The Strong Interaction Limit of the Møller-Plesset Adiabatic Connection
Authors:   , Daas Kimberly Jennifer 
Published: May 2024

All the information needed to describe chemical reactions can be obtained by solving the time dependent Schrödinger equation. However, this is only viable for the smallest of systems and for any chemically relevant system approximations are needed. The most used method for quantum chemical simulations is Density Functional Theory (DFT), which is formally exact and uses instead of the multidimensional wavefunction the three-dimensional electron density. However, for DFT calculations to be feasible and computationally inexpensive, approximations need to be made to the exchange correlation energy, which is the only part that cannot be calculated exactly. A systematic way to make approximations to the exchange correlation energy is the adiabatic connection, which links the non-interacting Kohn-Sham system, which can be solved exactly, to the physical system. Most DFT functionals can now be understood as linear extrapolations from the Kohn-Sham system to the physical system.

However, getting accurate results from extrapolating information is generally a hard problem, which even the most sophisticated machine learning algorithms struggle with, compared to interpolating them. Therefore, the mathematical structure of the strong interaction limit of DFT was derived, which is an exactly solvable system that can be used as the endpoint for future interpolations, which in turn lead to the creation of a new class of DFT functionals. Interestingly, we can also link a different non-interacting system, the Hartree-Fock system, to the physical system, which lead to the creation of the Møller-Plesset Adiabatic Connection (MPAC), which has as small coupling limit the Møller-Plesset Perturbation Theory (MPPT) series. This adiabatic connection allows us to obtain the correlation energy via interpolations functionals, although the strong coupling limit needs to be derived first.

In this work, the strong coupling limit of the MPAC was studied for the hydrogen atom and the results of the first three leading order terms were generalized to many-electron systems with different spins. After that accurate gradient expansion approximations were derived for the first two leading order terms to make these functionals more computationally viable. For this a compact representation, based on the large Z limit, is introduced to find the best coefficient for the gradient expansion. This inspired a subsequent investigation into the DFT adiabatic connection, which showed a surprising symmetry between the magnitude of the gradient expansion coefficient of the weak interaction limit (exchange energy) and strong interaction limit. Lastly a new class of interpolation functions was introduced for the MPAC to tackle non-covalent interactions (NCIs). These were shown to be competitive with dispersion corrected hybrid and double hybrid functionals at the computational cost of double hybrids. However, cost saving techniques as well as regularization were used to not only make the calculations computationally cheaper but also to further improve the accuracy of the method. This resulted in new functionals that can tackle a variety of NCIs and outperform dispersion corrected (double) hybrid functionals.