A theoretical model for the interacting upper states of the ν1, ν3, 2ν2, ν2 + ν4, and 2ν4 bands in methane

The effective vibration-rotation Hamiltonians complete to fourth order in the Amat-Nielsen scheme for the upper states of the ν₁, ν₃, 2ν₂, ν₂ + ν₄, and 2ν₄ bands in methane are reviewed, and the major vibration-rotation interactions (H₃₀, $\text{H}\text{?}{}_{40}$, $\text{H}\text{?}{}_{21}$, $\text{H}{}_{31}$, $\text{H}\text{?}{}_{22}$) connecting the different vibrational states are discussed. Explicit matrix elements in a basis of harmonic oscillator-symmetric rotor basis functions are given for the purely vibrational terms and for the vibration-rotation interactions. Expressions for spectral intensities of infrared and Raman spectra are presented, and the selection rules and transition moment matrix elements are stated. A computer program is described which, incorporating all these features, can be used for prediction of infrared and Raman spectra and for determination of molecular constants from observed spectra by a least-squares routine. As an example the program is applied to the 2ν₄ isotropic Raman spectrum of ¹²CH₄, leading to a very good agreement between the experimental and calculated spectra.     

The ground state of methane 12CH4 through the forbidden lines of the ν3 band

High resolution spectra of the ν₃ band of methane, ¹²CH₄, were recorded by using a “third generation vacuum Fourier interferometer”; a large pressure range (from 0.009 to 10 Torr) with a sample path fixed at eight meters was used, enabling observation of transitions with intensity ratios as low as $\text{1}\text{10 000}$. More than 350 forbidden transitions of the ν₃ band, including about 125 transitions of the Q⁺ branch, were unambiguously identified. Of the 277 transitions retained for computations, one-hundred have 11 ≤ J ≤ 16. From combination difference relations using pairs of transitions having the same upper state energy level (forbidden-allowed and forbidden-forbidden pairs were used), 276 independent differences between ground state energy levels could be determined with uncertainties of about 0.001 cm^?1.These data yielded the following values for the ground state structure constants of ¹²CH₄ along with their standard deviations (in cm^?1): $\text{β}{}^{\mathrm{o}}\text{hc}\text{=5.2410356±0.0000096}$, $\text{γ}{}^{\mathrm{o}}\text{hc}\text{=(?1±0.00074) 10}{}^{\mathrm{?4}}$, $\text{π}{}^{\mathrm{o}}\text{hc}\text{=(5.78±0.18) 10}{}^{\mathrm{?9}}$, $\text{?}{}^{\mathrm{o}}\text{hc}\text{=(?1.4485±0.0023) 10}{}^{\mathrm{?6}}$, $\text{?}{}^{\mathrm{o}}\text{hc}\text{=(1.768±0.126) 10}{}^{\mathrm{?10}}$, $\text{ξ}{}^{\mathrm{o}}\text{hc}\text{=(?1.602±0.067) 10}{}^{\mathrm{?11}}$, Thus, for the first time, the scalar constant π⁰ has been evaluated and ir values have been obtained for the two tetrahedral constants ?⁰ and ξ⁰; furthermore, these values are in very good agreement with the ones recently determined from radiofrequency data, i.e., in cm^?1: $\text{?}{}^{\mathrm{o}}\text{hc}\text{=(?1.45061±0.00014) 10}{}^{\mathrm{?6}}$, $\text{?}{}^{\mathrm{o}}\text{hc}\text{=(1.7634±0.0068) 10}{}^{\mathrm{?10}}$, $\text{ξ}{}^{\mathrm{o}}\text{hc}\text{=(?1.5432±0.0040) 10}{}^{\mathrm{?11}}$ From these values, the 276 differences can be reproduced with an overall rms deviation equal to 0.0009 cm^?1.Finally, the ground state energies of ¹²CH₄ have been calculated for J ≤ 16.     

