Weak bands in the far-infrared spectrum of HCNO

Several weak transitions in the far-infrared spectrum of H¹²C¹⁴N¹⁶O between the (0000_v) levels with v = 2, 3, and 4 have been analyzed. Vibrational levels of improved accuracy have been calculated for both the (0000_v) series (v ≦ 5) and the (0001_v) series (v ≦ 3). For the latter, some inconsistencies in previous assignments have been removed. Two transitions from the (00020)² level have been assigned tentatively. The two lowest bands of the (0000_v) series of H¹³C¹⁴N¹⁶O have been found. Two new types of graphical plots have been used in the assignment.     

Ion-electron coincidence study of the thermal He(23S) + H2 Penning reaction

A new Penning-electron-Penning-ion coincidence method is described. It is applied to the study of the thermal reaction of He(2³S) with H₂. The main results reported are separate electron energy spectra that are coincident with the three different ions formed: HeH₂⁺, HeH⁺ and H₂⁺. Based on these results it is shown that the Penning reaction of the He(2³S)/H ₂ system proceeds in two well-separated steps: (i) ionization at distances R (HeH₂) ? 6a₀ in which H₂⁺ (v) is formed in different vibrational states; and (ii) reactive collision of H₂⁺ (v) with He. For the second step the variation of the branching ratios with vibrational quantum numbers v = 0 to v = 10 is derived, and it is shown that these branching ratios may be regarded as relative vibrational-energy-dependent cross-sections for the collision of H₂⁺ (v) with He at an average relative kinetic energy of ～20 meV.     

Absorption measurements of H2O at high temperatures using a CO laser

Absorption of CO laser radiation (v = 8→7, J = 14→15 transition at 1901.762 cm^-1) by H₂O has been studied in shock-heated H₂/O₂/Ar mixtures over the temperature range 1300–2300 K. This laser transition is nearly coincident with the v₂-band 12_3,10←11_2,9 transition of H₂O at 1901.760 cm^-1, thereby providing a convenient and sensitive absorption-based H₂O diagnostic useful for studies of combustion. The collision-broadening parameter for this H₂O line, due to broadening by Ar, was determined to be 2γ (cm^-1atm^-1) = 0.027 (T/1300)^-0.9 in the temperature range 1300–2300 K. Calculations of the H₂O absorption coefficient (at 1901.762 cm^-1) based on this expression for 2γ are presented for the temperature range 300–2500 K and pressure range 0.3–1 atm.     

Assignment of the HCOOH CW-submillimeter laser

Twenty one laser lines of the 250–1000 GHz range have been assigned in the v₆ and v₈ excited states of the H¹²COOH molecule. The microwave study of these two states has allowed us to determine the molecular constants and to calculate the energy levels up to J = 50. The values of the energy levels of the ground state are well known and allow the frequency calculation of infrared rovibrational transitions near the 9.6–10.6 μm region and the comparison with the frequencies of the CO₂ laser lines. A microwave infrared double-resonance experiment has also been performed to confirm assignment based on the calculation of the energy levels. The value of the two band centers has been determined.     

Microwave spectrum of methyl fluoride in excited vibrational states: Coriolis interaction and anomalous l-doubling transitions

The microwave spectrum of CD₃F in the v₂ = 1, v₃ = 1, v₅ = 1, and v₆ = 1 states was observed, including the direct l-doubling transitions in the v₅ = 1 and v₆ = 1 states. The Coriolis interaction between the v₂ = 1 and v₅ = 1 states was analyzed in detail. An anomaly in the Stark effect was noticed in some of the direct l-doubling transitions in the v₆ = 1 states, and was explained in terms of accidental degeneracy between the Kl₅ = 1 and the Kl₅ = ? 2 levels. Molecular constants associated with the vibrational and rotational motions were determined through an analysis of these spectra.The J = 1 ← 0 transitions of ¹²CH₃F in the v₂ = 1, v₃ = 1, v₅ = 1, and v₆ = 1 states and of ¹³CH₃F in the v₃ = 1 and v₆ = 1 states were observed, as well as the direct l-doubling transitions of ¹²CH₃F in the v₅ = 1 state. A preliminary analysis was carried out on the strong Coriolis interaction between the v₂ = 1 and v₅ = 1 states.     

