Molecular structure and puckering potential of gas-phase 1-pyrroline as determined by microwave and infrared spectroscopy

The microwave spectrum of 1-pyrroline has been measured from 8 to 48 GHz. The transitions have been assigned to those of the ground state and the four lowest excited states of the ring-puckering vibration of monomer, which is a five-membered ring molecule with one CN double bond. The trimer, which exists in the liquid phase, has not been detected in the gas phase. The geometrical structure of the monomer has been estimated by an ab initio calculation and the trimer by a molecular mechanics calculation. The former is consistent with the experimental rotational constants. A gas-phase infrared spectrum has also been measured, and the ring-puckering potential has been determined by an analysis of the combination bands of the ring-puckering mode and the ring-stretching modes. The potential is described using a puckering coordinate, z, as V(z) = az² + bz⁴, where $\text{a = ?3.358(16) × 10}{}^4\text{cm}{}^{\mathrm{?1}}\text{A}\text{?}{}^{\mathrm{?2}}$ and $\text{b = 1.345(9) × 10}{}^6\text{cm}{}^{\mathrm{?1}}\text{A}\text{?}{}^{\mathrm{?4}}$; these values are intermediate of the corresponding values for cyclopentene and 1-pyrazoline. The nuclear quadrupole coupling constants, χ_aa = ?4.39(10), χ_bb = 1.04(10), and χ_cc = 3.35(10) MHz, have been determined by an analysis of well-resolved hyperfine splittings. These constants have been reproduced by an ab initio calculation with a 4-31G(N¹) basis set.     

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 $\text{Br}{}^{\mathrm{+}}\text{(}{}^3\text{P}{}_2\text{) +}\text{Br}{}^{\mathrm{?}}\text{(}{}^1\text{S}{}_0\text{)}\text{is 34 700 cm}{}^{\mathrm{?1}}$.     

Surface temperature modulation in molecular beam relaxation spectrometry applied to catalytic decomposition of CH3OH on NiO

A new modification of molecular beam relaxation spectrometry (MBRS) of surface processes is described making use of partial modulation in order to study nonlinear processes: a constant particle beam is directed towards the catalyst surface, the surface temperature is modulated due to absorption of a modulated beam of UV light, reaction products are analyzed by use of phase sensitive mass spectrometric detection. The application of the method is shown by a study of catalytic decomposition of methanol on polycrystalline NiO. Formation of CO was found to be a monomolecular, formation of H₂ and H₂O bimolecular processes. The resulting mechanism may be described as follows:

Rate constants in dependence from surface temperature T₀ are η = 1.8 × 10³$\text{exp(?}\text{46}\text{RT}{}_{\mathrm{o}}\text{kJ}\text{mol}\text{)}$; k_d1 = 1.8 × 10¹⁰$\text{exp(?}\text{92}\text{RTl}{}_0\text{kJ}\text{mol}\text{)}$ s^?1; k_d2 = 1.2 × 10^?2$\text{exp (?}\text{88}\text{RT}{}_0\text{kJ}\text{mol}\text{)}$ cm² particles^?1 s^?1; k_d3 = 3.5 × 10^?4$\text{exp(?}\text{88}\text{RT}{}_0\text{kJ}\text{mol}\text{)}$ cm² particles^?1 s^?1. Average surface residence times of the intermediates are: $\text{27 ?}{}^{\mathrm{\tau }}\text{HCO}\text{}\text{?}\text{1 ms}$ at 550 ? T₀ ? 650 K; $\text{42 ?}{}^{\mathrm{\tau }}\text{H ? 7 ms}$ at 540 ?T₀ ? 610 K; $\text{177 ?}{}^{\mathrm{\tau }}\text{OH ? 19 ms}$ at 550 ? T₀ ? 645 K.     

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).     

