Molecular Quantum Electrodynamics – molQED

The molQED team is a collaboration between theoretical chemists, physicists and mathematicians. We address our objective in two steps. In a first pragmatic step we will incorporate effective QED potentials, already available for atoms, into molecular calculations. Our platform for development will be the DIRAC program which is presently the leading program for 2- and 4-component relativistic molecular calculations with extensive functionality for molecular properties. In a second, more ambitious and therefore more risk-prone step we plan to formulate and implement a variational approach to QED in the framework of existing quantum chemical methods such as Hartree-Fock and Density Functional Theory. A key challenge will be real-space renormalisation to curb the singularities known from previous QED work. The success of this step hinges on the the mathematicians of the molQED team.

We have completed the implementation of effective QED potentials in the DIRAC code for relativistic molecular calculations. This provides unique functionality. We are presently investigating the effect of QED on molecular geometries and electric field gradient and will next extend our study to Mössbauer spectroscopy, NMR parameters, X-ray absorption spectroscopy as well as the (possible) electric dipole moment of the electron.

Molecular calculations use basis set expansions of orbitals and this requires careful design. The special consideration for molecules with many heavy atoms have been carefully analyzed mathematically.

The molQED project aims at providing a definite answer as to whether QED effects are important in the description of molecular properties. This is in itself important information, in particular for highly accurate calculations, e.g. providing precise values of NMR and Mössbauer parameters. However, such calculations go beyond purely chemical applications. Accurate calculations of the electric field gradient at nuclear positions combined with experiment allows the precise determination of nuclear quadrupole moments. Accurate calculations combined with atomic and molecular spectroscopy may ultimately allow the extraction of physical data normally only available from high-energy experiments such as the large hadron collider. One example are electroweak interactions leading to non-conservation of parity in chiral molecules which may shed new light on the origins of biochirality, the fact that Nature favors D-sugars and L-amino acids. Another example is the search for an electric dipole moment of fundamental particles such as the electron, which may
indicate new physics beyond that of the standard model of particle physics.

The molQED project furthermore attempts to provide a variational formulation of QED, in contrast to the usual perturbative formulation. This will provide a deeper understanding of the underlying physics of renormalization and very likely provide new mathematical techniques adapted for use within the finite basis approximation. It will allow the study of processes where a perturbative approach is no longer valid, such as the collision of heavy atoms with the fleeing creation of atomic species of charge beyond a critical value that might lead to a charge vacuum and new physics. An even more tantalizing aspect of such a variational formulation of QED would be that it might provide leads as to obtain variational formulations of quantum field theory for other forces in Nature, such as the strong force, where a perturbative approach is less justified.

Talks and posters at international conferences.

During the past thirty years it has been realized that relativistic effects have a profound impact on chemistry. It may be asked whether relativity was the last train from physics to chemistry, or whether further refinement is needed by taking into account the effects of quantum electrodynamics (QED). The present proposal aims at providing a definite answer to this question as well as providing tools for its exploration.

Previous studies indicate that the effect of QED on valence properties, such as electron affinities and ionization energies, is to reduce the relativistic effects by about five percent, which is rather modest. The situation for properties that depend on the electron density in the vicinity of nuclei is less clear. We therefore plan to investigate QED effects in chemistry with emphasis on such properties, notably on NMR parameters, on core and Mössbauer spectroscopies and on electric field gradients (which allows the determination of nuclear electric quadrupole moments).

Another domain in which QED effects may come into play concerns spectroscopic tests of fundamental physics. Spectroscopic experiments of extreme precision have been carried out on atoms and molecules in order to probe the standard model of the universe, as well as alternative models. Examples of such experiments concern the non- conservation of parity of chiral molecules as well as the search for a possible electric dipole moment of fundamental particles such as the electron. These experiments depend on theory for guidance and for the extraction of the quantities of interest. Ultimately the combination of theory with atomic and molecular spectroscopy may allow the determination of physical observables normally obtained from high-energy experiments such as the large hadron collider, but this would require not only experiments, but also theoretical calculations of very high accuracy, hence the need to know the importance of QED effects for such properties.

We address our objective in two steps. In a first pragmatic step we will incorporate effective QED potentials, already available for atoms, into molecular calculations. Our platform for development will be the DIRAC program which is presently the leading program for 2- and 4-component relativistic molecular calculations with extensive functionality for molecular properties. In a second, more ambitious and therefore more risk-prone step we plan to formulate and implement a variational approach to QED in the framework of existing quantum chemical methods such as Hartree-Fock and Density Functional Theory. A key challenge will be real-space renormalisation to curb the singularities known from previous QED work, but now to be carried out in the framework of finite basis set expansions. The success of this step hinges on the multidisciplinary character of the molQED team, involving theoretical chemists, physicists and mathematicians