Rotational Analysis of the ÃA1-X?A1 Band System of Yttrium Dicarbide, YC2

The 000-000 and 3¹₀ bands of the 775-nm electronic transition of YC₂(òA₁←X?²A₁) have been studied at high resolution, using the laser-induced fluorescence from a supersonic jet expansion. Three types of experiment have been carried out. First, the complete rotational and hyperfine structures of the two bands were recorded. To measure the small asymmetry splittings in the K=2 levels of the X?²A₁ state, portions of the b-type 3¹₀ band were then recorded in the presence of a weak static electric field. Finally, a number of pure rotational transitions between the K=0 levels of the ground state were recorded by pump/probe microwave optical double resonance. A few small rotational perturbations occur in the upper electronic state but, omitting the perturbed lines, the combined data sets could be modeled using an effective Hamiltonian operator appropriate for the rotation, electron spin, and hyperfine structure of a rigid asymmetric top molecule. The molecule is confirmed as being “T-shaped,” where the Y atom is bonded to the side of a C₂ group; the rotational constants determined are for the òA₁, 3¹ level, A=1.76128, B=0.189949, C=0.170056 cm⁻¹, and for the X?²A₁, v=0 level, A=1.742731, B=0.201947, C=0.181285 cm⁻¹. Allowing for electron orbital corrections to the rotational constants, the geometrical structures are found to be òA₁ state, r (Y-C)=2.2795 Å, r (C-C)=1.2630 Å, ∠C-Y-C=32.17°; X?²A₁ state, r (Y-C)=2.1946 Å, r (C-C)=1.2697 Å, ∠C-Y-C=33.63°. A molecular orbital diagram is given for the states of YC₂ and the interpretation of the electron spin and hyperfine parameters is discussed.     

Rotationally resolved electronic spectrum of propadienylidene

The rotationally resolved electronic spectrum of a vibrational band in the transition of the cumulene carbon chain C₃H₂ was measured in the 625 nm region in a supersonic discharge using cw cavity ring down spectroscopy. The rotational structure was analysed using a conventional Hamiltonian for an asymmetric top molecule, and the constants A′, B′, and C′ in the upper state were determined. The observed band is assigned to a combination of a₁ and b₂ vibrations with the frequency around 2000 cm⁻¹. The geometries in the ¹A₁, ¹A₂, ¹B₁ states and the intersection point between the latter two were obtained using ab initio calculations. The effective structure in the measured vibrational level of the ¹A₂ state was inferred from the determined constants.     

Fourier transform emission spectroscopy of Δv = 2 sequence bands of the CO molecule in the ground electronic state

High-resolution emission spectroscopy of rovibrational Δv = 2 sequence bands is carried out from a low-pressure discharge through pure CO gas. The effect of rare gases on the production of the Δv = 2 sequence bands is also studied. The v′ → (v′-2) sequence bands up to v′ = 17 are observed. Bands involving 8 ? v′ ? 17 in the Δv = 2 sequence are reported for the first time. The 16-14 and 17-15 bands could be observed only in the presence of xenon as a buffer gas. Accurate molecular constants (T, B, D, H) for different vibrational states of the ground electronic state of ¹²C¹⁶O are determined from a global fit.     

High-precision frequency measurements of the ν1 + ν3 combination band of C2H2 in the 1.5 μm region

A pair of 1.5 μm semiconductor laser frequency standards have been developed for optical telecommunications use, stabilised to transitions of ¹²C₂H₂ and ¹³C₂H₂, using cavity-enhanced Doppler-free saturation absorption spectroscopy. The absolute frequencies of 41 lines of the ν₁ + ν₃ band of ¹²C₂H₂, covering the spectral region 1520-1545 nm, have been measured by use of a passive optical frequency comb generator, referenced to ¹³C₂H₂ transitions of known frequency. The mean experimental uncertainties (coverage factor k = 1) of the frequency values are 3.0 kHz (type A) and 10 kHz (type B). Improved values of the band origin ν₀, rotational constants B′ and B″, and centrifugal distortion coefficients D′, D″, H′, and H″ are presented.     

