Accurate level energies in the EF1, GK1, H1, B1, , B′1, , , J1Δgstates of H2

Photolysis Production and Spectroscopic Investigation of the Highest Vibrational States in H2 (X1Σg+ v = 13, 14)

Rovibrational quantum states in the X1Σg+ electronic ground state of H2 are prepared in the v = 13 vibrational level up to its highest bound rotational level J = 7, and in the highest bound vibrational level v = 14 (for J = 1) by two-photon photolysis of H2S. These states are laser-excited in a subsequent two-photon scheme into F1Σg+ outer well states, where the assignment of the highest (v,J) states is derived from a comparison of experimentally known levels in F1Σg+, combined with ab initio calculations of X1Σg+ levels. The assignments are further verified by excitation of F1Σg+ population into autoionizing continuum resonances, which are compared with multichannel quantum defect calculations. Precision spectroscopic measurements of the F-X intervals form a test for the ab initio calculations of ground state levels at high vibrational quantum numbers and large internuclear separations, for which agreement is found.

The spin-forbidden vacuum-ultraviolet absorption spectrum of 14N15N

Photoabsorption spectra of ¹⁴N¹⁵N were recorded at high resolution with a vacuum-ultraviolet Fourier-transform spectrometer fed by synchrotron radiation in the range of 81-100 nm. The combination of high column density (3 × 10¹⁷ cm^-2) and low temperature (98 K) allowed for the recording of weak spin-forbidden absorption bands' exciting levels of triplet character. The triplet states borrow intensity from ¹Π_u states of Rydberg and valence character while causing their predissociation. New predissociation linewidths and molecular constants are obtained for the states C³Π_u(v = 7, 8, 14, 15, 16, 21), G³Π_u(v = 0, 1, 4), and F³Π_u(v = 0). The positions and widths of these levels are shown to be well-predicted by a coupled-Schrödinger equation model with empirical parameters based on experimental data on ¹⁴N₂ and ¹⁵N₂ triplet levels.

Solving the Schrödinger equation of hydrogen molecules with the free-complement variational theory: essentially exact potential curves and vibrational levels of the ground and excited states of the Σ symmetry

The Schrödinger equation of hydrogen molecules was solved essentially exactly and systematically for calculating the potential energy curves of the electronic ground and excited states of the ¹Σ_g, ¹Σ_u, ³Σ_g, and ³Σ_u symmetries. The basic theory is the variational free complement theory, which is an exact general theory for solving the Schrödinger equation of atoms and molecules. The results are essentially exact with the absolute energies being correct beyond μ-hartree digits. Furthermore, all of the present wave functions satisfy correct orthogonalities and Hamiltonian-orthogonalities to each other at every nuclear distance along the potential curve, which makes systematic analyses and discussions possible among all the calculated electronic states. It is noteworthy that these conditions were not satisfied in many of the accurate calculations of H₂ reported so far. Based on the present essentially exact potential curves, we calculated and analyzed the vibrational energy levels associated with all the electronic states. Among them, the excited states having double-well potentials showed some interesting features of the vibrational states. These results are worthy of future investigations in astronomical studies.

Invited Review Article: Photofragment imaging

Photodissociation studies in molecular beams that employ position-sensitive particle detection to map product recoil velocities emerged thirty years ago and continue to evolve with new laser and detector technologies. These powerful methods allow application of tunable laser detection of single product quantum states, simultaneous measurement of velocity and angular momentum polarization, measurement of joint product state distributions for the detected and undetected products, coincident detection of multiple product channels, and application to radicals and ions as well as closed-shell molecules. These studies have permitted deep investigation of photochemical dynamics for a broad range of systems, revealed new reaction mechanisms, and addressed problems of practical importance in atmospheric, combustion, and interstellar chemistry. This review presents an historical overview, a detailed technical account of the range of methods employed, and selected experimental highlights illustrating the capabilities of the method.

Nonadiabatic effects on the positions and lifetimes of the low-lying rovibrational levels of the GK 1Σ and H 1Σ states of H2

The term values of rovibrational levels of the GK 1Σ+g and H 1Σ+g states of H2 have been measured with absolute and relative accuracies down to 10-4 cm-1 (≈3 MHz) and 10-6 cm-1 (≈30 kHz), respectively, by measuring transitions to long-lived high-n Rydberg states using single-mode cw laser radiation and a collimated supersonic beam of cold H2 molecules. The term values are compared with those determined in earlier experimental and theoretical investigations and the comparison points at discrepancies and a need for improved theoretical treatments of nonadiabatic, relativistic and radiative corrections for these states. The lifetimes of several low-lying rovibrational levels of the GK, H and I+ 1Πg states have been determined in pump-probe experiments. These lifetimes reveal a significant dependence on the electronic, vibrational and rotational excitation and also deviate from results obtained in earlier experimental and theoretical investigations.

