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

One-Particle Operator Representation over Two-Particle Basis Sets for Relativistic QED Computations

This work is concerned with two-spin-1/2-fermion relativistic quantum mechanics, and it is about the construction of one-particle projectors using an inherently two-particle, "explicitly correlated" basis representation necessary for good numerical convergence of the interaction energy. It is demonstrated that a faithful representation of the one-particle operators, which appear in intermediate but essential computational steps, can be constructed over a many-particle basis set by accounting for the full Hilbert space beyond the physically relevant antisymmetric subspace. Applications of this development can be foreseen for the computation of quantum-electrodynamics corrections for a correlated relativistic reference state and high-precision relativistic computations of medium-to-high-Z helium-like systems, for which other two-particle projection techniques are unreliable.

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.

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

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.

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.