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42 L. Thøgersen, J. Olsen / Chemical Physics Letters 393 (2004) 36–43
values in the range 745–762 kJ/mol for the experimental
electronic contribution. Adding our estimate of quadruples
correction to the estimated CCSDT limit of 748
kJ/mol result of Feller and Sordo gives a value of 752 kJ/
mol for the electronic atomization energy for CN.
3.5. The vertical electron affinity
An FCI calculation for the CN anion using the aug 0 -
cc-pVDZ basis was carried out at the experimental
equilibrium geometry of the radical. The FCI calculation
contains about 20 billion Slater determinants and
sparsity of the CI-vectors was only used to reduce discstorage,
not computation time. This FCI calculation
represents one of the largest FCI calculations we hitherto
have carried out. The FCI energy for the anion was
obtained as )92.627391(2) E h . Combining this energy
with the FCI energy of )92.497766 E h for the radical in
the same basis set leads to an FCI value of 0.12962 E h
for the vertical electron affinity. CC expansions using
spin–orbital occupations for restrictions of excitations
were also carried out for the radical and the anion in the
aug 0 -cc-pVDZ basis and the resulting electron affinities
are given in Table 6.
As the differences between the CC calculations using
orbital and spin–orbital restrictions already have been
shown to be small, no orbital-restricted calculations
were carried out. Already at the CCSD level, the calculated
electron affinity differs from the FCI affinity by
less than 1 mE h , and at the CCSDT level the calculated
electron affinity differs from the FCI result by less than
0.1 mE h . The deviations of the CC energies from the
FCI energies for the radical and the anion are also listed
in Table 6. It is seen that the high accuracy of the CC
affinities is caused by cancellation of the errors of the
radical and anion – the deviation of the affinity is
roughly an order of magnitude smaller than the deviation
of the individual energies. It is also interesting to see
that the electron affinity converges from above – the CC
affinities are larger than the FCI affinity. As seen from
the other columns of Table 6, the CC expansion converges
slightly faster for the anion than for the radical.
The faster convergence of the anion may seem surprising
as the anion contains one more electron than the radical
but is probably caused by CN being slightly more
multiconfigurational than the anion. The electron affinity
of CN calculated using CC calculations in large
basis sets has been the subject of several recent studies
[33,34]. These studies also found small contributions to
the electron affinity from triple excitations.
4. Conclusion
Full configuration interaction calculations using the
cc-pVDZ basis and CC calculations using the cc-pVDZ
and cc-pVTZ basis sets have been carried out for the CN
radical at various geometries. Single reference configuration
interaction calculations were also carried out
using the cc-pVDZ basis at the experimental internuclear
distance. At the CCSDT level, the energies differ
from the FCI energy by 1.5 mE h , and at the CCSDTQ
level, the energies are 0.2 mE h from the FCI energy. The
CC energies converge toward the FCI energy in an approximately
linear fashion with a decrease in the deviation
by about a factor of 10 for each added excitation
level. This is in contrast to an analysis based on perturbation
theory, predicting that adding even orders
give larger decreases in the deviations than adding odd
orders. The observed convergence for CN in the ccpVDZ
basis is very similar to the convergence previously
reported for N 2 , indicating that the open-shell nature of
CN does not affect the convergence. A comparison of
the FCI and CC energies at various internuclear distances,
reveals that the deviations of the CC approaches
do not occur suddenly for large internuclear distances.
The deviations are instead nearly linear functions of the
internuclear distance.
At the FCI level, the equilibrium geometry and harmonic
frequency are obtained as 1.1969 A and 2020.1
cm 1 , respectively. The CCSDT and CCSDTQ frequencies
are 25 and 5 cm 1 above the FCI value, respectively.
The quadruple corrections to both the
equilibrium distance and the harmonic frequency were
found to be nearly identical in the cc-pVDZ and ccpVTZ
basis sets. The major errors of the CC frequencies
come from the errors of the distances where these are
evaluated.
For the electronic contribution to the atomization
energy, a value of 667.0 kJ/mol is obtained at the FCI
level using the cc-pVDZ basis set. The CCSDT and
CCSDTQ atomization energies are 4 and 0.5 kJ/mol
below the FCI atomization energy, respectively. The
quadruple contributions in the cc-pVDZ and cc-pVTZ
Table 6
The vertical electron affinity (E h ) of CN calculated in the aug 0 -cc-pVDZ basis
EA EA EA FCI E CN EFCI CN
E CN –EFCI
CN
CCSD(spin–orb) 0.13025 0.00063 0.01529 0.01466
CCSDT(spin–orb) 0.12977 0.00014 0.00154 0.00140
CCSDTQ(spin–orb) 0.12966 0.00003 0.00020 0.00016
FCI 0.12962