  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$_2$, CO, HCN, HNC, C$_2$H$_2$, and H$_2$CO), 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 $1^1\mathrm{B_{u}}$ and the doubly-excited
$2^1\mathrm{A_{g}}$ states, in excellent agreement with highly accurate
semistochastic heat-bath configuration interaction results, while EOM-CCSD
overestimates the energy of the $2^1\mathrm{A_{g}}$ state by almost 1 eV. Our
results demonstrate that linear-response DCT is a promising theoretical
approach for excited states of molecules.