The ground state of molecular hydrogen

The v = 0?0 quadrupole spectrum of H₂ has been recorded using a 0.005-cm^?1 resolution Fourier transform spectrometer. The rotational lines S(1) through S(5) are observable in the spectra, in the region 587 to 1447 cm^?1. The spectral position for S(0) was also obtained from its v = 1-0 ground-state combination difference. The high accuracy of the H₂ measurements has permitted a determination of four rotational constants. These are (in cm^?1) B₀ = 59.33455(6); D₀ = 0.045682(4); H₀ = 4.854(12) × 10^?5; L₀ = ?5.41(12) × 10^?8. The hydrogen line positions will facilitate studies of structure and dynamics in astrophysical objects exhibiting infrared H₂ spectra. The absolute accuracy of frequency calibration over wide spectral ranges was verified using 10-μm CO₂ and 3.39-μm CH₄ laser frequencies. Standard frequencies for 5-μm CO were found to be high by 12 MHz (3.9 × 10^?4 cm^?1).     

Non-adiabatic potentials for H2 +

In principle exact non-adiabatic pseudo-potentials for H₂ ⁺ and D₂ ⁺ are formulated in terms of the theory of conditional probability amplitudes in wave mechanics. Numerical results for the v = 0 and v = 1 (J = 0) states of H₂ ⁺ are derived from previously computed accurate non-adiabatic wave-functions. These results indicate that the non-adiabatic pseudo-potentials only differ from the adiabatic potential by small energies of the same magnitude as the non-adiabatic corrections to the adiabatic energy levels.     

Improved potential energy curve and vibrational energies for the electronic ground state of the hydrogen molecule

The potential energy curve for the electronic ground state of the hydrogen molecule has been recomputed for intermediate and large internuclear separations. for 2.4 ≤ R ≤ 8.0a.u. the previous potential energy curve has been improved. The largest improvement amounts to 5.5 cm^?1, and was obtained in the vicinity of R = 4.4a.u.. Using the new potential energy curve, and the adiabatic and relativistic corrections, the vibrational and rotational energy levels have been calculated for H₂, HD, and D₂. The deviations of the calculated energy levels G(v) of H₂ and D₂ from the observed values follow very closely the nonadiabatic corrections resulting from the Van Vleck formula.     

The pentad rotation-vibrational states of 12CD4: Wavenumber analysis of infrared and Raman spectra of the ν1, ν3, 2ν2, ν2 + ν4, and 2ν4 bands

The so-called pentad of ¹²CD₄ consists of the vibrational states v₁ = 1(symmetry A₁), v₃ = 1(F₂), v₂ = 2(A₁ + E), v₂ = v₄ = 1(F₁ + F₂), and v₄ = 2(A₁ + E + F₂). All states are located in the 1950 to 2250-cm^?1 region and all are strongly interacting. In the present work we have assigned more than 5000 infrared rotation-vibrational transitions and 163 isotropic Raman transitions from the vibrational ground state to the pentad. We have used infrared and Raman spectra of a resolution better than 0.01 cm^?1. From the experimental wavenumbers 2567 pentad rotation-vibrational energy levels with J ≦ 20 have been determined. These levels are reported in the paper. The levels have been used for refinements of the spectroscopic constants of two physically different effective Hamiltonians for the pentad states. For all levels with J ≦ 12 an unweighted standard deviation of 0.004 cm^?1 is obtained for both Hamiltonians, whereas the standard deviation increases more or less rapidly with J above 12 due to the imperfections of the Hamiltonians. The values of the spectroscopic constants of both Hamiltonians (85 and 106, respectively) are reported and the effects of the approximations are discussed.     

Calculation of centrifugal distortion constants for diatomic molecules from RKR potentials

Expressions are developed for computing the centrifugal distortion constants D_v, H_v, and L_v directly from the Rydberg-Klein-Rees rotationless potential of a diatomic molecule. These expressions involve summations over integrals of the wavefunctions of all neighboring vibrational levels. Application is made to the X¹Σ⁺ state of CO and the $\text{X}{}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{?}}$ state of O₂. In these applications, we have neglected the contributions of the continuum wavefunctions. For higher vibrational levels, particularly those near the dissociation limit, this approximation would be expected to fail. For the lowest vibrational levels of an electronic state, this method gives the same results for D_v, H_v, and L_v as the Dunham relations. However, for intermediate vibrational levels the present method is an improvement since expressions for only a few coefficients of the Dunham expansion are available. The use of D_v and H_v values calculated from Rydberg-Klein-Rees potentials in an iterative improvement of the reduction of spectroscopic data is described.     

