3dn Configurations Research Articles

Racah Parameter Ratio C/B for the 3d3-Configuration Ions Like Mn4+ and Cr3+ in the Tanabe-Sugano Diagram

The 3d3-configuration transition metal ions like Mn4+ and Cr3+ are very important activator ions for the realization of warm white-LED lighting and indoor plant cultivation applications using an UV/blue-chip InGaN device. The Racah parameters in conjunction with the Tanabe−Sugano energy-level diagram are widely used as a means of describing the effects of electron−electron repulsion within the transition metal complexes in coordination chemistry. In constructing the Tanabe−Sugano diagram for specific ions of 3dn configuration, an approximate value of C/B is assumed and an excited-state energy divided by B is plotted as a function of Dq/B. Once the various optical spectra have been identified a more refined comparison can then be made between theory and experiment, and more accurate values of Dq (crystal-field strength), B and C can be deduced. The present study discusses an importance of the Racah parameter ratio C/B ≡ r for better understanding of the Tanabe−Sugano energy-level diagram. A new calculation model for the Racah and related parameters is reported for this purpose. A comparison of its results with the generally accepted model results is made by focusing on the Mn4+-activated phosphors. Results are successfully interpreted by considering a value of r = 4.7 for such phosphors.

Visible spectrum of highly charged ions: The forbidden optical lines of Kr, Xe, and Ba ions in the Ar I to Kr I isoelectronic sequence

We present experimental data on visible transitions in highly charged ions observed in the Lawrence Livermore National Laboratory (LLNL) electron beam ion traps, including results from lines within the ground-state configuration and the first excited configuration. Measurements of lines produced by Kr (q = 11+ to 22+), Xe (q = 18+ to 35+), and Ba (q = 28+ to 36+) ions, corresponding mainly to 3sl 3pm 3dn configurations, were carried out. The ionization stages were determined experimentally by sweeping the electron beam energy over the ionization threshold of each species. We propose possible identifications for the lines with the help of simple atomic structure calculations. However, most observed lines remained unidentified, demonstrating that the understanding of visible spectra from highly charged ions, even if obtained under nearly "ideal" experimental conditions, is still in its infancy. These spectral data may be useful for the diagnostics of magnetically confined plasmas and may set the stage for future measurements of radiative lifetimes. In our experiments, we used the emission from visible lines to image the intersection of the electron beam with a beam of neutral atoms injected into the trap at a right angle as well as the ion cloud in the trap. Under some conditions, the diameter of the ion cloud may be an order of magnitude larger than that of the electron beam. PACS Nos.: 32.30Jc, 39.30+w, 52.59Rz

Ab Initio Structures and Stabilities of Doubly Charged Diatomic Metal Helides for the First Row Transition Metals

The electronic structure and molecular properties of doubly charge transition metal helides, HeX2+ (where X = Sc−Cu), have been investigated using the all-electron ROHF−UCCSD(T) method. Basis sets have been developed for the first row transition metals to elucidate trends in bonding, dissociation energies, and vibrational frequencies. The ground state for all the doubly charged helides exhibited a 3dn configuration. In addition, states with configurations that have holes in the metal 3dσ orbital exhibited greater binding energies. Relativistic effects have also been investigated using the Cowan-Griffin ansatz. Anharmonic vibrational frequencies have been determined variationally.

Visible Spectrum of Highly Charged Ions: the Forbidden Optical Lines of Kr, Xe, and Ba Ions in the Ar I to Ni I Isoelectronic Sequence

We present experimental data on visible lines produced by Kr (q = 11+ to 22+), Xe (q = 18+ to 35+), and Ba (q = 28+ to 36+) ions, corresponding mainly to 3sl 3pm 3dn configurations, obtained with the LLNL electron beam ion traps. Tentative assignments for the lines are made.

