On calculations of correlated wave functions with heavy configurational mixing

Abstract

ABSTRACT:We discuss aspects of the theory and computation of wave functions and energies of discrete states of polyelectronic atoms that are represented in zero order by configurations with holes in subshells below the valence subshell. Both in zero order and in the remaining correlation components, such wave functions have particularities stemming from the state-specific self-consistent field and the heavy configurational mixing associated with near-degeneracies and hole-filling correlations. By referring to a variety of examples from small-and large-scale calculations, it is noted that appropriate penetration into the many-body problem can provide, in an economic and physically transparent way, reliable interpretations and semi-and fully quantitative understanding of issues related to states with inner holes and to cases of near-degeneracies that result in strongly correlated wave functions. Whenever hole-filling correlations are allowed, multiple correlations (i.e., beyond single-and double-orbital substitutions in the single reference configuration) acquire increased importance relative to that in ordinary electronic structures. This is demonstrated via large-scale multiconfigurational HartreeFock (MCHF) plus configuration interaction (CI) calculations on the Cl KL3s3p 6 2 S discrete state, which is the lowest of its symmetry. The calculations incorporated correlations up to selected sextuple orbital excitations from the M shell. MCHF plus CI calculations at the level of quadruple orbital substitutions were also carried out for the Cl KL3s 2 3p 5 2 P o ground state and the excitation energy at this level of calculation was found to be 85,364 cm Ϫ1 , in excellent agreement with the experimental value of the finestructure-weighted average, 85,385 cm Ϫ1 (10.59 eV). Within the approximations of the calculation, the hole-filling triple and quadruple orbital correlations, which, of course, are absent from the 2 P o state, contribute about 1 eV, which is significant.

Regular series of doubly excited states inside two-electron continua: Application to2s2-hole states in neon above the Ne2+

“…(2) is obtained, (in modern times, this is done systematically for many types of structures), it is possible to compute the main effects of electron correlation and of the multichannel continuum via advanced but practical methods that are based on the use of appropriate function spaces (e.g., Refs. [10][11][12]19]). …”

“…In contradistinction, an SST calculation, by obtaining state-specific zero-order orbitals and corresponding optimized correlation configurations, immediately reduces the magnitude of calculation while considerably increasing its accuracy. Specifically, the calculation of X loc involves the proper construction of symmetry-adapted configurations consisting of MCHF and of virtual orbitals and their variational optimization, separately (if needed), and via the minimization into a local minimum of the total energyE 0 using orthonormal or nonorthonormal configuration-interaction techniques [11].…”

“…Related discussions can be found in Refs. [11,[23][24][25]. These techniques were applied in the present paper when necessary in addition to ones specific to the problem-see Sec.…”

“…For this reason, the relevant formalisms and methodologies have been named collectively the state-specific theory (SST) (e.g., Ref. [11] and references therein).…”

Autoionizing states of atomic boron

“…In the case of a neutral boron atom, however, the photoionization cross sections record is still rather scant. Various studies examined in detail the ground-state energy, the discrete spectrum [42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59], the electron affinity [60,61], the electron impact excitation and ionization [62][63][64][65][66], and the 1s core excitation [67] and core photoionization [68,69] of the boron atom. Discrete and photoionization spectra of the B + parent ion have also been computed [70][71][72][73][74][75].…”