The effect of the breakdown of the Born-Oppenheimer approximation on the rotation-vibration Hamiltonian of a triatomic molecule

The rotation-vibration-electronic Hamiltonian of a triatomic molecule has been derived in a manner similar to that used by J. T. Hougen, P. R. Bunker, and J. W. C. Johns [J. Mol. Spectrosc.34, 136 (1970)] in deriving the rotation-vibration Hamiltonian. An effective rotation-vibration Hamiltonian for the ground electronic state has been obtained from this, by using the perturbation technique of P. R. Bunker and R. E. Moss [Mol. Phys.33, 417 (1977)], in order to account for the effect of the breakdown of the Born-Oppenheimer approximation to second order. The same form of effective rotation-vibration Hamiltonian, in which the breakdown of the Born-Oppenheimer approximation is allowed for, will be obtained for any molecule. This Hamiltonian contains effective moments of inertia (these involve rotation g-factor corrections) and effective nuclear masses (likely to be close to the atomic masses). Following the procedure of A. R. Hoy and P. R. Bunker [J. Mol. Spectrosc.74, 1 (1979)] the effective rotation-bending Hamiltonian is derived from the effective rotation-vibration Hamiltonian, and this could be used to fit the rotation-bending energy levels.     

A Theoretical Study of MgNC and MgCN in the X?Σ Electronic State

The MgNC radical was the first Mg-containing species to be observed in interstellar space. This fact has stimulated considerable spectroscopic interest in this molecule, and in its isomer MgCN, but nevertheless the only rotationally resolved spectroscopic data presently available for X?²Σ⁺ MgNC comprise the rotational spectrum (K. Kawaguchi et al., 1993, Astrophys. J.406, L39-L42; K. Ishii et al., 1993, Astrophys. J.410, L43-L44; M. A. Anderson and L. M. Ziurys, 1994, Chem. Phys. Lett.231, 164-170; E. Kagi et al., 1996, J. Chem. Phys.104, 1263-1267; E. Kagi and K. Kawaguchi, J. Mol. Spectrosc. 2000, 199, 309-310) together with a few vibronic bands, all originating in the vibronic ground state and belonging to the òΠ←X?²Σ⁺ electronic transition (R. R. Wright and T. A. Miller, 1999, J. Mol. Spectrosc.194, 219-228). For MgCN, only the rotational spectrum in the vibrational ground state is known (M. A. Anderson, T. C. Steimle, and L. M. Ziurys, 1994, Astrophys. J.429, L41-L44). We report here potential energy surfaces calculated by the Averaged Coupled-Pair Functional (ACPF) method with TZ3P+f (Mg), TZ2P+f(N,C) basis sets including core-valence correlation due to the Mg 2s and 2p electrons. The ab initio results are used for determining the standard spectroscopic constants of X?²Σ⁺ MgNC and MgCN. Also, we report variational calculations of the rotation-vibration energies, and variational simulations of the lowest rotation-vibration bands, carried out with the MORBID program system (P. Jensen, 1988, J. Mol. Spectrosc.128, 478-501). We hope that our theoretical results will encourage and facilitate further characterization of X?²Σ⁺ MgNC and MgCN by high-resolution spectroscopy.     

Real-time 3D electromagnetic field measurement instrument with direct visualization

Nowadays, a wide variety of terminals are proposed to nomadic users. Generally these terminals provide wireless communication operating at frequencies between one and a few GHz. For technical reasons, including multiple access to the communication channel and battery autonomy, these terminals transmit only during very short periods i.e. transmission bursts. For a direct observation of certain characteristics of the transmitted signals radiated by such terminals, only a few measurement setups exist. This article proposes such a novel real-time 3D electromagnetic field measurement instrument with direct visualization. The prototype used for validation is based on an array of probes regularly attached on a non-conductive rigid loop which is put into fast rotation around the terminal under test. To cite this article: J. Rioult et al., C. R. Physique 10 (2009).     

