Effect of removing the no-virtual pair approximation on the correlation energy of the He isoelectronic sequence. II. Point nuclear charge model

Abstract

The correlation energies (CEs) of the He isoelectronic sequence Z=2-116 with a point nuclear charge model were investigated with the four component relativistic configuration interaction method. We obtained CEs with and without the virtual pair approximation which are close to the values from Pestka et al.'s Hylleraas-type configuration interaction calculation. We also found that the uniform charge and point charge models for the nucleus differ substantially for Z > or = 100.

Going beyond “no-pair relativistic quantum chemistry”

“…is incorrect, as compared either to E (1) np (35) or E (1) (62). As a matter of fact, H CS [a] (33) corresponds to a truly filled Dirac sea, at variance with H FS [a] (28) where the filled Dirac sea is introduced only as a formal step to avoid conceptually the so-called radiation catastrophe associated with the empty Dirac sea.…”

“…There have been two approaches in the field of RQC for handling the NES, i.e., the configuration space (CS) approach [30][31][32][33][34][35] associated with the empty Dirac picture and the Fock space (FS) approach 37-41 associated with the filled Dirac picture. While they yield identical results for one-electron properties of any order, the two approaches are completely different in the contribution of NES to two-electron properties beyond first order, including electron correlation.…”

“…Since the replacement of S F (x 2 , x 1 ) with S C (x 2 , x 1 ) changes the nature of NES completely, it is clear that the CS approach is not an approximation of QED, the Holy Grail of electromagnetic interactions between charged particles. In particular, the anti-correlating contribution of NES in the CS approach (i.e., energy increasing when included in the correlation treatment) [30][31][32][33][34][35] is not part of QED effects, sometimes claimed though. Again, this should not be confused with the anti-correlating contribution of 1s to He2s 2 : While the Schrödinger He2s 2 is truly unstable, the Dirac He1s 2 is certainly stable even in the presence of NES.…”

Relativistic Hamiltonians for Chemistry: A Primer

“…This bars, however, the complete relaxation of the one-particle basis and thus the projectors to the full instantaneous potential seen by the electrons of the system and implies that a full CI in this determinantal space cannot be considered as the exact solution of the optimal projected Dirac-Coulomb Hamiltonian. Various authors [70][71][72] have reported CI calculations using an N-particle basis constructed from both positive-and negative-energy orbitals. Pestka and coworkers [73] have reported a procedure in which the electronic ground state is treated as a resonance and extracted from the continuum by a complex-coordinate rotation technique.…”

Distinguished Self-Adjoint Extension of the Two-Body Dirac Operator with Coulomb Interaction

“…Such operators are generically unbounded below and therefore often dismissed as unphysical. Nonetheless, they are frequently employed in numerical studies in relativistic quantum chemistry-see [16] for an overview and concerning spectral properties, e.g., [12], [16], [21], [22], [32], [33]. It is therefore desirable to understand these unprojected two-body Dirac operators better also from a mathematical point of view.…”