Rotationally Resolved REMPI Spectra of CaH in a Molecular Beam

Rotationally resolved spectra of the CaH radical using a supersonic molecular beam are reported. Thus, high energy resolution of the (1+1′) REMPI spectra corresponding to the A←X and B←X electronic transitions were measured which allowed for the first time a clear and precise analysis of the low rotational part (J≤7) of the CaH spectrum. A comparison with previous studies revealed that the commonly accepted energy separation between the two band heads of B−X (v′=1, v′=0) of 10 cm⁻¹ is not correct. A value of ca. 1.6 cm⁻¹ was found to be more realistic. On the other hand, the present study confirmed that the perturbation appears only for v′=1, N′>3 of the B state.     

The BΣ state of the SO radical

Spectra of the B³Σ⁻- X³Σ⁻ transition in SO above the first dissociation limit are recorded using degenerate four wave mixing. These spectra are combined with earlier work involving laser induced fluorescence, absorption spectra and Fourier transform emission spectra, to enable a rotational analysis and deperturbation of vibrational levels of the B state up to v′ = 16. Numerous perturbations were noted within the B³Σ⁻ state, and the origin of these is discussed. In a number of cases, these perturbations can be attributed to interactions with specific other electronic states of SO, such as A³Π, C³Π, d¹Π, and A″ ³Σ⁺.     

Elastic constants of solids and fluids with initial pressure via a unified approach based on equations-of-state

The second and third-order Brugger elastic constants are obtained for liquids and ideal gases having an initial hydrostatic pressure p₁. For liquids the second-order elastic constants are C₁₁ = A + p₁, C₁₂ = A − p₁, and the third-order constants are C₁₁₁ = −(B + 5A + 3p₁), C₁₁₂ = −(B + A − p₁), and C₁₂₃ = A − B − p₁, where A and B are the Beyer expansion coefficients in the liquid equation of state. For ideal gases the second-order constants are C₁₁ = p₁γ + p₁, C₁₂ = p₁γ − p₁, and the third-order constants are C₁₁₁ = −p₁(γ² + 4γ + 3), C₁₁₂ = −p₁(γ² − 1), and C₁₂₃ = −p₁ (γ² − 2γ + 1), where γ is the ratio of specific heats. The inequality of C₁₁ and C₁₂ results in a nonzero shear constant C₄₄ = (1/2)(C₁₁ − C₁₂) = p₁ for both liquids and gases. For water at standard temperature and pressure the ratio of terms p₁/A contributing to the second-order constants is approximately 4.3 × 10⁻⁵. For atmospheric gases the ratio of corresponding terms is approximately 0.7. Analytical expressions that include initial stresses are derived for the material ‘nonlinearity parameters’ associated with harmonic generation and acoustoelasticity for fluids and solids of arbitrary crystal symmetry. The expressions are used to validate the relationships for the elastic constants of fluids.     

ESR and optical study of Mn doped potassium hydrogen sulphate

The ESR spectrum of Mn²⁺ doped potassium hydrogen sulphate at liquid nitrogen temperature (77 K) has been analyzed and site of entered Mn²⁺ in the lattice has been discussed. The values of the zero field parameters that give good fit to the observed ESR spectra have been obtained. The obtained g, A, B, D, E and a values are 2.0002, 66×10⁻⁴ cm⁻¹, 26×10⁻⁴ cm⁻¹, 59×10⁻⁴ cm⁻¹, 32×10⁻⁴ cm⁻¹ and −8×10⁻⁴ cm⁻¹, respectively. The percentage of covalency of the metal-ligand bond has also been estimated. From the optical absorption study at room temperature, the distortion has been suggested. The observed bands are assigned as transitions from the ⁶A_1g(S) ground state to various excited quartet levels of Mn²⁺ ion in a cubic crystalline field. The electron repulsion and crystal field parameters B, C, Dq and α providing good fit to the observed optical spectra have been evaluated and the values obtained for the parameters are B=627 cm⁻¹, C=2580 cm⁻¹ , Dq=790 cm⁻¹ and α=76 cm⁻¹.     

