Accurate calculation of C1s core electron binding energies of some carbon hydrates and substituted benzenes

Approaches, using density functional theory (DFT), to calculate accurate adiabatic and vertical carbon 1s core electron binding energies (CEBE) of some alkanes, alkenes, alkynes and methyl- and fluorine-substituted benzenes are investigated.

The approaches tested can be schematized as follows; $\Delta E_{\text{KS}}(\text{PW}86\times -\text{PW}91\text{c}/\text{TZP}+C_{\text{rel}})//\text{DFT}(\text{PW}86\times -\text{PW}91c/\text{TZP})$ where ΔE_KS is the difference between the Kohn–Sham total energy of the core–hole cation M⁺, E_KS(M⁺), and the Kohn–Sham total energy of the neutral ground state molecule M, E_KS(M). The geometry of M is optimized with DFT(PW86x-PW91c/TZP). For the adiabatic C1s CEBE calculation, the geometry of M⁺ is optimized whereas, for the vertical C1s CEBE calculation, the geometry of M⁺ is identical to the neutral ground state molecule M. C_rel represents relativistic corrections. We tested two cases; C_rel = 0 eV, and C_rel = 0.05 eV. The relativistic correction turned out to be not necessary, because inclusion of the relativistic correction always increased deviation. The current results suggest a systematic error in the calculations that is fortuitously offset by the neglect of relativistic effects. The best approach resulted in average absolute deviations (maximum absolute deviations) from adiabatic experimental values of 0.045 eV (0.130 eV) for calculations of the corresponding C1s CEBE of the alkanes, alkenes, and substituted benzenes for 120 cases. The absolute uncertainty in the experimental measurements is estimated to be 0.03 eV. The average absolute deviation of 0.045 eV is close to the magnitude of the experimental uncertainty. Agreement between theory and experiment is better for adiabatic C1s CEBE than for vertical C1s CEBE.