Example 1: P3+ / 6-311G(2df,2pd) calculations of vertical ionization potentials (VIPs) of water molecule

Input to G16 program:

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

           

           Title: P3+ calculations for VIPs of water.

           

           0 1

            H                

            O 1 0.957        

            H 2 0.957 1 104.2

            

            2 4

The option ept(p3,ReadOrbitals) invokes the EPT calculations in the renormalized partial third-order (P3+) approximation and requests the program to read an additional line (the last line of the input) containing orbitals for which electron binding energies will be calculated. In this case, these are orbitals 2 through 4, where numbering starts with the first correlated orbital. As the standard frozen-core approximation is a default in Gaussian calculations (in this case one lowest-energy occupied orbital is frozen), the line 2 4 requests a calculation of vertical electron detachment energies (VEDEs) for HOMO-2, HOMO-1, and HOMO orbitals. The resulting output gives these VEDEs as:

   
            Summary of results for alpha spin-orbital   2    P3:
 Koopmans theorem:            -0.70477D+00 au  -19.178 eV
 Converged second order pole: -0.66713D+00 au  -18.153 eV  0.921 (PS)
 Converged 3rd order P3 pole: -0.68842D+00 au  -18.733 eV  0.939 (PS)
 Renormalized (P3+)  P3 pole: -0.68535D+00 au  -18.649 eV  0.936 (PS)

 Summary of results for alpha spin-orbital   3    P3:
 Koopmans theorem:            -0.57443D+00 au  -15.631 eV
 Converged second order pole: -0.50721D+00 au  -13.802 eV  0.905 (PS)
 Converged 3rd order P3 pole: -0.53772D+00 au  -14.632 eV  0.930 (PS)
 Renormalized (P3+)  P3 pole: -0.53273D+00 au  -14.496 eV  0.926 (PS)

 Summary of results for alpha spin-orbital   4    P3:
 Koopmans theorem:            -0.50156D+00 au  -13.648 eV
 Converged second order pole: -0.42117D+00 au  -11.460 eV  0.899 (PS)
 Converged 3rd order P3 pole: -0.45510D+00 au  -12.384 eV  0.926 (PS)
 Renormalized (P3+)  P3 pole: -0.44939D+00 au  -12.228 eV  0.921 (PS)

Note that besides the P3+ number, results are also reported for lower-order approximations, namely Koopmans's theorem (which is simply equal to the orbital energy), diagonal second-order method (D2) and partial third-order (P3) method.

The last column contains the pole strength (PS) values. PS is equal to the norm of a Dyson orbital corresponding to a given VEDE and is calculated from a residue at this VEDE. 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. VIP is a negative of VEDE and hence all above examples correspond to an endoenergetic process of electron removal.

Note that instead of the 6-311G(2df,2pd) basis, we could have used another triple-zeta quality basis containing polarization functions, e.g., the correlation-consistent cc-pVTZ basis. These bases ensure results close to the basis-set limit for VIPs [].