The C 2 ‐DIIS convergence acceleration algorithm

We present a theoretical and numerical comparison between two DIIS algorithms to which we refer herein as C 1 ‐ DIIS and C 2 ‐ DIIS . The C 2 ‐ DIIS algorithm is shown to be equivalent to the traditional C 1 ‐ DIIS algorithm near convergence and more stable numerically as regards the accumulation of round‐off error when the C 1 ‐ DIIS equations become (nearly) singular. The C 2 ‐ DIIS algorithm also offers alternative solutions to the DIIS equations when anharmonicities or numerical difficulties are problematic. These properties of the C 2 ‐ DIIS algorithm allow the use of much larger DIIS spaces, obviating the need for truncation of the DIIS space, which, when done, usually results in a loss of information contained in the iterated subspace. The C 2 ‐ DIIS method can be considered to be a variant of the singular value decomposition method. © 1993 John Wiley & Sons, Inc.