Interconfigurational Energy Research Articles

First-Principles calculations of the interconfigurational transition energies of 4f - 4f-15d of Ln3+ ions in LiYF4 and CaF2

In studying the design of novel phosphors and solid-state laser materials, luminescence with a characteristically long lifetime originates from f - f emissions (infrared, visible and ultraviolet). However, due to high demand for novel luminescence materials which excite in the ultraviolet (UV) and vacuum ultraviolet (VUV) ranges, the interconfigurational f - d transition has been of great interest. In this work, we investigated the 4 f n - 4 f n -1 5 d transition energy of trivalent lanthanide ions in LiYF 4 and CaF 2 host crystals (LiYF 4 : Ln 3+ and CaF 2 : Ln 3+ ) without referring to any empirical parameters. These crystals are considered to be promising fluoride hosts for solid-state laser crystals. LnF 8 5− atomic clusters were built based on the crystal structures of LiYF 4 and CaF 2 . The relativistic MO calculations were done using the relativistic Discrete Variational Xα (DV-Xα) algorithm. The relativistic version of discrete variational multi-electron method (DVME) algorithm was used to calculate the multiplet energies. We considered the effect of lattice relaxation by a simple estimation using Shannon's crystal radii. Given that the theoretical transition energies are typically underestimated due to the underestimation of the corresponding effects, the absolute transitional energies have received corrections based on one-electron calculations utilizing the Slater's transition-state technique. The in-depth study indicates that the lattice-relaxation effect does not substantially impact LiYF 4 : Ln 3+ , but greatly affects the transitional energy of heavy lanthanides doped in CaF 2 from 4 f n - 4 f n -1 5 d . The energy corrections based on Slater's transition-state method are necessary to improve the accuracy of our calculations. By a combination of these two methods, the transition energies of 4 f n - 4 f n -1 5 d of LiYF 4 : Ln 3+ and CaF 2 : Ln 3+ agree very well with the experimental data. This research is important to providing guidance in the search for new lanthanide-based phosphors in UV or VUV regions. • The 4 f n - 4 f n -1 5 d transition energies of LiYF 4 :Ln 3+ and CaF 2 :Ln 3+ have been studied. • Effect of lattice relaxation was simply estimated based on Shannon's crystal radii. • Energy corrections utilizing Slater's transition-state method were considered. • The lattice relaxation greatly affects the transitional energy of heavy CaF 2 :Ln 3+ . • The energy corrections are necessary to improve the accuracy.

Structure and properties of pure and mixed transition metal dimers on graphene

Small Fe, Co and Ni clusters are known to exhibit high magnetic moments and are therefore investigated rather intensely for the purpose of developing novel magnetic materials with high magnetisation densities. The reduced bond density of these clusters compared to their respective bulk states, results in them being particularly sensitive to their environment. The choice of a substrate for these clusters is therefore of particular importance. Graphene has been shown to exhibit many novel phenomena and it is therefore interesting to investigate the suitability of using graphene as a support material for these metal clusters and if this would allow for an integration of technologies. In this paper, we report the results of plane–wave density functional theory (DFT) calculations of Fe, Co and Ni adatoms, and homonuclear and heteronuclear dimers, including mixing with Pt, adsorbed on graphene. We investigated the adsorption site structure, and stability, the projected density of states and electron populations, and magnetic moments. Calculations were performed using the Perdew–Burke–Ernzerhof (PBE) functional for the wavefunction with energy cutoffs of 40Ry and 480Ry for the wavefunction and density respectively. Brillouin zone sampling was performed with a Monkhorst–Pack grid of (8 ? 8 ? 1). We find that the adatoms bind weakly to graphene and that the magnetic moment of the most stable adatom configuration (the hole site configuration) is reduced by 2 ?B compared to the free adatom, and that the most stable dimer configuration is one where the dimer bond axis is oriented perpendicular to the graphene plane. The stability of the adatoms and dimers on graphene can be explained by considering the electronic interconfigurational energy change that accompanies the desorption of these clusters as well as the amount of charge transferred from cluster to graphene. Therefore, the accuracy of these calculations will depend rather strongly on how adequately the 3d–4s exchange correlation inter–action is treated.

