Essentials of Computational Chemistry

7.6 PRACTICAL ISSUES IN APPLICATION 233
Table 7.3 Singlet–triplet splittings (kcal mol −1 )forp-benzyne and N-protonated 2,5-pyridyne a
Level of Theory p-Benzyne N-Protonated 2,5-Pyridyne
HF 87.8 87.4
MP2 −25.3 −4.1
MP2 (cc-pVTZ) −27.8 11.4
MP3 22.8 42.0
MP4SDQ 14.3 10.1
MP4 −20.9 −21.0
CCSD 16.8 17.3
CCSD (cc-pVTZ) 18.4 18.9
CCSD(T) −4.5 −29.4
QCISD 16.2 4.7
QCISD(T) −4.1 −5.9
BD 17.0 17.0
BD(T) −4.1 −5.1
CAS(8,8) −2.7 −2.4
CASPT2(8,8) −5.1 −5.1
Experiment or best estimate −4.2 −5.0
a Basis set cc-pVDZ unless otherwise indicated; geometries from BPW91/cc-pVDZ density functional calculations
(see Chapter 8).
states, but inclusion of triples via the (T) formalism gives for the most part rather good
results. A significant exception is the CCSD(T) result for the 2,5-pyridynium ion, where
the triples correction drastically overcorrects. This is an example of instability arising from
large singles amplitudes in the CCSD expansion. In p-benzyne, the symmetry of the bonding
and antibonding combinations of the σ orbitals is different, so a single excitation from one
orbital to the other cannot contribute to the closed-shell wave function. In the less symmetric
2,5-pyridynium ion, however, these orbitals are the same symmetry, so such excitations are
allowed and are major contributors to the wave function (Figure 7.6). In such instances,
BD(T) calculations are to be preferred over CCSD(T), and indeed, the BD(T) level of theory
performs very nicely for this problem (in this particular case the QCISD(T) level also seems
to be more robust than CCSD(T) with respect to sensitivity to singles, but this is the reverse
of the situation that normally obtains).
As for basis-set convergence, triple-ζ calculations at the MP2 and CCSD levels are
provided for comparison to the double-ζ results. For this particular property, the results
for p-benzyne are not terribly sensitive to improvements in the flexibility of the basis set. In
the pyridynium ion case, the CCSD results are also not very sensitive, but a large effect is
seen at the MP2 level. This has more to do with the instability of the perturbation expansion
than any intrinsic difference between the isoelectronic arynes.
Note that when multiconfigurational character is explicitly accounted for, by an MCSCF
calculation using a complete active space including the relevant σ orbitals and electrons as
well as the six π orbitals and electrons, the results even without accounting for dynamical
electron correlation are fairly good. Including dynamical correlation at the CASPT2 level
improves them to the point where they are quite good.