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Example 4: Vertical excitation energies (VEEs) of nitrogen monoxide radical inferred from P3+ / 6-311+G(2df) calculations of vertical attachment energies (VEAEs) of nitorgen monoxide cation

Input to G16 program:

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

Title: P3+ calculations for VEAEs of nitorgen monoxide cation.

+1 1
O 1 1.150

6 8

This input is similar to the one of Example 1. Calculations are carried out for nitorgen monoxide cation, which has 14 electrons in 7 molecular orbitals. 2 out of these 7 occupied orbitals will be frozen by default and the remaining occupied orbitals used for correlation will be numbered from 1 through 5. The above input therefore requests (through the last line 6 8) vertical electron attachment energy (VEAE) calculations to LUMO (which is doubly degenrate and corresponds to orbitals no. 6 and 7) and LUMO+1 (orbital no. 8). The resulting output gives these VEAEs as:

 Summary of results for alpha spin-orbital   6    P3:
 Koopmans theorem:            -0.32437D+00 au   -8.827 eV
 Converged second order pole: -0.35889D+00 au   -9.766 eV  0.918 (PS)
 Converged 3rd order P3 pole: -0.35208D+00 au   -9.581 eV  0.915 (PS)
 Renormalized (P3+)  P3 pole: -0.35270D+00 au   -9.598 eV  0.915 (PS)
 Orbitals  7 and  6 are degenerate.  Skipping orbital  7

 Summary of results for alpha spin-orbital   8    P3:
 Koopmans theorem:            -0.10630D+00 au   -2.893 eV
 Converged second order pole: -0.12132D+00 au   -3.301 eV  0.987 (PS)
 Converged 3rd order P3 pole: -0.11816D+00 au   -3.215 eV  0.989 (PS)
 Renormalized (P3+)  P3 pole: -0.11863D+00 au   -3.228 eV  0.989 (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 stress once again that: PS values below 0.85 indicate that the diagonal self-energy approximations (i.e., D2, D3, OVGF, P3, P3+) are unreliable!!!

A state obtained after attachment of an electron to orbital no. 6 (LUMO) of nitorgen monoxide cation is the ground state of nitorgen monoxide radical, whereas the state obtained after electron attachment to orbital no. 8 (LUMO+1) is the first excited state of this radical. VEAEs are negative showing that both states of the radical are bound (see the sign convention notes for VEAEs in Example 2).

The first vertical excitation energy (VEE) of the radical may be obtained as VEAE for LUMO+1 minus VEAE for LUMO, which in P3+ approximation gives VEE of 6.370 eV.

Note that 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.