Photoabsorption in formaldehyde: Intensities and assignments in the discrete and continuous spectral intervals

Abstract

Theoretical investigations of total and partial-channel photoabsorption cross sections in molecular formaldehyde are reported employing the Stieltjes-Tchebycheff (s-T) technique and separated-channel static-exchange (!YO) calculations. Vertical one-electron dipole spectra for the 2b 2 (n), lb 1(7T), 5a 1(a), I b 2 , and 4a 1 canonical molecular orbitals are obtained using Hartree-Fock frozen-core functions and large basis sets of compact and diffuse normalizable Gaussians to describe the photoexcited and ejected electrons. The calculated discrete excitation spectra provide reliable zeroth-order approximations to both valence and Rydberg transitions, and, in particular, the 2b 2 (n)-msa 1 , npa 1 , npb 2 , and nda 2 IVO spectra are in excellent accord with recent experimental assignments and available intensity measurements. Convergent (S-T) photoionization cross sections in the static-exchange (IVO) approximation are obtained for the 15 individual partial channels associated with ionization of the five occupied molecular orbitals considered. Resonance features in many of the individual-channel photoionization cross sections are attributed to contributions frorn valencelike a 1 a*(CO), a 1 a*(CH), and b 2 a*(CH)/7Ty *(CO) molecular orbitals that appear in the photoionization continua, rather than in the corresponding one-electron discrete spectral intervals. The vertical electronic cross sections for 1 A 1 -+ 1 B 1 , 1 B 2 , and 1 A 1 excitations are in generally good accord with previously reported CI (s-T) predictions of continuum orbital assignments and intensities, although some discrepancies due to basis-set differences are present in the 1 B 1 and 1 B 2 components, and larger discrepancies apparently due to channel coupling are present in the 1 A 1 -+ 1 A 1 cross section. Partialchannel vertical electronic cross sections for the production of the five lowest parent-ion electronic states are found to be in general agreement with the results of very recent synchrotron-radiation photoelectron branching-ratio measurements in the 20 to 30 eV excitation energy interval. Most important in this connection is the tentative verification of the predicted orderings in intensities of the partial-channel cross sections, providing support for the presence of a strong ka 1 <r*(CO) resonance in the (5a 1 -1 ) 2 A 1 channel. Finally, the total vertical electronic cross sections for absorption and ionization are in general accord with photoabsorption measurements, photoionization-mass-spectrometric studies, and the previously reported CI (s-T) calculations. Although further refined calculations including vibrational degrees of freedom and autoionization line shapes are required for a more precise quantitative comparison between theory and experiment, the present study should provide a reliable zeroth-order account of discrete and continuum electronic dipole excitations in molecular formaldehyde.

Spectral properties of minimal‐basis‐set orbitals: Implications for molecular electronic continuum states

“…Calculations of SECI excitation spectra in mo- Ϫ1 photoionization branching ratio ( 2b 2 / total ) in H 2 CO. The experimental values (data points) are obtained from synchrotron-radiation photoelectron spectroscopy measurements [14], whereas the theoretical values (solid line) are obtained from single-channel SECI calculations [5]. (b) Polarization-symmetry contributions to the 2b 2 Ϫ1 photoionization cross section in H 2 CO, as indicated, obtained from single-channel SECI calculations employing extended basis sets [5].…”

“…The experimental values (data points) are obtained from synchrotron-radiation photoelectron spectroscopy measurements [14], whereas the theoretical values (solid line) are obtained from single-channel SECI calculations [5]. (b) Polarization symmetry contributions to the 5a 1 Ϫ1 photoionization cross section in H 2 CO, as indicated, obtained from single-channel SECI calculations employing extended basis sets [5]. (Note that the energy scale employed is different from that of Figure 3 selected ka 1 continuum molecular orbitals in H 2 CO, the latter obtained from single-channel SECI calculations employing extended basis sets [5].…”

“…The latter results are obtained in the single-channel SECI or IVO approximation employing Eqs. (4) and (5) (i ϭ 2b 2 ; j ϭ ka 1 , kb 2 , ka 2 ) and a much larger orbital basis set than the minimal basis referred to in Tables I and II [5]. Evidently, the very strong threshold feature in the experimental data of Figure 2(a) can be attributed to corresponding features in the 2b 2 3 kb 2 and ka 1 symmetry components of Figure 2(b), which are seen from Table II (4) and (5) in a minimal basis set [19] for the indicated hole states.…”

“…Previously reported theoretical and experimental studies of the formaldehyde molecule (H 2 CO) [4,5,14] are employed in combination with recently calculated continuum orbital amplitudes as a particularly interesting illustration of such spectral characteristics. Additional comments on the presence of virtual orbitals in the discrete excited states of selected diatomic molecules (N 2 , F 2 , HF) [15][16][17] emphasize that spectral concentration in the continuum becomes the more familiar Rydberg-valence mixing below the ionization threshold.…”

“…His particularly clear and insightful description and application of single-excitation configuration interaction (SECI) methods for excited electronic states [3], employing both minimal-and extended-basis Hartree-Fock orbitals represented in the now familiar Gaussian forms he helped to popularize, influ-enced our own studies of the electronic continua of molecules beginning in the 1970s [4,5] and aided us in obtaining a general understanding of the dependence of photoionization cross sections on molecular geometry, orbital occupancy, and other molecular attributes [6].…”