Rubidium Tetrachlorocadmate: X-Ray Diffraction Measurements and an Electronic Structure Study

The structure of Rb₂CdCl₄single crystal at room temperature has been determined from X-ray diffraction of the MoKαline (λ=0.7107 Å). After refinement through blocked least-squares methods, the reliability factorRin the final cycle is 3.07%. The following results have been obtained: tetragonal system, space groupI4/mmm,a=b=5.195(1) Å,c=16.130(1) Å;F(000)=380;Dm=3.243 g/cm³;Z=2. The structure can be viewed as made of layers of CdCl₆octahedra chains (Cd–Cl(1)=2.597(1) Å and Cd–Cl(2)=2.572(1) Å) separated by double slabs of rubidium atoms perpendicular to thecdirection. First-principles density functional theory calculations have been carried out to determine the electronic density distribution. The calculated equilibrium structure is in satisfactory agreement with the experimental data. Electronic density maps have been drawn from ab initio wavefunctions calculated both at the experimental and theoretical equilibrium geometries. Analysis of the calculated atomic populations confirms the highly ionic character of the electronic charge distribution in the crystal.     

X-ray diffraction and ab initio determinations of the structure of Rb4CdCl6

The structure of Rb₄CdCl₆ has been examined both at the experimental and at the ab initio levels. Experimentally, new X-ray diffraction measurements have been performed on a single crystal grown at room temperature from aqueous solution. The compound is confirmed to crystallize with a rhombohedral unit cell (space group ) but with a distorsion from cubic symmetry noticeably smaller than in a previous study [Kristallografiya, 37 (1992) 815]. From the ab initio point of view, three distinct sets of first-principles density functional theory calculations (Perdew-Wang generalized-gradient-approximation (PWGGA), Perdew, Burke and Ernzerhof parametrization and Becke-Lyp exchange-correlation functions) have been carried out. These ab initio results corresponding to the ideal crystal (i.e. infinite, periodic in a definite phase and defect-free) are in correct agreement with our own experimental findings, especially for the distorsion. Nevertheless, due to the relative flatness of the ideal crystal potential energy surface with respect to distorsion around the minimum, it is quite plausible the two presently available X-ray diffraction analyses, made on two different real (imperfect) samples, are both correct even though they come out onto significantly different mean distorsion parameters. The shape, orientation and relative sizes of the thermal vibration ellipsoids are discussed in relation with relevant aspects of the calculated potential energy surface. The PWGGA wavefunction is used to plot valence electronic charge density maps. The comparison of the charge distribution in Rb₄CdCl₆ with that in Rb₂CdCl₄ is discussed in terms of compound structures.     

Ab initio study of a Bi3+ impurity in Cs2NaYCl6 and Y2O3: comparison of perturbative and variational electron correlation methods

Ab initio study of excitation energies and oscillator strengths for absorption towards the (3)P(1) and (1)P(1) states of the Bi(3+) ion has been performed for the Bi(3+) ion in gas phase and as a dopant of the cubic elpasolite Cs(2)NaYCl(6) and the yttria Y(2)O(3) crystal using the ab initio embedded-cluster method. The ground and excited states were computed with a relativistic spin-orbit configuration interaction approach suited for heavy elements. Electron correlation was treated in the scalar relativistic scheme with perturbative, variational, and coupled-cluster methods. Intermediate coupling is included via an effective-Hamiltonian based spin-orbit configuration interaction approach. Small-core (60 electrons) and large-core (78 electrons) relativistic effective core potentials (ECPs) have been used to describe the bismuth ion. The best match with experiment was obtained with the small-core ECP. The accuracy of excitation energies strongly depends on the electron correlation method used. The agreement between experimental data and the results obtained using second-order multiconfigurational perturbation theory is greatly improved with the shifted zeroth-order Hamiltonian proposed by Ghido et al. [Chem. Phys. Lett. 396, 142 (2004)]. Although quite time consuming, coupled-cluster and variational methods yield good agreement with experimental data. The first absorption band recorded for the doped elpasolite crystal is positioned with an excellent accuracy while the computed energy of the second absorbing manifold is in poorer agreement with experimental data. This suggests that interactions with neglected close-lying excited states with a ligand-to-metal charge transfer character may be significant. Calculations of the spectrum of Bi(3+) doping yttria in both the S(6) and C(2) site symmetries indicate that the absorbing manifold arises from electronic excitations localized on the Bi(3+) doping ion with main triplet 6s6p character. Our results predict the first absorbing peak to lie about 0.5 eV lower for the S(6) sites than for the C(2) site, thus attributing the violet and the green emission wavelengths to the S(6) and C(2) sites, respectively. A subsequent study of Stokes shift and emission wavelength should hopefully lead to a final assignment of the measured excitation spectra.     