Alignment of the hydrogen molecule under intense laser fields

Alignment of the electronically excited E,F state of the H₂ molecule is studied using the velocity mapping imaging technique. Photofragment images of H⁺ due to the dissociation mechanism that follows the 2-photon excitation into the (E,F; ν = 0, J = 0) electronic state show a strong dependence on laser intensity, which is attributed to the high polarizability anisotropy of the H₂ (E,F) state. We observe a marked structure in the angular distribution, which we explain as the interference between the prepared J = 0 and Stark-mixed J = 2 rovibrational states of H₂, as the laser intensity increases. Quantification of these effects allows us to extract the polarizability anisotropy of the H₂ (E,F J = 0) state yielding a value of 312 ± 82 a.u. (46 ų). By comparison, CS₂ has 10 ų, I₂ has 7 ų, and hydrochlorothiazide (C₇H₈ClN₃O₄S₂) has about 25 ų meaning that we have created the most easily aligned molecule ever measured, by creating a mixed superposition state that is highly anisotropic in its polarizability.

Precision measurements and test of molecular theory in highly excited vibrational states of H2 (v = 11)

Accurate E F 1 Σ g + - X 1 Σ g + transition energies in molecular hydrogen were determined for transitions originating from levels with highly excited vibrational quantum number, v = 11, in the ground electronic state. Doppler-free two-photon spectroscopy was applied on vibrationally excited H 2 ∗ , produced via the photodissociation of H2S, yielding transition frequencies with accuracies of 45 MHz or 0.0015 cm-1. An important improvement is the enhanced detection efficiency by resonant excitation to autoionizing 7 p π electronic Rydberg states, resulting in narrow transitions due to reduced ac-Stark effects. Using known EF level energies, the level energies of X(v = 11, J = 1, 3-5) states are derived with accuracies of typically 0.002 cm-1. These experimental values are in excellent agreement with and are more accurate than the results obtained from the most advanced ab initio molecular theory calculations including relativistic and QED contributions.

Observations of high vibrational levels of the 4fσ4(1)Σu (+) state of H2

Resonantly enhanced multiphoton ionization via the EF(1)Σg (+), v' = 6 double-well state has been used to probe the energy region below the third dissociation limit of H2 where several high vibrational levels of the 4(1)Σu (+) state are expected. Theoretical ab initio potential energy curves for this state predict a deep inner well and shallow outer well where vibrational levels above v = 8 are expected to exhibit the double-well character of the state. Since the 4(1)Σu (+) state has f-state character, transitions to it from the ground state are nominally forbidden. However, the d character of the outer well of the EF(1)Σg (+) state allows access to this state. We report observations of transitions to the v = 9-12 levels of the 4(1)Σu (+) state and compare their energies to predicted energies calculated from an ab initio potential energy curve with adiabatic corrections. Assignments are based on measured energies and linewidths, rotational constants, and expected transition strengths. The amount of agreement between the predicted values and the observations is mixed, with the largest discrepancies arising for the v = 9 level, owing to strong nonadiabatic electronic mixing in this energy region.

VIS and VUV spectroscopy of 12C17O and deperturbation analysis of the A1Π, υ = 1–5 levels

The reduced T(J) − B_AJ(J + 1) + D_AJ²(J + 1)² term values for the ¹²C¹⁷O A₁Π (υ = 5) level and for the hypothetical unperturbed crossing rovibronic levels of the perturbers.

Communication: Test of quantum chemistry in vibrationally hot hydrogen molecules

Precision measurements are performed on highly excited vibrational quantum states of molecular hydrogen. The v = 12, J = 0 - 3 rovibrational levels of H2 (X(1)Σg (+)), lying only 2000 cm(-1) below the first dissociation limit, were populated by photodissociation of H2S and their level energies were accurately determined by two-photon Doppler-free spectroscopy. A comparison between the experimental results on v = 12 level energies with the best ab initio calculations shows a good agreement, where the present experimental accuracy of 3.5 × 10(-3) cm(-1) is more precise than theory, hence providing a gateway to further test theoretical advances in this benchmark quantum system.