Crystal field analysis of the 3d N ions at low symmetry sites including the ‘‘imaginary’’ terms

The crystal field (CF) package applicable to orthorhombic or higher symmetry has been extended to enable calculations of energy levels and ligand field states for 3dN ions in crystals at arbitrary symmetry sites by taking into account the contributions of the ‘‘imaginary’’ CF terms. The full Hamiltonian matrix, including the electrostatic terms, Trees correction, the spin–orbit interaction, and the ligand field terms, is diagonalized within the whole 3dN configuration. Several techniques based on the transformation properties of the crystal field Hamiltonian have been devised to test the package for internal consistency. The package is especially suitable for analysis of the low symmetry effects for transition metal ions at sites with the tetragonal and trigonal symmetry involving the imaginary CF terms as well as monoclinic and triclinic symmetry. It can be useful in analyzing the electron paramagnetic resonance spectra of 3dN ions and in correlating the ligand field parameters with the spin Hamiltonian parameters.

Analysis of the spectrum of six times ionized zinc (Zn VII): the 3d6–3d54p transition array

The spectrum of zinc was photographed in the 100-300 Å region on a 10.7 m grazing incidence spectrograph using a triggered spark light source. 335 lines were classified in the Zn VII 3d6–3d54p transition array, resulting in the establishment of 30 of the 34 levels of the 3d6 configuration and 103 of the 214 levels of the 3d54p. The ground configuration 3d6 was described by a generalized least-squares fit (GLSF) involving orthogonal operators to a set of 3dN configurations. This yielded a mean error of 3 cm−1 for its level values. The excited configuration was described by the conventional Slater Condon parameter set, giving a mean error of 105 cm−1.

Ligand field analysis of the 3dN ions at orthorhombic or higher symmetry sites

A computer package has been developed to calculate the energy levels and the ligand field states for a full Hamiltonian including the electrostatic terms, Trees correction, the spin-orbit interaction and the ligand field interactions within the 3dN configuration (N = 2 to 8). The program can deal with various cubic and non-cubic site symmetries of the 3d ion, namely the tetragonal, trigonal and orthorhombic ones. The package may be very useful in analyzing the EPR spectra of 3dN ions and in correlating the ligand field parameters with spin Hamiltonian parameters derived from the orbital singlet states for some F-term (S = 1, 32) and S-term (S = 52) ions as well as the 3d4 and 3d6 ions with high-spin S = 2. Numerous examples of these ions in various crystals exist in the literature. Other spin states arising from strong ligand fields can also be dealt with.

Determination of potential energy curves for ground and metastable excited state transition metal ions interacting with helium and neon using electronic state chromatography

Reduced zero field mobilities of Cr+, Co+, and Ni+ in their ground state configuration (3dn) and their metastable excited state configuration (3dn−14s1) have been measured in He and Ne as a function of temperature. Parameters for a n−6−4 interaction potential are obtained by fitting the mobility vs temperature curve. Bond dissociation energies, vibrational frequencies, and equilibrium bond lengths are extracted from these curves and compared with data from traditional equilibrium measurements and ab initio theory. Dramatic changes in bonding are observed for the 3dn and 3dn−14s1 configurations; the 3dn configuration yielding very much stronger bonds and very much shorter equilibrium bond lengths than the 3dn−14s1 configuration. The presence of multiple potential curves in the interaction of Co+(3F,3d8) and Ni+(2D,3d9) with He/Ne make interpretation of the ground state mobility data ambiguous. The analysis of each system is discussed in some detail.

Parametric description of 3dN 4s configurations using orthogonal operators

Parametric fits to the 3dN 4s configurations in the III to VI spectra of the iron sequence are reported, using a set of orthogonal operators consisting of electrostatic operators up to four-body character and magnetic operators up to two-body character. The results are presented for all operators. The parameter values behave regularly among neighbouring ions and, for the 3dN core, compare well to those for the corresponding 3dN configurations. For comparison, ab initio calculated values of some operators are given as well.

Energies of N equivalent electrons expressed in terms of two-electron energies and independent three-electron parameters: a new complete set of orthogonal operators. III. Ab initio calculations