Analysis of the Raman spectrum of SF6

The Raman active fundamentals ν₁(A1g), ν₂(Eg), ν₅(F2g), and the overtone 2ν₆ of SF₆ have been investigated with a higher resolution and the band origins were estimated to be: ν₁ = 774.53 cm^?1, ν₂ = 643.35 cm^?1, ν₅ = 523.5 cm^?1, and 2ν₆ = 693.8 cm^?1. Raman and infrared data have been combined for estimation of several anharmonicity constants. The ν₆ fundamental frequency is calculated as 347.0 cm^?1. From the analysis of the ν₂ Raman band, the following rotational constants of both the ground and upper states have been calculated:

$\text{B}{}_0\text{= 0.09111 ± 0.00005}\text{cm}{}^{\mathrm{?1}}\text{; D}{}_0\text{= (0.16±0.08)10}{}^{\mathrm{?7}}\text{cm}{}^{\mathrm{?1}}$

;

$\text{B}{}_2\text{= 0.09116 ± 0.00005}\text{cm}{}^{\mathrm{?1}}\text{; D}{}_2\text{= (0.18±0.04)10}{}^{\mathrm{?7}}\text{cm}{}^{\mathrm{?1}}$

.     

Vibrational spectra and force constants of symmetric tops: High resolution spectra of monoisotopic H3SiCl in the 2200-cm−1 region and rovibrational analysis of the ν1 and ν4 fundamentals

The gas phase infrared spectra of monoisotopic H₃Si³⁵Cl and H₃Si³⁷Cl have been studied in the $\text{ν}{}_1\text{ν}{}_4$ region near 2200 cm^?1 with a resolution of 0.012 and 0.04 cm^?1, respectively, and rotational fine structure for ΔJ = ±1 branches has been resolved. In addition, some information on ν₃ + ν₄ of H₃Si³⁵Cl near 2750 cm^?1 has been obtained. ν₁ and ν₄ are weakly coupled by Coriolis x, y resonance, $\text{B}\text{Ω}{}_{14}\text{ζ}{}_{14}\text{～ 2 × 10}{}^{\mathrm{?3}}\text{cm}{}^{\mathrm{?1}}$, only the upper states K′ = 2, l = 0 and K′ = 1, l = ?1 being substantially affected. Local perturbation due to rotational l(±1, ±1)-type resonance with ν₃ + ν₅⁺¹ + ν₆⁺¹ and ν₃ + ν₅⁺¹ + ν₆^?1 is revealed in the ΔK = +1 and ?1 branches, respectively. From a fit of the experimental line positions, standard deviations of 1.4 and 3.8 × 10^?3 cm^?1, respectively, to a model with five interacting levels conventional excited state parameters and interaction constants have been obtained. In $\text{H}{}_3\text{Si}{}^{35}\text{Cl}\text{H}{}_3\text{Si}{}^{37}\text{Cl}$ the fundamentals are ν₁, $\text{2201.94380(15)}\text{2201.9345(7)}$ and ν₄, $\text{2209.63862(8)}\text{2209.6254(2)}\text{cm}{}^{\mathrm{?1}}$, respectively. Q branches of the “hot” band (ν₃ + ν₄) ? ν₃ and of ν₄ of the ²⁹Si and ³⁰Si species have been detected.     

Lithium mobility in the layered oxide Li1−xCoO2

The Li⁺-ion chemical diffusion coefficient in the layered oxide Li_0.65CoO₂ has been measured to be $\text{D}\text{?}\text{= 5 × 10}{}^{\mathrm{?12}}$ m² s^?1 by three independent techniques: (1) from the Warburg prefactor, (2) from the transition frequency for semi-infinite to finite diffusion lengths in steady-state ac-impedence measurements and (3) from a modified Tubandt method that uses ac-impedance data to distinguish interfacial and surface-layer resistances from the bulk resistance of the sample. This value and a small increase in D? with (1 ? x) in Li_1?xCoO₂, 0.45 < (1 ? x) < 0.80, compare favorably with the $\text{D}\text{?}\text{= 5}\text{to}\text{7 × 10}{}^{-12}\text{m}{}^2\text{s}{}^{-1}$ obtained by Honders for this system with pulse techniques. A qualitative discussion is presented as to why this composition dependence and why D? for this system is a factor of five larger than that for Li⁺-ion diffusion in Li_xTiS₂.     

