Multiconfiguration Dirac-Hartree-Fock

Figure 13. Valence spinors of the Db atom in the 6d 7s ground state configuration from average-level all-electron (AE, dashed lines) multiconfiguration Dirac-Hartree-Fock calculations and corresponding valence-only calculations using a relativistic energy-consistent 13-valence-electron pseudopotential (PP, solid lines). A logarithmic scale for the distance r from the (point) nucleus is us in order to resolve the nodal structure of the all-electron spinors. The innermost parts have been truncated.

As fully numerical Multiconfiguration Dirac-Hartree-Fock programs (MCDHF) [83-85] became available a rigorous approach was undertaken to systematically improve orbital spaces and the correlation treatment in hyperfine structure calculations. 

Metz, B., StoU, H., Dolg, M. SmaU-core multiconfiguration Dirac-Hartree-Fock-adjusted pseudopotentials for post-4 main group elements Application to PbH and PbO, J. Chem. Phys. 2000, 113, 2563. 

All-electron (AE) multiconfiguration Dirac-Hartree-Fock (MCDHF) calculations. 

One further distinguishes ECPs by the kind of their adjustment, i.e., energy-consistent PPs (see Section 6.3.1) and shape-consistent PPs/MPs (see Section 6.3.2). Furthermore, ECPs are categorized by the size of their core, e.g., one differs between f-in-valence small-core [21,22] and f-in-core large-core PPs (LPP) [7-12] for the f elements. Finally, the accuracy of the underlying AE reference data determines the ECP type, e.g., for early actinides scalar-relativistic Wood-Boring (WB) [22] or relativistic multiconfiguration Dirac-Hartree-Fock (MCDHF) [23,24] small-core PPs (SPP) are available. 

Recently, new energy-consistent, small-core (60 electron) PPs for the f-block elements adjusted to extensive multiconfigurational Dirac-Hartree-Fock reference data (with contributions from the Breit interaction) have been reported for Ac-U [42,43]. In these cases the PPs were tested on both atomic and molecular calculations using large ANO basis sets. As in previous work the primitive sets were optimized primarily for the f"s states with diffuse d and p functions added. The ANO contractions were based on either CASSCF or MRCI averaged density matrices. 

The mixing coefficients can be determined by a multiconfigurational Dirac or Hartree-Fock procedure (MCDF, MCHF). In the present case, however, numerical values are not of interest, only the fact that A0 is smaller than unity due to the presence of virtual excitations in the normalized correlated wavefunction. 

Fig. 11.13. The 1000 eV noncoplanar-symmetric momentum profiles for lead (Frost et al., 1986). Curves show the plane-wave impulse approximation. The experiment is normalised at the peak of the 6p-manifold profile (a). The 14.6 eV and 18.4 eV states of the 6s manifold are indicated by (b) and (c). Spectroscopic factors are given in table 11.2. For (a), (b) and (c) respectively the Hartree—Fock calculation (broken curve) is normalised to multiconfiguration Dirac—Fock (solid curve) by factors 0.82, 0.70 and 0.64.

Fig. 5.18. Spin-orbit splittings for the nf series of Ba+, showing that good agreement is obtained between g Hartree and experimental values. For comparison, Dirac-Fock (labelled DHF) and multiconfigurational Dirac-Fock (labelled MCDF) curves computed from the same code are also shown (after J.-P. Con-nerade and K. Dietz [230]).

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