hand-power or electricity. There were also, in astronomy at least, armies of women
arithmeticians called computers – the original meaning of the word).
If we calculate the electronic energy simply as twice the sum of the energies of
the occupied MO orbitals, as with the simple and extended H€uckel methods, we get
a much higher value than from the correct procedure (Eq.5.147); with a 0.800 A ̊
bond length and the converged results this naive electronic energy is
2(!1.4470) h¼!2.8940 h, while the correct electronic energy (not given in
Table5.1– the HF energies there are electronic plus internuclear repulsion) is
!3.7668 h, i.e. 30% lower when we correct for the fact that simply double-summing
the MO energies counts electron repulsion terms twice (Section 5.2.3.6.4).
A geometry optimization for HHe+can be done by calculating the Hartree–Fock
energy (electronic plus internuclear) at different bond lengths to get the minimum-
energy geometry. The results are shown in Fig.5.11; the optimized bond length for the
STO-1G basis set is ca. 0.86 A ̊. Note that it is customary to report ab initio energies in
hartrees to five or six decimal places (and bond lengths in A ̊to three decimals); the
truncated values used here are appropriate for these illustrative calculations.
Summary of the steps in a single-point Hartree–Fock (SCF) calculation using the
Roothaan–Hall LCAO expansion of the MO’s
- Specify a geometry, basis set, and orbital occupancy (this latter is done by
specifying the charge and multiplicity, with an electronic ground state being
the default).
–2.4300–2.4350–2.4400–2.4450–2.45000.700 0.800 0.900.
.
.
.
.
E,
hartrees r, AFig. 5.11 STO-1G energy versus bond lengthrfor H–He+. The calculation forr¼0.800 A ̊was
done largely “by hand” (see Section “Using the Roothaan–Hall Equations to do Ab initio
Calculations – an Example”); the others were done with the program Gaussian 92 [ 29 ]
230 5 Ab initio Calculations