Toward a parallel, quadrature-based second-order algebraic diagrammatic construction method for electronic excitations: Møller–Plesset ground state and first order

Large-scale applications of wavefunction-based excited-state methods are hindered by the enormous storage demands of electron repulsion integrals (ERIs) and by the computational scaling of Hamiltonian matrix element evaluations. At the same time, conventional formulations of these methods are not well suited for parallelization due to complex coupling patterns inherent to the evaluated expressions. In this work, we present the reformulation of an algebraic diagrammatic construction (ADC) scheme using a seminumerical ERI decomposition approach together with the well-established Laplace transform technique. In contrast to previous studies, we maintain a molecular-orbital (MO) formulation, exploiting its intrinsically reduced dimensionality. With the goal of developing a quadrature-based second-order ADC [Q-ADC(2)] method, we here begin with a detailed investigation of computational aspects inherent to this novel methodology by applying it to full second-order Møller-Plesset (MP2) perturbation theory and to the first-order ADC [ADC(1)] scheme, thereby establishing the Q-MP2 and Q-ADC(1) methods. Compared to conventional implementations, both memory requirements and computational scaling are reduced by one order. We thoroughly investigate the accuracy of the new methods depending on the numerical integration grids used and compare different algorithmic variants arising from the MO-based formulation. Furthermore, the effects of the approximation on the ERI symmetry are discussed in detail. The potential of this novel methodology for large-scale applications is demonstrated by simulating UV-Vis absorption spectra of important fluorophores using up to 1978 basis functions. The ability to systematically balance accuracy and computational effort makes this quadrature-based approach particularly promising for extension to the ADC(2) scheme, which will be presented in a subsequent publication.