Vibration-rotation energies of harmonic and combination levels in tetrahedral XY4 molecules: Analysis of the 2ν2 and ν2 + ν4 bands of 12CH4

The theory and the extrapolation method described in the previous paper are used to analyze the v₂ = 2 and v₂ = v₄ = 1 levels of ¹²CH₄. In addition to the well-known parameters of the ground, v₂ = 1, and v₄ = 1 states, the computation of energy levels involves only 6 new parameters for 2ν₂ and 13 for ν₂ + ν₄ up to the fourth order of approximation. These parameters have been determined from Raman and infrared data. Forty-four Raman lines observed by Berger in the region from 3060 to 3090 cm^?1 have been assigned to the 2ν₂ band. The standard deviation obtained by fitting 39 of these transitions with the 6 corresponding parameters is 0.025 cm^?1. The calculated frequencies of ν₂ + ν₄ are compared with moderate resolution ir spectra recorded in our laboratory and the recent spectra of Hunt et al. Totally polarized weak Raman lines observed by Berger in the region from 2850 to 2900 cm^?1 have been assigned to the ν₂ + ν₄ band arising through a second-order Coriolis interaction with the ν₁ band. A project of a comprehensive treatment of the energy levels of methane between 2550 and 3650 cm^?1 is discussed.     

The vibration-rotation spectrum of methinophosphide: l-Type doubling, l-type resonance and the ν2, 2ν2, and 3ν2 bands of H12CP; The ν1 and ν2 bands of H13CP

The vibration-rotation bands ν₂, 2ν₂, and several “hot” bands of H¹²CP have been recorded and assigned. The states with v₂ = 2, perturbed by l-type resonance and l-type doubling effects have been analyzed on the basis of the existing theory. The energy difference between the 02²0 and the 02⁰0 states was found to be 17.5095 (19) cm^?1. Because of insufficient data, the states with v₂ = 3 could not be corrected for l-type resonance interaction and therefore only an effective l-type doubling constant was obtained. The ν₁ and ν₂ bands of the H¹³CP isotopic molecule (present at natural concentration) were also identified and their spectroscopic constants obtained. The value of I_e for H¹²CP is found to be 25.18793 (26) amu Ų.     

High-resolution infrared and microwave spectroscopy of the ν4 and 2ν2 bands of 14NH3 and 15NH3

More than two thousand Stark resonances of the ν₄ and 2ν₂ band transitions of ¹⁴NH₃ and ¹⁵NH₃ were observed at Doppler-limited resolution with a CO laser. Fourier transform infrared spectroscopy on ¹⁵NH₃ is also carried out. Thirty-six new microwave transitions including seven perturbation-enhanced transitions are observed in the v₄ = 1 excited vibrational state of ¹⁴NH₃ and ¹⁵NH₃. Accuracies of all available spectroscopic data on the v₄ = 1 and the v₂ = 2 states are evaluated and analyses of the vibration-rotation spectra are performed. The Coriolis interaction between the closely lying v₄ = 1 a (antisymmetric level) and v₂ = 2 s (symmetric level) states is explicitly included in the analysis. Smaller Coriolis interactions between the v₄ = 1 a and the v₂ = 1 s states and between the v₂ = 2 s and the v₂ = v₄ = 1 a states (i.e., (v₁, v₂, v′₃, v′₄) = (0 1 0⁰ 1¹)) are also taken into consideration. The accuracy in determination of the principal molecular constants is 10^?6. The parameters thus obtained reproduce the frequencies of the vibration-rotation transitions and inversion transitions within the accuracy of 0.0024 cm^?1.     

Spectroscopic determination of Fisher information on vibrational states of diatomic molecules using the example of the X 1Σ g + state of a Li2 molecule

An expression governing Fisher information of vibrational states of a diatomic molecule is obtained in the first-order Wentzel-Kramers-Brillouin (WKB) approximation, and a quantitative criterion of its applicability is proposed. The expression is determined only by the dependence of energy of vibrational levels on quantum number v and the reduced mass of the molecule; it is not related to any additional model assumptions and does not require knowledge of vibrational wavefunction. It is established that the dependence of Fisher information on v attains maximum at certain value v ₀. The efficiency of the obtained expression is demonstrated by calculating the Fisher information of vibrational levels v = 0–40 of the X ¹Σ _g ⁺ state of the ⁷Li₂ molecule. It is established that v ₀ = 23 for this electronic state. Calculation of the Fisher information of levels v = 0–38 of this state with the help of the obtained relation is in excellent (within mean-square deviation σ? = 0.01%) agreement with the results of calculation based on numerical solution of the Schrödinger equation by using the earlier-published semi-empirical potential curve of this state. At the same time, the expressions available in the literature based on the Wilson-Sommerfeld quantization rule describe the Fisher information of these levels only qualitatively (σ? = 18%). It is established that the reason for deviation for levels v = 39 (σ = 0.3%) and v = 40 (σ = 1.9%) is not related to using the WKB approximation but is due to the numerical differentiation procedure of strongly nonlinear (in the vicinity of the upper bound of v) dependence of the energy of vibrational terms on v appearing in the obtained expression.     