Density functional theory study of Fe, Co, and Ni adatoms and dimers adsorbed on graphene

Metal clusters have been investigated rather intensely for both fundamental and technological reasons. In this work we report the results of plane-wave density functional theory calculations of Fe, Co, and Ni adatoms and dimers adsorbed on graphene. We study both homonuclear and heteronuclear dimers, and the latter includes mixed dimers of Fe, Co, and Ni along with dimers of these elements with Pt. Our work is motivated by the fundamental interest in their configurational and magnetic properties. We calculated the adsorption site, the structure and relative stabilities of various adsorption configurations, the band structures, the atomic projected electronic density of states, and the magnetic moments of the adatoms and dimers. Contrary to previous work, our results show that adatoms bind weakly to graphene with binding energies ranging from 0.2 to 1.4 eV depending on the adsorption site and species. For both homonuclear and heteronuclear dimers the binding energies per atom are lower than the respective adatom cases, ranging from 0.1 to 0.5 eV per metal atom. The most strongly bound configurations for all the dimers studied are those with the dimer axis (nearly) perpendicular to the graphene plane and bound at the hole site. These configurations, which, to our knowledge, have not been considered in previous work, also turn out to have the largest enhancement of the magnetic moment at least for the atom farther from the graphene. The binding energies of these most strongly bound dimers are dependent on three factors, namely, the interconfigurational energy change in the dimer atom farther from graphene upon desorption, the charge transfer from the dimer to the graphene, and the adsorption site favored by the atom closer to the graphene sheet. The first factor is dominant for all the dimers studied here except for CoPt and NiPt. The relatively high electronegativity of Pt affects the character of the charge transfer from the dimer to graphene. In most of the dimers we investigated, charge is transferred almost exclusively from the dimer atom closer to the graphene except for heteronuclear dimers with Pt where charge is also transferred between the two dimer atoms upon adsorption. Thus, our calculations of the electronic structure allow us to understand the trends in binding energy and the magnetic moment in these dimers.

Interconfigurational energies and ionization potentials: Test of a correlation energy functional

A recently proposed correlation energy functional [S. Ragot, P. Cortona, J. Chem. Phys. 121 (2004) 7671] has been tested by calculating the interconfigurational energies and the ionization potentials of the third row transition metal atoms and the ionization potentials of a selected set of molecules. A great and almost systematic improvement, with respect to the results of standard local-density calculations, has been found for the ionization potentials: the accuracy of the new approximation is similar to that of the B3LYP hybrid functional. The interconfigurational energies are also improved, but the improvement is smaller than in the case of the ionization potentials. This is due to the fact that the local-density results largely benefit from the compensation of the errors. Calculations performed correcting the exchange-correlation functional for the self-interaction effects (by the D-SIC method) have also been done for the transition metal atoms: a further general improvement of the results is found.

Relaxed core projector-augmented-wave method

We extend the full-potential projector-augmented-wave method beyond the frozen core approximation, i.e., include the self-consistent optimization of the core charge density, in such a manner that the valence wave functions remain orthogonal to the core. The method consists of an on-the-fly repseudization of the all-electron problem, solving for the self-consistent core charge density within a spherical approximation. The key ideas in our procedure are to keep the projector functions fixed throughout the electronic minimization and to derive the new pseudopartial waves from these original projector functions, at each step of the electronic minimization procedure. Results of relaxed core calculations for atomic interconfigurational energies, structural energy differences between bulk phases of Fe, atomization energies of a subset of Pople's G2-1 set, and the Rh 3d surface core level shifts for the (log3 x log3)-Rh(111) surface at 1/3 CO coverage are presented.