Determination of the spin-spin centrifugal distortion parameters for deuterated selenoformaldehyde in its first excited triplet state

Recently-formulated centrifugal distortion corrections to the spin-spin Hamiltonian have been used to analyse the first excited triplet state (ã³A₂) of deuterated selenoformaldehyde. By including six spin-spin centrifugal distortion parameters, it is possible to account for the energy levels of this state using a single set of three rotational constants, A, B, and C, where previously nine spin-dependent parameters were required.     

Direct observation of the D′ 2g(P2)-A′ Π(2u) system for Cl2 by laser induced fluorescence spectroscopy: Determination of the absolute position of the A′ state

In a discharged supersonic jet of Cl₂, transitions of the D′ 2_g(³P₂)-A′ ³Π(2_u) system for ³⁵Cl₂ were observed directly by laser induced fluorescence spectroscopy. By a discharge in Cl₂, the Cl₂ molecules were populated into the A′ state, which is a metastable and optically forbidden state, from the state. An ultraviolet laser radiation excites the molecules to the D′ ion-pair state. A set of Dunham parameters for the A′ state is determined from a global least-squares fitting for 59 vibronic bands with v″ = 0-7. In the fitting, the previously reported data, T(v) and B(v) for the v = 14 and 15 bands of the A′ state [T. Ishiwata, A. Ishiguro, K. Obi, J. Mol. Spectrosc. 147 (1991) 300-320], were included. Y₀₀ = 57295.723(5) cm⁻¹ of the D′ state [J.-H. Si, T. Ishiwata, K. Obi, J. Mol. Spectrosc. 147 (1991) 334-345] was also included in the global fitting in order to determine the absolute position of the A′ state. The determined parameters of the A′ state are Y₀₀ = 17171.506(14), Y₁₀ = 255.915(85), Y₂₀ = −4.465(70), Y₃₀ = −8.7(23) × 10⁻², Y₄₀ = 6.3(35) × 10⁻³, Y₅₀ = −4.9(26) × 10⁻⁴, Y₆₀ = 1.43(69) × 10⁻⁵, Y₀₁ = 0.16282(15), Y₁₁ = −2.363(68) × 10⁻³, Y₂₁ = −5.01(93) × 10⁻⁵, and Y₃₁ = −3.01(36) × 10⁻⁶ (in cm⁻¹ and one standard deviations of the fit in parentheses). The absolute position of the A′ state is determined with good accuracy.     

EPR and optical study of Mn doped ammonium oxalate monohydrate

Studies on fine and hyperfine structures of paramagnetic resonance spectra in single crystals of Mn²⁺: ammonium oxalate monohydrate are reported. As sufficient numbers of lines were not obtained at room temperature, measurements have been done at liquid nitrogen temperature and at the frequency of X-band. The Mn²⁺ spin Hamiltonian parameters have been evaluated employing a large number of resonant line positions observed for various orientations of the external magnetic field and the surrounding crystalline field has been discussed. The values of the zero field parameters that give good fit to the observed EPR spectra have been evaluated. The values obtained for g, A, B, D, E and a are 2.0002±0.0002, (100±2)×10⁻⁴, (79.5±2)×10⁻⁴, (257±2)×10⁻⁴, (85±2)×10⁻⁴ and (−18±1)×10⁻⁴ cm⁻¹, respectively. The percentage of covalency of the metal-ligand bond is also determined. The optical absorption study has been done at room temperature. The observed bands are assigned as transitions from the ⁶A_1g(S) ground state to various excited quartet levels of Mn²⁺ ion in a cubic crystalline field. The electron repulsion parameters (B and C), the crystal field splitting parameter(Dq) and the Trees correction (α) providing good fit to the observed optical spectra have been estimated and the values obtained for the parameters are B=897, C=2144, Dq=910 and α=76 cm⁻¹.     

