channel equations involved and compare the calculated cross sections with the available experimental data.