Nonadiabatic corrections to rovibrational levels of H2

Pachucki, Krzysztof; Komasa, Jacek

doi:10.1063/1.3114680

Cited by 160 publications

(199 citation statements)

References 23 publications

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“…Adiabatic and nonadiabatic corrections are subsequently calculated perturbatively in powers of the electron-nucleus mass ratio. This procedure results in nonrelativistic binding energies accurate to a few parts in 10 −4 cm −1 [47]. The u − g symmetry-breaking is taken into account for the specific case of HD [34].…”

Section: Qed Calculations In Neutral and Ionic Molecular Hydrogenmentioning

confidence: 99%

Bounds on fifth forces from precision measurements on molecules

et al. 2013

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Highly accurate results from frequency measurements on neutral hydrogen molecules H2, HD and D2 as well as the HD + ion can be interpreted in terms of constraints on possible fifth-force interactions. Where the hydrogen atom is a probe for yet unknown lepton-hadron interactions, and the helium atom is sensitive for lepton-lepton interactions, molecules open the domain to search for additional long-range hadron-hadron forces. First principles calculations in the framework of quantum electrodynamics have now advanced to the level that hydrogen molecules and hydrogen molecular ions have become calculable systems, making them a search-ground for fifth forces. Following a phenomenological treatment of unknown hadron-hadron interactions written in terms of a Yukawa potential of the form V5(r) = β exp(−r/λ)/r current precision measurements on hydrogenic molecules yield a constraint β < 1 × 10 −7 eV·Å for long-range hadron-hadron interactions at typical force ranges commensurate with separations of a chemical bond, i.e. λ ≈ 1Å and beyond.

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Section: Qed Calculations In Neutral and Ionic Molecular Hydrogenmentioning

confidence: 99%

Bounds on fifth forces from precision measurements on molecules

et al. 2013

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“…The nonrelativistic energy E (0) is obtained by first producing a Born-Oppenheimer potential with 15 digit accuracy [26], and then solving the Schrödinger equation and calculating adiabatic and nonadiabatic corrections perturbatively in powers of the electron-nucleus mass ratio [27]. The resulting nonrelativistic binding energies are accurate to a few parts in 10 −4 cm −1 [27] and are in excellent agreement with the direct nonadiabatic calculations (a variational approach) for rotationless molecular hydrogenic levels, performed by Adamowicz and co-workers for the case of H 2 [28].…”

Section: × 10mentioning

confidence: 99%

Fundamental Vibration of Molecular Hydrogen

et al. 2013

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The fundamental ground tone vibration of H2, HD, and D2 is determined to an accuracy of 2 × 10 −4 cm −1 from Doppler-free laser spectroscopy in the collisionless environment of a molecular beam. This rotationless vibrational splitting is derived from the combination difference between electronic excitation from the X 1 Σ + g , v = 0 and v = 1 levels to a common EF 1 Σ + g , v = 0 level. Agreement within 1σ between the experimental result and a full ab initio calculation provides a stringent test of quantum electrodynamics in a chemically-bound system.Quantum electrodynamics (QED), the fully quantized and relativistic version of electromagnetism, solves the problem of infinities associated with charged point-like particles and includes the effects of spontaneous particleantiparticle generation from the vacuum. QED is tested to extreme precision by comparing values for the electromagnetic coupling constant α obtained from measurements of the g-factor of the electron [1] and from interferometric atomic recoil measurements [2]. These experiments and the Lamb shift measurements in atomic hydrogen [3,4] have made QED the most accurately tested theory in physics. Concerning molecules, significant progress has been made recently in theoretical [5] and experimental [6,7] investigations of QED phenomena in the HD + molecular ion, where multiple angular momenta (rotational, electronic and nuclear spins) play a role. Neutral hydrogen has also recently been targeted for QED-tests, via a measurement of the dissociation energy of the H 2 [8], HD [9], and D 2 [10] molecules, and the experimental determination of rotationally excited quantum levels inThe rotationless fundamental ground tone (i.e. the vibrational energy splitting between the v ′′ = 0, J ′′ = 0 and v ′ = 1, J ′ = 0 quantum states) of the neutral hydrogen molecule is an ideal test system for several reasons. The total electronic angular momentum is zero for the X 1 Σ + g ground state and the total nuclear spin for the rotationless J = 0 state of para-H 2 is also zero resulting in a simple spectrum without hyperfine splitting. The hyperfine splitting is extremely small in HD (down to the Hz level [12]) and D 2 in the absence of an I · J interaction for the J = 0 ground state. The recent progress in theory allows for calculations involving relativistic and QED-effects up to order α 4 [13,14]. Energy contributions in the calculation cancel to a large degree for the fundamental ground tone, leading to a significant reduction in the uncertainty, thereby allowing for accurate QED tests.The present study focuses on a precise laser spectroscopic measurement of the rotationless fundamental quantum of vibration in H 2 , HD and D 2 . In the absence of rotation a one-photon transition between the FIG. 1. (Color online)A schematic layout of the experimental setup. The oscillator cavity is seeded by a cw Ti:Sa laser, the pulsed output of which makes multiple passes in an amplifier stage. The amplified output is frequency up-converted in two frequency doubling (SHG) stages leadin...

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“…63 This work demonstrates what is needed for the precise ab initio determination of ro-vibrational energy levels. It transpires that the non-relativistic problem can be solved equally accurately using a direct fully nonadiabatic approach 64 or using the more traditional BO separation approach of solving the frozen geometry electronic structure problem 65 augmented by diagonal (adiabatic) 66 and off-diagonal (non-adiabatic) 67 corrections to the BO approximation. Rather remarkably, the current largest source of uncertainty is the treatment of quantum electrodynamic (QED) effects; 68 in this it echoes high precision calculations on the isoelectronic helium atom.…”

Section: Hydrogenic Systems As Benchmarksmentioning

confidence: 99%

Perspective: Accurate ro-vibrational calculations on small molecules

Tennyson

2016

The Journal of Chemical Physics

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In what has been described as the fourth age of quantum chemistry, variational nuclear motion programs are now routinely being used to obtain the vibration-rotation levels and corresponding wavefunctions of small molecules to the sort of high accuracy demanded by comparison with spectroscopy. In this perspective, I will discuss the current state-of-the-art which, for example, shows that these calculations are increasingly competitive with measurements or, indeed, replacing them and thus becoming the primary source of data on key processes. To achieve this accuracy ab initio requires consideration of small effects, routinely ignored in standard calculations, such as those due to quantum electrodynamics. Variational calculations are being used to generate huge lists of transitions which provide the input for models of radiative transport through hot atmospheres and to fill in or even replace measured transition intensities. Future prospects such as the study of molecular states near dissociation, which can provide a link with low-energy chemical reactions, are discussed. Published by AIP Publishing. [http://dx

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Nonadiabatic corrections to rovibrational levels of H2

Cited by 160 publications

References 23 publications

Bounds on fifth forces from precision measurements on molecules

Bounds on fifth forces from precision measurements on molecules

Fundamental Vibration of Molecular Hydrogen

Perspective: Accurate ro-vibrational calculations on small molecules

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