Scaled opposite-spin atomic-orbital based algebraic diagrammatic construction scheme for the polarization propagator with asymptotic linear-scaling effort: Theory and implementation

A novel local approach for the quantum-chemical computation of excited states is presented, where the concept of the atomic-orbital formulation of the second-order Moller-Plesset energy expression is extended to the second-order algebraic diagrammatic construction scheme by virtue of the Laplace transform. The scaled opposite-spin second-order algebraic diagrammatic construction method with Cholesky decomposed densities and density-fitting, or CDD-DF-SOS-ADC(2) for short, exploits the sparsity of the two-electron repulsion integrals, the atomic ground-state density matrix, and the atomic transition density matrix to drastically reduce the computational effort. By using a local density-fitting approximation, it is shown that asymptotically linear scaling can be achieved for linear carboxylic acids. For electron-dense systems, sub-cubic scaling can be achieved if the excitation is local, and hence the transition density is sparse. Furthermore, the memory footprint and accuracy of the CDD-DF-SOS-ADC(2) method are explored in detail.