Polarization and polarization transfer in the 2H(d,n)3He reaction at 10 MeV

Angular distributions of six polarization transfer coefficients $\text{K}{}_{\mathrm{x}}{}^{\mathrm{x\prime }}\text{(θ), k}{}_{\mathrm{x}}{}^{\mathrm{z\prime }}\text{(θ), K}{}_{\mathrm{z}}{}^{\mathrm{<mtext>x</mtext><mtext>?</mtext>}}\text{(θ), K}{}_{\mathrm{z}}{}^{\mathrm{<mtext>z</mtext><mtext>?</mtext>}}\text{(θ),}\text{and}\text{K}{}_{\mathrm{yy}}{}^{\mathrm{<mtext>y</mtext><mtext>?</mtext>}}\text{(θ)}$; of the four analyzing powers A_y(θ), A_xx(θ), A_yy(θ), and A_zz(θ); and of the polarization function P^ý(θ), have been measured atE_d = 10.00 MeV for the reaction ²H(d, n)³He. Measurements were made for neutron lab angles between 0° and 80° in 10° steps. Additionally the y-axis associated quantities were measured at θ_1ab = 99°. Most of the measured coefficients are large at some angles and all show considerable variation with angle.     

On the universality classes of the Henon map

Within an appropriate renormalization framework, we discuss a¹(b) and δ associated with the bifurcation road to chaos of a Hénon-like map generalized as follows: (x_t+1, y_t+1) = (1?a|x_t|^z + y_t, ?bx_t); (b?0, z?1). For fixed z, we obtained (i) only two universality classes, namely the conservative (b = 1) and non-conservative (b≠1) ones and (ii) $\text{a}{}^1\text{(}\text{1}\text{b}\text{) =}\text{a}{}^1\text{(b)}\text{b}{}^{\mathrm{z}}$. For b = 1, δ(z) presents a minimum, and diverges for z → 1 and z → ∞ (this contrasts with the b≠1 case).     

Semiconducting properties of pure and Mn-doped chromium disilicides

The phase analysis was carried out for the system (l?x) CrSi₂ + xMnSi₂ in the range 0?x?0.5 by X-ray technique. The solid solution Cr_1?xMn_xSi₂ was identified in the composition range 0?x?0.225, where the added Mn-atoms occupied substitutionally the Cr-atom sites in the CrSi₂ structure. Resistivity, Hall coefficient as well as thermoelectric power were measured as functions of temperature in the range, 80–1200 K and composition x in the single phase region, 0 ?x?0.225. The pure CrSi₂ (x = 0) was a p-type degenerate semiconductor, whose hole concentration was determined to be 7.7 × 10²⁰ cm^?3 at room temperature. Mn-atoms introduced in the CrSi₂ crystal were found to act as donors. The forbidden energy gap was determined to be 0.30 eV from the Hall-data in the intrinsic region. With increasing x, a conversion from p- into n-type semiconductor took place in Cr_1?xMn_xSi_y. From the analysis of Hall- as well as resistivity-data, the mobility ratio b was obtained as a function of composition x. It was revealed that b increased with increasing x from 0.01 for x = 0 to 0.12 for x = 0.182. The electron-hole concentration product could be expressed as $\text{np = 1.2 × 10}{}^{35}\text{T}{}^{35}\text{exp}\text{(?}\text{3480}\text{T}\text{)}$, and the hole mobility as $\text{μ}{}_{\mathrm{p}}\text{= 7.0 × 10}{}^4\text{T}{}^{\mathrm{<mtext>?</mtext><mtext>3</mtext><mtext>2</mtext>}}$ in the acoustic scattering region. The effective mass of hole was found out to be 3.2 m₀ and independent of x, whereas that of electron varied from 20.2 m₀ for x = 0 to 7.5 m₀ for x = 0.182. When these parameters are used, the theoretical temperature variation of the thermoelectric power curve was found out to be in good agreement with the measurement.     