For pt.I see ibid., vol.17, p.23-75 (1984). As an illustration of the theory developed in the first paper in this series, a set of five orthogonal parameters is used to describe all electrostatic two-particle excitations in the 3dN configurations completely to second order. These parameters represent the term energies of d2 and, consequently, the 3dN configurations are perceived as a collection of 1/2N(N-1)d2 pairs, the total energy of the configuration being the sum of the corresponding pair energies. As regards their effects, the parameters are partitioned into a structural and an additive part; the structural part is found to behave as a linear function of N, whereas the additive part is proportional to the average energy of the configuration. In order to take into account all electrostatic one-particle effects as well, two orthogonalised three-body parameters T1 and T2 are used, the first corresponding to the well known Trees parameter and the second covering the remaining class of one-electron excitations. With a least-squares fitting procedure, both the d2 energies and the three-electron parameters are determined for the dN ground configuration in the III, IV, V and VI spectra of the iron group elements. Surprisingly, the effects of T2 turn out to be important, especially for the lower ionisation stages. Amongst other things, old problems concerning the far-off position with respect to calculations of the 12D term in the 3d6, and parameter irregularities in the 3d7 configurations, seem to be solved with the introduction of T2. As a result, the mean error of the fit in some of these cases is reduced by factors of three to four. Using the above set of parameters, a prediction of the 3d4 ground configuration of Mn IV is made.

Energies of N equivalent electrons expressed in terms of two-electron energies and independent three-electron parameters: a new complete set of orthogonal operators. II. Application to 3dNconfigurations

For pt.I see ibid., vol.17, p.23-75 (1984). As an illustration of the theory developed in the first paper in this series, a set of five orthogonal parameters is used to describe all electrostatic two-particle excitations in the 3dN configurations completely to second order. These parameters represent the term energies of d2 and, consequently, the 3dN configurations are perceived as a collection of 1/2N(N-1)d2 pairs, the total energy of the configuration being the sum of the corresponding pair energies. As regards their effects, the parameters are partitioned into a structural and an additive part; the structural part is found to behave as a linear function of N, whereas the additive part is proportional to the average energy of the configuration. In order to take into account all electrostatic one-particle effects as well, two orthogonalised three-body parameters T1 and T2 are used, the first corresponding to the well known Trees parameter and the second covering the remaining class of one-electron excitations. With a least-squares fitting procedure, both the d2 energies and the three-electron parameters are determined for the dN ground configuration in the III, IV, V and VI spectra of the iron group elements. Surprisingly, the effects of T2 turn out to be important, especially for the lower ionisation stages. Amongst other things, old problems concerning the far-off position with respect to calculations of the 12D term in the 3d6, and parameter irregularities in the 3d7 configurations, seem to be solved with the introduction of T2. As a result, the mean error of the fit in some of these cases is reduced by factors of three to four. Using the above set of parameters, a prediction of the 3d4 ground configuration of Mn IV is made.

Gaussian basis sets for molecular calculations. The representation of 3d orbitals in transition-metal atoms

Augmented (4d) and (5d) Gaussian basis sets are presented which provide a balanced description of the 4s23dn−2, 4s3dn−1, and 3dn configurations of transition−metal atoms. When compared to accurate Hartree–Fock calculations, the (4d) and (5d) expansions in the literature, which have been optimized for the 4s23dn−2 configuration, can lead to errors of several eV for states of the latter configurations where the 3d orbitals become more diffuse. The augmented sets reported here consist of a single diffuse basis function added to the original sets, where the orbital exponent of the added function was optimized for the 3dn configuration. Basis sets and contraction schemes are presented for the atoms Sc through Cu.

Simple analytical wavefunctions for the ions of the iron group elements

Simple analytic model wavefunctions consisting of two Slater-type orbitals are constructed for the 3d shells of singly ionized iron-group atoms in the 3dn configuration. The parameters are optimized by a Hartree-Fock variation procedure, keeping the inner orbitals fixed. For these latter a simplified description is given, particularly suitable for the present purpose. It is shown that the values of one- and two-electron integrals associated with the 3d orbitals can be calculated to an accuracy of about 5% within the framework of these wavefunctions.

Optical properties of transition metal impurities in CdSe. I. Crystal‐field spectra

AbstractThe absorption spectra of Ti (d2), V (d3), Cr (d4), Fe (d6), Co (d7), Ni (d8), and Cu (d9) in CdSe crystals are presented. The main features of the spectra are successfully interpreted using crystal‐field theory for the states of 3dn configuration in a potential of predominantly Td symmetry. It is found that the oscillator strengths of the observed absorption bands are in the range 10−2to 10−5 due to transitions within the 3dn shell. The crystal‐field parameters, Δ, and the Racah parameters, B and C, are determined where possible, and discussed.