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The solutions of
Eqs. (7.4) and (7.7) are expanded in a
subspace of which is iteratively expanded (Davidson method
[83]). The iteration is stopped when the Euclidean
norm of the residual vector is smaller than . The default
for is , which usually gives excitation energies accurate to
digits and properties accurate to digits ( 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.

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