Stochastic Resolution\nof Identity to CC2 for Large\nSystems: Ground State and Triplet Excitation Energy Calculations

An implementation of stochastic resolution of identity\nto the CC2\n(sRI-CC2) ground state energy followed by triplet excitation energy\ncalculations is presented. A set of stochastic orbitals is introduced\nto further decouple the expensive 4-index electron repulsion integrals\non the basis of RI approximation. A Laplace transformation of the\norbital energy difference denominators into numerical summations is\nadopted to obtain a third-order overall scaling. We select a series\nof hydrogen dimer chains with nearly thousands of electrons, as well\nas some other molecules, for sRI-CC2 energies and test the accuracy\nand time consumption in comparison with those of RI-CC2. Our sRI-CC2\nresults reproduce a modest agreement with the RI-CC2 in Q-Chem program\npackage and it allows a steep scaling reduction from <i>O</i>(<i>N</i><sup>5</sup>) to <i>O</i>(<i>N</i><sup>3</sup>). Besides, the unrestricted sRI-CC2 calculations also\nfit well with the restricted results. Thus, our sRI-CC2 implementation\nof ground state energy and triplet excitation energy provides a cost-efficient\nalternative approach, especially for some large-sized systems.