Comparisons of the RPA, SCRPA, Tamm–Dancoff, and full CI methods by analysis of their transition density matrices, oscillator strengths, and energy moments of oscillator strengths for the electric dipole transitions from the ground state of the B+ ion (frozen K‐shell model)

Abstract

AbstractThe RPA, SCRPA, Tamm–Dancoff, and full CI methods are compared by analyzing their transition density matrices, oscillator strengths, and energy moments of oscillator strengths for the 1Sground – 1Podd transitions of the 4‐electron B+ ion in the frozen K‐shell approximation. It is found that the RPA gives transition density matrices that are aligned nearly as well as possible along those of the full CI, but have vector lengths that are significantly too long. The corresponding transition energies are significantly too small. These errors compensate to give oscillator strengths for the dominant transition that, for all forms of the oscillator strength, are within 1.6% of the corresponding full CI values. The SCRPA gives better transition density matrices than the RPA, but poorer oscillator strengths. The Tamm‐Dancoff approximation gives very good values for the mixed length‐velocity form of the oscillator strength. The RPA gives a static electric dipole polarizability that is nearly 20% larger than that of the full CI. The SCRPA gives a value 15% smaller than—and the Tamm‐Dancoff approximation gives a mixed length‐velocity value that is 11% larger than—that of the full CI. Other energy moments of oscillator strengths are also reported. Certain other approximations related to the RPA and the SCRPA are reported as well.