Strengths and lorentz broadening coefficients for spectral lines in the ν3 and ν2 + ν4 bands of 12CH4 and 13CH4

Line strengths and self- and nitrogen-broadened half-widths were measured for spectral lines in the ν₃ and ν₂ + ν₄ bands of ¹²CH₄ and ¹³CH₄ from 2870–2883 cm^?1 using a tunable diode laser spectrometer. From measurements made over a temperature range from 215 to 297 K, on samples of ¹²CH₄ broadened with N₂, we deduced that the average temperature coefficients n, defined as $\text{b}{}_{\mathrm{<mtext>L</mtext>}}{}^0\text{(T) = b}{}_{\mathrm{<mtext>L</mtext>}}{}^0\text{(T}{}_0\text{)(}\text{T}\text{T}{}_0\text{)}{}^{\mathrm{?n}}$, of the Lorentz broadening coefficients for the ν₃ and ν₂ + ν₄ bands of ¹²CH₄ were 0.97 ± 0.03 and 0.89 ± 0.04, respectively. A smaller increase is observed in line half-width with increasing pressure for E-species lines, for both self- and nitrogen-broadening, than for other symmetry species lines over the range of pressures measured, 70 to 100 Torr.     

Some effects of spin-orbit interaction on rotational levels and rotational line intensities in vibrationally unexcited 2A, 2E, and 2F electronic states of open-shell XY4 molecules

Rotational energy levels in vibronic ground states of ²A, ²E, and ²F electronic states of open-shell XY₄ molecules, as well as rotational line intensities for allowed transitions between such states, are discussed, including the effects of spin-orbit interaction and tetrahedral splittings. Jahn-Teller effects are assumed to be small, and are only taken into account implicitly, through their contributions to various parameters in the effective Hamiltonian. Qualitative information is obtained by considering several limiting-case coupling schemes among the electron spin angular momentum S, the electron orbital angular momentum L, and the pure rotational angular momentum R. These limiting cases are similar in spirit to Hund's coupling cases in diatomic molecules, but differ sufficiently from the latter to make detailed correspondences unhelpful. Quantitative information on rotational energy levels and line intensities is obtained numerically by diagonalizing a Hamiltonian matrix set up in a basis set characterized by uncoupled moleculefixed projections of S, L, and the total angular momentum J, and symmetrized so that all basis set functions belong to a definite species in the subgroup D_2d of the true point group T_d. Hamiltonian matrix elements are determined by ladder operator techniques. Three sample calculated spectra, corresponding to $\text{p(}{}^2\text{F}{}_2\text{)-s(}{}^2\text{A}{}_1\text{)}$, $\text{d(}{}^2\text{E)-p(}{}^2\text{F}{}_2\text{)}$, and $\text{d(}{}^2\text{F}{}_2\text{)-p(}{}^2\text{F}{}_2\text{)}$ are presented. As one might expect, when the spin-orbit constant A is set equal to zero, then both qualitative and quantitative aspects of the rotational-electronic problem in open-shell XY₄ molecules can be mapped easily onto discussions of the rotation-vibration problem from the CH₄ literature.     

Structure,vibrational study and conductivity of the trihydrated uranyl bis(dihydrogenophosphate): UO2(H2PO4)2·3H2O

The X-ray structure (293 K) of UO₂(H₂PO₄)₂·3H₂O has been refined (R = 0.062): M_r = 518g, space group: P2₁/c (Z = 4); $\text{a = 10.816(1)}\text{A}\text{?}$, $\text{b = 13.896(2)}\text{A}\text{?}$, $\text{c = 7.481(1)}\text{A}\text{?}$, β = 105.65(1)^°, $\text{V = 1082.7(2)}\text{A}\text{?}{}^3$; D_c = 3.17 Mg m^?3. The structure consists of infinite chains along the (101) axis with U atoms bridged by two H₂PO₄ groups. The U atom is surrounded by a pentagonal bipyramid of oxygen atoms, one of them being an equatorial water molecule. The cohesion between the chains is ensured by hydrogen bonds involving the two last water molecules. An assignment of IR and Raman bands with isotopic substitution spectra is proposed. A phase transition at 128 K was made evident by DSC and spectroscopy. The room-temperature phase is characterized by a high disorder of the OH bond orientation while in the low-temperature phase H₂O and POH species appear well oriented. The conductivity seems to occur by proton transfer and protonic-species rotation at the POH-water molecular interface between the chains. ac conductivity has been determined by means of the complex-impedance method ($\text{σ}{}_{\mathrm{<mtext>RT</mtext>}}\text{～ (3?12) × 10}{}^{\mathrm{?5}}\text{Ω}{}^{\mathrm{?1}}\text{cm}{}^{\mathrm{?1}}$; E ～ 0.20 eV).     

