The time-independent electronic Schr\"odinger equation \eqref{eq:time-independent-schrodinger-equation} is the starting point for a fundamental understanding of the behaviour of electrons and, thence, of chemical structure, bonding and reactivity.  
Indeed, the past 80 years have provided overwhelming evidence that, as Dirac observed in the early days of the quantum mechanical revolution \cite{Dirac29},

\begin{quote}
	\textit{``the underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble.''}
\end{quote}

Contemporary quantum chemistry has developed in two directions: wave function-based models \cite{Helgaker} and density-based models \cite{ParrYang}.
Both spring from the Schr\"odinger equation but each reformulates this second-order partial differential equation in terms of integrals.  
For this reason, it is no exaggeration to say that the mathematical operation of integration lies at the heart of the field.  
If integration of functions were a trivial task, quantum chemistry would be likewise trivialised.  
But, it is not. 

