We present an implementation of single
residues for response functions
to arbitrary order using a recursive approach. Explicit expressions
in terms of density-matrix-based response theory for the single residues
of the linear, quadratic, cubic, and quartic response functions are
also presented. These residues correspond to one-, two-, three- and
four-photon transition matrix elements. The newly developed code is
used to calculate the one-, two-, three- and four-photon absorption
cross sections of para-nitroaniline and para-nitroaminostilbene, making this the first treatment of four-photon
absorption in the framework of response theory. We find that the calculated
multiphoton absorption cross sections are not very sensitive to the
size of the basis set as long as a reasonably large basis set with
diffuse functions is used. The choice of exchange–correlation
functional, however, significantly affects the calculated cross sections
of both charge-transfer transitions and other transitions, in particular,
for the larger para-nitroaminostilbene molecule.
We therefore recommend the use of a range-separated exchange–correlation
functional in combination with the augmented correlation-consistent
double-ζ basis set aug-cc-pVDZ for the calculation of multiphoton
absorption properties.