PAM analysis of the microwave spectra of thioacetic acid,CH3COSH and CH3COSD

The microwave spectra of two isotopic species of thioacetic acid, CH₃COSH and CH₃COSD, have been studied. Using the principal axis method (PAM), including terms through n = 6 in the perturbation series and the denominator correction, the spectra were analyzed and 45 lines for CH₃COSH and 40 lines for CH₃COSD were assigned. The parameters obtained by the least-squares analysis are A = 9913.29 ± 0.56 MHz, B = 4923.11 ± 0.23 MHz, C = 3354.60 ± 0.24 MHz, θ = 57.080 ± 0.030°, s = 6.2980 ± 0.0012, and I_α = 3.198 ± 0.020 amu$\text{A}\text{?}{}^2$ for CH₃COSH, and A = 9662.80 ± 0.78 MHz, B = 4810.74 ± 0.26 MHz, C = 3273.92 ± 0.18 MHz, θ = 55.097 ± 0.024°, s = 5.9742 ± 0.0016, and I_α = 3.171 ± 0.020 amu$\text{A}\text{?}{}^2$ for CH₃COSD. The barrier to internal rotation of the methyl group is V₃ = 222.6 ± 1.4 cal/mole for CH₃COSH and V₃ = 212.9 ± 1.4 cal/mole for CH₃COSD. The Stark effect measurements of A species transitions for CH₃COSH led to the dipole moment μ = 1.821 ± 0.013 D with the components μ_a = 0.191 ± 0.010 D and μ_b = 1.811 ± 0.013 D.     

Chemical diffusion in nonstoichiometric chromium sulfide,Cr2+yS3

Using the re-equilibration kinetic method the chemical diffusion coefficient in nonstoichiometric chromium sesquisulfide, Cr_2+yS₃, has been determined as a function of temperature (1073–1373 K) and sulphur vapour pressure (10?10⁴ Pa). It has been found that this coefficient is independent of sulphur pressure and can be described by the following empirical equation: $\text{D}\text{?}\text{Cr}{}_{\mathrm{2+y}}\text{S}{}_3\text{=50.86}\text{exp(-39070 cal/mole/}\text{RT)}\text{(cm}{}^2\text{s}{}^{\mathrm{?1)}}$. It has been shown that the mobility of the point defects inCr_2+yS₃ is independent of their concentration and that the self-diffusion coefficient of chromium in this sulfide has the following function of temperature and sulphur pressure: . (cm²s^?1).     

Ultraviolet absorption spectra of Zn2 and Cd2 in solid argon and krypton at 10 K

Zinc and cadmium atoms have been condensed with argon and krypton at 10 K. The most intense absorption is due to the ${}^1\text{P}{}_1\text{←}{}^1\text{S}{}_0$ atomic transition, and a weak band is due to the ${}^3\text{P}{}_1\text{←}{}^1\text{S}{}_0$ atomic absorption. Structured absorptions at 252 and 254 nm in solid argon and krypton with vibrational spacings of 140-120 cm^?1 are due to the ${}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{←}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ transition of Zn₂. Similar 273 and 277 nm absorptions with 110-90 cm^?1 vibrational spacings are due to Cd₂ in solid argon and krypton, respectively.     

