On the multimode quadratic vibronic coupling problem: An open-ended solution using a parallel Lanczos algorithm

We introduce an algorithm to solve the secular equation that arises in the time independent multimode expansion of the quadratic vibronic coupling problem in parallel. The implementation can handle expansions of arbitrary length, with the open-ended character of the algorithm achieved through the use of fine grained parallelism to partition the trial vectors. The characteristics of the algorithm are discussed and its utility is illustrated by determining a model photoelectron spectrum of the ethoxy radical (C2H5O) using a vibronic expansion involving more than 1 billion vibronic basis states. This calculation also represents the first determination of a photoelectron spectrum obtained using a diabatic Hamiltonian obtained with a recently introduced ab initio surface reshaping procedure.