Example 3: P3+ / 6-311G(2df) calculations of vertical detachment energy (VEDE) of chloride ion

Input to G16 program:

   
           #p ept(p3,ReadOrbitals) 6-311G(2df)

           

           Title: P3+ calculations for VEDEs of chloride ion.

           

           -1 1

            Cl               

            

            4 4

This input is similar to the one of Example 1. Calculations are carried out for chloride ion, which has 18 electrons in 9 molecular orbitals. 5 out of these 9 occupied orbitals will be frozen by default and the remaining occupied orbitals used for correlation will be numbered from 1 through 4. The above input therefore requests (through the last line 4 4) vertical electron detachment energy (VEDE) calculations from HOMO. The resulting output gives this VEDE as:

   
            Summary of results for alpha spin-orbital   4    P3:
 Koopmans theorem:            -0.14401D+00 au   -3.919 eV
 Converged second order pole: -0.11439D+00 au   -3.113 eV  0.911 (PS)
 Converged 3rd order P3 pole: -0.12112D+00 au   -3.296 eV  0.917 (PS)
 Renormalized (P3+)  P3 pole: -0.12027D+00 au   -3.273 eV  0.916 (PS)

Similarly as in Example 1, results are reported not only for P3+, but for Koopmans's theorem, D2 and P3, as well.

Pole strengths (PS) reported in the last column are equal to the norms of a Dyson orbitals corresponding to VEDEs and are calculated from residues at VEDEs. We re-emphasize that: PS values below 0.85 indicate that the diagonal self-energy approximations (i.e., D2, D3, OVGF, P3, P3+) are unreliable!!!

Sign convention: Numbers reported above are VEDEs defined as the total energy of the N-electron system minus the total energy of the (N-1)-electron system. A negative value of VEDE therefore means that the N-electron system is bound. The above example thus shows that the chloride ion is bound, i.e., it is energetically more stable than the chlorine atom.

Note that instead of the 6-311G(2df) basis, we could have used another triple-zeta quality basis containing polarization functions, e.g., the correlation-consistent cc-pVTZ basis.