Numerical Challenges in a Cholesky-Decomposed Local Correlation Quantum Chemistry Framework

This chapter discusses local electron correlation approximation to multireference configuration interaction theory (MRCI) and numerical implementation of this method in the code called TigerCI. The most common variant of MRCI is called multireference singles and doubles configuration interaction (MRSDCI). The chapter describes the basic approach the algorithm takes to MRCI and the local electron correlation approximation. It provides an overview of the numerical importance of the major components in the method. The chapter reviews the Cholesky decomposition of the two-electron integrals. The two-electron integrals represent one of the largest computational hurdles in a correlated wavefunction calculation. The cost of the two-electron integrals can be further reduced by exploiting their linear dependencies. The Cholesky decomposition is only stable for positive semi-definite matrices when pivoting is used. Finally, the chapter describes rebuilding the two-electron integrals after decomposition, buffering and storage of the associated data structures and the algorithm to evaluate matrix-vector products.