By way of illustration, we have carried out some W1 theory calculations on trans-1,3-butadiene and benzene. All relevant computed and observed results are summarized in Table VIII. The example of benzene is representative and will be discussed here in detail -- it should be mentioned that the calculation was carried out in its entirety on an SGI Octane workstation with 2x18 GB external SCSI disks.
The reference geometry was obtained at the B3LYP/cc-pVTZ level[74]. The zero-point energy at that level, after scaling by 0.985, is found to be 62.04 kcal/mol.
The SCF component of TAE is predicted to be 1044.95 kcal/mol at the one-particle basis set limit, of which only 0.39 kcal/mol is covered by the geometric extrapolation. Of the CCSD valence correlation component of 291.07 kcal/mol, however, some 10.11 kcal/mol is covered by the extrapolation, which also accounts for 2.13 kcal/mol out of the 26.55 kcal/mol connected triple excitations contribution.
The inner-shell correlation contribution is quite sizable
at 7.09 kcal/mol, although this number is not qualitatively
different from that for three acetylenes or three ethylenes.
Finally, Darwin and mass-velocity terms contribute a small
but significant -0.96 kcal/mol, and atomic spin-orbit
splitting another -0.51 kcal/mol. All adds up to 1367.95
kcal/mol at the bottom of the well, or 1305.92 kcal/mol
at 0 K, which is in excellent agreement with the experimental
value of 1306.1
0.12 kcal/mol from the NIST WebBook[75].
The CCSD/VQZ calculation took 10h10' with MOLPRO on the Octane, the CCSD(T)/VTZ calculation 1h48' on a single CPU on the Origin 2000. By far the most time-consuming part of the calculation was the inner-shell correlation contribution, at 67h46', to which another 4h52' should be added for the Darwin and mass-velocity contribution. We see similar trends in the results for trans-butadiene, which agree with experiment to virtually within the stated experimental uncertainty; for allene, we obtain a value intermediate between the two experimental values proposed in the WebBook.
We find for both molecules that the sum of core-correlation and relativistic contributions can be quite well estimated by additivity approximations. For instance, the core correlation and scalar relativistic contributions with the same basis set for C2H4 are +2.360 and -0.330 kcal/mol, respectively, adding up to 2.030 kcal/mol. Assuming 2 and 3 times this `C=C bond equivalent' for butadiene and benzene, respectively, yields estimated contributions of 4.06 (trans-butadiene), and 6.09 (benzene) kcal/mol, which agree excellently with the directly computed values of 4.02 and 6.12 kcal/mol, respectively. Considering that inner-shell correlation effects should be fairly local in character, such schemes should work quite well for larger organic systems where the valence calculation would still be feasible but the explicit inner-shell calculation would not be.