Rotational analysis of a 2Δ-2Π system of NiF

A ²Δ-²Π system of NiF has been obtained in emission from a “composite wall hollow cathode” in the blue region. High-dispersion rotational analysis has led to the following constants (in cm^?1):

     

5.

Laser spectroscopy of CaBr: A²Π-X²Σ⁺ and B²Σ⁺-X²Σ⁺ systems     

P.F. Bernath  R.W. Field  B. Pinchemel  Y. Lefebvre  J. Schamps 《Journal of Molecular Spectroscopy》1981,88(1):175-193

Laser excitation spectra have been recorded for Ca⁷⁹Br and Ca⁸¹Br in the spectral region 600–630 nm. The use of a 1-m monochromator as a narrow band pass filter (1–2 cm^?1) has allowed rotational analysis of the 0-0, 1-1, and 2-2 bands of the B²Σ⁺ - X²Σ⁺ transition and the 0-0 and 1-1 bands of the A²Π - X²Σ⁺ transition. A few additional lines of the 0-1, 1-2, 1-0, and 2-1 bands of the B-X system were used to obtain band origins for vibrational analysis. The main constants for Ca⁷⁹Br are (in cm^?1):

	2Π1/2	2Π3/2	2Δ3/2	2Δ5/2
B	0.3861	0.3886	0.3772	0.3792
D × 106	0.46	0.35	0.40	0.37
p	0.154
pj	?3.8 × 10-6

     

6.

Electronic structure and perturbations: Interpretation in the SiO valence states     

J.M. Robbe  J. Schamps  H. Lefebvre-Brion  G. Raseev 《Journal of Molecular Spectroscopy》1979,74(3):375-387

Using SCF-CI wavefunctions, we have calculated energies and spectroscopic constants of low-lying states of SiO. Special attention has been paid to the ³Π states and has led to the prediction of a new state lying close to the observed c³Π_i state. Ab initio calculations of parameters characteristic of the perturbations occurring between the valence states of SiO have been performed and compared to experimental deperturbation analysis of Field, Lagerqvist, and Renhorn.     

7.

Rotational analysis of a red $\text{A′}{}^2\text{Σ}{}^{\mathrm{+}}\text{-X}{}^2\text{Π}{}_{\mathrm{i}}$ system of CuO     

Y Lefebvre  B Pinchemel  J Schamps 《Journal of Molecular Spectroscopy》1977,68(1):81-88

High dispersion rotational analysis of a red CuO band system has led to the identification of an $\text{A′}{}^2\text{Σ}{}^{\mathrm{+}}\text{-X}{}^2\text{Π}{}_{\mathrm{i}}$ transition. The anomalous appearance of the branches is due to a very large spin splitting of the ²Σ upper state. The influence of centrifugal distortion effects on this spin splitting (γ_D and γ_H parameters) is essential for explaining the band structure. A reassignment of electronic symmetries of all the ²Σ states of CuO is proposed.     

8.

The A 1Π ∼ D 1Δ rotation-electronic interaction in CO     

André Le Floch  Joëlle Rostas  Joël Schamps 《Molecular physics》2013,111(4):677-684

All available experimental data pertinent to the A ¹Π (v = 0-4) and D ¹Δ state of CO have been used to derive five independent values for the rotation-electronic interaction parameter b(A ～D). The experimental values concern a narrow R centroïd region (1·21 < R < 1·32 Å). The mean value b(A ～D) = 0·12 ± 0·01 is much smaller than the value (0·48) predicted by ab initio SCF-CI calculations which have been carried out for several internuclear distances. The experimental and calculated values for the A ¹Π ～I ¹Σ^- and a ³Π ～ a′³Σ⁺, e ³Σ^-, d ³Δ rotation-electronic perturbations available in the literature are also discussed.     

