Relativistic configuration-interaction matrix

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],... 

DHF calculations on molecules using finite basis sets require considerably more computational effort than the corresponding nonrelativistic calculations and cause several problems due to the presence of the Dirac one-particle operator. It is therefore desirable to find (approximate) relativistic Hamiltonians for many-electron systems which are not plagued by unboundedness from below and therefore do not cause problems like the variational collapse at the self-consistent field level or the Brown-Ravenhall disease at the configuration interaction level. It is also desirable to find forms in which the quality of a matrix representation of the kinetic energy is more stable than for the Dirac Hamiltonian, i.e., forms which are not affected by the finite basis set disease . 

The comparison of the calculated spectra of the free ions and the ones in the crystal is not straightforward. Indeed, in the crystal, the presence of the first coordination shell increases the number of electrons and basis functions in the calculations, resulting in a blow-up of the Cl expansion, mainly due to the generated doubly-excited configurations. One should bare in mind that this increase is about six time as fast in double group symmetries as in the non-relativistic symmetry. In a non effective Hamiltonian method, the only way to keep the size of the DGCI matrix to an affordable size of few million configurations, is to cut down the number of correlated electrons. This may essentially deteriorate the quality of electron correlation as the contributions of the spin-orbit interaction... 

As with most Cl schemes of that period, the construction of the Hamiltonian matrix and its direct diagonalization effectively limited the size of calculations to a few thousand determinants. One possible strategy for extending the capability of this type of calculation is to introduce some sort of selection criterion for the A -particle functions, and to leave out those that do not contribute appreciably. Such methods had been developed within the framework of multireference Cl (MR-CI) calculations, and Hess, Peyerimhoff, and coworkers (Hess et al. 1982) extended this to the case of spin-orbit interactions. Their procedure was based on performing a configuration-selected non-relativistic MR-CI, followed by extrapolation to zero threshold. This technique may be applied in a one-step scheme, where selection criteria are introduced not only for the correlating many-particle states, but also for those that couple to the reference space via spin-orbit interaction. The size of the calculation that has to be performed in the double group may thereby be reduced. The errors introduced by these selection procedures appear to be small. 

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