Invited lecture: A QFT-based theory for molecular properties Fundamentals and some applications to NMR spectroscopic parameters

GUSTAVO A. AUCAR

Smolenice

Congreso; XI REHE (2014); 2014

Comité organizador

During the last few years several attempts to introduce relativistic quantum methods in a QED framework were published1. One of the main difficulties is related to merging electron correlation and QED effects on the same theoretical framework. The path integral formalism was developed long time ago as an alternative to the wave function based formalism. Both are completely equivalent, though the first one is mostly applied by the quantum field community of physicist, and the second one is more traditionally applied by quantum chemist and molecular physicist. Scientists working with polarization propagators are in between. Even though calculations of atomic and molecular response properties with polarization propagators at second-order level of approach, SOPPA, are today among the most reliable, they are still not widely applied by quantum chemists, perhaps by historical reasons2. The path integral formalism is the natural quantum language that gives solid grounds to derive polarization propagators. I am going to show in this lecture how to do it and what can we learn doing it: there is a rule to write propagators within the path integral formalism as a representation. One can work out generating functionals from which to obtain double-time Green functions or polarization propagators. So the physical insights that are intrinsic to the path integral formulation of quantum mechanics are nicely applied to our propagators. Indeed one is aware now on why polarization propagators are defined with exactly the same formal expressions within both regimes, relativistic and non-relativistic: it is due to its foundations on the path integral formalism3. On the other hand, within the relativistic regime new operators shall replace the spin-adapted tensor operators. The most natural generalization are the well-known Kramers operators that span a new basis. When the matrices of the principal propagator are expressed in this last tensor basis, making c →∞ they become the NR spin-adapted matrices. This finding gives strong support on what the Kramers operators mean, and also on the physical information that the principal propagator contain at any regime. Working within the relativistic regime one should change the non relativistic way of thinking to get deeper though unusual physical insights3. My main concern is to show that from this new theoretical development, it shall be possible to find out new roads for properly including QED and electron correlation effects, on atomic and molecular properties. Why not for going even further?