Evaluation of the Bethe logarithm: from atom to chemical reaction

Ferenc, Dávid; Mátyus, Edit

doi:10.48550/arxiv.2208.03033

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References 45 publications

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“…To test the implementation, the Bethe logarithm was evaluated for several test systems and compared with the literature values in Table 4.4 [174]. The agreement supports the correctness of our code.…”

Section: Evaluation Of the Bethe Logarithmsupporting

confidence: 65%

“…The validity of this approximation is well illustrated in Table 4.5 for light atoms and Table 4.6 [25]. Table 4.4: Numerical tests of our implementation [174] for He, H + 2 , and H 2 with respect to benchmark lnk 0 values available in the literature. For the case of H 2 the authors of Ref.…”

Section: Evaluation Of the Bethe Logarithmmentioning

confidence: 87%

“…Nevertheless the most accurate method, that is directly applicable to many-electron molecules as well is nearly exactly the one proposed by Schwartz. Schwartz' method was implemented to obtain values for the Bethe logarithm of small molecules, within the BO approximation [174]. The process starts with the solution of the electronic Schrödinger equation Eq.…”

Section: Evaluation Of the Bethe Logarithmmentioning

confidence: 99%

“…[179] estimated the error to be in the last digit. To go beyond that approximation we evaluated the Bethe logarithm for several excited states of hydrogen, He + 2 , H + 3 and for the equilibrium geometry of a reactive PES, H 3 with a collinear nuclear configuration [174]. The obtained values for these systems are listed in Table 4.7.…”

Section: Evaluation Of the Bethe Logarithmmentioning

confidence: 99%

“…7: The Bethe logarithm computed in Ref [174]. for selected electronically excited states of the H 2 molecule, the ground state of H + 3 and H 2 +H at the equilibrium structures.…”

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confidence: 99%

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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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Section: Evaluation Of the Bethe Logarithmsupporting

confidence: 65%

Section: Evaluation Of the Bethe Logarithmmentioning

confidence: 87%

Section: Evaluation Of the Bethe Logarithmmentioning

confidence: 99%

Section: Evaluation Of the Bethe Logarithmmentioning

confidence: 99%

“…7: The Bethe logarithm computed in Ref [174]. for selected electronically excited states of the H 2 molecule, the ground state of H + 3 and H 2 +H at the equilibrium structures.…”

mentioning

confidence: 99%

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Relativistic QED developments for precision spectroscopy

Ferenc

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Evaluation of the Bethe logarithm: from atom to chemical reaction

Cited by 1 publication

References 45 publications

Relativistic QED developments for precision spectroscopy

Relativistic QED developments for precision spectroscopy

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