VOLUME 59, NUMBER 20 PHYSICAL REVIEW LETTERS 16 NOVEMBER 1987 Ground States of Ca and Sc from Two Theoretical Points of View Charlotte Froese Fischer Department of Computer ScienceV, anderbilt University, NashvilleT, ennessee 37235 and Jolanta B. Lagowski and S. H. Vosko Department of Physics, University of Toronto, Toronto, Ontario, Canada M5SlA7 (Received 24 February 1987) Multiconfiguration Hartree-Fock theory and density-functional theory both show that the negative ions Ca and Sc have stable ground states, the extra electron being a 4p electron. The multicon- figuration Hartree-Fock method, with a relativistic shift correction, predicts an electron affinity of 0. 045 eV for Ca, a result in excellent agreement with recent experiment. A less accurate calculation for Sc yields an electron affinity of 0. 152 eU. Density-functional theory gives a simple explanation of why the extra electron goes into the 4p orbital rather than a 3d orbital. PACS numbers: 31. 20. — d, 35. 10. Hn Stable and metastable negative ions have been of con- siderable interest in recent years. Theoretical calcula- tions of their structure are complicated by the fact that correlation-energy contributions to electron amenities (EA) often are as large as EA's themselves and thus play a crucial role. In this work we consider two methods for studying the low-lying states of Ca and Sc: the high- ly accurate multiconfiguration Hartree-Fock (MCHF) method, ' which serves as a benchmark for the less accu- rate but easily interpretable density-functional theory (DFT). Unexpectedly, and in contrast to the other ele- ments in the fourth period, the additional electron in Ca and Sc goes into the 4p orbital. By using the two methods, we are able to gain some insight into how these bound states of Ca and Sc occur. The first theoretical studies for negative ions were per- formed by Weiss for the alkali-metal ions Li, Na and K and the alkaline earths Be and Mg, using superposition techniques with an analytic basis. A more comprehensive study of bound states of negative ions for the elements hydrogen to calcium has since been per- formed by Bunge et a/. , also using an analytic basis. These calculations confirmed that stable Be ions do not exist, that the bound 2s2p P state lies in the 2s k/ D and S continua and hence, because of spin-orbit interac- tion with the 2s 2p D and S states, may slowly au- toionize. Similar calculations were reported for Mg and Ca, but now spin-orbit interactions are expected to be larger and autoionization rates greater. Beck con- firmed that the lowest configuration in Mg was 3s3p P and predicted the lifetimes of the J= —, ', —, ', and levels to be 7.8, 9.8, and 1. 6 ns, respectively. A few years ago, Pegg et a/. began an experimental investigation of the structure of Ca using an electron spectroscopic technique. The apparatus, which had been successfully tested on the metastable He ion, failed to detect an electron signal that was expected to be the sig- nature of autodetachment Of the Ca ion formed in the metastable state. They concluded that either the ion was stable or it was formed in a very long-lived metastable state whose lifetime was at least greater than the few mi- croseconds time delay between the production and detec- tion regions of their apparatus. This is consistent with the earlier observations of Heinicke et a/. who, on the basis of the transit time of Ca ions through their ap- paratus, put a lower limit on the lifetime of the ion at about 10 ps. Unpublished estimates of the lifetimes of the 4s4p P levels obtained by Beck indicate that these levels would not survive the delay to the detection region. The same experimental techniques were then applied to Be . Kvale et a/. report the observation of a peak in the Be autodetachment electron-energy spectrum, a signature for the decay of the metastable negative-ion state. The center-of-mass energy of the autodetaching electrons was in good agreement with the theoretical pre- dictions. Now, after redesigning their experiment and using photoelectron spectroscopy, Pegg et a/. have shown that the Ca ion is stably bound, being formed in the 4s 4p P state. They have found the electron affinity of Ca to be 0.043+ 0.007 eV. Adjacent to calcium in the periodic table is scandium. For the ground state of Sc, the identification first pro- posed by Feigerle, Herman, and Lineberger ' was 3d4s 4p 'D or D. This identification has been con- firmed by Jeung" through a configuration-interaction calculation. He obtained an EA of 0. 14 eV for the 'D state, in good agreement with the observed EA of 0. 189 eV for the lowest state, thus identifying the LS term of the ground state. Motivated by the earlier experimental evidence for Ca and with the identification of the ground state for Sc known, an independent theoretical study was under- taken for Ca ~ By use of the MCHF atomic-structure package' modified for the Cray X/MP, it has been 1987 The American Physical Society 2263