Effects of molecular potential and geometry on atomic core-level photoemission over an extended energy range: The case study of the CO molecule

We report an experimental and theoretical study of single-molecule inner-shell photoemission measured over an extended range of photon energies. The vibrational intensity ratios $I(\nu =1)/I(\nu =0)$ from the C $1s$ photoelectron spectra of carbon monoxide, although mostly determined by the bond length change upon ionization, are shown to be affected also by photoelectron recoil and by scattering from the neighboring oxygen atom. Static-exchange density functional theory (DFT) is used to encompass all these effects in a unified theoretical treatment. The ab initio calculations show that the vibrational ratio as a function of the photoelectron momentum is sensitive to both the ground-state internuclear distance and its contraction upon photoionization. We present a proof-of-principle application of DFT calculations as a quantitative structural analysis tool for extracting the dynamic and static molecular geometry parameters simultaneously.

Figure 1

Carbon $1s$ photoelectron spectrum, measured at $h\nu =425$ eV at SOLEIL. Cirles: experiment; solid lines: least-squares fit of the vibrational progression.

Figure 2

Static-exchange DFT calculations of vibrational ratios. Bold middle curves in both panels are obtained with $R_0=R_{\mathrm{lit}}$ and $\Delta R=\Delta R_{\mathrm{lit}}$. (a) Variations of $R_0=0.95...1.05R_{\mathrm{lit}}$ (from blue to red) and (b) $\Delta R=0.99...1.01\Delta R_{\mathrm{lit}}$ (from blue to red). Horizontal line in panel a marks the value from Franck-Condon calculation and the the dashed curve reprents the photoelectron recoil effect.

Figure 3

Experimental and calculated intensity ratios of the vibrational peaks in C $1s$ photoelectron spectra of CO. Open cirles: measurements at SPring8; full circles: measuments at SOLEIL; double triangles: Ref. [8]. Bold solid red line: fit of the static-exchange DFT theory; thin red line: DFT theory with literature input values; dashed blue line: fit of analytical formula.