Vibrational Level Spacings Research Articles

Interatomic potentials of A 3+ and B 31 states of HgHe, HgNe, and HgAr van der Waals complexes

Rotational structures of A–X and B–X vibronic transitions of HgHe, HgNe, and HgAr van der Waals (vdW) complexes formed in supersonic free jets have been investigated. An analysis of the rotational contours shows that rotational structures for the six isotopic species, mHgHe, mHgNe, or mHgAr (m=204,202,201,200,199, and 198), are overlapped, and the observed isotopic splittings are utilized for the definite assignment of the vibrational quantum numbers in the A and B states. Based on the vibrational level spacings and the rotational constants, interatomic potentials for the A and B states of HgNe and HgAr are determined with good accuracy. In the case of the B state of the 199HgRg and 201HgRg (Rg=Ne or Ar), magnetic dipole hyperfine splittings are observed and analyzed.

The characterization of the complete set of bound vibronic states of HNO in its excited [formula omitted] electronic state

Laser-induced fluorescence excitation spectra of the HNO A ̃ 1A″- X ̃ 1A′ band system have been recorded with high sensitivity. This has enabled detection of the Franck-Condon unfavored vibronic bands (002)-(000) and (003)-(000), thereby completing the set of fully bound vibronic levels in the A ̃ state. Extensions have also been made to other bands. A strong Coriolis resonance between the K a 1 = 8 levels of the excited (010) vibronic state and the K a 1 = 9 levels of the (001) state leads to rotational perturbations of up to 9 cm −1. The (100-000) band includes weak axis-tilting branches. It is concluded from the vibrational energy level spacings that vibronic interaction makes an important contribution to the energies of the higher bending levels, consistent with the correlation of the A ̃ 1A″ state with a component of a 1Δ state for linear HNO.

Relation between total cross section data and the interaction potential; A comparison with closely connected data

The information on the spherical interaction potential contained in total collision cross section data in the glory region is investigated. The amplitude of the glory undulations is found to be a predominant measure for the curvature of the potential around its minimum. The information on the potential from the amplitude is strongly related to the information that can be obtained from spectroscopic data on the vibrational level spacings. The location of the glory extrema yields a measure for the area of the potential well. A strong correlation is shown to be present between the value of the area parameter and the low temperature second virial coefficient and its temperature derivative. To the non-glory total cross section a rather well defined probing distance can be attributed, suggesting that a scheme for direct inversion of such data into potential data may be worked out.

The electronic structure and spectra of the X 1Σ+g and A 1Σ+u states of Li2

The potential energy curves for the X 1Σ+g and the A 1Σ+u states of Li2 have been calculated on the single configuration Hartree–Fock–Roothaan (HF) level, and on the multiconfiguration self-consistent-field (MCSCF) level. The MCSCF results give binding energies De (X 1Σ+g) =8297 cm−1 and De (A 1Σ+u) =9299 cm−1; a semiempirical scaling which reproduces the experimental vibrational energy level spacings suggests ’’most-likely’’ dissociation energies De′ (X 1Σ+g=8450±100 cm−1 and De′ (A (1Σ+u) =9400±100 cm−1.

Spin densities in LiH+

Electronic energies and spin density distributions for LiH+ have been determined by spin-polarized self-consistent-field and full configuration interaction calculations with several basis sets. For the 2Σ ground state Re, De ,the dipole moment, and vibrational level spacings have been estimated. The lowest 2Π state is purely repulsive, but the vertical excitation energy to it from the rovibronic ground state has been estimated. Spin densities have been investigated at the nuclei and as distributions in space. Direct and spin-polarization contributions are discussed. Spin densities at the nuclei are found to be sensitive to inclusion in the basis set of very compact functions, and to correlation.

