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\chapter{Summary}
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The goal of this work is to develop computational methods for
large-scale correlated electronic structure calculations which provide
better performance than the traditional methods and effectively
utilize massively parallel computers.  The resolution of the identity
(RI) and orbital invariant (OI) approaches are both very promising for
different types of chemical problems, but both require further
development before they can be considered as viable alternatives to
traditional correlated calculations in the general case.

This proposal describes a research program that will carry out the
necessary developments, using second-order many-body perturbation
theory (MP2) as the initial context in which to develop the RI and OI
approaches:
%\begin{itemize}
\begin{list}{{$\bullet$}}{\itemsep 0pt}  
\item Understand the requirements on, and the behavior of, the RI
fitting basis, developing a strategy to derive suitable fitting sets
automatically from the user's chosen AO basis.
\item Examine the sparsity of electronic interactions in large
systems, apropos of both the OI approach and other methods which
depend on locality.
\item Incorporate sparsity effectively into the Global Array
programming model, in accord with the ``experimental'' findings
above.
\item Develop and implement analytic gradients for OI- and
RI-MP2.
\item Apply these methods to problems in the areas of metal binding to
18-crown-6 ethers, and electronic materials.
\end{list}
%\end{itemize}

Since the primary focus of this proposal is the development of new
{\em methodology} for the treatment of large molecules, the impact of
this work will extend well beyond this particular project.  These
tools, which will be available as part of the NWChem computational
chemistry package, can and will be applied to a broad range of
chemical problems, of course.  But the ideas behind them also have
application in other, higher level correlated methods.  Similarly, the
specific knowledge gained about the behavior of electronic
interactions in large systems will benefit other methods under
development which rely on locality, including attempts to apply
``linear scaling'' techniques to correlated methods.

In that goal of this research program is to push the boundaries of
large-scale calculations, it is also important to take full advantage
of the capabilities of high-performance computers, which means
parallel implementations.  This work will use the NWChem parallel
computational chemistry code, and the Global Array programming model
as its base.  Building on the substantial experience with parallel
correlated electronic structure techniques embodied in NWChem,
parallelism can be incorporated into this work with almost no
additional effort or risk. The benefits of this work will include
enhancements to the public domain Global Array Toolkit, which is
widely used in the chemistry community and elsewhere, as well as the
practical experience, on which others will be able to draw to further
the incorporation of parallel computing into the standard ``tool box''
of our field.

Finally, this work includes demonstrations the effectiveness of these
approaches by applying them to problems of environmental and materials
interest, such as the design of organic light emiting diodes and the
binding of metal cations to crown ethers.