Absorption spectra of Ni2+ in (NH4)2Mg(SO4)2·6H2O and Co2+ in Na2Zn(SO4)2·4H2O

Optical absorption spectra of Ni²⁺ in (NH₄)₂Mg(SO₄)₂·6H₂O and Co²⁺ in Na₂Zn(SO₄)₂·4H₂O single crystals have been studied at room and liquid nitrogen temperatures. From the nature and position of the observed bands, a successful interpretation could be made assuming octahedral symmetry for both the ions in the crystals. The splitting observed for ${}^3\text{T}{}_{\mathrm{1g}}\text{(F)}$ band in Ni²⁺ and ${}^4\text{T}{}_{\mathrm{2g}}\text{(F)}$ band in Co²⁺ at liquid nitrogen temperature have been explained as due to spin-orbit interaction. The extra band observed at 16,325 cm^-1 in the case of Ni²⁺ at low temperature has been interpreted to be the superposition of vibrational mode of SO^2-₄ radical on ${}^3\text{T}{}_{\mathrm{1g}}\text{(F)}$ band. The observed band positions in both the crystals have been fitted with four parameters B, C, Dq and ζ.     

Electrical transport and magnetic properties of Nd2(WO4)3

Measurements of the molar magnetic susceptibility (X_m) of a powdered sample of Nd₂(WO₄)₃ in the temperature range 300–900 K, and the electrical conductivity (σ) and dielectric constant (?$\text{)}\text{?}$ of pressed pellets of the compound in the temperature range 4.2–1180 K are reported. X_m obeys the Curie-Weiss law with a Curie constant C= 3.13 K/mole, a paramagnetic Curie temperature θ= ?60 K and a moment of Bohr magnetons, p= 3.49 for the Nd³⁺ ion. The electrical conductivity data can be explained in terms of the usual band model and impurity levels. Both the σ and ?$\text{\$}\text{?}$data indicate some sort of phase transition round 1025 K. The conductivity follows Mott's law $\text{σ = A exp (?B/T}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}\text{)}$ in the temperature range $\text{200 < T < 3000}\text{K with}\text{B = 45.00 (}\text{K}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}\text{and}\text{A = 1.38 × 10}{}^{\mathrm{?5}}\text{Ω}{}^{\mathrm{?1}}\text{cm}{}^{\mathrm{?1}}$. The dielectric constant increases slowly up to 600 K, as is usual for ionic solids. The increase becomes much faster above 600 K, which is attributed to space-charge polarization of thermally generated charge carriers.     

Hole mobility in evaporated layers of As2S3.CdI2

The hole drift mobility in As₂S₃.CdI₂ has been determined using Spear's method. The room-temperature value is 10^?4$\text{cm}{}^2\text{Vs}$, the activation energy 0.2 eV. The hole yield appears to be controlled by geminate recombination.     

Tabulation of hyperfine splittings in rotational F1 and F2 levels of the ground vibrational state of 12CH4 for J ≤ 20

To a good approximation, hyperfine splittings for F₁ and F₂ rotational levels of the ground vibrational state of ¹²CH₄ depend linearly on three hyperfine interaction parameters. Coefficients in these linear expressions have been computed in a relatively simple manner and tabulated for levels with 1 ≤ J ≤ 20. The hyperfine pattern for the $\text{J = 7 F}{}_2{}^{\mathrm{(2)}}$ level computed from these expressions using values for the three hyperfine interaction parameters reported recently by Yi, Ozier and Ramsey (1) agrees well with the pattern obtained from new HeNe laser measurements of Hall and Bordé (2) on the $\text{P(7) F}{}_2{}^{\mathrm{(2)}}$ line of the ν₃ band of methane.     

Ni2+ emission in MgO,KMgF3, KZnF3 and MgF2

The emission of Ni²⁺ ions in MgO, KMgF₃, KZnF₃ and MgF₂ crystals has been investigated. The fine structure on the bands at about 20 000 cm^-1 and 13 000 cm^-1 has been studied in detail and from this and the excitation spectra these bands are assigned to ${}^1\text{T}{}_{\mathrm{2g}}\text{→}{}^3\text{A}{}_{\mathrm{2g}}$ and ${}^1\text{T}{}_{\mathrm{2g}}\text{→}{}^3\text{T}{}_{\mathrm{2g}}$ transitions respectively.     

