The Non-Orthogonality Problem and Orthogonalization Procedures

Re, Giuseppe Del

doi:10.1007/978-1-4757-1659-7_5

Cited by 4 publications

(1 citation statement)

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“…As the basis size increases, at some point the finite numerical precision (typically double-precision (64 bit) is used) will be insufficient to properly represent and invert a near-singular overlap matrix. There are several strategies to avoid that, for instance the Löwdin's canonic orthogonalization is commonly used [104,105,106,81]. This however proved to be inefficient when optimizing a basis set, since the omission of a linearly dependent basis function increases the energy, and further optimization only resulted in the exclusion of an increasing number of basis functions.…”

Section: Avoiding Linear Dependenciesmentioning

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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Section: Avoiding Linear Dependenciesmentioning

confidence: 99%