Nitrogen correlation energy

In the nitrogen molecule, we found no significant difference in the CT energies between using NOs and canonical CAS orbitals over the potential curve, unlike in the H2O case. However, it is still important to optimize the orbitals, as the CASCI-based L-CTD does not yield a correct potential curve. Finally, as in the water calculations, the L-CTSD(2) approximation recovers most of L-CTSD correlation energy across the potential energy curve. 

Table 4 Components of the calculated correlation energy for the nitrogen molecule...

For the nitrogen molecule calculations were performed for nuclear separations of 1.75, 2.00, 2.25, and 2.50 bohr and these values interpolated to obtain a correlation energy at the equilibrium nuclear geometry. The empirical correlation energy for the nitrogen molecule is -0.538 hartree. The calculated correlation energy obtained by interpolation is -0.4501 hartree which represents 83.7% of the estimate. 

The results of the distributed basis set study of the second-order correlation energy for the nitrogen molecule(83) is compared with the second-order correlation energies obtained by employing other recently reported basis sets for this system in Figure 1. 

In (a), all the electrons stay away from each other owing to their Fermi holes, as given already by the No significant correction appears in x for such a three-electron same-spin "collision . Even the total correlation energy of 2 in the S state of the nitrogen atom is only 0.1 ev (see Fig. 1), most of which is due to the pairwise effect... 

Equation (85) has been confirmed very recently for the first row atoms (Gladney and Allen later obtained similar empirical values), dementi evaluated the correlation energies of these atoms and their ions empirically using his H.F. results and estimates of relativistic effects. The additivity observed is within the empirical uncertainty of the data. Figures 1 and 2 are based on his data and show the correlation energy increments in nitrogen and neon ions and atoms as more and more electrons are added. 

Fig. 1. Correlation energies of nitrogen ions and atom (based on the empirical data of E. Clementi, Reference 67).

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