Orbital angular momentum in triatomic molecules

The effects of electronic angular momentum in triatomic linear molecules are considered. An effective vibronic hamiltonian is derived and second order energy level expressions are obtained for the bending levels in an electronic Π state. The formulae allow for the anharmonicity of the bending potentials and for the variation of the expectation value <L_z > with bond angle; effects of electron spins are also included. The vibronic levels predicted by the analytic expressions are compared with those calculated using a full matrix treatment of the orbital angular momentum; it is shown that they are far more accurate than the levels predicted by the formulae currently available in the literature. The relationship between the anharmonic corrections and the deviation of <L_z > from unity is discussed in terms of an electrostatic interaction between linear molecule states of different symmetry.     

Rydberg states of the HeH+ ion calculated by ab initio methods: potential energies and effective principal quantum numbers

More than 80 excited electronic states of the hydrohelium ion HeH⁺ of ^{1, 3}Σ⁺, ^{1, 3}Π, ^{1, 3}Δ, ^{1, 3}Φ and ^{1, 3}Γ symmetry have been calculated ab initio up to n = 6 for internuclear distances ranging from 0.5 to 100 bohr. The computations involve a configuration interaction (CI) treatment based on a home-made suite of programs that uses special basis sets designed for the representation of molecular Rydberg states. The results are compared with previous computations where these are available (up to n = 4), and it is found that except for the very lowest excited states, the present energies are consistently lower than those obtained previously, with an average lowering corresponding to several hundred cm^?1. It is shown that with the exception of its ground state, HeH⁺ is an effective one-electron system having an overall electronic structure similar to H⁺₂. The interaction of the excited electron with the He⁺ 1s core electron causes small singlet–triplet splittings to appear and ?-mixing interactions to occur, that are not present in H⁺₂.     

Das „Floating Gaussian Orbital”-Modell als Hilfsmittel zur Interpretation von Photoelektronen-Spektren

Zusammenfassung Die Floating-Gaussian-Orbital (FGO)-Methode von Frost [5] macht einfache ab-initio-SCF-Rechnungen für mittelgroße Moleküle möglich. Wir vergleichen gemäß Koopmans Theorem die Orbitalenergien von (z.T. modifizierten) FGO-Rechnungen für CH₄, C₂H₂, C₂H₄, C₂H₆, C₃H₆, C₄H₈ mit den entsprechenden Photoelektron-Spektren.

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The interpretation of photoelectron spectra by the Floating Gaussian Orbital-model

With Frost's Floating Gaussian Orbital (FGO)-method [5] simple ab-initio-SCF-calculations for medium-size molecules are possible. Based on Koopmans theorem we compare the orbital energies of (partially modified) FGO-calculations for CH₄, C₂H₂, C₂H₄, C₂H₆, C₃H₆, C₄H₈ with the corresponding photoelectron spectra.

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Résumé Avec la méthode des Floating Gaussian Orbitals (FGO) de Frost [5] il est possible d'effectuer des calculs simples SCF-ab-initio pour des molécules de largeur moyenne. Nous comparons suivant le théorème de Koopmans les énergies orbitales des calculs FGO (partiellement modifiés) pour CH₄, C₂H₂, C₂H₄, C₂H₆, C₃H₆, C₄H₈ avec les spectres de photoionisation correspondants.

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Diese Arbeit ist Teil des Projekts Nr. SR 2.120.69 des Schweizerischen Nationalfonds. Die Rechnungen wurden auf der Univac 1108 der Firma Sandoz AG, Basel durchgeführt. Wir danken der Leitung und dem Personal des Rechenzentrums für Rechenzeit und für sorgfältige Arbeiten.     

Theoretical assignments of the electronic spectrum of acetylene

Non empirical calculations of energies and properties of some excited states of acetylene are presented. A frozen core approximation is used and excitations to , and MO's are taken into account. Both valence and Rydberg states are considered. Assignments of the UV and electron impact spectra are proposed and some questions are raised.     

On equivariant self-similar wave maps

By variational methods, we establish the existence of an infinite number of self-similar wave maps which evolve from smooth, compactly supported data and develop a singularity in finite time.     

The transition probabilities from the ground state to the excited J = 0 1Σu(+) levels of H2: measurements and ab initio quantum defect study

The energies, widths and absolute intensities of the P(1) v' = 0, J' = 1 absorption transitions of H(2) have been measured in the spectral range of 81-75 nm using monochromatized synchrotron radiation. This work completes and extends previous observations, in particular those of Herzberg and Jungen [J. Mol. Spectrosc. 41, 425 (1972)]. Ab initio multichannel quantum defect theory (MQDT) is used to corroborate the spectral analysis of the experimental data. Line intensities and decay widths are also calculated using MQDT.     

