Atomic and molecular2pbinding energies of P, As, and Se from many-body calculations and x-ray photoelectron spectroscopy

The $2p_{\frac{1}{2},\frac{3}{2}}$ levels in ${\mathrm{As}}_4$ and the $2p_{\frac{3}{2}}$ level in ${\mathrm{Se}}_{5,6}$ have been measured by x-ray photoelectron spectroscopy with the use of 1486.6-eV ($\mathrm{Al}K\alpha$) radiation. The $2p_{\frac{1}{2}}$ binding energies have been calculated for the atomic species, as well as for atomic phosphorus, as the difference between the total energies of the $2p_{\frac{1}{2}}$ hole state and the ground (neutral) state $\Delta$ SCF ($\Delta$ self-consistent field method), using the Dirac-Fock program of Desclaux, to which is added the respective correlation-energy difference between the two states. The calculated values of 140.70 eV for $\mathrm{P}2p_{\frac{1}{2}}$, 1368.89 eV for $\mathrm{As}2p_{\frac{1}{2}}$, and 1484.88 eV for $\mathrm{Se}2p_{\frac{1}{2}}$ include a 0.7-1.0-eV increase due to the effects of correlation, consistent with earlier work done on the K and Zn atoms. The $2p_{\frac{3}{2}}$ atomic binding energies were calculated similarly with the use of available Dirac-Slater $\Delta$ SCF values. When we combine these with the measured molecular binding energy of ${\mathrm{P}}_4$, ${\mathrm{As}}_4$, and ${\mathrm{Se}}_{5,6}$ we obtain corresponding $2p$ chemical shifts (atom-molecule) of 3.5, 3.0, and 2.4 eV, respectively. Comparison is also made between the atomic, molecular, and solid-state binding energies of As and Se, and it is found that the solid-state binding energy is the lowest of the three in both cases, as expected from consideration of extra-atomic relaxation.