Benchmarking approximate density functional theory. I. s/d excitation energies in 3d transition metal cations

The performance of a number of different implementations of density functional theory (DFT) for predicting the s/d interconfigurational energies of the 3d transition metal cations is investigated. Systematic comparisons of computed results with experimental data indicate that gradient corrected correlation functionals, like the LYP GGA, efficiently correct the flaws of the LDA, but reveal shortcomings in the treatment of exchange by currently available GGAs. The admixture of exact exchange in hybrid functionals eventually leads to largely reduced errors. Several basis sets available for the 3d elements are tested in combination with the B3LYP functional. Finally, the influence of variations of the admixture of exact exchange is systematically tested. The results reveal that computed s/d excitation energies obtained for the individual ions depend in markedly different ways on the amount of exact exchange admixture and that there is no single optimal and transferable exchange parameter to create a hybrid functional that yields improved results for all ions alike. Several of the recently devised functionals perform as good as or slightly better than the B3LYP functional in the present study. But given the fact that the B3LYP functional has been identified as the most successful DFT method in an overwhelming number of systematic investigations in very many areas of chemical research, there is no persuasive motivation to recommend its replacement by one of the other functionals, as much less is known about their robustness.

Gradient-corrected density-functional potential with correct asymptotic behavior: Application to interconfigurational energies in transition-metal atoms

Based upon the optimized effective potential with the self-interaction correction, we present in this paper an alternative gradient-corrected density-functional approximation with the proper long-range behavior of the effective potential. As applied to the study of the interconfigurational energies of the whole transition-metal atoms, the present combination of the gradient-corrected contribution and the modified optimized effective potential lead the s ionization to the excellent agreement with the experiment. The calculated d ionizations and s-d transition energies are also discussed.

Relativistic density-functional all-electron calculations of interconfigurational energies of lanthanide atoms

The interconfigurational energies (ICEs) of the lanthanide atoms, including the s ionization energies, the f ionization energy, and the fd transition energy, are studied based on the fully relativistic density-functional theory (RDFT). The exchange-correlation energy functional by the local-spin-density approximation (RLSD), the generalized gradient approximation (RGGA), and the approximation within the framework of the Krieger-Li-Iafrate treatment of the optimized effective potential (ROEP) incorporated by an explicit self-interaction correction term are used to perform the calculation. In addition, results obtained from the simple perturbation with the mass-velocity correction and the Darwin shift are also presented for comparisons. It is found that the ROEP, with the proper description of the long-range behavior of the outermost electron, yields the most best computations for the two s ionizations. For the f ionization potential and the fd transition energy, the RGGA surpasses the RLSD and the ROEP, reflecting the importance of the gradient expansion in dealing with the more localized f or d electron densities. The excellent satisfaction of the Koopmans' theorem for the two s binding energies is demonstrated within the ROEP framework. As predicted in previous work [C. Y. Ren, H. T. Jeng, and C. S. Hsue, Phys. Rev. B 66, 125105 (2002)], the perturbative ICEs for the first s ionization are almost the same with those by the fully RDFT through the whole lanthanide atoms, with a deviation smaller than 0.1 eV. However, the similarity of calculations by means of the fully RDFT and the standard perturbation method is destroyed in the cases of the f ionization and the fd transition energy.

Relativistic density-functional calculations of interconfigurational energies for second and third transition-metal rows

Relativistic density-functional calculations of interconfigurational energies for second and third transition-metal rows

Investigation of the use of density functionals in second‐ and third‐row transition metal dimer calculations

AbstractWe explore the use of density functionals in calculating the equilibrium distances, dissociation energies, and harmonic vibrational frequencies of the homonuclear diatomics of the second‐row transition metals, platinum, and gold. The outermost s–d interconfigurational energies (ICEs) and the outermost s and d ionization potentials (IPs) were also calculated for the second‐ and third‐row transition metal atoms. Compared with the first‐row transition metal dimer calculations (J Chem Phys 2000, 112, 545–553), the binding energies calculated using the combination of the Becke 1988 exchange and the one‐parameter progressive correlation (BOP) functional and Becke's three‐parameter hybrid (B3LYP) functional are in better agreement with the experiment. However, the pure BOP functional still gives the deep and narrow dissociation potential wells for the electron configurations containing high‐angular‐momentum open‐shell orbitals. Analysis of the s–d ICEs and the s and d IPs suggests that the overestimation may be due to the insufficient long‐range interaction between the outermost s and d orbitals in the exchange functional. The hybrid B3LYP functional seems to partly solve this problem for many systems by the incorporation of the Hartree–Fock exchange integral. However, this still leads to an erroneous energy gap between the configurations of fairly different spin multiplicity, probably because of the unbalance of exchange and correlation contributions. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1995–2009, 2001

