An overview of the graphically contracted function (GCF) method is presented.  The GCF method is based on an explicit underlying wave function expansion using the graphical unitary group approach (GUGA), but it is parameterized in such a way that the 1-RDM and 2-RDM can be computed with only O(n2) and O(n4) effort respectively for n molecular orbitals. The efficient computation of the hamiltonian matrix in a GCF basis is based on computing the 1-RDM and 2-RDM elements which are then immediately contracted with the appropriate hamiltonian integrals.  Spin-density matrices, which can be used to compute spin-dependent expectation values, can be computed with O(n2) effort by combining particular 1-RDM and 2-RDM elements recursively.

Reduced density matrices within the graphically contracted function method

242nd National Meeting (2011)

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