A Tensorial Formalism Adapted to the Rovibronic Couplings in the Colored Hexafluorides: Application to the nu(5)(F(2g)) and nu(3)(F(1u)) Modes

A tensorial formalism adapted to the case of transition-metal hexafluorides in a degenerate electronic state has been developed on the basis of preceding works about spherical-top molecules in a nondegenerate electronic state. We have introduced electronic operators constructed using group theory features and some physical considerations. Vibronic couplings (Jahn-Teller effect, etc.) have been reviewed for the triply degenerate vibrational modes nu(5)(F(2g)) and nu(3)(F(1u)) leading to the identification of the main vibronic parameters. For the first time, an effective rovibronic Hamiltonian as well as the effective transition moment operators (dipole moment and polarizability) for rovibronic transitions have been studied qualitatively thanks to the tensorial algebra properties. Copyright 2000 Academic Press.     

Development of the Hamiltonian and transition moment operators of symmetric top molecules using the O (3) ⊃ C∞v ⊃ C3v group chain

We present a development of the Hamiltonian, dipole moment, and polarizability operators for XY₃Z molecules. These rovibrational operators are written with the aid of a tensorial formalism derived from the one already used in Dijon and adapted to the XY₃Z symmetric tops in a recent paper [A. El Hilali, V. Boudon, M. Loëte, J. Mol. Spectrosc. 234 (2005) 166-174]. We use the O (3) ⊃ C_∞v ⊃ C_3v group chain. Expressions for the matrix elements are derived for these operators.     

Spectroscopy of XY2Z2 (C2v) Molecules: A Tensorial Formalism Adapted to the O(3)⊃Td⊃C2v Chain. Application to the Ground State of SO2F2

A tensorial formalism adapted to the case of quasi-spherical XY₂Z₂ asymmetric tops such as SO₂F₂ has been developed as an extension of the usual one for the tetrahedral molecules. We use the O(3)⊃T_d⊃C_2v group chain. All the coupling coefficients and formulas for the computation of matrix elements are given for this chain. Such relations are then deduced in the C_2v group itself. We also present a development of the Hamiltonian, dipole moment, and polarizability operators for the molecules under consideration using this formalism. These operators are involved in the calculation of the energies and intensities of rovibrational transitions and are essential for spectrum simulations. Expressions for the matrix elements are derived for these operators. A first application to the ground state of SO₂F₂ is presented. Programs for spectrum simulation and fit using these methods are freely available at the URL http://www.u-bourgogne.fr/LPUB/c2vTDS.html.     

Spectroscopy of X2Y4 (D2h) molecules: tensorial formalism adapted to the O(3)⊃D2h chain, Hamiltonian and transition moment operators

A tensorial formalism adapted to the case of the X₂Y₄ molecules with D_2h symmetry has been developed in the same way as in the previous works on XY₄ (T_d) and XY₆ (O_h) spherical tops and XY₅Z (C_4v) symmetric tops. Here, we use the O(3)⊃D_2h group chain. All the coupling coefficients and formulas for the computation of matrix elements are given for this chain and used in the case of the Hamiltonian and transition moment operators.     

Calculated energy levels and intensities for the ν1 and 2ν2 bands of HDO

A Hamiltonian taking explicitly into account both Fermi and Coriolis interactions has been set up for triatomic molecules of symmetry C_s and used to reproduce, very satisfactorily, the available rotational energy levels of the {(100), (020)} interacting states of HDO, providing us with realistic wavefunctions as well as precise rotational constants and vibrational energies. Then, to calculate line intensities, these wavefunctions were used together with suitably chosen transition moment operators expanded up to degree 2 in $\text{J}$ and having the correct symmetry in the C_s group, leading to hybrid bands of both A and B type., Using this formalism, it has been possible to determine, from the fit of the existing experimental intensities, the coefficients appearing in the expansions of the transition moment operators of the 2ν₂ and ν₁ bands of HDO. In this way, we have improved upon the F-factor formalism which needs much more parameters to reproduce the line intensities with the same precision. Finally, using the transition moments as well as the wavefunctions and energy levels deduced from the diagonalization of the Hamiltonian matrix, we have calculated the whole spectrum of the ν₁ and 2ν₂ bands of HDO.     

The ground state rotational spectrum of SO2F2

The analysis of the ground state rotational spectrum of SO₂F₂ [K. Sarka, J. Demaison, L. Margulès, I. Merke, N. Heineking, H. Bürger, H. Ruland, J. Mol. Spectrosc. 200 (2000) 55] has been performed with the Watson’s Hamiltonian up to sextic terms but shows some limits due to the A and S reductions. Since SO₂F₂ is a quasi-spherical top, it can also be regarded as derived from an hypothetical XY₄ molecule. Thus we have developed a new tensorial formalism in the O(3)⊃T_d⊃C_2v group chain (M. Rotger, V. Boudon, M. Loëte, J. Mol. Spectrosc. 216 (2002) 297]. We test it on the ground state of this molecule using the same experimental data (10 GHz-1 THz region, J up to 99). Both fits are comparable even if the formalisms are slightly different. This paper intends to establish a link between the classical approach and the tensorial formalism. In particular, our tensorial parameters at a given order of the development are related to the usual ones. Programs for spectrum simulation and fit using these methods are named C_2vTDS. They are freely available at the URL:http://www.u-bourgogne.fr/LPUB/c2vTDS.html.     

