Example 2: P3+ / 6-311+G(2df) calculations of vertical electron affinities (VEAs) of sodium chloride molecule

Input to G16 program:

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

           

           Title: P3+ calculations for VEAs of sodium chloride.

           

           0 1

            Na        

            Cl 1 2.360

            

            5 6

This input is similar to the one of Example 1. Calculations are carried out for sodium chloride molecule, which has 28 electrons in 14 molecular orbitals. 10 out of these 14 occupied orbitals will be frozen by default and the remaining occupied orbitals used for correlation will be numbered from 1 through 4, and the LUMO orbital will have no. 5. The above input therefore requests (through the last line 5 6) vertical electron attachment energy (VEAE) calculations to LUMO and LUMO+1 orbitals. The resulting output gives these VEAEs as:

   
            Summary of results for alpha spin-orbital   5    P3:
 Koopmans theorem:            -0.19916D-01 au   -0.542 eV
 Converged second order pole: -0.22971D-01 au   -0.625 eV  0.995 (PS)
 Converged 3rd order P3 pole: -0.23094D-01 au   -0.628 eV  0.994 (PS)
 Renormalized (P3+)  P3 pole: -0.23085D-01 au   -0.628 eV  0.995 (PS)

 Summary of results for alpha spin-orbital   6    P3:
 Koopmans theorem:             0.12671D-01 au    0.345 eV
 Converged second order pole:  0.12076D-01 au    0.329 eV  0.999 (PS)
 Converged 3rd order P3 pole:  0.12035D-01 au    0.327 eV  0.999 (PS)
 Renormalized (P3+)  P3 pole:  0.12038D-01 au    0.328 eV  0.999 (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 VEAEs and are calculated from residues at VEAEs. We recall 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 VEAEs defined as the total energy of the (N+1)-electron system minus the total energy of the N-electron system. A negative value of VEAEs therefore means that the (N+1)-electron system is bound. VEA is a negative of VEAE and hence above results for orbital no. 5 (LUMO) correspond to an exoenergetic process of electron attachment and show that sodium chloride anion is more stable than the neutral species. In contrast, electron attachment to orbital no. 6 (LUMO+1) of sodium chloride is an exoenergetic process.

Note an important change in the basis set compared to Example 1: now the "+" sign has been added to the basis set name, which denotes that the basis set has been augmented with diffuse functions, necessary to span the space in the outer regions of the molecule where the electron attachment process takes place. Note that only one "+" is added, since there are no hydrogen atoms in the molecule; for the same reason, the "2pd" part has been dropped in the parenthesis compared to Example 1. Instead of the 6-311+G(2df) basis, we could have used another triple-zeta quality basis containing both polarization and diffuse functions, e.g., the correlation-consistent aug-cc-pVTZ basis.