This memoir concerns the research activities I have been involved in after the end of my PhD.

In a nutshell, my PhD work deals with excited electronic states of macromolecules, such as proteins, enzymes and DNA fragments, as well as the development of QM/MM methods which combine quantum mechanics and molecular mechanics methods. 
Martin Karplus, Micheal Levitt and Arieh Warshel have been awarded the 2013 Nobel Prize in Chemistry for the seminal development of these methods. 

During the three years of my PhD, I worked on the development of a new efficient hybrid QM/MM method, as well as its implementation in a quantum chemistry package \cite{Fornili06, SLBO07}.
Part of my research project aimed at investigating spectroscopic properties and solvation effects on large systems (core ionisations, UV/Vis and IR spectra of chromophoric units) with the help of density-functional theory (DFT) and its time-dependent version (TD-DFT) \cite{CI07, AB08}. 
I have also made a series of more technical contributions, including:
\begin{itemize}
	\item combination of orthogonalisation procedures \cite{CI07};
	\item non-orthogonal molecular orbitals (biorthogonal basis sets) \cite{SLBO07};
	\item variationally-optimised strictly localized orbitals \cite{SLBO07};
	\item coupled-perturbated Hartree-Fock equations with non-variational orbitals;
	\item TD-DFT/MM coupling \cite{AB08}.
\end{itemize}
Towards the end of my PhD, I turned to new chemical situations (DNA damage, Ru@DNA complexes, reducible disulfide bonds) for which one has to ensure a proper treatment of electronic attachment \cite{SS08a, SS08b, SS08c, SS09, DNA09, RuDNA10}. 

After completing my PhD, I worked for four years as a postdoctoral fellow at the Research School of Chemistry (RSC) at the Australian National University (ANU) under the supervision of Prof.~Peter Gill.
During these years, I worked extensively on two-electron systems \cite{TEOAS09, EcLimit09, Frontiers10, Concentric10, Ballium10, EcProof10, QuasiExact09, Hook10, ExSpherium10, QR12, Exciton12}.
I also co-supervised one third-year undergraduate student (Yan Zhao) \cite{Yanium11} and one exchange student from Switzerland (Julian Strauss).
Some of this work is summarised in Chapter \ref{chap:two-electron}.

From 2013 to 2017, I was a DECRA recipient (roughly equivalent to a \textit{``ANR JCJC''}), which allowed me to concentrate on my research and steadily build my research group.
During that time, I was the group leader of the Mathematical and Theoretical Chemistry group at the RSC.
In 2014, I was awarded a Discovery Project (equivalent to a \textit{``Projet ANR''}), and I was promoted to senior lecturer.
Thanks to this Discovery Project grant, I hired a postdoctoral fellow (Dr Davids Agboola) on a one-year contract, followed by Dr Marat Sibaev on a two-year contract. 
In 2016, I was a full-time lecturer at the ANU and a visiting Erskine fellow at the University of Canterbury.
I also organise with Deborah Crittenden (University of Canterbury, New Zealand) the \textit{2nd Quantum and Computational Chemistry Student Conference} in Christchurch NZ.

During my time at the ANU, I supervised three Master students (Anneke Knol, Sam Backwell and Fergus Rogers). 
I also co-supervised two PhD students (Caleb Ball and Giuseppe Barca), who have both recently successfully completed their PhD.
In addition, I also supervised a dozen of undergraduate students: Dominic Weiller, Amy Kendrick, Ee-Faye Chong, Stuart Ferrie, Matt Plowman, Nathaniel Bloomfield, Anneke Knol, Daniel Hills, Nilupuli Senadhira, Wenqi Zhang, Harrison Barnett and Fergus Rogers.

During these years, I made several contributions on the uniform electron gas (UEG) models.
In particular, we introduced a new paradigm to study the UEG based on spherical geometry \cite{Glomium11}.
We showed that this new model is mathematically simple and well-suited to address some unsolved problems in the field. 
I also worked on more conventional UEG models, and we published three papers reporting the derivation of the closed-form expression of energy expansion coefficients \cite{2DEG11, 3DEG11, 1DEG13}.
Some of the work we performed during that time is summarised in Chapter \ref{chap:DFT-UEG}.
More recently, I have devoted part of my time to the construction of accurate trial wave functions incorporating explicit electronic correlation.
Some of this work is discussed in Chapter \ref{chap:ManyElectronIntegrals}.

Since February 2017, I have been a CNRS researcher at the \textit{Laboratoire de Chimie et Physique Quantiques} at the Universit\'e Paul Sabatier in Toulouse.
The research projects we are currently pursuing are summarised in Chapter \ref{chap:future}.
