Density matrices in full configuration interaction quantum Monte Carlo: Excited states, transition dipole moments and parallel distribution

We present developments in the calculation of reduced density matrices (RDMs) in the full configuration interaction quantum Monte Carlo (FCIQMC) method. An efficient scheme is described to allow storage of RDMs across distributed memory, thereby allowing their calculation and storage in large basis sets. We demonstrate the calculation of RDMs for general states by using the recently-introduced excited-state FCIQMC approach [J. Chem. Phys. 143, 134117 (2015)] and further introduce calculation of transition density matrices (TDMs) in the method. These approaches are combined to calculate excited-state dipole and transition dipole moments for heteronuclear diatomic molecules, including LiH, BH and MgO, and initiator error is investigated in these quantities.