A study of valency changes of vanadium ions in Al2O3 by γ irradiation

The effect of γ irradiation at 300 K on the concentrations of vanadium ions V³⁺, V⁴⁺ and V²⁺ in Al₂O₃ has been studied quantitatively, using three techniques: optical absorption (V³⁺), low temperature thermal conductivity measurements (V⁴⁺) and EPR (V²⁺). Several single crystals of Al₂O₃ doped with vanadium in a large range of concentration $\text{(2.8 × 10}{}^{18}\text{? 1.3 × 10}{}^{20}\text{at.}\text{cm}{}^3\text{)}$ have been measured. The evolution of the respective concentrations by γ irradiation as a function of the total vanadium content C is quite different in the two regions $\text{C< 1.2 × 10}{}^{19}\text{at.}\text{cm}{}^3$ and C larger than this value. A consistent analysis of the results has nevertheless been achieved, leading to the determination of the absolute concentrations of the three ions in the as-received and γ irradiated states for all samples with $\text{C<4.2 × 10}{}^{19}\text{at.}\text{cm}{}^3$ (room temperature annealing is observed above this value). The concentrations of V⁴⁺ and V²⁺ ions are always small, but V⁴⁺ ions are more stable: they are present in the as-received state at a level of 1% of the total concentration and a maximum value of $\text{/}\text{?}\text{2.3 × 10}{}^{18}\text{at.}\text{cm}{}^3$ is observed in the γ irradiated state; on the other hand there are less than 4.7 × 10¹⁵V²⁺ ions per cm³ in the as-received state and the maximum value is only $\text{4.2 × 10}{}^{17}\text{at.}\text{cm}{}^3$. Charge transfer between V ions only is not sufficient to explain the experimental results and other defects must be involved in the γ irradiation effect.     

Bounded diffusion in solid solution electrode powder compacts. Part II. The simultaneous measurement of the chemical diffusion coefficient and the thermodynamic factor in LixTiS2 and LixCoO2

Two electrochemical methods - involving the application of a long-time galvanostatic current pulse and a small potentiostatic voltage step to a M/M_xSSE cell - are presented. From the overvoltage, respectively current response the chemical diffusion coefficient ($\text{D}{}_{\mathrm{M}}{}^{\mathrm{+}}$) and the thermodynamic factor (? ln a/? ln c) are obtained. The methods have been applied to the cells: Li/1M·LiClO₄ in propylenecarbonate/Li_xTi_1.03S₂ 0.05 < x < 0.95, T = 20°C; and Li_xCoO₂ 0.10 < × < 1, T = 20°C. From the application of the current pulse/voltage decay method it followed: $\text{D}{}_{\mathrm{<mtext>Li</mtext>}}{}^{\mathrm{+}}\text{(}\text{Li}{}_{\mathrm{x}}\text{Ti}{}_{1.03}\text{S}{}_2\text{) = 1?4 × 10}{}^{\mathrm{?8}}\text{cm}{}^2\text{s}{}^{\mathrm{?1}}$, with a slight tendency to increase with decreasing x; $\text{D}{}_{\mathrm{<mtext>Li</mtext>}}\text{C}\text{(}\text{Li}{}_{\mathrm{x}}\text{CoO}{}_2\text{) = 2?40 × 10}{}^{\mathrm{?9}}\text{cm}{}^2\text{s}{}^{\mathrm{?1}}$, decreasing with decreasing x. These values are among the highest found for solid state Li⁺-ion diffusion, and will be closely evaluated and compared with data reported by other workers. The x-dependence of the thermodynamic factor, determined from kinetic data, for Li_xTi_1.03S₂ (x = 0.05-0.95) and Li_xCoO₂ (x = 0.60-1.00) is in accordance with a simple thermodynamic model. Unlike for Li_xTi_1.03S₂, the thermodynamic factor for Li_xCoO₂, determined from the EMF-x relation, cannot be accounted for by this model. Furthermore, a fast, but crude method to determine the average chemical diffusion coefficient in Li_xTi_1.03S₂ and Li_xCoO₂ is discussed.     

