Born–Oppenheimer potentials for Π, Δ, and Φ states of the hydrogen molecule

Siłkowski, Michał; Pachucki, Krzysztof

doi:10.1080/00268976.2022.2062471

Cited by 8 publications

(3 citation statements)

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“…For the calculation for a highly excited state, the nonadiabatic perturbation theory (NAPT) gives an accuracy of about 10 À4 cm À1 . 64,65 The next coefficient E (4) is the leading relativistic correction. It has been calculated for the ground electronic state ( 1 S + g ) using the nonadiabatic explicitly correlated Gaussian (ECG) functions with a precision below 10 À6 cm À1 .…”

Section: Theoretical Energy Levelsmentioning

confidence: 99%

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Precision spectroscopy of molecular hydrogen

Liu,

Tan,

Cheng

et al. 2023

Phys. Chem. Chem. Phys.

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Section: Theoretical Energy Levelsmentioning

confidence: 99%

“…For the calculation for a highly excited state, the nonadiabatic perturbation theory (NAPT) gives an accuracy of about 10 −4 cm −1 . 64,65…”

Section: Theoretical Energy Levelsmentioning

confidence: 99%

Precision spectroscopy of molecular hydrogen

Liu,

Tan,

Cheng

et al. 2023

Phys. Chem. Chem. Phys.

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“…where α 1 , α 2 and β 1 , β 2 are variational parameters. More than fifty years after the original work, the Kołos-Wolniewicz basis set is still used with great success for the ground [54] and excited states of hydrogen [55,56].…”

Section: Explicitly Correlated Basis Functionsmentioning

confidence: 99%

Relativistic QED developments for precision spectroscopy

Ferenc

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Many of the topics, discussed in this thesis are beyond the scope of the usual quantum chemistry curriculum. Sadly there is no truly comprehensive, up-to-date textbook, which would serve as a guide through the relevant chapters of relativistic quantum theory of bound states, hence I decided to give a detailed and general theoretical introduction to the field. Wherever it is appropriate to the discussed topic my contribution to the field is presented in the form of numerical examples or methodological developments. The precise details of the computations are found in the referenced original papers.The thesis is divided into four main chapters. At first the non-relativistic theory of interacting charged particles is considered in a somewhat broader sense than usual, including methods, that do not separate the nuclear and electronic degrees of freedom. The second chapter starts with a quick revision of special relativity and continues with the discussion of the basics of relativistic quantum mechanics, in a simple traditional manner, yet based on rigorous theoretical considerations. In Chapter 4-since there are many excellent textbooks on QED-a more practical approach is taken, and I focus on the correction terms arising in atomic-and molecular bound states. The last section of that chapter sets the scene for Chapter 5 where the fully relativistic developments are discussed. The appendix contains some useful formulas and derivations for the sake of deeper understanding and completeness of the material. i Acknowledgement I am grateful to Edit Mátyus for her support and kindness during the past five years. I feel very lucky that I have had the opportunity to do my PhD under her supervision. I am also especially grateful to Péter Jeszenszki, once for proofreading my thesis and twice for the his inspiring attitude towards scientific research. I would like to thank all members of the Molecular Quantum Dynamics research group, especially Tibor Keresztesi for the tremendous amount of help with any (im)possible issue, Alberto Martín Santa Daría and Gustavo Avila for creating a great environment in the group (and in our office) and Eszter Saly for her work and commitment towards our research topics. I am gratefully for the help of Dániel Nógrádi, to whom I could frequently turn with my questions regarding quantum field theory.Finally I would like to thank my family, especially my parents, my sister, and Szilvia Tóth for their endless support during my studies.iii Contents Preface i Acknowledgement iii Notations and conventions vii List of abbreviations BO Born-Oppenheimer BP Breit-Pauli BS Bethe-Salpeter CCR complex coordinate rotation COM center of mass DC Dirac-Coulomb DC(B) Dirac-Coulomb(-Breit) DCB Dirac-Coulomb-Breit ECG explicitly correlated Gaussian GVR global vector representation KB kinetic balance LF laboratory frame NRQED nonrelativistic quantum electrodynamics pBO pre-Born-Oppenheimer PEC potential energy curve PES potential energy surface PG point group QED quantum electrodynamics QFT quantum field theory RKB re...

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Advances in cavity-enhanced methods for high precision molecular spectroscopy and test of fundamental physics

Gianfrani,

Hu,

Ubachs

2024

Riv. Nuovo Cim.

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Cavity-enhanced spectroscopic techniques are highly sensitive laser-based methods for interrogating the atomic and molecular constituents of any gaseous medium that is confined into an optical resonator. A first advantage over conventional absorption spectroscopy comes from the extremely long path length of the laser radiation inside the stable, high-finesse, optical cavity, which allows the sample to be probed over several tens of kilometers. After more than 30 years of research and development, techniques like cavity ring-down spectroscopy, cavity-enhanced absorption spectroscopy, and noise-immune cavity-enhanced optical-heterodyne molecular spectroscopy, have reached extraordinary levels of detection sensitivity, such that it is possible to measure light absorption from molecules in trace amounts or extremely weak spectral lines of more abundant species. A second advantage of the use of high-finesse cavities lies in the power amplification achieved inside the optical resonator, making it possible to saturate even weak transitions, thus reducing the width of spectral lines by some three orders of magnitude. Combining these methods with frequency comb technologies has further enhanced their capabilities, adding metrology-grade qualities to spectroscopic determinations such as transition frequencies of molecular resonances, which can be measured with sub-kHz accuracy. In this review article, we discuss the current status of highly precise and highly sensitive laser spectroscopy for fundamental tests and measurements. We describe state-of-the-art molecular spectroscopy methods and their application to a few selected molecules of fundamental importance in understanding quantum chemistry theories or testing quantum electrodynamics.

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Born–Oppenheimer potentials for Π, Δ, and Φ states of the hydrogen molecule

Cited by 8 publications

References 62 publications

Precision spectroscopy of molecular hydrogen

Precision spectroscopy of molecular hydrogen

Relativistic QED developments for precision spectroscopy

Advances in cavity-enhanced methods for high precision molecular spectroscopy and test of fundamental physics

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