Biomedical Engineering Reference
In-Depth Information
obtained basis sets have sufficient flexibility to be a most useful starting set for molecular
computations, as noted by Richardson. With the addition of 3d and 4f functions, the reported
atomic basis sets provide a molecular basis set which duplicates quantitatively most of the
chemical information derivable by the more extended basis sets needed to obtain accurate
Hartree-Fock molecular functions.
Clementi thus doubled the number of atomic orbitals and so used two slightly different
1s orbitals, two slightly different 2s orbitals and so on. Once again, he optimized the
orbital exponents by systematic variations and a small sample from his results is shown in
Table 16.2. We refer to such a basis set as a
double zeta
basis set. Where the single zeta
basis set for atomic lithium has a 1s exponent of 2.6906, the double zeta basis set has two
1s orbitals with exponents 2.4331 and 4.5177 (the inner and outer 1s orbitals).
Table 16.2
A selection from Clementi's double zeta basis set
Atom
1s exponents
2s exponents
2p exponents
He
1.4461
2.8622
Li
2.4331
0.6714
4.5177
1.9781
Be
3.3370
0.6040
5.5063
1.0118
B
4.3048
0.8814
1.0037
6.8469
1.4070
2.2086
C
5.2309
1.1678
1.2557
7.9690
1.8203
2.7263
N
6.1186
1.3933
1.5059
8.9384
2.2216
3.2674
O
7.0623
1.6271
1.6537
10.1085
2.6216
3.6813
F
7.9179
1.9467
1.8454
11.0110
3.0960
4.1710
Ne
8.9141
2.1839
2.0514
12.3454
3.4921
4.6748
The lowest energy HF-LCAO atomic orbital for a lithium atom will be a combination of
the four s-type basis functions, and we call this combination 'the' atomic 1s orbital.
16.8.3 Polarization Functions
There is a second point to notice fromClementi's paper, where he speaks about 'the addition
of 3d and 4f functions...'with reference to first- and second-row atoms respectively. Any
chemist would write the fluorine electronic ground state configuration
F:1s
2
2s
2
2p
5
and so the d and f orbitals are unoccupied. When atoms combine to form molecules the
atomic charge density may well distort from spherical symmetry and such
polarization
functions
are needed to accurately describe this distortion.
