1.2 Ground and Excited State Multiplets

The computation of multiplets can be carried out with adf, using the input key SLATERDETERMINANTS.

The method described in [1] for the calculation of the energies of proper spin and spatial symmetry adapted Configuration State Functions is based on the calculation of the energies of single determinantal wavefunctions. The densities corresponding to those Slater determinants are inserted in the approximation used for the exchange-correlation energy.

The procedure as detailed above is somewhat involved. Moreover, one would like to have an easy procedure to calculate many determinants. This is particularly desirable if one wishes to calculate the energies of all Slater determinants of a given configuration, for instance if one wishes to calculate certain averages in view of the inconsistencies of the method.

We have implemented a semi-automatic procedure, using the key SLATERDETERMINANTS.

The general idea of this method is to first perform a restricted calculation in the symmetry that is appropriate for the molecule. This is called the average-of-configuration (AOC) calculation. This AOC calculation generates the orbitals which will be used in all the Slater determinants.

The AOC is the fragment that must be used in all subsequent calculations. The subsequent calculations are characterized by having the AOC as the (only) fragment, and by specifying the keyword SLATERDETERMINANTS. This key is a general key: it may be used as a simple key (it must then have an argument) or as a block type key (no argument, but a data block). If an argument is given this must be a file name. The named file should contain the occupations for the determinants (see below). If no file name is specified the key should be a block key and the occupations should be specified in the data block.

The required information, on file or in the data block, is the specification of the determinant or determinants that are to be calculated in the form of orbital occupation numbers for the AOC orbitals, using the irrep labels of the point group of the AOC calculation, see below for format. All specified determinants will be calculated, and the obtained energy will always be the energy difference with respect to the AOC. Default occupations for all subspecies of the AOC fragment are the occupations of the AOC itself. Therefore, only the open (modified) subspecies have to be specified.

One has to be careful with respect to the point group symmetry to use in the SLATERDETERMINANTS calculation. The density belonging to a specific determinant is usually lower than the AOC symmetry (which is the full symmetry group of the system). In that case this lower point group symmetry has to be specified in the SLATERDETERMINANTS calculation. Everything will always work fine if one just does not use any symmetry at all (nosym). However, if for reasons of computational efficiency one does want to use a subgroup of the system that corresponds to the determinant density or densities, this is perfectly possible. However, all the densities of the determinants specified must then have this (or a higher) symmetry. The program does not check on this, it is the user's responsibility to make sure that this condition is satisfied for all the determinants. The only check that is performed is that occupations of equivalent representations (subspecies of one irrep) in the lower point group of the SLATERDETERMINANTS run, that result from the specified occupations of the subspecies of the AOC symmetry, are equal.