Ultraviolet laser-induced fluorescence spectrum of fluorochlorocarbene in solid argon

CFCl has been produced for spectral investigation by matrix reactions of alkali metal atomic beams with CFCl₃ in argon followed by rapid quenching to 15°K on a tilted copper wedge. When these samples were irradiated with near uv light from a krypton ion laser, a very intense, highly structured fluorescence spectrum was observed. This emission system extended from about 25 000 cm^?1 to 15 000 cm^?1 and peaked in intensity at about 22 000 cm^?1. The three most intense progressions are assigned to transitions from a common excited state to ground state levels (0v₂0), (1v₂0) and (1v₂1). New molecular constants determined from these progressions include $\text{ω}{}_2{}^0\text{= 446}\text{cm}{}^{\mathrm{?1}}$, x₂₂ = ?1.2 cm^?1, x₁₂ = ?3 cm^?1, x₂₃ = ?4 cm^?1, and x₁₃ = ?6 cm^?1. CFCl was also produced by in situ photolysis of CFCl₃ using laser plasma emission and by alkali metal atom reactions with CF₂Cl₂, CF₂ClBr, and CHFCl₂.     

Simultaneous diffusion of calcium and strontium in KCl single crystals

Concentration dependent diffusion coefficients for ⁴⁵Ca²⁺ and ⁸⁵Sr²⁺ in purified KCl were measured using a sectioning method. KCl was purified by an ion exchange — Cl₂?HCl process and the crystals grown under $\text{1}\text{6}$ atmosphere of HCl. The tracers were purified on small disposable ion exchange columns to remove precessor and daughter impurities prior to use in a diffusion anneal. Isothermal diffusion anneals were made in the temperature range from 451% to 669%C. At temperatures above 580%C (the lowest melting eutectic in this system) diffusion was from a vapor source: below 580%C surface depositied sources were used. The saturation diffusion coefficients. enthalpies and entropies of impurity-vacancy associations were calculated using the common ion model for simultaneous diffusion of divalent ions in alkali halides. In KCl the saturation diffusion coefficients D_S(ca) and D_s(Sr) are given by

$\text{D}{}_{\mathrm{s}}\text{(Ca) = 9.93 × 10}{}^{\mathrm{?5}}\text{exp(?0.592}\text{eV}\text{kT}\text{)}\text{cm}{}^2\text{sec}$

(1) and

$\text{D}{}_{\mathrm{s}}\text{(Sr) = 1.20 × 10}{}^{\mathrm{?3}}\text{exp(?0.871}\text{eV}\text{kT}\text{)}\text{cm}{}^2\text{sec}$

(2) for calcium and strontium, respectively. The Gibbs free energy of association of the impurity vacancy complex in KCl for calcium can be represented by

$\text{Δg(Ca) = ?-0.507 eV + (2.25 × 10}{}^{\mathrm{?4}}\text{eV}\text{\%K}\text{)T}$

(3) and that for strontium by

$\text{Δg(Sr) = ?0.575 eV + (2.90 × 10}{}^{\mathrm{?4}}\text{eV}\text{\%K}\text{)T}$

. (4)     

