Convergence improvement for coupled cluster calculations

Convergence problems in coupled-cluster iterations are discussed, and a new iteration scheme is proposed. Whereas the Jacobi method inverts only the diagonal part of the large matrix of equation coefficients, we invert a matrix which also includes a relatively small number of off-diagonal coefficients, selected according to the excitation amplitudes undergoing the largest change in the coupled cluster iteration. A test case shows that the new IPM (inversion of partial matrix) method gives much better convergence than the straightforward Jacobi-type scheme or such well-known convergence aids as the reduced linear equations or direct inversion in iterative subspace methods. Letter to the Editor 2 The coupled cluster (CC) method is widely used in electronic structure calculations. The CC theory has been described in many reviews (see, e.g., [1, 2, 3, 4, 5]), and will not be presented here. The basic equation for the CC method is the Bloch equation ΩHΩ = HΩ, (1) where H is the Hamiltonian and Ω is the wave operator. The resulting equations have the general algebraic form A i + N j=1 B(t) ij t j = 0, where t j are the cluster or excitation amplitudes to be determined, N is the number of the unknown amplitudes, A is a vector and B(t) is a square matrix which in general depends upon t. For simplicity, we consider the case when B does not depend upon t,