A long-range correction scheme for generalized-gradient-approximation exchange functionals

We propose a new long-range correction scheme that combines generalized-gradient-approximation (GGA) exchange functionals in density-functional theory (DFT) with the ab initio Hartree–Fock exchange integral by using the standard error function. To develop this scheme, we suggest a new technique that constructs an approximate first-order density matrix that corresponds to a GGA exchange functional. The calculated results of the long-range correction scheme are found to support a previous argument that the lack of the long-range interactions in conventional exchange functionals may be responsible for the underestimation of 4s−3d interconfigurational energies of the first-row transition metals and for the overestimation of the longitudinal polarizabilities of π-conjugated polyenes in DFT calculations.

Relativistic density-functional calculations of interconfigurational energies in transition-metal atoms

The relativistic local-spin-density approximation and the relativistic generalized gradient approximation (RGGA) are employed to calculate interconfiguration energies including $4s$-$3d$ transition energies, $4s$ ionization energies, and $3d$ ionization energies for the first transition-metal atoms. For $3d$ ionizations, the RGGA, which includes relativistic corrections as well as gradient effects, yields the best results. For $4s$-$3d$ transitions, the relativistic effects also systematically improve the accuracies of the results. However the $4s$ removal energies from the relativistic schemes are slightly too large, whereas the self-interaction-correction local-spin-density approximation, which provides correct long-range effective potentials, gives accurate results.

An investigation of density functionals: The first-row transition metal dimer calculations

The performance of different density functional theory (DFT) methods was investigated in the calculations of the bond length and the binding energy of the first-low transition metal dimers. The 4s–3d interconfigurational energies and 4s and 3d ionization potentials were also calculated for the first-row transition metal atoms. In general, the hybrid DFT method, B3LYP, yields the bond lengths that are too short compared to the experimental ones. In contrast, the optimized bond lengths by nonhybrid DFT methods such as BOP or PW91 are in good agreement with the experiment. It was also found that nonhybrid DFT methods overestimate the binding energies, because they have a tendency to overstabilize the electron configurations that contain the atomic and molecular orbitals in a higher angular momentum open shell. The hybrid DFT method yields more accurate binding energies, but it estimates rather poor energy gaps between states whose spin multiplicity is quite different.

On the dissociation energy of Ti(OH2)+. An MCSCF, CCSD(T), and DFT study

The dissociation energy of the Ti(OH2)+ ion–molecule complex was calculated by the multiconfigurational self-consistent field theory, coupled cluster theory, and two density functional theory based methods, using both all-electron basis sets and effective core potentials. The calculations show that approximate density functional theory gives results in better agreement with experiment than either the multiconfigurational self-consistent field theory or the coupled cluster theory, with both all-electron basis sets and effective core potentials. Nevertheless, the optimized geometries and harmonic vibration frequencies are very similar, irrespective of the level of theory used. The interconfigurational energy ordering of the two valence electronic configurations dn−1s and dn−2s2 of the 4F electronic state of the titanium cation were also calculated and are discussed. Key words: ab initio, dissociation energy, ion–molecule complex, effective core potentials, transition metals.

The theory of vibronic transitions in rare earth compounds

The theory of vibronic transitions in rare earth compounds is re-examined in the light of a more reliable representation for the ligand field Hamiltonian than the crude electrostatic model. General expressions that take into account the relevant contributions from the forced electric dipole and dynamic coupling mechanisms are derived for the vibronic intensity parameters. These include additional terms, from charge and polarizability gradients, which have not been considered in previous work. Emphasis is given to the relative signs of these various contributions. Under certain approximations these expressions may be conveniently written in terms of accessible ligand field parameters. A comparison with experimental values for the compounds Cs 2NaEuCl 6 and LiEuF 4 is made and satisfactory agreement between theory and experiment is found. A discussion is given on the sensitivity of the calculated intensities to the values of radial integrals, interconfigurational energy differences and ligand field parameters that may be used. Finally, the problem in which a vibronic and an electronic level are in resonance, or near resonance, is analyzed. Suitable expressions to describe the effects of the even-rank components of the vibronic Hamiltonian are obtained. It is found that, depending on the strength of the vibronic interaction and the resonance conditions, the admixture between these two levels may lead to intensities of nearly equal values.

