title: Efficient algorithms for solving the non-linear vibrational coupled-cluster equations using full and decomposed tensors.
abstract: Vibrational coupled-cluster (VCC) theory provides an accurate method for calculating vibrational spectra and properties of small to medium-sized molecules. Obtaining these properties requires the solution of the non-linear VCC equations which can in some cases be hard to converge depending on the molecule, the basis set, and the vibrational state in question. We present and compare a range of different algorithms for solving the VCC equations ranging from a full Newton-Raphson method to approximate quasi-Newton models using an array of different convergence-acceleration schemes. The convergence properties and computational cost of the algorithms are compared for the optimization of VCC states. This includes both simple ground-state problems and difficult excited states with strong non-linearities. Furthermore, the effects of using tensor-decomposed solution vectors and residuals are investigated and discussed. The results show that for standard ground-state calculations, the conjugate residual with optimal trial vectors algorithm has the shortest time-to-solution although the full Newton-Raphson method converges in fewer macro-iterations. Using decomposed tensors does not affect the observed convergence rates in our test calculations as long as the tensors are decomposed to sufficient accuracy.
authors.affiliation: Department of Chemistry, Aarhus University, 8000 Aarhus C, Denmark.
authors.forename: Niels K
authors.initials: NK
authors.lastname: Madsen
authors.affiliation: Department of Chemistry, Aarhus University, 8000 Aarhus C, Denmark.
authors.forename: Ian H
authors.identifier: 0000000150342293
authors.initials: IH
authors.lastname: Godtliebsen
authors.affiliation: Department of Chemistry, Aarhus University, 8000 Aarhus C, Denmark.
authors.forename: Ove
authors.identifier: 000000019215571X
authors.initials: O
authors.lastname: Christiansen