Performance Optimization of Tensor Contraction Expressions for Many Body Methods in Quantum Chemistry Albert Hartono, † Qingda Lu, † Thomas Henretty, † Sriram Krishnamoorthy, † Huaijian Zhang, † Gerald Baumgartner, ‡ David E. Bernholdt, ¶ Marcel Nooijen, § Russell Pitzer, † J. Ramanujam, ‡ and P. Sadayappan ∗,† The Ohio State University, Louisiana State University, Oak Ridge National Laboratory, and University of Waterloo E-mail: saday@cse.ohio-state.edu Abstract Complex tensor contraction expressions arise in accurate electronic structure models in quantum chemistry, such as the coupled cluster method. This paper addresses two complemen- tary aspects of performance optimization of such tensor contraction expressions. Transforma- tions using algebraic properties of commutativity and associativity can be used to significantly decrease the number of arithmetic operations required for evaluation of these expressions. The identification of common subexpressions among a set of tensor contraction expressions can result in a reduction of the total number of operations required to evaluate the tensor contrac- tions. The first part of the paper describes an effective algorithm for operation minimization † The Ohio State University ‡ Louisiana State University ¶ Oak Ridge National Laboratory § University of Waterloo 1