High-resolution infrared spectrum of the ν2 and ν8 bands of CH2D2

A high-resolution infrared spectrum of methane-d₂ has been measured in the C-D stretching band region (2025–2435 cm^?1). Rotational structures of the ν₂ and ν₈ bands have been assigned by use of the ASSIGN-diagram method, and the c-type Coriolis interaction between ν₂ and ν₈ has been analyzed. The band origins, ν₂ = 2203.22 ± 0.01 cm^?1 and ν₈ = 2234.70 ± 0.01 cm^?1, the rotational constants and the centrifugal distortion constants for the two bands, and the Coriolis coupling constant, $\text{∥;ξ}{}_{28}{}^{\mathrm{c}}\text{∥; = 0.182 ± 0.015}\text{cm}{}^{\mathrm{?1}}$, have been determined.     

Etude du comportement non-debye des courant de depolarisation stimules thermiquement (TSDC) dans le Ce2(S04)3 · 9H2O monocristallin

TSDC (thermally stimulated depolarization current) measurements on Ce₂(SO₄)₃· 9H₂O single crystals show non-Debye behaviour An analytical study has been made on the basis of the well-known general kinetics analysis of thermally stimulated processes (TSPs) involving the kinetic order q, related to dipolar interactions We define a complex relaxation time, $\text{τ = (}\text{P}{}_0\text{P}\text{)}{}^{\mathrm{q?1}}\text{exp}\text{(}\text{E}\text{kT}\text{)}$, that is, a function q and the dipolar concentration Some experimental evidence, which shows the influence of the dipolar concentration on the characteristic relaxation parameters, is obtained.     

Laser-excited phosphorescence spectrum of C3S2 in an Ar matrix

The phosphorescence spectrum of C₃S₂ was observed in a low-temperature Ar matrix with excitation of an Ar⁺ laser. The spectrum consists of a very strong 0-0 band at 18 287 cm^?1 and well-resolved progressions in the ν₂, ν₅, ν₆, and ν₇ vibrations. Side bands were found on the high-energy sides of some transitions. The separation between the main and side bands is 23 cm^?1. Polarization analysis suggests that C₃S₂ is linear symmetric in the Phosphorescent state as in the ground electronic state. On the basis of symmetry considerations and a qualitative evaluation of spin-orbit coupling, the phosphorescent state is assigned to ³Σ_u^? with Σ_u⁺ and Π_u components split by spin-spin interaction. The Σ_u⁺ level is lower than the Π_u one by 23 cm^?1 and the main and side band emissions start from the Σ_u⁺ and Π_u levels, respectively. The Σ_u⁺ component seems to acquire allowed character from a ¹Σ_u⁺ state by spin-orbit coupling and from bent ${}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{?}}\text{(}{}^1\text{B}{}_2\text{)}$ and ${}^1\text{Δ}{}_{\mathrm{g}}\text{(}{}^1\text{A}{}_1\text{+}{}^1\text{B}{}_2\text{)}$ states by ν₅ vibronic coupling. Mixing of the Σ_u⁺ and Π_u components through ν₅ is responsible for most of the side bands. The ν₅ frequency is estimated to be 160 ± 20 cm^?1 in the ³Σ_u^? state from the intensities of ν₅ progression bands and from the ground-state frequency, 411 cm^?1.     

The bending vibration bands ν4 and ν5 of HCCI

The bending vibration bands ν₄ and ν₅ of HCCI were studied. From the observed rotational structure the rotational constant B₀ and the centrifugal distortion constant D₀ were obtained. The results were B₀ = 0.105968(7) cm^?1 and D₀ = 1.96(7) × 10^?8 cm^?1 from ν₄ and B₀ = 0.105948(8) cm^?1 and D₀ = 1.96(11) × 10^?8 cm^?1 from ν₅. The structure of the hot bands 2ν₅(Δ) ← ν₅(Π) and 3ν₅(φ) ← 2ν₅(Δ) was also resolved and hence the values α₅ = ?3.033(8) × 10^?4 cm^?1 and q₅ = 9.3(3) × 10^?5 cm^?1 could be derived. The other most intense hot bands following ν₅ could be explained in terms of the Fermi diads $\text{ν}{}_3\text{2ν}{}_5{}^0$ and $\text{ν}{}_3\text{+}\text{ν}{}_5{}^{\mathrm{\pm 1}}\text{3ν}{}_5{}^{\mathrm{\pm 1}}$. Of the numerous hot bands accompanying ν₄, only those between different excited states of ν₄ could be assigned. Then estimates for α₄ and q₄ were also obtained. In addition, several vibrational constants were derived.     

