  Attosecond nonlinear Fourier transform (NFT) pump probe spectroscopy is an
experimental technique which allows investigation of the electronic excitation,
ionization, and unimolecular dissociation processes. The NFT spectroscopy
utilizes ultrafast multiphoton ionization in the extreme ultraviolet spectral
range and detects the dissociation products of the unstable ionized species. In
this paper, a quantum mechanical description of NFT spectra is suggested, which
is based on the second order perturbation theory in molecule-light interaction
and the high level ab initio calculations of CO2 and CO2+ in the Franck-Condon
zone. The calculations capture the characteristic features of the available
experimental NFT spectra of CO2. Approximate analytic expressions are derived
and used to assign the calculated spectra in terms of participating electronic
states and harmonic photon frequencies. The developed approach provides a
convenient framework within which the origin and the significance of near
harmonic and non-harmonic NFT spectral lines can be analyzed. The framework is
scalable and the spectra of di- and triatomic species as well as the
dependences on the control parameters can by predicted semi-quantitatively.
