Non-closed Shell Many-electron Theory Research Articles

CI Methods for the calculation of hyperfine structures, lifetimes, and molecular potential energy surfaces

The “charge wave function,” which is the sum of the internal, and semi-internal correlations of the Non-Closed Shell Many-Electron Theory (ncmet) of Sinanoǧlu and co-workers, has been calculated by Sinanoǧlu and Oksuz and more recently by Schaefer and Harris for atomic systems, and for molecules by Das and Wahl, and recently by Schaefer. The results on optical transition probabilities, on hyperfine structures and on molecular pe curves are summarized and the extent of agreement with the initial result of the ncmet theory as given earlier by Sinanoǧlu that the “charge wave function”, a finite ci function, should yield these properties well, and the main features of pe curves, is examined.

An approximate method for the evaluation of electron correlation effects on atomic energy differences

A relatively simple approximate ab initio method for the evaluation of correlation effects on atomic energy differences is developed. In this method, which is a modification of the semiempirical version of Sinanoglu's non-closed-shell many-electron theory (NCMET), the all-external contributions to the correlation energies are evaluated by a scheme based on the knowledge of second-order pair energies calculated for approximate closed-shell atomic systems. The present method can be applied to a much larger set of atomic systems than the semiempirical NCMET. To test the reliability of the present approach extensive calculations are performed for energy differences involving states of the 1s22sm2pn configurations for various atomic numbers. These calculations could be to a large extent based on previously published values of both the 'charge' contributions to the energies and the relevant pair energies. The results for (i) term splittings within a single configuration for neutral atoms as well as positive and negative ions, (ii) excitation energies, (iii) ionisation potentials and (iv) electron affinities prove that the present approach can be used for reliable predictions of atomic energy differences. Since the method is non-relativistic, some attempts have been made to account for the relativistic corrections. In all cases considered the inclusion of these corrections has further improved the agreement with the experimental results.

Oscillator strengths for O(II) ions

Oscillator strengths between various doublet states of O(II) ions are calculated with extensive use of multi-configuration wave functions. The lower levels for the transition are in the 2 p 3 2 D 0 and 2 p 3 2 P 0 states, and the upper levels are 2 p 4, 3 s, and 3 d states. The results, which are estimated to have errors of less than 10% for individual transitions, agree quite well with beam-foil experiments, as well as with calculations made by the use of the non-closed-shell many-electron theory (NCMET). The present ratios of transition probabilities are estimated to have errors of less than 20%. A comparison with recent branching ratio measurements indicates that agreement between theory and experiment is within the overlap of the error bars except for the 538 581 Å pair. Agreement with rocket measurements is only within the overlap of the error bars for the 718 797 Å pair.

Rydberg—valence mixing in atoms and molecules

Interactions of Rydberg electronic configurations with excited intravalency configurations have a large influence on atomic spectra as well as molecular electronic spectra. The 1134 Å resonance transition of the nitrogen atom is used to illustrate the progress which has been achieved in treating these effects in atoms. In addition, the first-order theory of oscillator strengths (FOTOS) is shown to be an approximation to the non-closed shell many-electron theory (NCMET) of Sinanoǧlu as applied to oscillator strengths.

Theory of atomic structures including electron correlation. V. Excited states not lowest of their symmetry and oscillator strengths in neutral and singly ionized atoms

The non-closed-shell many-electron theory (NCMET) of Sinano\ifmmode \breve{g}\else \u{g}\fi{}lu is applied to excited states which are not the lowest of their symmetry. Variational collapse towards lower states of the same symmetry is prevented by use of the Hylleraas-Undheim-MacDonald theorem. The procedure for calculating such states is described. Using it, variationally correct charge wave functions are obtained and for the first time for several $2s2{p}^{n}$ excited states in neutral and singly ionized atoms of carbon, nitrogen, oxygen, and fluorine. The configuration labels of these states and lower energy states of the same symmetry are found in agreement with the experimentally assigned orderings in each case. Optical oscillator strengths are calculated with these wave functions and are found in good agreement with experiment where previous calculations in the literature had shown large discrepancies.