Nuclear hyperfine interactions in spherical top molecules

The nuclear hyperfine Hamiltonian for XY₄ and XY₆ spherical top molecules in their ground electronic state is built up by a tensor method, and is given by a linear combination of invariant tensor products in the group ^L0(3) × G(G = T_d or 0_h); the case when an external magnetic field is applied is also considered. For the study of a given vibrational state, the appropriate restriction is easily determined; as examples were consider the ground vibronic state and a triply degenerate fundamental state.     

Spectroscopy of XY3Z (C3v) molecules: A tensorial formalism adapted to the O (3) ⊃ C∞v ⊃ C3v group chain

A tensorial formalism adapted to the case of XY₃Z symmetric tops has been developed. We use the O (3) ⊃ C_∞v ⊃ C_3v group chain. All the coupling coefficients and formulas for the computation of the matrix elements are given for this chain. Such relations are also deduced in C_3v group itself.     

Ground state properties of CsCoCl3

The electronic spectra of CsCoCl₃ are fit to a Hamiltonian that includes terms for interelectron repulsion, octahedral and trigonal crystal fields, and spin-orbit coupling. The fit adequately accounts for both the optical spectrum and the electronic Raman spectrum. The fitted parameters give empirical estimates of the radial expectation values 〈r^?1〉 and 〈r^?3〉 as well as the charge on the cobalt. The ground state wave functions generated from the fit are used to calculate the following properties: parallel and perpendicular g factors, Co hyperfine field, ⁵⁹Co quadrupole splitting, anisotropy of magnetic exchange, the magnetic moment of Co²⁺, and the spin flop field. The agreement between calculated values and observed values for this variety of independently obtained properties is reasonable in all cases.     

Vibrational anharmonicity and the inversion potential function of NH3

The nonrigid bender formulation of the vibration-inversion-rotation Hamiltonian for an XY₃ pyramidal molecule (V. ?pirko, J. M. R. Stone, and D. Papou?ek, J. Mol. Spectrosc.60, 159 (1976)) is improved by allowing for anharmonicity in all the vibrations. To model the anharmonic potential function of an XY₃ molecule with a low barrier to inversion a Plíva-type empirical potential (J. Plíva, Collect. Czech. Chem. Commun.23, 777 (1958)) is used. A fitting procedure that involves the numerical integration of the effective inversion Schrödinger equation (the nonrigid bender equation) and diagonalization of some resonance matrices is used to determine the equilibrium structure and the anharmonic potential function of the ammonia molecule.     

A comparative study of electronic structure and magnetic properties of SrCrO3 and SrMoO3

A comparative study of electronic structure and magnetic properties of SrCrO₃ and SrMoO₃ has been carried out using FPLAPW method with density-functional theory. The calculated results suggest that both compounds are nonmagnetic (NM) metal in cubic structures at room temperature, and they exhibit very similar band structure and electronic properties except more extend Mo 4d orbitals than Cr 3d electronic states. However, the electronic structure and magnetic properties exhibit remarkable differences between them in the low temperature phases. SrCrO₃ is with a C-AFM ground state with magnetic moment of 1.18μ_B/Cr in the tetragonal structure, while SrMoO₃ is with a NM ground state in the orthorhombic structure. It is assumed that the extend 4d orbitals may be the reason which results in NM solution at low temperature phase of SrMoO₃.     

Spectroscopy of XY(5)Z (C(4v)) Molecules: Development of the Hamiltonian and the Transition Moment Operators Using a Tensorial Formalism

We present a development of the Hamiltonian, dipole moment, and polarizability operators of XY(5)Z (C(4v)) molecules using a tensorial formalism derived from the one developed previously in Dijon for XY(6) molecules. These operators are involved in the calculation of the energies and intensities of rovibrational transitions and are essential for spectrum simulations. Expressions for the matrix elements are derived for all these operators. Copyright 2000 Academic Press.     

The ν1 + 3ν2 + 3ν3 and 4ν1 + ν2 + ν3 bands of ozone by CW-cavity ring down spectroscopy between 5900 and 5960 cm

The absorption spectrum of ozone, ¹⁶O₃, has been recorded in the 5903-5960 cm⁻¹ region by high sensitivity CW-cavity ring down spectroscopy (α_min ∼ 5 × 10⁻¹⁰ cm⁻¹). The ν₁ + 3ν₂ + 3ν₃ and 4ν₁ + ν₂ + ν₃ A-type bands centred at 5919.15 and 5947.07 cm⁻¹ were newly observed. A set of 173 and 168 energy levels could be experimentally determined for the (1 3 3) and (4 1 1) states, respectively. Except for a few K_a = 5 levels of the (4 1 1) state, the rotational structure of the two states was found mostly unperturbed. The spectroscopic parameters were determined from a fit of the corresponding line positions by considering the (1 3 3) and (4 1 1) states as isolated. The determined effective Hamiltonian and transition moment operators were used to generate a list of 785 transitions given as Supplementary Material.     