Efficient ultraviolet photorefraction in LiNbO3

A nominally undoped LiNbO₃ crystal with a slightly broadened absorption edge is used to study beam coupling effects in the UV at 351 nm. At this wavelength the crystal exhibits a diffusion-dominated charge transport mechanism, which allows steady state beam amplification of up to 700 times, comparable to BaTiO₃ in the visible. The used crystal material was characterized by an absorption coefficient =2.68 cm^–1 at 351 nm and a maximal gain coefficient =13.94 cm^–1. This high gain value in the UV can be attributed to a hole diffusion-dominated charge transport mechanism together with a low bulk photovoltaic effect. We measured photovoltaic fields of the order of 550 V/cm.     

Excited states of the polyacetylenes. Analysis of the near ultraviolet spectra of diacetylene and triacetylene

The 2000–2800 Å system of diacetylene and the 2300–3000 Å system of triacetylene have been investigated. Analysis of the vibrational structure indicates that we observe transitions to a ¹Δ_u upper electronic state for both molecules and transitions to a ¹Σ^?_u state for diacetylene.     

Potential Energy Surfaces for the Na(3p)N2, Na(3p)HCN and Na(3p)C2H2 Complexes: Ab Initio Calculations and Model Considerations

Highly correlated ab initio calculations for the potential‐energy surfaces of the systems Na−N₂, Na−HCN, and Na−C₂H₂ have been performed, where the Na atom is in the 3s ground state or in the 3p excited state, and the molecules are kept fixed in their equilibrium configurations. The purpose of these calculations was to enable computer simulation of optical‐scattering experiments. In this paper, model considerations are presented that allow easy qualitative understanding of the shapes of the calculated surfaces.     

High-resolution millimeter wave spectroscopy and multichannel quantum defect theory of the hyperfine structure in high Rydberg states of molecular hydrogen H2

Experimental and theoretical methodologies have been developed to determine the hyperfine structure of molecular ions from detailed studies of the Rydberg spectrum and have been tested on molecular hydrogen. The hyperfine structure in l=0-3 Rydberg states of H2 located below the X 2Sigmag+(v+=0,N+=1) ground state of ortho H2+ has been measured in the range of principal quantum number n=50-65 at sub-MHz resolution by millimeter wave spectroscopy following laser excitation to np and nd Rydberg states using a variety of single-photon and multiphoton excitation sequences. The np1(1), nd1(1), and the nf1(0-3) Rydberg states were found to be metastable and to have lifetimes of more than 5 micros beyond n=50. Members of other series, such as the nd1(2), nd1(3), and the np1(0) series, were found to have lifetimes of more than 1 mus. Local perturbations induced by low-n Rydberg states belonging to series converging on rovibrationally excited levels of H2+ reduce the lifetimes in narrow ranges of n values. The hyperfine structure is strongly dependent on the value of the orbital angular momentum l. In the penetrating s and p states at n approximately 50 the exchange interaction dominates over the hyperfine interaction and the levels can be labeled by the total electron spin angular momentum quantum number S (S=0 or 1). In the less penetrating d and f Rydberg states, the hyperfine interaction between the core nuclear and electron spins is larger than the exchange interaction and the Rydberg states are of mixed singlet and triplet character. A procedure based on the Stark effect and on the systematic analysis of selection rules and combination differences was developed to determine the orbital and the total angular momentum quantum numbers l and F and to construct an energy map of p and f Rydberg levels between n=54 and 64 with relative positions of an accuracy of better than 1 MHz. Multichannel quantum defect theory (MQDT) was extended to treat the hyperfine structure in molecular Rydberg states and was used to analyze the observed hyperfine structure of the p and f Rydberg states of H2. The frame transformation between the Born-Oppenheimer channels described by the angular momentum coupling scheme (abetaJ) and the asymptotic channels described by the (e[bbetaS+]) coupling scheme was derived and enables an elegant treatment of all intermediate coupling cases. Purely ab initio quantum defect theory reproduced the experimentally determined positions to within 40 MHz for the p levels and 13 MHz for the f levels. By slight adjustments of the quantum defect functions and their energy dependences and by consideration of the p-f interaction, of the singlet-triplet splittings of the f levels, and of the departure of the ionic levels from pure coupling case (bbetaS+), the agreement between theory and experiment could be improved to 600 kHz. By comparing the results of MQDT calculations of the hyperfine structure of f Rydberg levels with those of coupled equations calculations, the frame transformation approximation of MQDT was shown to be accurate to within 300 kHz. The extrapolated ionic hyperfine structure of the X 2Sigmag+(v+=0,N+=1) ionic level corresponds to the ab initio prediciton of Babb and Dalgarno [Phys. Rev. A 46, R5317 (1992)] within the experimental error.