Far infrared pure rotational spectrum of methylacetylene

The pure rotational spectrum of methylacetylene has been recorded in the far infrared region between 10 and 60 cm^?1 with a Fourier transform spectrometer whose theoretical resolution was 0.025 cm^?1. From the measured wavenumbers it has been possible to determine the rotational constants in the ground state and in the v₅ = 1, v₈ = 1, v₁₀ = 1, 2, 3, 4 levels.     

Rate coefficient and transition probability of XeO

Rate coefficients of XeO(¹S) at various vibrational levels (v = 0, 1 and 2) were observed by measuring absolute intensities of the spectrum in the low-pressure d.c. glow of an Xe-O₂ mixture discharge. The association coefficients at the various levels are K_a0 = 2.4×10^-34 cm⁶ at v = 0, K_a1 = 1.1 × 10^-34 cm⁶ atv = 1, and K_a2 = 9.1 × 10^-35 cm⁶ at v = 2. The transition probability from XeO(¹S)₀ to $\text{XeO(}{}^1\text{D)u}$ is estimated to be A₀ = 1.3 × 10⁵ sec^-1.     

High-resolution infrared spectrum of acetylene in the region of the bending fundamental v 5

The infrared spectrum of C₂H₂ in the region of the bending fundamental v ₅ has been studied at a resolution of about 0·015 cm^-1. The molecular constants G ₀(v ₅=1) = 730·3341 (1) cm^-1 and B ₀ = 1·176641 (2) cm^-1 have been derived. In addition to the fundamental, all the hot bands starting from the levels v ₄ and v ₅ have been investigated. The vibrational, vibration-rotation coupling and centrifugal constants for the excited vibrational states v ₅ = 2 and v ₄ = v ₅ = 1 have been derived using the vibration-rotation energy matrix.     

Nuclear magnetic resonance in ferromagnetic HCP and FCC 59cobalt

The ⁵⁹Co nuclear magnetic resonance spectra of powdered metal have been investigated in the temperature range from 3 K – 295 K. Both HCP resonance lines, coming from nuclei at the center and the edge of the domain walls (v₁ = 221 MHzv₂ = 214 MHz at 295 K, respectively) have been observed as in bulk material. The quadrupole splitting, directly measured only by Kawakami et al., was verified. The line spacing v_q = 3e²Qq/2I(2I - 1)h is v_q = (178 ± 5) kHz at 295 K. A new line with v = 221.7 MHz at 295 K was found, which is probably due to a stacking fault.The temperature behaviour of the FCC-linewidth is anomalous. Between 3 and 10 K a line splitting due to frequency pulling, already predicted by De Gennes et al. in 1962, was discovered. The frequency shift derived from the splitting of the FCC line at 3 K is δω₀ ≈ 2.51 MHz. The corresponding anisotropy field and zero field ferromagnetic resonance frequency of FCC cobalt are H_A ≈ 1.25 × 10² Oe and ω_e ≈ 2.27 × 10⁹ Hz, respectively.     

Study of the torsion-rotation Hamiltonian for symmetric tops using the millimeter wave spectrum of methyl silane

The torsion-rotation Hamiltonian for symmetric tops has been tested in methyl silane by combining recent anticrossing molecular beam measurements in the ground torsional state (v = 0) with pure rotational spectra taken for v as high as 4. The earlier microwave data set which consisted of J = 1 ← 0 and 2 ← 1 has been greatly extended by studying millimeter transitions for J = 4 ← 3, 5 ← 4, and 13 ← 12. An analysis of the 72 rotational frequencies for v ≤ 2 and the 15 anticrossing data for v = 0 yielded an excellent fit using 14 rotational, torsional, and distortion constants including the effective values for the A rotational constant and the barrier height V₃. No satisfactory fit could be obtained when the data set was extended to include measurements for (v = 3) or (v = 4). For each of these higher torsional levels, the difference between the observed frequencies and the predictions based on the best (v ≤ 2) constants can be expressed in terms of a shift δB_v in the B rotational constant, where δB_v is a smooth function of the torsional energy. This disagreement is of particular interest because it may result from the fact that the molecule passes from hindered to free rotation as v is increased from 2 to 4. The possibility of perturbation by a low-lying vibrational level is considered briefly. The information contained in the different types of spectra is discussed; the redundancy relations are treated and a Fourier expansion of the diagonal torsional matrix elements is introduced. For ¹²CH₃²⁹SiH₃, ¹²CH₃³⁰SiH₃, and ¹³CH₃²⁸SiH₃ pure rotational spectra for v = 0 were studied briefly in natural abundance. The results were combined with existing data for two deuterated symmetric rotors to obtain a structure based only on symmetric top rotational constants.