Multiconfiguration Dirac-Fock

Vilkas, M.J., Ishikawa, Y. and Koc, K. (1998) Quadratically convergent multiconfiguration Dirac-Fock and multireference relativistic configuration-interaction calculations for many-electron systems. Physical Review E, 58, 5096-5110. 

Of the five group-13 elements, only B and A1 have experimentally well characterized electron affinities. Lists of recommended EAs [50,51] show errors ranging from 50% to 100% for Ga, In, and T1. Very few calculations have appeared for the latter atoms. These include the multireference configuration interaction (MRCI) ofAmau etal. using pseudopotentials [52], our relativistic coupled cluster work on T1 [45], and the multiconfiguration Dirac-Fock (MCDF) computation of Wijesundera [53]. 

For the relativistic Hamiltonian the procedure is called multiconfiguration Dirac—Fock. A computer program for structure calculations in this approximation has been described by Grant et al. (1980). The non-relativistic procedure has been described by Froese-Fischer (1977) and implemented by the same author (Froese-Fischer, 1978). 

R(q) is momentum-dependent. Both the extended-average-level and the optimal-level multiconfiguration Dirac—Fock methods were tried. The results are illustrated in fig. 11.12. The sensitivity of electron momentum spectroscopy is shown by the fact that the former calculation is completely... 

Fig. 11.12. The experimental and theoretical branching ratios for the 1000 eV ionisation of lead to the 6ps/2 and 6pi/2 states of Pb+, plotted against recoil momentum p (Frost et al, 1986). The calculations with target-state correlations in the plane wave impulse approximation are indicated by MCDF, multiconfiguration Dirac—Fock EAL, extended average level OL, optimal level. Cl indicates ion-state configuration interaction.

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.

The computations of 2p-core ionization energies were performed using a pattern similar to that used for Is- and 2s-core ionization energies [9]. Here again we have used Bruneau s multiconfiguration Dirac-Fock (MCDF) ab initio program [26-28], which is based on a numerical resolution of the Dirac equation corrected for Breit terms, vacuum polarization, and radiative (qed) contributions, and nuclear size and motion (nuc) effects. 

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]).

Uncovering two-step autoionisation involved a combination of techniques the photoabsorption spectrum of Ba was obtained using synchrotron radiation and classical spectroscopy of high dispersion [358]. The analysis was performed using the multiconfigurational Dirac-Fock method, which allowed the limits to be identified [359]. The doubleionisation spectrum was obtained by photoion spectroscopy using syn-... 

The emergence of Wigner statistics can be approached from the point of view of ab initio multiconfigurational Dirac-Fock theory. Although a full calculation for the 5p spectrum of Ba presents a formidable challenge and has not yet proved possible, fairly extensive calculations have proved fea-... 

Fig. 10.7. Nearest neighbour spacings in multiconfigurational Dirac-Fock calculations for the 4p spectrum of strontium (after J.-P. Connerade et al. [550]).

Fig. 11.4. The inner-shell absorption spectrum of Sm vapour. Also included are results of multiconfigurational Dirac-Fock calculations for the free atom (after B.K. Sarpal et al. [627]).

J. Bieron, I. P. Grant, C. FVoese Fischer, Multiconfiguration Dirac-Fock calculations of the hyperfine structure constants and determination of the nucleeir quadrupole moment of yttrium 90, Phys. Rev. A 58 (1998) 4401-4405. 

The all-orders relativistic many-body perturbation theory approach [82], [83], the combination of this approach with the multiconfiguration Dirac - Fock method [84] or the relativistic coupled-cluster approach [85] allow for the evaluation of the energy levels for valence electrons with accuracy of the order of... 

Atomic calculations. Most atomic calculations for the heaviest elements were performed by using Dirac-Fock (DF) and Dirac-Slater (DS) methods [20-24,58] and later by using multiconfiguration Dirac-Fock (MCDF) [64-72] and Dirac-Coulomb-Breit Coupled Cluster Single Double excitations (DCB CCSD) [73-85] methods, with the latter being presently the most accmate one. 

J. Desclaux, A multiconfiguration relativistic Dirac-Fock program. Comp. Phys. Comm. 9 (1975) 31-45. 

Desclaux JP (1975) A multiconfiguration relativistic DIRAC-FOCK program. Comput Phys Commun 9(l) 31-45... 

These elements possess well-developed multiplet structure in the soft X-ray spectra of the condensed phase, which can be compared with the spectrum of the fiee atom by performing ab initio Dirac—Fock calculations, the actual 4f occupancy in the solid can be deduced. An example is shown in figs. 4 and 5. The first point to note is that the multiplet structure of the atom survives in the solid, because of the strong localization of the 4f electrons, so that soft X-ray spectroscopy provides a useful probe of the 4f occupancy. To emphasize this point, we show, in fig. 4, a comparison between spectra of Sm vapour and Sm in the solid phase, which reveals the great similarity of structure between them. A multiconfigurational atomic structure calculation (fig. 5 Sarpal et al. 1991) demonstrates that, even in this complex situation, it is possible to deduce from ab initio atomic structure calculations what the 4f occupancy is. 

The observed 3d-4f multiplet structures for Sm atoms and small clusters at low temperature were compared to multiconfigurational Dirac-Fock (DF) calculations (Sarpal et al. 1991). As mentioned above, these unsealed ab initio calculations also yield positions of levels in the F manifold in agreement with observed optical data (Dupont 1967). The results of our ab initio calculations (fig. 5) for transitions firom the Fq groimd state give Mv and Miv multiplet lines whose total intensities (fig. 10) are comparable to those observed for Sm atoms and clusters at low temperature. These calculations, by including the transitions from the 1 l v l (populated according to Boltzmann s distribution)... 

---