Oscillator strengths for transitions involving excited states not lowest of their symmetry: Carbon I and fluorine II transitions

Theoretical f values are reported for the 1657 and 1329 Å transitions of carbon I and the 485, 549, 457, and 513 Å transitions of fluorine II. These involve excited states not lowest of their symmetry. We calculate these using the nonclosed shell many electron theory (NCMET) of Sinanoğlu and proper application of the variational theory required for such nonlowest of symmetry states. The results of this work differ from Hartree–Fock and other values in previous literature by factors of 2–5. Experimental values, where available, are in good agreement with the results of this work. New experimental measurements by methods such as beam foil spectroscopy are recommended for several transitions.

Oscillator strengths for transitions involving excited states not lowest of their symmetry oxygen I and oxygen II transitions

Theoretical f values and transition rates we calculate using the nonclosed shell many electron theory (NCMET) of Sinanoğlu for the OI 792 Å transition and the OII 538 and 581 Å transitions are reported and compared to experiment. Good agreement is obtained resolving the discrepancies which existed in previous literature. Results are also reported for the OI 811 and 878 Å transitions and the OII 617 and 673 Å transitions.

The large effects of electron correlation on the multiplet generalized oscillator strengths of non-closed shell systems: Be 1s 22s 21S → 1s 22s2p 1P 0 and B 1s 22s 22p 2p 0 → 1s 22s2p 22D

Correlation effects are shown to change generalized oscillator strengths and inelastic form factors by large factors as large as 10, from the Hartree-Fock values. The effects are fully included in the charge wavefunctions of the non-closed shell many-electron theory by Sinanoǧlu. We calculate the charge wavefunctions and obtain from the generalized oscillator strength F 0η( q) versus ln q 2 and the integrated cross section σ 0η( E) versus ln E 1 for BeI 2s 2 1S → 2s2p 1P 0 and BI 2s 22p 2P 0 → 2s2p 2 2D cases, exemplifying the method.

Test of the non-closed shell many-electron theory in a solvable model

The non-closed shell many-electron theory of Sinanoĝlu is applied to the two-particle problem in a solvable model called the pseudoatom. The results for overlaps and electric dipolar transitions probabilities are discussed for the approximate and exact solutions.

Prediction of molecular excited state properties, potential energy curves, and the non-closed shell many-electron theory

Prediction of molecular excited state properties, potential energy curves, and the non-closed shell many-electron theory

Electric dipole transitions in the carbon isoelectronic sequence calculated with symmetric states obtained from superposition of configurations

Sinanoğlu's nonclosed shell many electron theory (NCMET) is used to determine and analyze symmetry-adapted correlated wavefunctions for states of the F(IV) ion belonging to the 1s 22s 22p2 and 1s 22s 2p3 configurations. We argue that these wavefunctions contain those specific correlation effects important in calculating accurate oscillator strengths for allowed transitions between states of these two configurations. The types of correlations included, the reasons for their importance, the methods of approximating them, and the necessity and techniques for introducing symmetry into these calculations are discussed. Comparison of results using Hartree-Fock as opposed to correlated wavefunctions clearly shows the necessity of including correlation effects in calculating the electric-dipole oscillator strengths in F(IV). The conclusion follows for both the dipole-velocity and the dipole-length formulations. These new results for the six electric-dipole transitions in F(IV) are combined with previously published results for the same transitions in the isoelectronic species C(I), N(II), O(III) in order to extrapolate the Z dependence of these transitions and thereby make reasonable predictions of the oscillator strengths for the heavier ions. We conclude with a formalism, based on plausible but as yet unproven speculations, which shows in a transparent way what correlation effects are of significance in the general problem of computing oscillator strengths.

