We make a detailed assessment of which form of the dipole operator to use incalculating high order harmonic generation within the framework of the strongfield approximation, and look specifically at the role the form plays in theinclusion of multielectron effects perturbatively with regard to thecontributions of the highest occupied molecular orbital. We focus on how thesecorrections affect the high-order harmonic spectra from aligned homonuclear andheteronuclear molecules, exemplified by $\mathrm{N}_2$ and CO, respectively,which are isoelectronic. We find that the velocity form incorrectly finds zerostatic dipole moment in heteronuclear molecules. In contrast, the length formof the dipole operator leads to the physically expected non-vanishingexpectation value for the dipole operator in this case. Furthermore, the socalled "overlap" integrals, in which the dipole matrix element is computedusing wavefunctions at different centers in the molecule, are prominent in thefirst-order multielectron corrections for the velocity form, and should not beignored. Finally, inclusion of the multielectron corrections has very littleeffect on the spectrum. This suggests that relaxation, excitation and thedynamic motion of the core are important in order to describe multielectroneffects in molecular high-order high harmonic generation.
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