Weighted-density exchange and local-density Coulomb correlation energy functionals for finite systems: Application to atoms.

A nonlocal exchange energy functional developed within the weighted spin-density approximation (WSDA) and a local Coulomb correlation energy functional are combined within the density-functional scheme for the calculation of the electronic structure of many-electron systems. Both functionals include alternative forms of the pair-correlation functions governing the size and shape of the Fermi and Coulomb holes. Self-consistent calculations have been performed for all atoms from He to Rn within the exchange-only WSDA scheme. These have been compared to the results of similar calculations using Becke's exchange functional. Besides, the results of calculations for all atoms from He to Ar, including both exchange and correlation, are compared with those of the self-interaction-corrected method. In addition to obtaining accurate total, exchange, and correlation energies, we perform a successful calculation of the s\ensuremath{\rightarrow}d interconfigurational energies (ICE's) for transition-metal atoms. The average error of the calculated ICE values for 3d atoms is only 0.2 eV.

Single-body methods in 3d transition-metal atoms.

We report results of calculations on atoms in the 3d transition-metal series, comparing the results of the local-spin-density approximation, Hartree-Fock exchange plus local correlation, and a semiempirical form of screened exchange. All data reported are calculated without any approximation on the angular dependence of the total and orbital densities, and are calculated fully self-consistently with both scalar-relativistic and spin-orbit effects included. We have found that a semiempirical screened exchange version of the local-spin-density approximation led to a marked improvement in the interconfigurational and spin-flip energies due to the inclusion of screening effects, while ionization potentials show little improvement.

Europium valencies in substituted EuCu2Si2 systems

Mossbauer studies of151Eu in EuCu2−xPt x Si2, EuCu2Si2−xGe x and Eu x Gd1−xMn2Si2 (x≤0.25) at temperatures between 90 K and 425 K have been performed. All spectra are composed of at least two subspectra, corresponding to stable Eu2+ and intermediate valent Eu. The isomer shift of the stable divalent Eu (ordered magnetically up to 400 K in Eu0.25Gd0.75Mn2Si2) isS2=−7.5 mm/sec in comparison toS2=−10.5 mm/s for stable Eu2+ in EuMn2Ge2. This shows that the Eu2+ is under heavy internal pressure in these systems. From the temperature dependence of the hyperfine interaction parameters and line intensities conclusions are derived concerning interconfigurational excitation energies, their inhomogeneous width and recoil free fraction behaviour.

Self-interaction correction: The transition-metal atoms.

The method that we have recently proposed to correct the local-density approximation of the density-functional theory for spurious self-interaction effects is used to calculate the interconfigurational energies and the ionization potentials of the transition-metal atoms. The results so obtained are compared with the corresponding quantities calculated by using the local-density approximation and the Perdew and Zunger self-interaction correction. In both cases we find very large improvements which are essentially due to a better description of the 3d electrons. The results of this paper show that the large local-density errors for these quantities are mainly due to the self-interaction terms. They also indicate that the latter are probably a major source of errors in the local-density calculations of the electronic properties of the transition-metal dimers and solids.

Two-photon excitation of the 4f5d band of Pr3+ and interconfigurational energy transfer in LaF3:(Pr3+,Gd3+).

Two-photon stepwise excitation of the 4f5d band of ${\mathrm{Pr}}^{3+}$ using as a real intermediate level $^{1}\mathrm{D}_{2}$ state is demonstrated in a Pr- and Gd-doped ${\mathrm{LaF}}_{3}$ crystal. Strong fluorescence arising from the $^{6}\mathrm{P}_{7/2}$ level of ${\mathrm{Gd}}^{3+}$ provides the first evidence of interconfigurational energy transfer between ${\mathrm{Pr}}^{3+}$ and ${\mathrm{Gd}}^{3+}$ ions in a solid. The mechanisms involved in this energy transfer are discussed.