Low-order scaling local electron correlation methods. IV. Linear scaling local coupled-cluster (LCCSD)

A new implementation of local coupled-cluster theory with single and double excitations (LCCSD) is presented for which asymptotically all computational resources (CPU, memory, and disk) scale only linearly with the molecular size. This is achieved by: (i) restricting the correlation space for each electron pair to domains that are independent of molecular size; (ii) classifying the pairs according to a distance criterion and treating only strong pairs at the highest level; (iii) using efficient prescreening algorithms in the integral transformation and other integral-direct procedures; and (iv) neglect of small couplings of electron pairs that are far apart from each other. The errors caused by the various approximations are negligible. LCCSD calculations on molecules including up to 300 correlated electrons and over 1000 basis functions in $C_1$ symmetry are reported, all carried out on a workstation.