9.

Ab initio embedded cluster study of the excitation spectrum and Stokes shifts of Bi3+-doped Y2O3     

Réal F  Vallet V  Flament JP  Schamps J 《The Journal of chemical physics》2007,127(10):104705

The ab initio embedded cluster method coupled with correlated spin-orbit calculations has been used to interpret the excitation spectrum of a Bi(3+)-doped yttria crystal. Our results indicate that the Bi(3+) impurity can absorb light over a wider energy range in the C(2) site than in the S(6) site. Even if the computed absorption energies seem to be about 0.4 eV too high with respect to the experimental peaks for both sites, it is noteworthy that the embedded cluster model renders 93% of the large crystal redshift, about 6 eV. The determination of the geometry relaxation of the first shell of oxygen neighbors upon electronic excitation shows that the Stokes shift is smaller in the S(6) site than in the C(2) site. Combining all these results confirms the assignment of the violet emission to the S(6) site and that of the green emission to the C(2) site, as proposed by Boulon [J. Phys. (Paris) 32, 333 (1971)]. In addition, the nature of the metastable states which lie below the emitting ones and are responsible for the temperature dependence of the fluorescence lifetimes is discussed.     

10.

Properties of r-centroids for equal-frequency harmonic oscillators     

J. Schamps 《Journal of Quantitative Spectroscopy & Radiative Transfer》1977,17(6):685-694

Basic properties of r-centroids are discussed in the model of harmonic oscillators with equal frequencies and different oscillation centers (r_e values). In this approximation, r-centroids are found to be given by a very simple formula. They are characteristic of each Δυ=constant sequence and change regularly from one sequence to the next. The corresponding change in r-centroid is inversely proportional to the distance between the oscillation centers. The important special case of two abutting levels is studied and it is found that the r-centroid of the two levels is their common turning point. The conditions under which r-centroids can be considered as mean internuclear distances are specified. Applications of these simple results to molecular vibronic interactions are discussed. It is shown that the r-centroid of degenerate perturbing vibronic levels is located at the crossing of the corresponding electronic potential curves, so that, contrary to transition moments, the variation of electronic perturbation parameters with the internuclear separation R cannot be accurately deduced from only experimental data.     

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	$\text{X}{}^2\text{Σ}{}^{\mathrm{+}}$	$\text{A}{}^2\text{Π}$	$\text{B}{}^2\text{Σ}{}^{\mathrm{+}}$
$\text{T}{}_{\mathrm{e}}$	0	15 958.41 (10)	16 383.137 (6)
$\text{ω}{}_{\mathrm{e}}$	285.732 (9)	288.56 (20)	285.747 (9)
$\text{ω}{}_{\mathrm{e}}\text{χ}{}_{\mathrm{e}}$	0.840 (4)	—	0.954 (4)
$\text{B}{}_{\mathrm{e}}$	0.094466141 (30)	0.0957343 (20)	0.0965151 (20)
$\text{α}{}_{\mathrm{e}}$	0.000403551 (40)	0.0004327 (20)	0.0004483 (15)
$\text{γ}{}_{\mathrm{e}}$ (spin-rot.)	0.00301484 (50)	—	0.068767 (79)
$\text{P}{}_{\mathrm{e}}$	—	?0.066834 (64)	—
$\text{A}{}_{\mathrm{e}}$	—	59.175 (1)	—

Laser spectroscopy of CaBr: A2Π-X2Σ+ and B2Σ+-X2Σ+ systems

Laser excitation spectra have been recorded for Ca⁷⁹Br and Ca⁸¹Br in the spectral region 600–630 nm. The use of a 1-m monochromator as a narrow band pass filter (1–2 cm^?1) has allowed rotational analysis of the 0-0, 1-1, and 2-2 bands of the B²Σ⁺ - X²Σ⁺ transition and the 0-0 and 1-1 bands of the A²Π - X²Σ⁺ transition. A few additional lines of the 0-1, 1-2, 1-0, and 2-1 bands of the B-X system were used to obtain band origins for vibrational analysis. The main constants for Ca⁷⁹Br are (in cm^?1):