Reference deconvolution. Elimination of distortions arising from reference line truncation

Reference deconvolution (G. A. Morris; J. Magn. Reson. 80, 547 (1988)) or reference lineshape adjustment (J. M. Wouters and G. A. Petersson, J. Magn. Reson. 28,81 (1977); J. M. Wouters, G. A. Petersson, W. C. Agosta, F. H. Field, W. A. Gibbons, H. Wyssbrod, and D. Cowburn, J. Magn. Reson. 28, 93 (1977)) relies on extracting the signal of a known reference material from an experimental spectrum and using a comparison between the experimental reference signal and that predicted by theory to correct instrumental contributions to the full experimental spectrum. Truncation of the reference line can produce unwanted artifacts and distortions in the final spectrum. The source of these anomalies usually lies in the dispersion-mode rather than in the absorption-mode data, as discontinuities are formed when the dispersion “wings” are truncated. These discontinuities can be reduced by a numerical extrapolation covering the lost region; this is sufficient to provide adequate results in most cases, but fails where spectra have baseline errors. A method of recreating the full dispersion signal directly from the corresponding adsorption data, based on the Hilbert transform relationship between the real and imaginary parts of a Fourier transform, is demonstrated here. This method results in the removal of truncation distortions from the deconvoluted spectrum, thus extending the range of application of the reference deconvolution technique.     

Multidimensional optimization of structural changes of molecules upon lonization in Franck-Condon factor calculations

Two different iterative methods, namely, the conjugate gradients method and the pattern search method, are applied to Franck-Condon factor calculations using the Coon et al. method (J. B. Coon, R. E. DeWames, and C. M. Loyd, J. Mol. Spectrosc.8, 235–299 (1962)) and the generating function method (T. E. Sharp and H. M. Rosenstock, J. Chem. Phys.41, 3453–3463 (1964); R. Botter, V. H. Dibeler, J. A. Walker, and H. M. Rosenstock, J. Chem. Phys.44, 1271–1278 (1966)). In such treatment, either the changes in normal coordinates or the changes in internal symmetry displacement coordinates are refined automatically until the weighted sum of square deviation between the calculated and the observed Franck-Condon factors is minimized. Some properties of the methods used are given and their applications to several cases are discussed in detail.     

Assignments of several groups of iodine (I2) lines in the B-X system

The spectra obtained by means of Fourier spectroscopy and the assignments of the B-X lines of I₂ in the vicinity of two argon ion laser lines (5145 and 5287 Å), three krypton ion laser lines (5208, 5308, and 5683 Å), and one HeNe laser line (6119 Å) are given. A detailed comparison, in the vicinity of the argon ion laser line (5145 Å), between the iodine wavenumbers calculated by means of the two sets of molecular constants previously published [Wei and Tellinghuisen, J. Mol. Spectrosc.50, 317–332 (1974); Barrow and Yee, J. C. S. Faraday II. 69, 684–700 (1973)] with those calculated from Fourier spectroscopy data, is presented.     

The influence of disorder on magnetocaloric effect and the order of transition in ferromagnetic manganite (La1−x Nd x )2/3(Ca1−y Sr y )1/3MnO3

Magnetocaloric effect and order of transition in (La_1?x Nd _x )_2/3(Ca_1?y Sr _y )_1/3MnO₃, prepared by conventional solid-state reaction, have been investigated. Using Banerjee criterion, we demonstrate first-order transition for (J1) and (J2 ) as well as second-order transition for (J3 ), (J4 ), and (J5 ) samples. The ΔS _M ^max is ranging between 9.18 Jkg^?1 K^?1 and 4.87 when Nd and Sr content changes leading to relative cooling power (RCP) varying between 330 and 229.35 J/kg. Both ΔS _M ^max and the RCP are found sensitive to the disorder σ ². The universal behavior obtained from ΔS variation curves confirmed the first-order transition for (J1) and (J2 ) samples and second-order transition for (J3), (J4), and (J5 ) samples obtained by Banerjee criterion. All samples with second-order phase transition exhibit inhomogeneous character estimated from local exponent n.     

Comment on “A new model of charge transfer during ice–ice collisions”: [C. R. Physique 3 (2002) 1293–1303]

A model which proposes modifications of a theory of collisional charging of ice is criticized. To cite this article: J.G. Dash, J.S. Wettlaufer, C. R. Physique 4 (2003).     

