Molecules built from fragments
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ADF analyzes the results in terms of user-specified subsystems from
which the total system is built. The program tells you how the
'Fragment orbitals' (FOs) of the chemically meaningful subunits mix
with FOs on other fragments to combine to the final molecular
orbitals.

ADF builds a molecule from user-defined fragments, which may be single
atoms or larger moieties, for example, ligands, functional groups, or
complete molecules in a donor-acceptor complex. In practice, this
means that the results of the ADF calculation on a fragment are saved
on a file and that the fragment files are then used in setting up the
calculation on the overall system. The fragment orbitals (FOs), i.e.,
the MOs from the calculations on the fragments, are employed as basis
functions in the new calculation. This does not imply a basis set
truncation or contraction because the virtual FOs are included: the
FOs constitute only a transformation of the basis set. If there are
symmetry-equivalent fragments, for example, the six CO molecules in
octahedral Cr(CO)_6 , the program generates symmetry combinations of
the FOs and uses the symmetrized fragment orbitals (SFOs) as basis
functions. The SFOs transform as the irreducible representations
(irreps) of the molecule, allowing a symmetry-driven analysis of the
results. In the absence of any symmetry the SFOs are identical to the
FOs.

The fragment approach offers considerable advantages. It enhances the
interpretative power of ADF as it leads to a more transparent picture
of bonding, which reduces from a complicated mixing of many primitive
basis functions (possessing little physical relevance) to a few key
interactions between meaningful fragment (frontier) orbitals. The
fragment approach also improves the numerical precision. In ADF,
energies are calculated directly, with respect to the fragments, by
one single numerical integral of the difference energy density
\epsilon[\rho,\mathbf{r}] - \sum_A \epsilon_A[\rho_A,\mathbf{r}]
between the overall molecule and the constituting fragments.

   \Delta E[\rho] = \int d\mathbf{r} \left( \epsilon[\rho,\mathbf{r}]
   - \sum_A \epsilon_A[\rho_A,\mathbf{r}] \right)

In other words, we evaluate the energy of the overall molecule,
E[\rho] = \int d\mathbf{r} \epsilon[\rho,\mathbf{r}], and the energies
of each of the fragments, say the atoms that constitute the overall
molecule, E_A[\rho] = \int d\mathbf{r} \epsilon_A[\rho_A,\mathbf{r}],
in the same numerical integration grid. This provides more accurate
relative energies than subtracting total energies from separate
calculations, because the same relative numerical integration error
applies to a much smaller quantity, yielding, in turn, a much smaller
absolute error.

Note that the user has the freedom to make their own choice of
fragments. This is, however, not a matter of plain arbitrariness, and
it does not make the analysis tools less meaningful. On the contrary,
this freedom simply reflects the many perspectives from which a
particular chemical phenomenon can be viewed.

In practice, many calculations are performed using as fragments the
so-called basic atoms, which are the smallest possible building blocks
in ADF. The basic atoms are not necessarily physically realistic
objects - indeed, usually they are not, as they must be spin-
restricted and spherically symmetric. The computed (bonding) energy
with respect to basic atoms, then, does not yield quantities that can
be compared to experimental data directly. Rather, one must correct
for the true ground state of the isolated single atoms.

Text is mostly taken from: *Chemistry with ADF* G. te Velde, F.M.
Bickelhaupt, E.J. Baerends, C. Fonseca Guerra, S.J.A. van Gisbergen,
J.G. Snijders, T. Ziegler Journal of Computational Chemistry 22, 931
(2001).

Link: How to make molecular fragments

Tutorial: ADF fragment analysis

Examples: analysis options
