Angular versus radial correlation effects on momentum distributions of light two-electron ions

2006

The question of how density functional theory (DFT) compares with Hartree-Fock (HF) for the computation of momentum-space properties is addressed in relation to systems for which (near) exact Kohn-Sham (KS) and HF one-electron matrices are known. This makes it possible to objectively compare HF and exact KS and hence to assess the potential of DFT for momentum-space studies. The systems considered are the Moshinsky [Am. J. Phys. 36, 52 (1968)] atom, Hooke's atom, and light two-electron ions, for which expressions for correlated density matrices or momentum densities have been derived in closed form. The results obtained show that it is necessary to make a distinction between true and approximate DFTs.

“…the electron pair[27]. Such a wavefunction has a simple momentum-space counterpart closed-form expressions to be derived for the 1RDM and momentum…”

mentioning

confidence: 99%

Exact Kohn-Sham versus Hartree-Fock in momentum space: Examples of two-fermion systems

2006

“…All the more, such deformations are very small compared with deformations due to intra-atomic correlation, which may contribute up to a few percent to 1-electron densities. 12,14,35 Accordingly, it is unlikely that the sole dispersive effects be observable through x-ray diffraction or Compton scattering experiments. (25) and (26).…”

Section: Discussionmentioning

confidence: 99%

“…In this respect, we adopt here a density-matrix description of electron correlation, as density matrices provide a natural basis for passing from direct to momentum space and vice versa. 12,13,14 Furthermore, electron correlation can be accounted for in the one-electron matrix and subsequently in the momentum density, in contrast with a DFT approach. 15 In the following, closed-form expressions for the one-and two-electron reduced density matrices for a general N-electron system are derived from a pairwise correlated wavefunction.…”

Section: Introductionmentioning

confidence: 99%

Closed-form expressions for correlated density matrices: Application to dispersive interactions and example of He2

Becker

2006

Empirically correlated density matrices of N-electron systems are investigated. Exact closed-form expressions are derived for the one-and two-electron reduced density matrices from a general pairwise correlated wave function. Approximate expressions are proposed which reflect dispersive interactions between closed-shell centro-symmetric subsystems. Said expressions clearly illustrate the consequences of second-order correlation effects on the reduced density matrices. Application is made to a simple example: the (He) 2 system. Reduced density matrices are explicitly calculated, correct to second order in correlation, and compared with approximations of independent electrons and independent electron pairs. The models proposed allow for variational calculations of interaction energies and equilibrium distance as well as a clear interpretation of dispersive effects on electron distributions. Both exchange and second order correlation effects are shown to play a critical role on the quality of the results.

Comments on the Hartree–Fock description of Hooke’s atom and suggestion for an accurate closed-form orbital

2008

The ground-state Hartree–Fock (HF) wavefunction of Hooke’s atom is not known in closed form, contrary to the exact solution. The single HF orbital involved has thus far been studied using expansion techniques only, leading to slightly disparate energies. Therefore, the present letter aims at proposing alternative definitions of the HF wavefunction. First, the HF limit is ascertained using a simple expansion, which makes it possible to formulate explicit expressions of HF properties. The resulting energy, 2.038 438 871 8 Eh, is found stable at the tenth digit. Second and more instructive, an analysis of the Hartree equation makes it possible to infer a remarkably simple and accurate HF orbital, i.e., φHF(r)=nHFe−αr2r2+β2, leading to an energy exceeding by 5.76×10−7 Eh only the above HF limit. This orbital makes it possible to obtain (near) Hartree–Fock properties in closed form, which in turn enables handy comparisons with exact quantities.