  We propose to improve the convergence properties of the single-reference
coupled cluster (CC) method through an augmented Lagrangian formalism. The
conventional CC method changes a linear high-dimensional eigenvalue problem
with exponential size into a problem of determining the roots of a nonlinear
system of equations that has a manageable size. However, current numerical
procedures for solving this system of equations to get the lowest eigenvalue
suffer from two practical issues: First, solving the CC equations may not
converge, and second, when converging, they may converge to other --
potentially unphysical -- states, which are stationary points of the CC energy
expression. We show that both issues can be dealt with when a suitably defined
energy is minimized in addition to solving the original CC equations. We
further propose an augmented Lagrangian method for coupled cluster (alm-CC) to
solve the resulting constrained optimization problem. We numerically
investigate the proposed augmented Lagrangian formulation showing that the
convergence towards the ground state is significantly more stable and that the
optimization procedure is less susceptible to local minima. Furthermore, the
computational cost of alm-CC is comparable to the conventional CC method.