Dissociation energies of ground-state HgX molecules (X = I, Br, Cl) from analysis of vibrational level spacings

Wieland's spectroscopic data on the mercury monohalides have been reexamined and analyzed via the LeRoy-Bernstein modified Birge-Sponer extrapolation procedure to yield improved values for their ground ( X 2Σ +) state dissociation energies. The result obtained for HgI is D 0 = 3120 ± 50 cm −1. For HgBr and HgCl the extrapolations are less secure, but the best estimated D 0 values are 6000 and 8600 cm −1, respectively. Each of these dissociation energies is significantly higher than the current literature value. Further experimental investigations are recommended to confirm the present results.

A re-examination of the adiabatic correction term for the hydrogen molecule

The adiabatic coupling correction term [Formula: see text] has been evaluated by two methods, the one used by Kołos and Wolniewicz in 1964 and the one suggested by Kari, Chan, Hunter, and Pritchard in 1973. The difference between the two procedures for H2 amounts to 0.04 cm−1 and is almost independent of internuclear separation in the range R = 1.0–1.8 a.u. Thus, the method of computing the ΔR-term does not affect the vibrational energy level spacings.

Atomic interactions in neon and helium

The first two quantum corrections to the second virial coefficients of the Smith-Thakkar potential are calculated. Parameters for neon and helium, gases in which quantum effects are important, are then determined by fitting to semiempirical dispersion coefficients and experimental second virial coefficients. Viscosity coefficients for both gases and vibrational energy level spacings for the neon dimer are calculated as independent tests of the potentials. Overall agreement with experiment is excellent for neon and moderate for helium. The previously determined parameters for argon are found to be only very slightly perturbed by the inclusion of quantum corrections in the calculated second virial coefficients.

Determination of the Interatomic Potential of Krypton

New measurements of the differential collision cross section for Kr + Kr are presented and, together with previously published data, are analyzed in terms of a Morse—Spline—van der Waals interatomic potential function. By means of a least-squares fitting procedure a potential is obtained which best describes the measurements. This potential also predicts second virial coefficients and vibrational-level spacings that agree well with experiment. Some of the difficulties that arise in attempting the inversion of scattering data in this and similar systems are discussed. Finally, we present a comparison with some low-temperature solid-state data.

Modeling of a pulsed CO/N2 molecular laser system. II. Effect of mixture components and temperature variation

The CO molecular laser model described in a previous publication has been used to investigate the effect of molecular mixture components and kinetic temperature variations on improving the gain of low-lying CO infrared transitions. Gas mixtures involving diatomic molecules with both larger and smaller vibrational level spacing than CO are investigated. Vibrational pumping of CO by a molecule having a smaller vibrational spacing leads to negligible laser gain predictions due to the nonspecific nature of vibrational exchange processes. The largest predicted gain in the low-lying transitions of CO is found for N2/CO mixtures at 77°K in which appreciable gain in the 2–1 transition is found.

ChemInform Abstract: SPECTROSCOPIC INFORMATION ON GROUND‐STATE AR2, KR2 AND XE2 FROM INTERATOMIC POTENTIALS

AbstractDie Rotations‐Schwingungsniveaus für die Grundzustände der zweiatomigen Edelgasmoleküle Arz, Kr, und Xez werden durch numerische Integration der radialen Schrödinger‐Gleichung berechnet.

Vibrational spacings for H2+, D2+and H2

New calculations are presented for the vibrational energy level spacings of the electronic ground states of H2 + and D2 + at the adiabatic level of approximation. A second-order perturbation method is used to find the non-adiabatic corrections to these spacings. The relevance of these results to the discrepancies between the observed and calculated vibrational spacings for H2 is discussed.