Polarization spectroscopy of the E0g+-B0u+ band system of Br2

The E-B (0_g⁺-0_u⁺) band system of Br₂ has been investigated at Doppler-limited resolution using polarization labeling spectroscopy. Merged E state data for the three naturally occurring isotopes in the range v_E = 0–16, expressed in terms of the constants for ⁷⁹Br₂, are (in cm^?1) Y_0,0 = 49 777.962(54), Y_1,0 = 150.834(22), Y_2,0 = ?0.4182(28), Y_3,0 = 6.6(11) × 10^?4, Y_0,1 = 4.1876(28) × 10^?2, Y_1,1 = ?1.607(16) × 10^?4, and Y_0,2 = 1.39(39) × 10^?8. The bond distance is $\text{r}{}_{\mathrm{<mtext>e</mtext>}}\text{= 3.194}\text{A}\text{?}$, and the diabatic dissociation energy to $\text{Br}{}^{\mathrm{+}}\text{(}{}^3\text{P}{}_2\text{) +}\text{Br}{}^{\mathrm{?}}\text{(}{}^1\text{S}{}_0\text{)}\text{is 34 700 cm}{}^{\mathrm{?1}}$.     

Thermodynamics and mobility of copper in bornite (Cu5FeS4)

The thermodynamics and kinetics of copper transport in bornite (Cu₅FeS₄) have been investigated. Coulometric titration experiments on single-crystal and hot-pressed polycrystalline materials indicated a restricted range of composition for substoichiometric single-phase bornite, with materials of copper contents less than Cu_4.95FeS₄ existing as a two-phase mixture of bornite and a chalcopyrite-type phase (Cu₃FeS₄). For the polycrystalline material the van der Pauw technique was used to obtain the electronic conductivity (σ_e) as a function of temperature and a six-point cell was used to measure the ionic conductivity (σ_i) as a function of composition. Typical results obtained at 170°C were $\text{σ}{}_{\mathrm{e}}\text{=230 Ω}{}^{\mathrm{?1}}\text{m}{}^{\mathrm{?1}}$, $\text{σ}{}_{\mathrm{i}}\text{= 11 Ω}{}^{\mathrm{?1}}\text{m}{}^{\mathrm{?1}}$, activation energy for electronic conduction = 15 kJ mol^?1. The transient behaviour of the electronic and ionic probe voltages during the six-point cell experiments have been tentatively interpreted in terms of the chemistry of the copper-iron sulphides.     

Magnetic circular dichroism of transition metal ions in solids—II K2NaGaF6: Cr3+

The absorption and MCD spectra of the ${}^4\text{A}{}_{\mathrm{2g}}\text{→}{}^4\text{T}{}_{\mathrm{2g}}$, ${}^4\text{A}{}_{\mathrm{2g}}$, ${}^4\text{A}{}_{\mathrm{2g}}\text{→}{}^4\text{T}{}_{\mathrm{1g}}{}^{\mathrm{a}}$ and ${}^4\text{A}{}_{\mathrm{2g}}\text{→}{}^4\text{T}{}_{\mathrm{1g}}{}^{\mathrm{b}}$ spin-allowed transitions of Cr³⁺ in K₂NaGaF₆ are reported. It is shown that transitions to the ${}^4\text{T}{}_{\mathrm{1g}}$. states are induced by T_1u vibratio the other spin-allowed transition, ${}^4\text{A}{}_{\mathrm{2g}}\text{→}{}^4\text{T}{}_{\mathrm{2g}}$, there are three competing intensity mechanisms: electric dipole induced by T_1u vibrations, electric dipole induced by T_2u vibrations and magnetic dipole, and an estimate is made of the relative importance of these. The magnetic dipole ${}^4\text{A}{}_{\mathrm{2g}}\text{→}{}^2\text{E}{}_{\mathrm{g}}$ zero-phonon line is observed to be accompanied by a vibrational sideband for which the coupling is predominantly with T_2u vibrations. Other weak transitions are observed in MCD spectra and their origin briefly discussed.