Electronic structure and perturbations: Interpretation in the SiO valence states

Using SCF-CI wavefunctions, we have calculated energies and spectroscopic constants of low-lying states of SiO. Special attention has been paid to the ³Π states and has led to the prediction of a new state lying close to the observed c³Π_i state. Ab initio calculations of parameters characteristic of the perturbations occurring between the valence states of SiO have been performed and compared to experimental deperturbation analysis of Field, Lagerqvist, and Renhorn.     

Rotational analysis of a red A′ 2Σ+-X 2Πi system of CuO

High dispersion rotational analysis of a red CuO band system has led to the identification of an $\text{A′}{}^2\text{Σ}{}^{\mathrm{+}}\text{-X}{}^2\text{Π}{}_{\mathrm{i}}$ transition. The anomalous appearance of the branches is due to a very large spin splitting of the ²Σ upper state. The influence of centrifugal distortion effects on this spin splitting (γ_D and γ_H parameters) is essential for explaining the band structure. A reassignment of electronic symmetries of all the ²Σ states of CuO is proposed.     

The A 1Π ∼ D 1Δ rotation-electronic interaction in CO

All available experimental data pertinent to the A ¹Π (v = 0-4) and D ¹Δ state of CO have been used to derive five independent values for the rotation-electronic interaction parameter b(A ～D). The experimental values concern a narrow R centroïd region (1·21 < R < 1·32 Å). The mean value b(A ～D) = 0·12 ± 0·01 is much smaller than the value (0·48) predicted by ab initio SCF-CI calculations which have been carried out for several internuclear distances. The experimental and calculated values for the A ¹Π ～I ¹Σ^- and a ³Π ～ a′³Σ⁺, e ³Σ^-, d ³Δ rotation-electronic perturbations available in the literature are also discussed.     

Ab initio embedded cluster study of the excitation spectrum and Stokes shifts of Bi3+-doped Y2O3

The ab initio embedded cluster method coupled with correlated spin-orbit calculations has been used to interpret the excitation spectrum of a Bi(3+)-doped yttria crystal. Our results indicate that the Bi(3+) impurity can absorb light over a wider energy range in the C(2) site than in the S(6) site. Even if the computed absorption energies seem to be about 0.4 eV too high with respect to the experimental peaks for both sites, it is noteworthy that the embedded cluster model renders 93% of the large crystal redshift, about 6 eV. The determination of the geometry relaxation of the first shell of oxygen neighbors upon electronic excitation shows that the Stokes shift is smaller in the S(6) site than in the C(2) site. Combining all these results confirms the assignment of the violet emission to the S(6) site and that of the green emission to the C(2) site, as proposed by Boulon [J. Phys. (Paris) 32, 333 (1971)]. In addition, the nature of the metastable states which lie below the emitting ones and are responsible for the temperature dependence of the fluorescence lifetimes is discussed.     

Properties of r-centroids for equal-frequency harmonic oscillators

Basic properties of r-centroids are discussed in the model of harmonic oscillators with equal frequencies and different oscillation centers (r_e values). In this approximation, r-centroids are found to be given by a very simple formula. They are characteristic of each Δυ=constant sequence and change regularly from one sequence to the next. The corresponding change in r-centroid is inversely proportional to the distance between the oscillation centers. The important special case of two abutting levels is studied and it is found that the r-centroid of the two levels is their common turning point. The conditions under which r-centroids can be considered as mean internuclear distances are specified. Applications of these simple results to molecular vibronic interactions are discussed. It is shown that the r-centroid of degenerate perturbing vibronic levels is located at the crossing of the corresponding electronic potential curves, so that, contrary to transition moments, the variation of electronic perturbation parameters with the internuclear separation R cannot be accurately deduced from only experimental data.