Deformed explicitly correlated Gaussians

Beutel, Matthew; Ahrens, Alexander; Huang, Chenhang; Suzuki, Y.; Varga, K.

doi:10.1063/5.0066427

Cited by 4 publications

(1 citation statement)

References 159 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…ECGs basis sets are applied in many fields of (quantum) few-body physics, including for instance nuclear structure computations [67] or in cavity quantum electrodynamics [68]. For the many applications and further theoretical details of ECG wave functions see Ref.…”

Section: Explicitly Correlated Basis Functionsmentioning

confidence: 99%

Relativistic QED developments for precision spectroscopy

Ferenc

View full text Add to dashboard Cite

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...

show abstract

Section: Explicitly Correlated Basis Functionsmentioning

confidence: 99%

Relativistic QED developments for precision spectroscopy

Ferenc

View full text Add to dashboard Cite

show abstract

Real-space, real-time approach to quantum-electrodynamical time-dependent density functional theory

Malave

Ahrens

Pitagora

et al. 2022

The Journal of Chemical Physics

View full text Add to dashboard Cite

The Quantum-Electrodynamical Time-Dependent Density Functional Theory (QED-TDDFT)equations are solved by time propagating the wave function on a tensor product of a Fock-space andreal-space grid. Applications for molecules in cavities show the accuracy of the approach. Examplesinclude the coupling strength and light frequency dependence of the energies, wave functions, op-tical absorption spectra, and Rabi splitting magnitudes in cavities, as well as a description of highharmonic generation in cavities.

show abstract

Regularized relativistic corrections for polyelectronic and polyatomic systems with explicitly correlated Gaussians

Rácsai,

Ferenc,

Margócsy

et al. 2024

The Journal of Chemical Physics

View full text Add to dashboard Cite

Drachmann’s regularization approach is implemented for floating explicitly correlated Gaussians (fECGs) and molecular systems. Earlier applications of drachmannized relativistic corrections for molecular systems were hindered due to the unknown analytic matrix elements of 1/rix1/rjy-type operators with fECGs. In the present work, one of the 1/r factors is approximated by a linear combination of Gaussians, which results in calculable integrals. The numerical approach is found to be precise and robust over a range of molecular systems and nuclear configurations, and thus, it opens the route toward an automated evaluation of high-precision relativistic corrections over potential energy surfaces of polyatomic systems. Furthermore, the newly developed integration approach makes it possible to construct the matrix representation of the square of the electronic Hamiltonian relevant for energy lower-bound as well as time-dependent computations of molecular systems with a flexible and high-precision fECG basis representation.

show abstract

Deformed explicitly correlated Gaussians

Cited by 4 publications

References 159 publications

Relativistic QED developments for precision spectroscopy

Relativistic QED developments for precision spectroscopy

Real-space, real-time approach to quantum-electrodynamical time-dependent density functional theory

Regularized relativistic corrections for polyelectronic and polyatomic systems with explicitly correlated Gaussians

Contact Info

Product

Resources

About