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Part 3<br />
Benchmarking for Radicals<br />
As expected, the cc-pVDZ basis set does not provide accurate geometries and frequencies, and the<br />
cc-pVTZ numbers are clearly more in the range of the experimental data than the cc-pVDZ<br />
numbers.<br />
CCSD displays its insufficiency for prediction of equilibrium properties by differing from the FCI<br />
values by 0.01Å in the geometry, 90 cm -1 in the frequency, and 35 kJ/mol in the atomization energy.<br />
The errors in R eq and ω e are reduced by a factor of four going to the CCSDT level and a factor of<br />
five going from the CCSDT to the CCSDTQ level. The error in the atomization energy is reduced<br />
by a factor of nine going to the CCSDT level and a factor of eight going from the CCSDT to the<br />
CCSDTQ level, but while the equilibrium geometry on the CCSDTQ level is only 0.0005Å from<br />
the FCI value, the harmonic frequency is still about 5 cm -1 too high.<br />
Both the equilibrium geometry and the harmonic frequency are apparently better approximated by<br />
the CCSDT method than the CCSDTQ. This is due to a favorable cancellation in errors for CCSDT<br />
calculations in small basis sets. By extrapolation to the larger aug-cc-pVQZ basis, 67,75 we get an<br />
equilibrium distance of 1.1759Å and a harmonic frequency of 2060cm -1 at the CCSDTQ level.<br />
3.3.4 The Vertical Electron Affinity of CN<br />
Calculations on CN - and CN were carried out in the aug´-cc-pVDZ basis at the experimental<br />
equilibrium geometry for CN. The FCI calculation on CN - is one of the largest FCI calculations<br />
carried out so far containing about 20 billion Slater determinants. The vertical electron affinity (EA)<br />
was found and is displayed in Table 3-2. Again only CC(spin-orb) calculations have been carried<br />
out because of the rather small difference in performance of CC(spin-orb) and CC(orb).<br />
Table 3-2 The vertical electron affinity of CN.<br />
EA / E h EA - EA FCI<br />
CCSD(spin-orb) aug’-cc-pVDZ 0.13025 0.00063<br />
CCSDT(spin-orb) aug’-cc-pVDZ 0.12977 0.00014<br />
CCSDTQ(spin-orb) aug’-cc-pVDZ 0.12966 0.00003<br />
FCI aug’-cc-pVDZ 0.12962 ---<br />
The convergence is remarkable; already at the CCSD level we are down to an error of 0.5% of the<br />
FCI value, on the CCSDT level it is 0.1% and on the CCSDTQ level 0.02%. The reason for the<br />
excellent convergence is found in a cancellation of errors that influence the result. The deviations of<br />
the individual energies are always roughly an order of magnitude larger than the deviation of the<br />
affinity, 75 but the errors cancel when the CN and CN - energies are subtracted. That the convergence<br />
is from above is also noteworthy. This is because the CC hierarchy converges faster for CN - than for<br />
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