CSF's required^{a} | ||||
Molecule | CISD | CISDT | CISDTQ | FCI |
BH | 568 | n/a | 28 698 | 132 686 |
H_{2}O | 361 | 3 203 | 17 678 | 256 473 |
NH_{3} | 461 | 4 029 | 19 925 | 137 321 |
HF | 552 | 6 712 | 48 963 | 944 348 |
H_{7}^{+} | 1 271 | 24 468 | 248 149 | 2 923 933 |
^{a}Data from reference [6] except for H_{7}^{+} data from | ||||
reference [17]. |
We can also see from Table 3 that the number of N-electron basis functions increases dramatically with increasing excitation level. It should be pointed out that while the calculations on BH, HF, and H_{7}^{+} used DZP basis sets, those on H_{2}O and NH_{3} used only DZ basis sets. A DZP basis should be considred the minimum adequate basis for a truly meaningful benchmark study, and even then it is desirable to use a high-quality basis such as an Atomic Natural Orbital (ANO) set. While it is generally possible to perform CISD calculations on small molecules with a good one-electron basis, the CISDTQ method is limited to molecules containing very few heavy atoms, due to the extreme number of N-electron basis functions required. Full CI calculations are of course even more difficult to perform, so that despite their importance as benchmarks, few full CI energies using flexible one-electron basis sets have been obtained.
The size of the full CI
space in CSF's can be calculated (including
spin symmetry but ignoring
spatial symmetry) by Weyl's dimension formula
as applied to the Distinct
row table (DRT).
If N is the number of electrons, n is the number
of orbitals, and S is the total spin, then the dimension of the CI
space in CSF's is given by
The dimension of the full CI
space in determinants (again, ignoring spatial symmetry) is computed simply by
(tex2html_deferredtex2html_deferred4.tex2html_deferred17D_n N S =
( ) ( ) ) |
Number of electrons | ||||
Orbitals | 6 | 8 | 10 | 12 |
10 | ||||
( ) | ( ) | ( ) | ( ) | |
20 | ||||
( ) | ( ) | ( ) | ( ) | |
30 | ||||
( ) | ( ) | ( ) | ( ) |