Correlation energy obtained in the RPA as a function of the imaginary frequency calculated from 400 eigenvalues of the dielectric matrix for , at the distance of 7.20 bohr (close to the equilibrium bond length). Circles are obtained by explicit diagonalization; the solid line is from TB calculations (see text). The figure clearly shows that full and TB calculations give almost identical results.
Comparison of BE curves for Ar dimer obtained using different DFT functionals (see text) and experiment. LDA (dashed) and GGA (dashed-dotted) functionals give very poor result as expected. EXX/RPA (red) performs better than vdW-DF (blue, from Ref. 33). Near the equilibrium position, the EXX/RPA curve is not as good as the one obtained from a recently proposed VV09 (purple) functional (Ref. 44), but it does approach the experimental curve (black solid) faster than any other ones in the asymptotic region.
BE curve of the Kr dimer as obtained using the EXX/RPA technique (see text), compared to those obtained from experiment and vdW-DF functional (from Ref. 33). The inset shows the same curves over a wider range of interatomic distances.
Dissociation energy curves of the Be dimer calculated using the EXX/RPA technique (see text) with different input wave functions: LDA (red squares), GGA (black circles), HF (blue diamonds), and hybrid functional PBE0 (purple triangles up). The curve denoted experiment is obtained by fitting an Expanded Morse oscillator function to recent experimental data (Ref. 46). Theoretical results from QMC and CI methods are also shown for comparison. Inset: total energies from EXX/RPA with exact-exchange only (top panel), i.e., no correlation, and RPA correlation energies (bottom panel). When a curve in the top panel is combined with a corresponding correlation energy part in the bottom one, the full EXX/RPA binding curve in the figure is recovered.
EXX of Be dimer as a function of Be–Be distances evaluated from the HF expression with different input wave-functions: LDA (red squares), GGA (black circles), and HF (blue diamonds).
Exact-exchange (left) and RPA correlation (right) energies evaluated from different input one-particle orbitals including the exact KS ones for He, Be, and Ne.
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