Spectroscopic information on ground-state Ar 2, Kr 2, and Xe 2 from interatomic potentials

Calculations of vibrational and rotational level spacings of homonuclear inert gas diatomic molecules by numerical integration of the radial Schrödinger equation are presented. The potentials which were used for the ground states of Ar 2, Kr 2, and Xe 2 were obtained from accurate fits to the molecular beam scattering data. From the calculated ΔG v+ 1 2 ' s and B v 's, the following spectroscopic constants (in cm −1) were fitted: for Ar 2 ω e = 31.92, ω e x e = 3.31, ω e y e = 0.11, B e = 0.060, α e = 0.004; for Kr 2 ω e ⋍ 23.99 , ω ex e ⋍ 1.30 , ω ey e ⋍ 0.021 , B e ⋍ 0.024 , α e ⋍ 0.001 ; for Xe 2 ω e ⋍ 21.26 , ω ex e ⋍ 0.75 , ω ey e ⋍ 0.008 , B e ⋍ 0.013 , α e ⋍ 0.0004 .

Classical dynamical investigations of reaction mechanism in three-body hydrogen-halogen systems

A theoretical investigation of the reaction mechanisms in eight different three-body hydrogen-halogen reactions has been accomplished by means of Monte Carlo averages over classical trajectories computed on reasonable semiempirical potential-energy surfaces. Two of the surfaces employed contain a single adjustable parameter characteristic of a halogen core charge while six others result from unadjusted computations. The analysis shows that dynamic effects resulting from momentum transfer require the reactions M2+X=MX+M (M=H,D, or T; X=Br or I) to proceed through excited vibrational states of M2. Reaction of the ground vibrational state is dynamically forbidden in each case. Reaction rate coefficients, associated activation energies, pre-exponential factors, and kinetic isotope effects calculated from rotationally averaged reaction cross sections are in reasonable agreement with experiment. The computations further suggest an origin for the isotope effect that is significantly different from that derived from statistical mechanical theory. A comparison of the relative magnitudes of the experimental activation energy and vibrational level spacing can be used to qualitatively predict the importance of dynamic effects in homogeneous gas-phase reactions of diatomic species.

The elastic constants of solid Ar

An interatomic potential for Ar 2 derived from high resolution elastic differential scattering cross sections, second virial coefficients and vibrational level spacings, by Parson et al. is used to calculate, by Monte Carlo methods, the elastic constants of solid Ar at 80°K and near zero pressure. The calculated solid state properties are compared with those of two other recently proposed Ar 2 potentials. Comparison with experiments confirm the presence of many body forces in the solid. Moreover, these appear to be almost quantitatively accounted for by the three body triple-dipole force.

Observations of Vibration–Vibration Energy Pumping between Diatomic Molecules

The simultaneous, coupled vibrational relaxation of two diatomic species is discussed theoretically. In conditions of high vibrational and low translational temperature the species with the smaller vibrational energy level spacing will be vibrationally pumped by the other species.

Vibrational Effects in Molecular Exciton Motion Along a Polymer

Two aspects of the effects of molecular vibrations on exciton motion are considered: First is the reversible evolution of an electronically excited state of a system of molecules, in each of which many vibrational excitations are possible upon electronic excitation. Vibrational structure of the ground state is ignored. The reversible, or coherent, propagation is found to depend on the parameter 2πν2δ—1, where ν2 is the intermolecular coupling energy of individual vibronic levels, and δ is the spacing of vibrational levels. Second is the irreversible effect of vibrational relaxation in individual molecules through interaction with the solvent. The result of a heuristic treatment is that simple diffusive motion occurs if the relaxation time is much smaller than 2πhδ—1, and the diffusion coefficient is calculated. Throughout, we deal with an infinite, linear array of molecules.

Situation of the A (3) Level in the Nitrogen Molecule

HERZBERG and Sponer1 have recently reported that the A(3) level of N2 lies 6.14 volts above the X (ground) level. They have assumed in deriving this value that Kaplan's new band system2 is indeed the intercombination A – X. For this hypothesis the spacing of Kaplan's upper vibrational levels affords some support. On the other hand, direct estimates of the position of this level by the method of electron collision, including Sponer's3 original determination, agree in placing it at least two volts higher than the above value.