PHYSICAL REVIEW A VOLUME 47, NUMBER 5 MAY 1993 Ground-state correlation energies for atomic ions with 3 to 18 electrons Subhas J. Chakravorty, Steven R. Gwaltney, and Ernest R. Davidson' Department of Chemistry, Indiana University, Bloomington, Indiana 47405 Farid A. Parpia and Charlotte Froese Fischer Department of Computer Science, Vanderbilt University, Nashville, Tennessee 37235 (Received 23 November 1992) Recently Davidson et al. [Phys. Rev. A 44, 7071 (1991)]have estimated nonrelativistic correlation en- ergies and relativistic corrections to ionization potentials for atomic ions with up to 10 electrons. In this work, this approach is extended to atomic ions with 11 to 18 electrons. The correlation energies for 3- to 10-electron atomic ions are also recomputed using more recent experimental and theoretical data. Un- like other work the method focuses on the correlation contribution to the individual ionization energies which are obtained by comparing experimental data with relativistic complete-valence-space energies. Ab initio estimates of correlation contributions to the ionization energies with extensive configuration- interaction calculations of 3- to 10-electron atomic ions with nuclear charge from 4 through 10 and 18, 36, 50, 72, 100, and 144 have been obtained. The correlation energies obtained from some density- functional models are also compared to these correlation energy data. PACS number(s): 35. 10. Hn, 31. 20.Tz, 31. 20.Di, 31. 30. Jv THEORETICAL BACKGROUND In a recent paper, Davidson et al. [1] estimated the ex- act ground-state correlation energies E, (N, Z) of hy- pothetical nonrelativistic atomic ions with N electrons and nuclear charge Z, for N up to 10 electrons. These en- ergies are of considerable interest to theoreticians. They are useful in calibrating density-functional methods and in estimating the basis-set limit of accurate molecular cal- culations. As most quantum chemistry for molecules is done with a stationary-point-nucleus, nonrelativistic Hamiltonian, it is important to know the atomic energies in this same approximation. In this study, the method used by Davidson et al. has been extended for atomic ions up to 18 electrons and the estimates of 2- to 10- electron-ion energies have been reanalyzed and improved. Scherr, Silverman, and Matsen [2] used tabulations of atomic ionization potentials to obtain correlation ener- gies for atomic ions. Clementi [3] estimated the correla- tion energies by actually calculating the relativistic corrections from Breit-Pauli perturbation theory [4]. More recently, Anno and Teruya [5] proposed a semiempirical refinement of the relativistic energies and computed the nonrelativistic energies and correlation en- ergies using Moore's revised tables [6]. With the recent improvements in theory [7,8] and ex- periment [6, 9], reasonably accurate estimates of all im- portant high-order corrections in the relativistic atomic model are possible. Further, it is possible with the avail- able recent experimental data [6,9] on ionization poten- tials to make a discernable refinement and augmentation of the atomic-correlation-energy tables presented in [1]. CORRELATION CONTRIBUTION TO THE IONIZATION ENERGY The total nonrelativistic, stationary-point-nucleus ener- gy E(N, Z) is defined as the exact ground-state eigenvalue of the nonrelativistic Hamiltonian defined as (in atomic units), T N N ( — —, ')V; — Zlr;+ g Ilr; %=E(N, Z)+ . E, (N, Z)=E(N, Z) EHF(N, Z) . — (2) One may show, by treating the electron-electron interac- tion as a perturbation term and expanding the resulting total energy, that E(N, Z)/Z can be expanded in a for- mal Laurent series in Z ' [2, 10 — 12], viz. , E(N, Z) =Bc(N)Z +Bi(N)Z+B2(N)+B3(N)Z +B4(N)Z + In cases where a single configuration with hydrogenic or- bitals is an adequate zeroth-order approximation, one can evaluate the leading terms Bo and B, . The spin- and symmetry-restricted Hartree-Fock energy also gives the correct Bo and B, so E, will begin with a constant term. For other systems a single configuration does not serve Here X denotes the number of electrons and Z the corre- sponding nuclear charge. The Hartree-Fock (HF) ap- proximation with spin- and symmetry-restricted orbitals furnishes the energy EHF(N, Z ) and the correlation ener- gy E, (N, Z) is defined by the relation 47 3649 1993 The American Physical Society