Periodic Reporting for period 3 - POLYQUANT (Theoretical developments for precision spectroscopy of polyatomic and polyelectronic molecules)
Reporting period: 2023-01-01 to 2024-06-30
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 theoretical and computational framework for molecular systems. Theoretical, methodological, and 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 the most precise spectroscopy experiments.
Motivated by the recent massive increase in the energy resolution of the best spectroscopy experiments, by sophisticated control of molecular quantum states and synchronization of spectrometers to atomic clocks, it is necessary to develop ultra-precise quantum chemistry, which must be six-to-nine orders of magnitude beyond the standard, ca. 1 mEh, chemical accuracy of traditional quantum chemistry. It is not just about solving the existing equations more precisely. It is necessary to go beyond the two fundamental approximations, the Born-Oppenheimer and the non-relativistic approximations, of the established molecular quantum mechanics framework.
New theoretical and computational approaches are being developed in POLYQUANT in order to establish this new realm of molecular computations for quantitative comparison with precision spectroscopy results to test the underlying physical equations and the fundamental physical constants used in the equations.
In the POLYQUANT project, theoretical, algorithmic and methodological developements have been carried out along these lines. As a result, the POLYQUANT team computed tight 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 for a series of few-particle atomic and molecular systems to extend the current boundaries of molecular quantum mechanics and to help interpreting experimental results and designing new experiments. Variational relativistic computations became possible with an unprecedented accuracy, and a 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. A new and robust approach was developed to compute regularized relativistic corrections for molecular systems in an automated fashion.
All in all, theoretical and methodological progress has been made for an ultra-precise quantum chemsitry framework to keep up with the progess of ultra-precise spectroscopy and providing possible guidance for quantum technology developments operating on a molecular platform.
New theoretical and computational approaches are being developed in POLYQUANT in order to establish this new realm of molecular computations for quantitative comparison with precision spectroscopy results to test the underlying physical equations and the fundamental physical constants used in the equations.
In the POLYQUANT project, theoretical, algorithmic and methodological developements have been carried out along these lines. As a result, the POLYQUANT team computed tight 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 for a series of few-particle atomic and molecular systems to extend the current boundaries of molecular quantum mechanics and to help interpreting experimental results and designing new experiments. Variational relativistic computations became possible with an unprecedented accuracy, and a 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. A new and robust approach was developed to compute regularized relativistic corrections for molecular systems in an automated fashion.
All in all, theoretical and methodological progress has been made for an ultra-precise quantum chemsitry framework to keep up with the progess of ultra-precise spectroscopy and providing possible guidance for quantum technology developments operating on a molecular platform.
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.
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.