Linear-Response Density Cumulant Theory for Excited Electronic States.

We present a linear-response formulation of density cumulant theory (DCT) that provides a balanced and accurate description of many electronic states simultaneously. In the original DCT formulation, only information about a single electronic state (usually, the ground state) is obtained. We discuss the derivation of linear-response DCT, present its implementation for the ODC-12 method (LR-ODC-12), and benchmark its performance for excitation energies in small molecules (N, CO, HCN, HNC, CH, and HCO), as well as challenging excited states in ethylene, butadiene, and hexatriene. For small molecules, LR-ODC-12 shows smaller mean absolute errors in excitation energies than equation-of-motion coupled cluster theory with single and double excitations (EOM-CCSD), relative to the reference data from EOM-CCSDT. In a study of butadiene and hexatriene, LR-ODC-12 correctly describes the relative energies of the singly excited 1B and the doubly excited 2A states, in excellent agreement with highly accurate semistochastic heat-bath configuration interaction results, while EOM-CCSD overestimates the energy of the 2A state by almost 1 eV. Our results demonstrate that linear-response DCT is a promising theoretical approach for excited states of molecules.