We explore and expand the known potential energy surface of Si6Li6 using quantum topology within the QTAIM formalism to include seventeen new unique topologies. To accommodate the non-nuclear attractors (NNAs) that exist for some isomers of Si6Li6, two types of 3-D quantum topology phase diagram are created to ensure unique solutions of the Poincare-Hopf relation. The position of the most energetically stable isomer on the quantum topology phase diagram contrasts strongly with earlier work on a range of isomer sets. A cage critical point (CCP) violating the condition of enclosing topological features is discovered for a topologically unstable molecular graph. (C) 2014 Elsevier B.V. All rights reserved.