Accurate calculation of quantum electron correlation effects is essential for understanding the molecular electronic structure of organometallic chemicals. Electron correlation and de- localization contribute to stabilization of chemical species, and provide a mechanism through which non-classical and non-intuitive chemical behaviors occur. Oxidation and reduction of metal complexes, for example, are classically thought to occur at the metal site; stabilization of delocalized electrons throughout the ligand field, however, can allow for ligand-centered redox processes. These ligand-centered processes, known as ligand non-innocence, are central to an emerging area of investigation relevant to the catalysis, chemical transformation, and energy transfer fields. Computation of the correlation effects in these large organometallic species is hindered by the exponential scaling of traditional wavefunction methods which explicitly treat electron correlation. I describe several methods that are based on the two- electron reduced density matrix (2-RDM) that avoid the exponential cost of computing the entire wavefunction. Since the energy of a quantum electronic system is an exact linear functional of the 2-RDM, direct determination of the 2-RDM with respect to the electronic Hamiltonian allows the determination of the energy and correlation effects with polynomially scaling algorithms. This favorable scaling allows for the description of electron correlation for organometallic systems which are far beyond the computational capabilities of traditional wavefunction techniques. I also describe the use of analytical gradient techniques in this methodological context and show how large-scale correlated calculations offer predicted geometries of metal complexes that differ from smaller correlated calculations.