HFS constants of Be I 1s 22s2p 3p 0, B I 1s 22s2p 24P and B I 1s 22s2p 22D obtained from the non-closed shell many-electron theory for excited states

Using the non-closed shell many-electron theory for excited states of Sinanoǧlu we compute the hyperfine structure constants of Be I 1s 22s2p 3P 0, B I 1s 22s2p 2 4P and B I 1s 22s2p 2 2D. The quadrupole moment of 9Be is also newly determined to be, Q = 0.05494 barns.

Variational calculations of correlated wavefunctions and energies for ground, low-lying as well as highly excited discrete states in many-electron atoms using a new atomic structure theory including electron correlation

The authors have calculated to a high degree of accuracy correlated wavefunctions and their corresponding energies containing all the non-dynamical correlations of the non-closed shell many-electron theory by Sinanoglu and co-workers (1970). Ground as well as highly excited states of atoms and ions with three to nine electrons from beryllium to silicon are considered. Special care is applied to obtain wavefunctions of highly excited hole-states having lower states of the same symmetry, like Be I 1s2 2p2 1S, B I 1s2 2s 2p2 2S, O I 1s2 2s 2p5 3P0, F II 1s2 2s 2p5 1P0 and others. The methods, presented in reasonable detail, yield correlated wavefunctions accurate to approximately 0.001 au readily applicable to transition probabilities, hyperfine structure, spin-orbit coupling and other properties. Accurate wavelengths, term-splitting ratios and multiplet oscillator strengths for lines in highly ionized silicon, are given as an example of the applicability of the wavefunctions and energies obtained.

Theoretical oscillator strengths for the beryllium 1s22s21S-1s22s2p1P0, 1s22s2p1P0-1s22p21D and 1s22s2p1P0-1s22p21S isoelectronic sequences

Accurate oscillator strengths (f-values) for the 1s22s2 1S-1s22s2p 1P0, 1s22s2p 1P0-1s22p2 1D, 1s22s2p 1P0-1s22p2 1S lines of the Beryllium sequences are calculated using wavefunctions (the 'charge wavefunctions' Psi c) containing all of the specifically non-closed shell type correlation effects given by Sinanoglu's (1970) non-closed shell many electron theory (NCMET). Comparison with the numerous Beam-Foil experimental results using both the dipole length and dipole velocity formulae, yields very good agreement except for the Be I 1s22s2p 1P0-1s22p2 1S line. For this line, the dipole length and velocity calculations yield fR=0.396, fV=0.100 while two experiments give f=0.122 and f=0.119.

Chemisorption and 1s binding energies in oxygen atom and negative ion

The use of accurate experimental 1s binding energies (B.E.) of an atom in its “free” and “adatom” states is proposed as a means of studying chemisorption forces. In the case of the oxygen atom, which is important for adsorption studies, there are no experimental results on the 1s binding energy of the free atom or negative ion. In this paper we report accurate, theoretical 1s B.E.'s for O 3P and O − 2P 0 obtained using Sinanog̈lu's non-closed shell many-electron theory (NCMET). We find: B.E. (O 3P) = 544.5 eV and B.E. (O −2P) = 528.6 eV. Hopefully these values will be useful for adsorption studies in the context of the approach outlined below.

Transition probabilities: New theory vs recent experimental results

Transition probabilities are calculated for various 1s 22s 22p n −1s 22s2p n+1 electric dipole transitions in the first row ions C II, N I, N II, N III, O II, O III, O IV, F II, Ne II. A Non-Closed Shell Many Electron Theory (N.C.M.E.T.) of atomic structure developed by Sinanoǧlu and co-workers, which treats electron correlation accurately in both ground and excited states, predicts novel correlation effects which are included in the wave functions used to calculate the multiplet oscillator strengths. The calculated values are in agreement with recent experimental results within 10%. It is found that the usual improvement of the Hartree-Fock wave-function by the inclusion of a few configurations traditionally thought to be important, is not sufficient to obtain agreement with experiment. It is concluded therefore that all novel correlation effects as analyzed within the framework of N.C.M.E.T. should be included in the wave function to obtain accurate oscillator strengths.