Relativistic configuration

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. 

Schwerdtfeger, P McFeaters, J.S., Stephens, R.L., Liddell, M.J., Dolg, M. and Hess, B.A. (1994) Can AuF be synthesized A theoretical study using relativistic configuration interaction and plasma modelling techniques. Chemical Physics Letters, 218, 362—366. 

Apparently, a large number of successful relativistic configuration-interaction (RCI) and multi-reference Dirac-Hartree-Fock (MRDHF) calculations [27] reported over the last two decades are supposedly based on the DBC Hamiltonian. This apparent success seems to contradict the earlier claims of the CD. As shown by Sucher [18,28], in fact the RCI and MRDHF calculations are not based on the DBC Hamiltonian, but on an approximation to a more fundamental Hamiltonian based on QED which does not suffer from the CD. At this point, let us defer further discussion until we review the many-fermion Hamiltonians derived from QED. 

TABLE 1. Transition energies (TE) between states averaged over the relativistic configurations of El 12 derived from HFDB calculations with Fermi nuclear model and the corresponding absolute errors of other all-electron calculations (in cm ). 

TABLE 13. One-electron energies, e, for some spinors from states averaged over the relativistic configurations of E112 (in a.u.). See footnotes in Tables 1 and 2. 

In consequence, the first group of terms in (23.82) corresponds to the interaction energy within a given relativistic configuration and the others... 

S. Fritzsche, Ch. Froese Fischer, G. Gaigalas, RELCI A program for relativistic configuration interaction calculations, Comput. Phys. Com-mun., 148, 103-123 (2002). 

K. Balasubramanian,/. Chem. Phys., 89, 5731 (1988). Relativistic Configuration Interaction... 

In table 2 our result is compared with the UV spectroscopic result of Klein et al. [26], Also shown are the theoretical results of Zhang et al. [2], Plante et al. [27], and Chen et al. [28], The first of these uses perturbation theory, with matrix elements of effective operators derived from the Bethe-Salpeter equation, evaluated with high precision solutions of the non-relativistic Schrodinger equation. This yields a power series in a and In a. The calculations of Zhang et al. include terms up to O(o5 hi a) but omit terms of 0(ary) a.u. The calculations of Plante et al. use an all orders relativistic perturbation theory method, while those of Chen et al. use relativistic configuration interaction theory. These both obtain all structure terms, up to (Za)4 a.u., and use explicit QED corrections from Drake [29],... 

Our above-mentioned conclusions are contrary to the results reported from previous less rigorous calculations e.g.. Hay et al. (11) concluded from an effective core potential (ECP) calculation using an approximate treatment of relativity that the 5d core does not appear to play a dominant role in the chemical bond in AuH this conclusion is incorrect in view of our result that 5d electrons cannot be left in the core in AuH. Our extended basis set (EBS), DF SCF calculation predicts a value of 1.682 eV for the D of AuH and our relativistic configuration interaction calculation with the... 

The correct nonrelativistic limit as far as the basis set is concerned is obtained for uncontracted basis sets, which obey the strict kinetic balance condition and where the same exponents are used for spinors to the same nonrelativistic angular momentum quantum number for examples, see Parpia and Mohanty (1995) and also Parpia et al. (1992a) and Laaksonen et al. (1988). The situation becomes more complicated for correlated methods, since usually many relativistic configuration state functions (CSFs) have to be used to represent the nonrelativistic CSF analogue. This has been discussed for LS and j j coupled atomic CSFs (Kim et al. 1998). 

Johnson W R and Cheng K T 1996 Relativistic configuration-interaction calculation of the polarizabilities of helium-like ions , Phys. Rev. A 53, 1375 -8... 

Many non-relativistic Configuration Interaction (Cl) algorithms are also suited for a relativistic no-pair formulation. In general it is best to use determinant expansions [33] of the wave function because the alternative... 

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...

Later, in Sec. 4, we will give a detailed discussion of the need for the no-pair Hamiltonian in relativistic calculations, its limitations, and its relation to QED. To establish a foundation for our studies of few-electron systems, we start in Sec. 2 with a discussion of the one-electron central-field Dirac equation and radiative corrections to one-electron atoms. In Sec. 3 we describe many-body perturbation theory (MBPT) calculations of few-electron atoms, and finally, in Sec. 4 we turn to relativistic configuration-interaction (RCI) calculations. 

An alternative approach to the perturbation theory in treating many-electron systems is the configuration-interaction (Cl) method which is based on the variational principle. Nonrelativistic Cl techniques have been used extensively in atomic and molecular calculations. The generalization to relativistic configuration-interaction (RCI) calculations, however, presents theoretical as well as technical challenges. The problem originates from the many-electron Dirac Hamiltonian commonly used in RCI calculations ... 

---