Analysis of the ν2 + ν3 band of 12CH4 and 13CH4

The ν₂ + ν₃ bands of ¹²CH₄ and ¹³CH₄ occurring in the region 4400–4650 cm^?1 have been studied from spectra recorded with a high-resolution Fourier transform spectrometer (resolution better than 0.01 cm^?1). Champion's Hamiltonian expansion, Canad. J. Phys.55, 1802 (1977), is applied to the problem of the two interacting F₁ and F₂ vibrational sublevels of this type of a band. As the P branch of ν₂ + ν₃ is strongly overlapped by neighboring bands, a combination-difference method, adapted to tetrahedral XY₄ molecules has been developed to help assignments of lines. A fit of 700 transitions has been performed using 13 new effective constants in the case of ¹²CH₄. In the case of ¹³CH₄, 532 transitions have been fit to 18 constants. The known parameters, relative to the vibrational ground state and the ν₃ state for both methanes, and the ν₂ state for ¹²CH₄ were fixed throughout. Most of the perturbed levels, up to J′ = 12, are well reproduced and the general agreement between experimental and calculated transitions is satisfactory with standard deviations of 0.047 cm^?1 (¹²CH₄) and 0.041 cm^?1 (¹³CH₄). The results (order of magnitude of obtained (ν₂ + ν₃) parameters and comparison of observed and computed intensities) indicate that the ν₂ + ν₃ band is perturbed by many other bands.     

Higher-order fine structure of the a4Πu state of O2+

It is shown that the quality of the fit of frequencies for the (4, 4) band of the b⁴Σ_g^?-a⁴Π_u transition of O₂⁺, obtained in an ion-beam experiment, can be significantly improved by the inclusion of a fine structure term of the form L_zS_z³ in the effective Hamiltonian for the a⁴Π_u state, where L_z and S_z are respectively the components of the total orbital and spin angular momenta along the internuclear axis. The various contributions to this term in the Hamiltonian are assessed from a general standpoint by the use of a new order-of-magnitude scheme. The separate contributions to the parameter involved, η, are then considered in detail by means of a perturbation treatment of the spin-orbit and spin-spin interactions through third order. Attempts to interpret the parameter values determined for the a⁴Π_u state of O₂⁺ are severely limited by the present lack of detailed knowledge of the properties of the various electronic states of O₂⁺.     

Jahn-Teller transition and electron-phonon interaction in Cr-doped manganites Sr0.9Ce0.1Mn1−yCryO3

Cr-doped manganites Sr_0.9Ce_0.1Mn_1−yCr_yO₃ (y=0, 0.05, and 0.10) have been systematically investigated by X-ray, magnetic, transport, and elastic properties measurements. For parent compound Sr_0.9Ce_0.1MnO₃, it undergoes a metal-insulator (M-I) transition at 318 K, which is suggested to originate from a first-order structural transition accompanied by Jahn-Teller (JT) transition. With increasing Cr doping content, the JT transition temperature decreases. The Cr doping suppresses the antiferromagnetic (AFM) state and makes the system spin-glass (SG) behavior at low temperatures. In the vicinity of JT transition temperatures, the softening of Young's modulus originating from the coupling of the orbital (quadrupolar) moment of the e_g orbital of Mn³⁺ ion to the elastic strain has been observed. The anomalous Young's modulus properties imply the electron-phonon coupling due to the JT effect may play an important role in the system.     

Antiferromagnetic order and spin glass behavior in Dy2CuIn3

The magnetic properties of the intermetallic compound Dy₂CuIn₃ have been investigated. Ac and dc-susceptibility measurements indicate an onset of antiferromagnetic ordering at T_N=19.5 K and an additional frequency dependent transition at T_ds∼9 K. Neutron diffraction studies confirm the ordered transition at 19.5±1 K. The magnetic unit cell can be described by the propagation vector k=(0.25,0.25,0) with the magnetic moment μ=2.63(4)μ_B/Dy³⁺ parallel to the c-axis. Nevertheless, neutron diffraction reveals no additional magnetic phase transition around or below 9 K, which suggests that, at lower temperatures, a spin glass state may be formed in coexistence with the antiferromagnetic mode as a result of frustration and the antagonism between ferromagnetic and antiferromagnetic exchange interactions.     

Electronic and magnetic properties of NdCrSb3: A first principles study

The electronic and magnetic properties of NdCrSb₃ are calculated by the first principles full-potential linearized augmented plane wave (FP-LAPW) method based on the density functional theory (DFT). Density of states (DOS), magnetic moments and band structures of the system are presented. For the exchange and correlation energy, local spin density approximation (LSDA+U) with the inclusion of Hubbard potential U is used. Our calculation shows that the 3d state electron of Cr and 4f state electrons of Nd contribute to the total DOS and the band structures. The effective magnetic moment is found to be 5.77μ_B, which is comparable to the earlier experimental results of NdCrSb₃.