The millimeter wave spectrum of the CO dimer

The millimeter wave spectrum of the isotopically substituted CO dimer, (¹³C¹⁶O)₂, has been studied for the first time, confirming and extending a recent infrared study. Eighty-seven transitions in the 77-180 GHz region have been assigned and analyzed in terms of a model-independent term value scheme involving 57 rotational levels with J=0-8. The levels can be classified into 7 “stacks” which have symmetry classifications of either A⁻/B⁺ or A⁺/B⁻ and K-values of either 0 or 1. For the normal isotope, symmetry and nuclear spin statistics cause alternate rotational levels to be missing, but for (¹³C¹⁶O)₂ all levels are present with an intensity alternation of 1:3 between A and B symmetries. The four A⁻/B⁺ stacks have not previously been observed, and the lowest of them establishes the tunneling splitting of (¹³C¹⁶O)₂ to be 3.769 cm⁻¹, slightly larger than the (¹²C¹⁶O)₂ value of 3.731 cm⁻¹. A large amount of precise experimental data is now available for the CO dimer, which should lead to greater theoretical insight into its structure and tunneling dynamics.     

EPR and optical absorption study of Cr-doped ammonium oxalate monohydrate single crystals

The electron paramagnetic resonance (EPR) study of the Cr³⁺-doped ammonium oxalate monohydrate (AOM) single crystal is done at room temperature. Two magnetically inequivalent sites for chromium are observed. The hyperfine structure for Cr⁵³ isotope is also obtained. The spin Hamiltonian parameters are evaluated as: D=(309±2)×10⁻⁴ cm⁻¹, E=(103±2)×10⁻⁴ cm⁻¹, g=1.9820±0.0002, A=(161±2)×10⁻⁴ cm⁻¹ for site I and D=(309±2)×10⁻⁴ cm⁻¹, E=(103±2)×10⁻⁴ cm⁻¹, g=1.9791±0.0002, A=(160±2)×10⁻⁴ cm⁻¹ for site II, respectively. On the basis of EPR data the site symmetry of Cr³⁺ doped single crystal is discussed. The optical absorption spectra are recorded in 195-925 nm wavelength range at room temperature. The energy values of different orbital levels are determined. On the basis of EPR and optical data, the nature of bonding in the crystal is discussed. The values of different parameters are B=803, C=3531, D_q=2208 cm⁻¹, h=0.59 and k=0.21, where B and C are Racah parameters, D_q is crystal field parameter and h and k are nephelauxetic parameters, respectively.     

Centrifugal distortion analysis of the rotational spectrum of aziridine: Comparison of different Hamiltonians

Previous measurements of rotational spectrum of aziridine up to 1.85 THz have been supplemented by new data in 225-660 GHz frequency range. A total of 1465 transitions (915 of them are newly assigned ones) with maximum values of J = 59 and K_c = 50 were fit to a standard Watson Hamiltonian using the S- and A-reductions and the representations I^r and III^r. Although aziridine is an asymmetric oblate top, the combination (A, III^r) gives the worst results. From the point of view of the convergence of the Hamiltonian, the best results are obtained with the combination (S, III^r). It is explained that the failure of the combination (A, III^r) is due to the large value of the parameter σ=(2C-A-B)/(A-B) which makes some sextic centrifugal distortion constants much too large impeding the convergence of the Hamiltonian. It is also shown that the calculation of the centrifugal distortion constants from a force field is sometimes an ill-conditioned operation. Finally, the use of a non-reduced Hamiltonian (with six quartic centrifugal distortion constants) was successful in the particular case thanks to the method of predicate observations.     

Spin substructure of space-time

In a spin space, with noncommutative spinorial coordinatesC ^A which satisfyx ^AB =1/2{C ^A ,C ^*B }, we investigatex-dependent spin coordinate transformations which correspond to a local fermi-bose symmetry. A concept of a spin vector corresponding to these local transformations is established, and spin space is provided with a spinorial vierbein field which determines non-nil-potent line and volume elements which are direct generalizations of the conventional relativistic ones.     

