MCDHF calculations

The best-known and widely-quoted tabulation of atomic Dirac-Hartree-Fock energies was published by Desclaux [11], covered elements in the range Z=1 to Z=120 using finite difference methods. A number of computer packages are available to perform MCDHF calculations [19]. Published DHF and Dirac-Fock-Slater (DFS) calculations for atoms are now too numerous to construct a comprehensive catalogue. It is, however, possible to sort the purposes for which these calculations have been performed into general classes. 

Figure 4. Contribution of relativistic configurations to LSI level of the ns np configuration of gC, j4Si, 32Ge, jflSn and gjPb from average-level MCDHF calculations. 1) p /2P3/2...

Fig. 29.1. Energy levels of Si VII relative to ground level ls22s22p4 3P2 in several approximations. E(0+1 <0+1+2> — calculations in the first and second order [233]. Eexp — experimental data [235]. EMCHFb — MCHF calculation results [229, 236], gMCDHFd — MCDHF calculation results [237], In parentheses — energy values of the levels with J = 1 and J = 0, respectively.

Average-level (AL) multi-configuration Dirac-Hartree-Fock (MCDHF) calculations corresponding to one nonrelativistic configuration (Dolg 1995). Only 4f was considered. 

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

Scattering MCDHF wavefunctions have recently been used as target states in electron-atom and electron-ion scattering calculations, based mainly on the relativistic R-matrix approach [187-190]. 

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. 

Bieron et al. [106] applied the MCDHF scheme to the light elements Be and F in order to obtain very accurate A and B values including nuclear recoil eflFects, the Breit interaction and corrections for omitted virtual orbitals via the I extrapolation technique described in [107]. Both constants were calculated for the Pz/2 state of the iBe" " ion... 

CCSD(T) calculations on three different gallium halides [139] finally gave 171 2 mb for the Ga NQM corroborating the atomic MCDHF value. The deviation can be attributed to basis set deficiencies caused by a neccessary reduction of the basis for the DHF-CCSD(T) calculations. Furthermore, additivity for the smaller contributions like SO, CCSD(T)/SO and vibrational averaging was assumed, but as these effects become larger the assumption of additivity certainly becomes a more serious source of errors due to the inconsistent theoretical framework the individual contributions were obtained in. 

In contrast to the LPPs for the more rigorous SPPs also SO operators [58,61] are available. However, it has to be noted that these SO operators are effective valence SO operators, i.e., they have to be applied in SO-CI calculations for the valence electrons (Ln 4f/5d/6p An 5f/6d/7p), where the semicore shells (Ln 4p/4d/5p An 5p/5d/6p) are frozen in their scalar-relativistic form, or a corresponding perturbative treatment. If the SO contributions of the semicore shells cannot be neglected, the recently developed MCDHF/DC+B SPPs [23,24] suitable for a variational two-component treatment or SO-CI calculations including excitations from semicore shells should be applied. However, these SPPs are still under construction and only available for Ac-U so far. 

Figure 16.2 Spread of energies of J levels and average energy gap between adjacent J levels for the Cr, Mo, W rfis (74 levels) and Cd, Cm fd (3106 / levels) configurations from MCDHF/DC calculations [2], Except for W the chosen configurations are the ones assigned for the experiment ll ground state...

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