Multiplet States

Calculations with adf yield results for one-determinant electronic states, which are not always the 'true' states of the molecule. The evaluation of the correct multiplet energies is not trivial in this approach; see the Theory document. The point is to evaluate a specific multiplet state as a linear combination of selected one-determinant functions, each computed in the field of the so-called Average-of-Configuration (AOC). Typically, in an open shell system, the AOC is the spin-restricted system in which all orbitals in the open shell are degenerate and equally occupied. The AOC serves then as a fragment for the subsequent calculations, in which the different open shell orbitals are occupied differently by specifying the appropriate occupation numbers as explained below.

Important: in these follow-up calculations it is imperative that the results are obtained in the AOC field: no SCF convergence must be carried out, because we only want to assign the electrons differently, while keeping exactly the AOC orbitals. To achieve this, the follow-up calculations must use the keyword SCF, and the subkey iterations must be set to 0.

Since adf requires that the point-group symmetry matches not only to the nuclear frame but also to the electronic charge density and MO occupations, these calculations must run in a lower pointgroup symmetry. Often you will also want to run the modified calculations spin-unrestricted. For an example, see the set of sample runs that come with the package and the discussion in the Examples document.

The calculation of the one-determinant states based on the AOC reference state is controlled with the key SLATERDETERMINANTS: . It is a general key; it can be used as a simple key and requires an argument then. It can also be used as a block key. For this particular key it is not correct to specify an argument and a data block.

SLATERDETERMINANTS file

When used as a simple key, the argument must be a file (including the path). The file must be an ASCII file containing data in the same format as you would supply in the data block when using the key as block type key, see below. All information on the file until the eof must be suitable for the data block, but no record 'end' on the file must be specified: only the contents of the data block.

The block format:

SLATERDETERMINANTS file
 title1
 irrep occups
 irrep occups
 ....
 subend
 title2
 irrep occups
 .....
 subend
 title3
 ....
 subend
 ....
end

Each 'title' functions as a subkey, but is otherwise an arbitrary string to label the resulting one-determinant calculation. Each such subkey block contains the occupation numbers for a single one-determinant calculation. It is necessary that the calculation uses the reference AOC run as its only fragment file. The occupations in the subkey blocks must be re-arrangements of the AOC open-shell electrons. In the Slaterdeterminants calculation you must explicitly specify the pointgroup symmetry in which you want to run; this must be a lower symmetry than the AOC one, otherwise you couldn't rearrange the open shell electrons. See the Theory document. An sample run is included in Examples document.

Each 'irrep occups' record specifies the occupations for the indicated irrep in the usual way (see for instance the occupations key). The irrep labels must correspond to the (lower) point group symmetry used in the slaterdeterminants calculation. Note that in an unrestricted calculations, occupations numbers must be given for both spins, using the double slash (//) to separate the occupations for spin-α and spin-β.

In this setup, the program will for each of the subkey blocks under the slaterdeterminants key execute an SCF calculation with only one cycle, i.e. no convergence, where the start-up field is the fragment field, i.e. the AOC field. So all one-determinant states in this calculation are evaluated in the AOC field. The resulting energies for the distinctly computed one-determinant states can then be combined to the desired multiplet values, corresponding to how the multiplet states are combinations of the one-determinant states.