Limits on a gravitational field dependence of the proton-electron mass ratio from H2 in white dwarf stars

Spectra of molecular hydrogen (H2) are employed to search for a possible proton-to-electron mass ratio (μ) dependence on gravity. The Lyman transitions of H2, observed with the Hubble Space Telescope towards white dwarf stars that underwent a gravitational collapse, are compared to accurate laboratory spectra taking into account the high temperature conditions (T∼13 000  K) of their photospheres. We derive sensitivity coefficients Ki which define how the individual H2 transitions shift due to μ dependence. The spectrum of white dwarf star GD133 yields a Δμ/μ constraint of (-2.7±4.7stat±0.2syst)×10(-5) for a local environment of a gravitational potential ϕ∼10(4) ϕEarth, while that of G29-38 yields Δμ/μ=(-5.8±3.8stat±0.3syst)×10(-5) for a potential of 2×10(4) ϕEarth.

VUV Fourier-transform absorption study of the Lyman and Werner bands in D2

An extensive survey of the D(2) absorption spectrum has been performed with the high-resolution VUV Fourier-transform spectrometer employing synchrotron radiation. The frequency range of 90,000-119,000 cm(-1) covers the full depth of the potential wells of the B (1)Σ(u)(+), B' (1)Σ(u)(+), and C (1)Π(u) electronic states up to the D(1s) + D(2l) dissociation limit. Improved level energies of rovibrational levels have been determined up to respectively v = 51, v = 13, and v = 20. Highest resolution is achieved by probing absorption in a molecular gas jet with slit geometry, as well as in a liquid helium cooled static gas cell, resulting in line widths of ≈0.35 cm(-1). Extended calibration methods are employed to extract line positions of D(2) lines at absolute accuracies of 0.03 cm(-1). The D (1)Π(u) and B'' (1)Σ(u)(+) electronic states correlate with the D(1s) + D(3l]) dissociation limit, but support a few vibrational levels below the second dissociation limit, respectively, v = 0-3 and v = 0-1, and are also included in the presented study. The complete set of resulting level energies is the most comprehensive and accurate data set for D(2). The observations are compared with previous studies, both experimental and theoretical.

QED effects in molecules: test on rotational quantum states of H2

Quantum electrodynamic effects have been systematically tested in the progression of rotational quantum states in the X 1Σ(g)(+), v=0 vibronic ground state of molecular hydrogen. High-precision Doppler-free spectroscopy of the EF 1Σ(g)(+)-X 1Σ(g)(+) (0,0) band was performed with 0.005  cm(-1) accuracy on rotationally hot H2 (with rotational quantum states J up to 16). QED and relativistic contributions to rotational level energies as high as 0.13  cm(-1) are extracted, and are in perfect agreement with recent calculations of QED and high-order relativistic effects for the H2 ground state.

First constraint on cosmological variation of the proton-to-electron mass ratio from two independent telescopes

A high signal-to-noise spectrum covering the largest number of hydrogen lines (90 H(2) lines and 6 HD lines) in a high-redshift object was analyzed from an observation along the sight line to the bright quasar source J2123-005 with the Ultraviolet and Visual Echelle Spectrograph on the European Southern Observatory Very Large Telescope (Paranal, Chile). This delivers a constraint on a possible variation of the proton-to-electron mass ratio of Δμ/μ=(8.5 ± 3.6(stat) ± 2.2(syst))×10(-6) at redshift z(abs) = 2.059, which agrees well with a recently published result on the same system observed at the Keck telescope yielding Δμ/μ=(5.6 ± 5.5(stat) ± 2.9(syst))×10(-6). Both analyses used the same robust absorption line fitting procedures with detailed consideration of systematic errors.

Spectral identification of diffuse resonances in H2 above the n = 2 dissociation limit

The resonance structure in molecular hydrogen above the n = 2 dissociation limit is experimentally investigated in a 1 XUV + 1 VIS coherent two-step laser excitation process, with subsequent ionization of H(n = 2) products. Diffuse spectral features exhibiting widths of several cm(-1) in the excitation range of 118,500-120,500 cm(-1) are probed. Information on angular momentum selection rules for parallel and crossed polarizations, combination differences, the para-ortho distinction, extrapolation from rovibrational structure in the bound region below the n = 2 threshold, and mass-selective detection of H(2)(+) parent and H(+) daughter fragments is used as input. This allows for an assignment of the diffuse resonances observed in terms of (1)Σ(g)(+), (1)Π(g), and (1)Δ(g) states, specified with vibrational and rotational quantum numbers.