Theoretical transition probabilities for the OH meinel system

An electric dipole moment function (EDMF) for the X²Π ground state of OH based on the complete-active-space self-consistent-field plus multi-reference-singles-plus-double-excitation configuration-interaction procedure using an extended Slater basis is reported. This EDMF and the recently published MCSCF(7)-self-consistent electron pairs (SCEP) EDMF of H-J. Werner, P. Rosmus, and E-A. Reinsch [J. Chem. Phys. 79, 905–916 (1983)] (WRR) are critically compared with the “experimentally” derived EDMF. Einstein coefficients calculated with both theoretical EDMFs are substantially different than those reported by F. H. Mies [J. Mol. Spectrosc. 53, 150–188 (1974)] based on the EDMF of W. J. Stevens, G. Das, A. C. Wahl, D. Neumann, and M. Krauss [J. Chem. Phys. 61, 3686–3699 (1974)]. By shifting the WRR EDMF by 0.03 Bohr to larger r, it is possible to reproduce the accurate experimental value for the difference in dipole moments between the v = 0 and v = 1 levels measured using the molecular beam electric resonance technique. Following the theory of Mies (except that Hill and Van Vleck's intermediate coupling approximation is used), revised Einstein coefficients are tabulated for Δv = v′ – v″ ranging from the fundamental transition, Δv = 1 to the Δv = 5 overtone for v′ = 1–9, and J′ = 0.5–15.5 using the “shifted” WRR EDMF. Theoretical emission spectra are also presented, and the potential for OH involvement in the surface glow of space vehicles is briefly discussed.     

On the rotational intensity distribution in the a1Δg → X3Σg− magnetic dipole transition of oxygen molecule

The relative intensity distribution in the rotational structure of the a¹Δ_g → X³Σ_g⁻ magnetic dipole transition of molecular oxygen is examined. Use is made of experimental data obtained from the high-resolution (0.02 cm⁻¹) FTS recording of the 0-0 band published by C. Amiot and J. Verges (Canad. J. Phys. 59, 1391–1398 (1981)). Comparison of the experimental and theoretical intensities indicates that rotational linestrength formulas containing purely vibronic transition moments are inadequate and need to be supplemented by two additional parameters of rovibronic origin.     

Élaboration et caractérisation d'un biomatériau à base de phosphates de calcium

The tricalcium phosphate–fluorapatite composite has a good aptitude to sintering at 1300 °C, so a densification rate of about 90% was reached with 33.16 wt% of fluorapatite. At 1300 °C, the increase of the content of fluorapatite in the composite favours the formation of the α tricalcium phosphate phase. The ³¹P MAS-NMR analysis reveals the presence of three tetrahedral P sites for the tricalcium phosphate, whereas the fluorapatite possesses only one. At temperatures higher than 1300 °C, the densification is hindered by grain growth and the formation of large pores. To cite this article: F. Ben Ayed, J. Bouaziz, C. R. Physique 8 (2007).     

Line assignments and intensities of the ν2 + ν3 − ν2 band of 12CH4

As part of a comprehensive effort to compile line parameters of methane from 2400 to 3200 cm^?1, the P and R branches of the ν₂ + ν₃ ? ν₂ band of CH₄ at 3010 cm^?1 were assigned through upper state J = 9. The process utilized the analysis of ν₂ + ν₃ at 4544 cm^?1 by J. C. Hilico, J. Degni, J. P. Champion, and G. Guelachvili (J. Mol. Spectrosc.81, 277–302 (1980)) and the ν₂ levels derived from the infrared spectrum by Margolis (in preparation) to predict the positions of the hot band. Experimentally determined lower-state energies were used to confirm assignments, and line intensities of the 300 transitions assigned are observed on the order of 10^?3 cm^?2 atm^?1 or less.     

An ab Initio Study of the ÃΠ State and the ÃΠ←X?Σ Electronic Transition of MgNC

We use the RENNER program system (see, for example, P. Jensen, G. Osmann, and P. R. Bunker, in “Computational Molecular Spectroscopy” (P. Jensen and P. R. Bunker, Eds.), Wiley, Chichester, 2000, and references therein) to make a detailed calculation of the rovibronic energies in the first excited electronic state, òΠ, of the MgNC radical. This calculation is based on ab initio data (supplemented here with points for larger bending displacements from linearity) calculated at the level of MR-SDCI(+Q)/[TZ3P+f(Mg), aug-cc-pVQZ (N and C)] by T. E. Odaka, T. Taketsugu, T. Hirano, and U. Nagashima (J. Chem. Phys.115, 1349-1354 (2001)). These authors employed ab initio derived spectroscopic constants to calculate vibronic energies using perturbation expressions (J. T. Hougen and J. P. Jesson, J. Chem. Phys.38, 1524-1525 (1963)), and their results suggested that an observed vibronic band belonging to the òΠ←X?²Σ⁺ electronic transition (R. R. Wright and T. A. Miller, J. Mol. Spectrosc.194, 219-228 (1999)) should be reassigned. The present work confirms this conclusion, which is further substantiated by the rotational structures calculated in the vibronic states and by Franck-Condon theory predicting relative intensities.     

