Intruder-free cumulant-truncated driven similarity renormalization group second-order multireference perturbation theory

Abstract

Accurate multireference electronic structure calculations are important for constructing potential energy surfaces. Still, even in the case of low-scaling methods, their routine use is limited by the steep growth of the computational and storage costs as the active space grows. This is primarily due to the occurrence of three- and higher-body density matrices or, equivalently, their cumulants. This work examines the effect of various cumulant truncation schemes on the accuracy of the driven similarity renormalization group second-order multireference perturbation theory. We test four different levels of three-body reduced density cumulant truncations that set different classes of cumulant elements to zero. Our test cases include the singlet–triplet gap of CH2, the potential energy curves of the XΣg+1 and AΣu+3 states of N2, and the singlet–triplet splittings of oligoacenes. Our results show that both relative and absolute errors introduced by these cumulant truncations can be as small as 0.5 kcal mol−1 or less. At the same time, the amount of memory required is reduced from O(NA6) to O(NA5), where NA is the number of active orbitals. No additional regularization is needed to prevent the intruder state problem in the cumulant-truncated second-order driven similarity renormalization group multireference perturbation theory methods.