Evaluation of the Bethe Logarithm: From Atom to Chemical Reaction

Bound-State Relativistic Quantum Electrodynamics: A Perspective for Precision Physics with Atoms and Molecules

Precision physics aims to use atoms and molecules to test and develop the fundamental theory of matter, possibly beyond the Standard Model. Most of the atomic and molecular phenomena are described by the quantum electrodynamics (QED) sector of the Standard Model. Do we have the computational tools, algorithms, and practical equations for the most possible complete computation of atoms and molecules within the QED sector? What is the fundamental equation to start with? Is it still Schrödinger's wave equation for molecular matter, or is there anything beyond that? This paper provides a concise overview of the relativistic QED framework and recent numerical developments targeting precision physics and spectroscopy applications with common features of the robust and successful relativistic quantum chemistry methodology.

The Bethe-Salpeter QED Wave Equation for Bound-State Computations of Atoms and Molecules

Interactions in atomic and molecular systems are dominated by electromagnetic forces and the theoretical framework must be in the quantum regime. The physical theory for the combination of quantum mechanics and electromagnetism, quantum electrodynamics has been "established" by the mid-twentieth century, primarily as a scattering theory. To describe atoms and molecules, it is important to consider bound states. In the nonrelativistic quantum mechanics framework, bound states can be efficiently computed using robust and general methodologies with systematic approximations developed for solving wave equations. With the sight of the development of a computational quantum electrodynamics framework for atomic and molecular matter, the field theoretic Bethe-Salpeter wave equation expressed in space-time coordinates, its exact equal-time variant, and emergence of a relativistic wave equation, is reviewed. A computational framework, with initial applications and future challenges in relation with precision spectroscopy, is also highlighted.

Relativistic two-electron atomic and molecular energies using LS coupling and double groups: Role of the triplet contributions to singlet states

The triplet contribution is computed to the 1 and 2 S0e1 states of the He atom, to the 1S0e1 state of the Li⁺ and Be²⁺ ions, and to the X¹Σ_g ⁺ ground state of the H₂ molecule by extensive use of double-group symmetry (equivalent to LS coupling for the atomic systems) during the course of the variational solution of the no-pair Dirac-Coulomb-Breit (DCB) wave equation. The no-pair DCB energies are converged within sub-parts-per-billion relative precision, using an explicitly correlated Gaussian basis optimized to the non-relativistic energies. The α fine-structure constant dependence of the triplet sector contribution to the variational energy is α⁴E_h at leading order, in agreement with the formal perturbation theory result available from the literature.