Analysis of the 2770-Å emission system in I2

A weak emission spectrum of I₂ near 2770 Å is reanalyzed and found to to minate on the A(1u³Π) state. The assigned bands span v″ levels 5–19 and v′ levels 0–8. The new assignment is corroborated by isotope shifts, band profile simulations, and Franck-Condon calculations. The excited state is an ion-pair state, probably the 1g state which tends toward $\text{I}{}^{\mathrm{?}}\text{(}{}^1\text{S) +}\text{I}{}^{\mathrm{+}}\text{(}{}^3\text{P}{}_1\text{)}$. In combination with other results for the A state, the analysis yields the following spectroscopic constants: T″_e = 10 907 cm^?1, $\text{D}$″_e = 1640 cm^?1, ω″_e = 95 cm^?1, $\text{R″}{}_{\mathrm{e}}\text{= 3.06}\text{A}\text{?}$; T′_e = 47 559.1 cm^?1, ω′_e = 106.60 cm^?1, $\text{R′}{}_{\mathrm{e}}\text{= 3.53}\text{A}\text{?}$.     

Isospin dependence of the nuclear level density

Experiments on $\text{(ft)}{}^{\mathrm{+}}\text{/(}\text{ft)}{}^{\mathrm{?}}$ for mirror Gamow-Teller β-decay are reanalyzed in the light of recent work and new values for the Kubodera, Delorme and Rho second class parameters are deduced: ξ = ? (0.8 ± 2.0) × 10^?3MeV^?1; λ = (3.4 ± 3.9) × 10^?3. These values are compared with recent correlation experiments.     

The rotational spectrum of the X 2Σ+ state of the SrF radical using laser microwave optical double resonance

The pure rotational spectrum of the $\text{X}{}^2\text{Σ}{}^{\mathrm{+}}$ state of the gaseous SrF radical has been measured using microwave optical double resonance (MODR) techniques. The analysis fully confirms the recent dye laser excitation spectrum and rotational assignment of the $\text{B}{}^2\text{Σ}{}^{\mathrm{+}}\text{-X}{}^2\text{Σ}{}^{\mathrm{+}}$ system. Transitions were measured in both the v″ = 0 and v″ = 1 states to give values of B_e″ = 0.250533 cm^?1, α_e″ = 1.546 × 10^?3 cm^?1 and γ″ (spin-rotation) = 2.49 × 10^?3 cm^?1. General qualitative features of MODR in ²Σ⁺ states are treated and suggested improvements for obtaining experimental hyperfine constants are discussed. The more precise ground state constants are merged with the B-X optical analysis to obtain a more accurate set of constants for both states.     

The spectroscopic study of excitation and ionization in the collision of two metastable atoms

Collisions between two excited atoms leading to an increase in the excitation energy of the particles have been under investigation. All measurements were made in the afterglow of gas-discharge plasma. The cross sections of the following reactions have been determined: $\text{Hg}\text{(6}{}^3\text{P}{}_{012}\text{) +}\text{Hg}\text{(6}{}^3\text{P}{}_{012}\text{) →}\text{Hg}{}^7\text{+}\text{Hg}\text{(6}{}^1\text{S}{}_0\text{),}\text{He}{}_{\mathrm{m}}\text{(2}{}^{\mathrm{1,3}}\text{S}\text{) +}\text{Xe}{}_{\mathrm{m}}\text{(}{}^3\text{P}{}_{\mathrm{0,2}}\text{) → (}\text{Xe}{}^{\mathrm{+}}\text{)}{}^1\text{+}\text{He}{}_0\text{+}\text{e}$. The cross section of the first reaction for different transitions lies in the region (2?35) × 10^?15 cm² and the cross section of the second, in (0.2?2.4) × 10^?16 cm². Possible systematic errors and the role of cascade transitions are discussed. Cross sections of the Penning reaction He_m + Xe₀ → He₀ + Xe⁺ + e have also been measured. The result is σ (2³S) = (1.4 ± 0.2) × 10^?15 cm², σ (2¹S) = (1.2 ± 0.3) × 10^?15 cm².     