Single crystal EPR and optical absorption study of Cr doped l-histidine hydrochloride monohydrate

EPR study of the Cr³⁺ ion doped l-histidine hydrochloride monohydrate single crystal is done at room temperature. Two magnetically inequivalent interstitial sites are observed. The hyperfine structure for Cr⁵³ isotope is also obtained. The zero field and spin Hamiltonian parameters are evaluated from the resonance lines obtained at different angular rotations and the parameters are: D=(300±2)×10⁻⁴ cm⁻¹, E=(96±2)×10⁻⁴ cm⁻¹, g_x=1.9108±0.0002, g_y=1.9791±0.0002, g_z=2.0389±0.0002, A_x=(252±2)×10⁻⁴ cm⁻¹, A_y=(254±2)×10⁻⁴ cm⁻¹, A_z=(304±2)×10⁻⁴ cm⁻¹ for site I and D=(300±2)×10⁻⁴ cm⁻¹, E=(96±2)×10⁻⁴ cm⁻¹, g_x=1.8543±0.0002, g_y=1.9897±0.0002, g_z=2.0793±0.0002, A_x=(251±2)×10⁻⁴ cm⁻¹, A_y=(257±2)×10⁻⁴ cm⁻¹, A_z=(309±2)×10⁻⁴ cm⁻¹ for site II, respectively. The optical absorption studies of single crystals are also carried out at room temperature in the wavelength range 195-925 nm. Using EPR and optical data, different bonding parameters are calculated and the nature of bonding in the crystal is discussed. The values of Racah parameters (B and C), crystal field parameter (Dq) and nephelauxetic parameters (h and k) are: B=636, C=3123, Dq=2039 cm⁻¹, h=1.46 and k=0.21, respectively.     

Relationship between the thermal expansion coefficient, plasmon energy, and bond length of ternary chalcopyrite semiconductors

A simple relation between the average bond length and plasmon energy, that is, d=15.30(?ω_p)^−2/3, has been proposed for A^IIB^IVC^V₂ and A^IB^IIIC^VI₂ chalcopyrite semiconductors. The average linear thermal expansion coefficient (α_L) of these semiconductors has been calculated using plasmon energy data. The linear expansion coefficients (α_a) and (α_c) of the lattice parameters a and c, respectively, have also been calculated. The calculated values of d, α_L, α_a and α_c have been compared with the experimental values and the values reported by different workers. A fairly good agreement has been obtained between them.     

Conventional and inverse magnetocaloric effects,and critical behaviors in Ni43Mn46Sn8In3 alloy

A systematic study of the conventional and inverse magnetocaloric effects, and critical behaviors in an alloy ingot of Ni₄₃Mn₄₆Sn₈In₃ has been performed. Our results reveal the sample exhibiting structural and magnetic phase transitions at temperatures T_C^M = 166 K (T_C of the martensitic phase), T_M–A = 260 K (the martensitic-to-austenitic phase transformation) and T_C^A = 296 K (T_C of the austenitic phase). The large values of refrigerant capacity (RC) around T_M–A and T_C^A are found to be RC_M–A = 172.6 and RC_A = 155.9 J kg⁻¹, respectively, under an applied field change of 30 kOe. Our critical analyses near the T_C^M and T_C^A reveal that a coexistence of the long- and short-range ferromagnetic order in the martensitic phase, while the long-range ferromagnetic order exists in the austenitic phase. Interestingly, at around T_C^A, the maximum magnetic entropy change (|ΔS_max|) versus magnetic field H obeys a power law, |ΔS_max| = a·Hⁿ, where the exponent n is found to be about 0.66.     

Painlevé analysis and integrability of the damped anharmonic oscillator equation

The Painlevé analysis is applied to the anharmonic oscillator equation . The following three integrable cases are identified: (i)C=0,d ²=25A/6,A>0,B arbitrary, (ii)d ²=9A/2,B=0,A>0,C arbitrary and (iii)d ²=−9A/4,C=2B ²/(9A),A<0,C<0,B arbitrary. The first two integrable choices are already reported in the literature. For the third integrable case the general solution is found involving elliptic function with exponential amplitude and argument.