Simultaneous vector iteration.

The solutions of Eqs. (7.4) and (7.7) are expanded in a subspace of L which is iteratively expanded (Davidson method [83]). The iteration is stopped when the Euclidean norm of the residual vector is smaller than 10^-k. The default for k is 5, which usually gives excitation energies accurate to 8 - 10 digits and properties accurate to 4 - 5 digits (k can be changed by specifying $rpaconv k). Several roots, i.e., several excited states or frequencies can be treated simultaneously, which is very effective and permits the calculation of whole excitation spectra and dispersion curves. During the iteration, the vectors are kept on scratch files vfile_<IR>,wfile_<IR>, and/or rhs_<IR>, where IR denotes an IRREP of the point group (see below). Before the programs terminate, the converged vectors are written onto formatted files 〈type 〉〈IR〉, where type is an abbreviation for the type of response calculation performed (cf. $scfinstab). Given these files in the working directory, escf and egrad calculations can be restarted or continued, e.g., with a larger number of roots.