Rotation-vibration analysis of the Coriolis-coupled ν5g, ν6g, ν8g and ν9 bands of H2CCO

Medium resolution infrared grating spectra of gaseous ketene, H₂CCO were recorded between 1000 and 400 cm^?1, both at instrument temperature (40°C) and with cooling (?40°C). Interferometric Fourier spectra were also measured at ?70°C with resolution 0.22 cm^?1 between 450 and 330 cm^?1. The K structure of the fundamentals ν₅, ν₆, ν₈, and ν₉ was assigned. These fundamentals are coupled by a-axis Coriolis interactions. These couplings were analysed on the symmetric top basis for setting up the perturbation matrix and by utilizing the K-dependent Coriolis shifts of levels. A preliminary analysis of the Coriolis intensity anomalies was also undertaken.Band center values from combination differences are $\text{ν}{}_5{}^0\text{= 587.30 (27)}$ and $\text{ν}{}_6{}^0\text{= 528.36 (39)}\text{cm}{}^{\mathrm{?1}}$. Synthetic spectra indicate the band origins of ν₈ and ν₉ to be close to 977.8 and 439.0 cm^?1, respectively. Estimates of Coriolis coupling constants obtained from synthetic spectra are $\text{ζ}{}_{58}{}^{\mathrm{a}}\text{= + 0.33 (5)}$, $\text{ζ}{}_{68}{}^{\mathrm{a}}\text{= + 0.714 (20)}$, $\text{ζ}{}_{59}{}^{\mathrm{a}}\text{= ? 0.774 (20)}$, and $\text{ζ}{}_{69}{}^{\mathrm{a}}\text{= ? 0.30 (2)}$. Approximate ratios of unperturbed vibrational transition moments obtained from spectral simulations are $\text{M}{}_8{}^0\text{:±iM}{}_5{}^0\text{:±iM}{}_6{}^0\text{:M}{}_9{}^0\text{≈ +2:?9:+10:+0.5}$.     

Transverse spin correlation function of the one-dimensional spin-12 XY model

The transverse spin pair correlation function p^x_n=<S^x_mS^x_m+n>=<S^x_mS^x_m+n> is calculated exactly in the thermodynamic limit of the system described by the one-dimensional, isotropic, spin-$\text{1}\text{2}$, XY Hamiltonian

$\text{H=?2J}\text{∑}\text{l=1}\text{N}\text{(S}{}^{\mathrm{x}}{}_{\mathrm{l}}\text{S}{}^{\mathrm{x}}{}_{\mathrm{l+1}}\text{+S}{}^{\mathrm{y}}{}_{\mathrm{l}}\text{S}{}^{\mathrm{y}}{}_{\mathrm{l+1}}\text{)}$

. It is found that at absolute zero temperature (T = 0), the correlation function ρ^x_n for n ≥ 0 is given by

$\text{ρ}{}^{\mathrm{x}}{}_{\mathrm{2p}}\text{=}\text{1}\text{4}\text{2}\text{π}{}^{\mathrm{2p}}\text{Π}\text{j=1}\text{p?1}\text{4j}{}^2\text{4j}{}^2\text{?1}{}^{\mathrm{2p?2j}}\text{if}\text{n=2p}$

,

$\text{ρ}{}^{\mathrm{x}}{}_{\mathrm{2p+1}}\text{=±}\text{1}\text{4}\text{2}\text{π}{}^{\mathrm{2p+1}}\text{Π}\text{j=1}\text{p}\text{4j}{}^2\text{4j}{}^2\text{?1}{}^{\mathrm{2p+2j}}\text{if}\text{n=2p+1}$

, where the plus sign applies when J is positive and the minus sign applies when J is negative. From these the asymptotic behavior as n → ∞ of |?^x_n| at T = 0 is derived to be $\text{|ρ}{}^{\mathrm{x}}{}_{\mathrm{n}}\text{| ～}\text{a}\text{n}$ with a = 0.147088?. For finite temperatures, ρ^x_n is calculated numerically. By using the results for ?^x_n, the transverse inverse correlation length and the wavenumber dependent transverse spin pair correlation function are also calculated exactly.