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Theoretical developments for precision spectroscopy of polyatomic and polyelectronic molecules

Periodic Reporting for period 2 - POLYQUANT (Theoretical developments for precision spectroscopy of polyatomic and polyelectronic molecules)

Reporting period: 2021-07-01 to 2022-12-31

POLYQUANT is about the fundamental theory of molecular matter. It aims to develop molecular quantum theory massively beyond the non-relativistic and Born‒Oppenheimer approximations, which underlie our current chemical theory. Theoretical, methodological, algorithmic developments are carried out, computations are performed to ultimately obtain numerical results from the theory and these numerical results are tested with respect to precision spectroscopy experiments.
The work performed during the first half of POLYQUANT includes theoretical, methodological, and algorithmic developments in relation with the non-adiabatic, pre-Born-Oppenheimer, relativistic and QED `corrections' using various forms of explicitly correlated (Gaussian) spatial basis functions. Motivated by the experimental energy resolution, the general relative accuracy goal in the computed atomic and molecular energies was 1:10^9 (parts-per-billion, ppb), and occasionally, we could achieve also the sub-ppb convergence regime (which resulted from several small technical and algorithmic developments during the work).

Variational energy upper bounds and also energy lower bounds (aiming for a computed error bar instead of a estimated one), non-adiabatic mass corrections, regularized perturbative relativistic corrections, and leading-order perturbative QED corrections have been computed for a series of few-particle atomic and molecular systems.

During the first half of the POLYQUANT project, variational relativistic computations (solution of the no-pair Dirac-Coulomb-Breit equation) became possible with an unprecedented accuracy, and a very systematic study was conducted to compare and validate the variational relativistic results with respect to benchmark perturbative relativistic values.

A Hylleraas-functional approach was developed for an efficient computation of the non-adiabatic mass correction for a single as well as a multi-dimensional electronic space, and a similar approach was implemented for an efficient computation of the non-relativistic Bethe logarithm required for the leading-order QED correction.

So, work has been started along several directions which is necessary to establish the general theoretical and practical methodological foundations of molecular quantum theory beyond the non-relativistic Born-Oppenheimer framework of standard quantum chemistry.
During the first half of POLYQUANT, it was possible to bridge the state-of-the-art perturbative relativistic approach (established in relation with the most precise spectroscopy experiments and specialized for the smallest systems) with the variational Dirac relativistic framework used in relativistic quantum chemistry (targeting compounds with heavy elements and high nuclear charge numbers).

During the second half of the project, radiative, retardation, and pair corrections will be better explored through the Dirac relativistic approach in relation with the already established perturbative route (which is limited to some finite order). Initial steps will be taken toward a pre-Born-Oppenheimer Dirac relativistic framework, and alternatively, a non-adiabatic relativistic approach will be explored for a series of small atomic and molecular systems.