1. Beyond the no-pair approximation
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1.1 Effective QED potentials
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We have reported the implementation of three such potentials in the DIRAC program package [https://doi.org/10.1063/5.0116140]: the Uehling potential for vacuum polarization (VP) as well as two effective potentials for electron self-energy.
1.2 Towards variational QED
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At the lowest level of bound-state QED in the S-matrix formalism one finds three contributions: i) Vacuum polarization ii) Electron self-energy and iii) Single-photon exchange [relativistic two-electron interaction]
1.2.1. Vacuum polarization (VP)
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In the atomic case, upon expansion of the VP density in orders of the nuclear charge, the linear term is divergent and the physical part, generating the Uehling potential, is only obtained after charge renormalization. For the non-linear part, we have developed a robust numerical machinery for the calculation of the non-linear part of the VP density [https://doi.org/10.1103/PhysRevA.108.012808] in a finite Gaussian basis. For the linear part, we are in the process of devising schemes for regularization and renormalization in a finite basis. We have developed a way to introduce a sharp momentum cutoff in a finite basis and are currently exploring its effect. We are also exploring the Pauli-Villars regularization scheme based on the use of auxiliary masses.
1.2.2 Electron self-energy
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We are investigating the partial wave renormalization scheme for calculating the electron self-energy in atomic systems, using finite Gaussian basis sets.
1.2.3 Relativistic two-electron interaction
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Work is in progress, but not completed, for the implementation of the Breit two-electron term at the SCF and correlated levels. We have implemented the Gaunt term (part of the Breit term) for the calculation of magnetic properties at the SCF level.
2.Coupled-cluster response theory
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We have developed a general-order coupled-cluster code generator, written in python and named tenpi. Using diagrammatic methods the basic equations are formulated and then both flop count and memory is optimized by defining suitable intermediates. The generator produces several output code types, including Fortran code for modern distributed memory tensor libraries designed to run on supercomputers, but also a python code which allows for rapid prototyping and testing of methods. The generated Fortran code has been included into the DIRAC program package and enabled it for the first time to run CCSDT and CCSDTQ calculations on multiple computing nodes in parallel.
Our first target property is the electric field gradient (EFG) at nuclear positions in a molecule, which, combined with experiment, allows to extract the value of nuclear electric quadrupole moments. In preparation for more accurate calculation, we have carried out a detailed study at the DFT level of the chemical information that can be extracted from knowledge of the EFG.
