Hylleraas-configuration-interaction analysis of the low-lying states in the three-electron Li atom and Be+ion

Abstract

The total energies of twenty eight bound S-, P-, D-, F-, G-, H-, and I-states in the three-electron Li atom and Be + ion, respectively, are determined with the use of the Configuration Interaction (CI) with Slater orbitals and L-S eigenfunctions, and the Hylleraas-configuration-interaction (Hy-CI) methods. We discuss the construction and selection of the configurations in the wave functions, optimization of the orbital exponents and advanced computational techniques. Finally, we have developed an effective procedure which allows one to determine the energies of the excited states in three-electron atoms and ions to high accuracy by using compact wave functions. For the ground and low lying excited states our best accuracy with the Hy-CI method was ≈ 1 · 10 −6 a.u. and 1 · 10 −4 a.u. for other excited states. Analogous accuracy of the CI method is substantially lower ≈ 1 · 10 −3 a.u. Many of the rotationally excited (bound) states in the three-electron Li atom and Be + ion have never been evaluated to such an accuracy. *

Application of Löwdin's canonical orthogonalization method to the Slater-type orbital configuration-interaction basis set

“…Although such type of basis has already been able to produce highly accurate results for low‐lying two‐electron states without using extend precision technique, it is very interesting to investigate the reduction effect of the orthogonalization method on the calculation of high‐lying Rydberg states where the required number of basis functions are generally large. Our work can also be considered as the prelusion of applying the orthogonalization method to more complicated systems, such as the three‐ and four‐electron atoms where STOs have been extensively used in full CI calculations and, in these cases, the dimension of basis set is also generally large. It is expected that Löwdin's canonical orthogonalization method would play important roles in overcoming the possible linearly dependent problem and, at the same time, reducing the dimension of basis and resulting in more efficient calculations of various properties relevant to computational and quantum chemistry.…”

Linear dependence in Hylleraas configuration‐interaction calculations of He atom

“…The Hylleraas bases are extremely accurate in calculating the ground and lower‐excited states for few‐electron atoms, while for higher‐lying and higher angular momentum states the double or even triple basis set method is utilized by the authors to obtain very high precision results . The Hy‐CI basis set would probably be more appropriate to describe the higher‐excited states and easier extension to multi‐electron systems …”

High precision analytical description of the allowed β spectrum shape

“…The description of shake-off has seen significant theoretical (Carlson et al, 1968;Freedman, 1974;Frolov and Ruiz, 2010;Green, 1957;Law and Suzuki, 1982;Levinger, 1953;Ruiz, 2013;Ruiz et al, 2013;Schwartz, 1953;Stephas andCrasemann, 1967, 1971;Suzuki and Jaw, 1982) and experimental (Carlson, 1963a,b;Carlson et al, 1963;Couratin et al, 2013Couratin et al, , 2012Schupp and Freedman, 1980;Scielzo et al, 2003;Snell and Pleasonton, 1957) effort. For practical reasons, this has mainly focused on the calculation of electron ejection from the K shell, which is a small effect in all nuclei 1 and not in our current interests.…”