Molecular structure and centrifugal distortion constants of isocyanic acid from the microwave,millimeter wave,and far-infrared spectra

The pure rotational spectra of HNCO and DNCO were measured in the far-infrared region from 80 to 350 cm^?1 by a Fourier transform spectrometer with a resolution of 0.1 cm^?1. The ^rR_K branches were measured and assigned for HNCO from K = 1 to 6, and for DNCO from K = 3 to 8. The measured transition wavenumbers were analyzed together with the microwave and millimeter wave data reported by Hocking, Gerry, and Winnewisser [Can. J. Phys.53, 1869–1901 (1975)] and with the far-infrared data of Krakow, Lord, and Neely [J. Mol. Spectrosc.27, 148–176 (1968)] in the low-wavenumber region. The microwave and millimeter wave data of H¹⁵NCO, HN¹³CO, and HNC¹⁸O reported by Hocking et al. were reanalyzed assuming several centrifugal distortion constants to be identical with those of the normal species. The molecular structure of HNCO was reevaluated using a modified substitution method from the rotational constants obtained in this work. The molecule has a bent structure in a trans configuration with $\text{r}\text{(NH) = 0.995}\text{A}\text{?}$, $\text{r}\text{(NC) = 1.314}\text{A}\text{?}$, $\text{r}\text{(CO) = 1.668}\text{A}\text{?}$, ∠HNC = 123.9°, and ∠NCO = 172.6°.     

Organic photovoltaic materials and devices

Organic photovoltaic solar cells bere an important potential of development in the search for low-cost modules for the production of domestic electricity. We review the principles and techniques needed for their development: organic semiconductors, their transport properties and photophysical characteristics, photovoltaic molecule and polymer structures, device technologies, electrical and optical behaviour of the cells, state of the art, limitations and perspectives. Despite some recent record efficiencies, research on organic solar cells is still in its infancy when stability and efficiency have to be compared with the performances of silicon cells. A nominal 10% solar efficiency is the research target for the next few years. To cite this article: J.-M. Nunzi, C. R. Physique 3 (2002) 523–542.     

Electron spin resonance of Gd in the intermetallic compounds YCu,YAg, and LaAg: Wave vector dependence of the exchange interaction

The discrepancy between the Gd EPR g shift and linewidth in YCu, YAg, and LaAg is resolved using a wave vector dependent exchange parameter J(k,k'). Various experimentally observable quantities are related to J(k,k') using a partial wave expansion.     

Stresses in compressed bubble rafts

We present a simple geometric method to determine the stress field in a compressed bubble raft. We show that bubble rafts exhibit arches phenomena as do granular materials, and examine the relaxation of stresses following a T₁ transformation. To cite this article: C. Ybert, J.-M. di Meglio, C. R. Physique 3 (2002) 555–559.     

Ab initio properties of gaseous helium

Recent ab initio calculations of the interaction potential of helium, and the effects of the new potentials on the calculated properties of helium gas (density and acoustic virials, viscosity, and thermal conductivity) are reviewed. To cite this article: J.B. Mehl, C. R. Physique 10 (2009).     

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.     

Reduced effective Hamiltonians for degenerate vibrational states of methane-type molecules

The ambiguity of effective Hamiltonians for the fundamental degenerate states of the methane-type molecules is studied. The transformations of these Hamiltonians to reduced forms which include only empirically determinable parameters are suggested. The set of parameters fitted by Champion and Pierre for the ν₄ band of CH₄ (J. Mol. Spectrosc.79, 225–280 (1980)) is found to be related to the set of parameters of Husson and Poussigue (J. Phys.32, 859–865 (1971)) by the unitary transformation of the effective Hamiltonian.